DPhil Thesis

The Effect of Magnetic Fields on

Autocatalytic Chemical Reactions

A thesis submitted for the degree of

Doctor of Philosophy at the

University of Oxford

by

Robert Evans

Worcester College &

Inorganic Chemistry Laboratory

Trinity Term 2007

CONTENTS Acknowledgements i Abstract ii

Physical constants, glossary iii

1: Introduction 1 1.1 Magnetic Fields 3 1.1.1 Bulk Properties 4 1.1.2 Microscopic Properties 5 1.2 Origins of Magnetic Field Effects 10 1.2.1 Lorentz Force 10 1.2.2 Magnetic Force 11 1.2.3 Radical Pair Mechanism 15 1.3 Feedback and Autocatalysis 22

PART I: MAGNETIC FIELD EFFECTS ON THE TRAVELLING WAVE REACTION BETWEEN CO(II)EDTA2− AND H2O2 2: Introduction 28 2.1 Magnetic Resonance Imaging 31 2.1.1 Basics of Magnetic Resonance 31 2.1.2 Spin Relaxation 33 2.1.3 Magnetic Resonance Imaging 36 2.2 Convective Effects and Chemical Fingering 43 3: Methods and Materials 47 3.1 Materials 47

3.2 Methods 47 3.2.1 Preliminary Experiments 47 3.2.2 MRI Experiments 51 4: Results 58 4.1 Preliminary Results 58 4.1.1 Magnetic Susceptibility Measurements 58 4.1.2 Magnetic Field Effect 59 4.1.3 Changes in Density and its Effect 61 4.1.3.1 Distortion of the Wavefront 62 4.1.3.2 Dilatometer Measurements 62 4.2 MRI Experiments 65 4.2.1 Application of Magnetic Field Gradients z/Bz ∂∂ 65 4.2.1.1 Flat Wave Fronts 66 4.2.1.2 Distorted Wave Fronts 67 4.2.1.3 Waves in a Porous Medium I 69 4.2.2 Application of Magnetic Field Gradients

x/Bz ∂∂ and 70 y/Bz ∂∂ 4.2.2.1 Formation of a Chemical Finger 71 4.2.2.2 Manipulation of a Chemical Finger 75 4.2.2.3 Waves in a Porous Medium II 82 5: Discussion 84 5.1 Interpreting the Effect 84 5.2 Future Work and Applications 94 5.2.1 Modelling 94 5.2.2 Velocity Imaging 106 5.2.3 Other Reactions 109

PART II: EFFECT OF MAGNETIC FIELDS ON THE OSCILLATIONS OF THE BELOUSOV-ZHABOTINSKY REACTION 6 Introduction 113 6.1 A Brief History of the Belousov-Zhabotinsky Reaction 113 6.2 Mechanism of the BZ 115 6.3 Possibility of a Magnetic Field Effect 123 7: Methods and Materials 127 7.1 Methods 127 7.1.1 Continuously-flowed Stirred Tank Reactor (CSTR) 127 7.1.2 Analysis 133 7.2 Materials 135 8. Results 139 8.1 Oscillations 139 8.2 Preliminary Results 145 8.2.1 Addition of Ag+ ions 146 8.2.2 Irradiation of Reaction 149 8.3 Application of Magnetic Field 153 8.4 Is there an effect? 156 8.4.1 Ferroin Catalysed Reaction 157 8.4.2 Cerium Catalysed Reaction 158 9. Discussion 161

PART III: USING SQUID MAGNETOMETRY TO FOLLOW CHEMICAL REACTIONS. 10 Introduction 171 10.1 Methods of Measuring Magnetic Properties 172 10.2 Other Methods of Following Chemical Reactions 175 10.2.1 Absorption Spectroscopy 175 10.2.2 Nuclear Magnetic Resonance 176 11: Methods and Material 177 11.1 Materials 177 11.2 Methods 178 11.2.1 pH Electrode Experiments 178 11.2.2 Absorption Spectroscopy Experiments 178 11.2.3 NMR Experiments 178 11.2.4 SQUID Experiments 179 11.2.5 Analysis 183 12: Results 185 12.1 Co(II)EDTA2−/H2O2 reaction 185 12.1.1 pH Electrode Experiments 185 12.1.2 Absorption Spectroscopy Experiments 187 12.1.3 NMR Experiments 194 12.1.4 SQUID Experiments 196 12.2 Other Reactions 203 12.2.1 Belousov-Zhabotinsky Reaction and Derivatives 203 12.2.1.1 Cerium-Catalysed Belousov-Zhabotinsky Reaction 204 12.2.1.2 Ferroin Clock Reaction 209 12.2.2 Vanadium Chemistry 214 13. Discussion 217 14: Summary and Conclusion 223

Appendices Appendix I: Corresponding to Introduction Systems of Magnetic Units I

Appendix II: Corresponding to Part I Derivation of Navier-Stokes equations IV Appendix III: Corresponding to Part II Data acquisition program X Appendix IV: Corresponding to Part III

SQUID Magnetometry XXVI References And Notes I

ACKNOWLEDGEMENTS

In spite of me being slightly more demanding for time than Fraser, Chris Timmel has

been a top class supervisor. I guess any apologies for being mental myself should go

here. Sorry.

Without Melanie Britton, I doubt there’d be this thesis in this form. There is really not

much more that can be added. You’ve been great. Yiannis Ventikos and Mike Heyward

have allowed me to use their time, space and resources and helped out whenever I hit a

brick wall in those pieces of work. Peter Hore has also added just the right advice, at the

right times. Nick Rees and Nick Green, as well. Both helpful whenever ambushed on

South Parks Road.

The rest of the CRT and PJH groups, from Kevin, Kim and Fillipo all the way to Part II

students that I’m really struggling to remember, have been great company. Certainly

Kevin and Kim have been a great help throughout. Janet, Wedge and Alex have all put

up with my rather skewed take on life. They deserve medals. Shiny ones.

I have to mention lab services and work shops, both in the PTCL and ICL. Friendly and

helpful, they have helped with the two, three lab moves as the group and I have roamed

across the science area. The football chat with the ICL guys when I was alone in the

basement there certainly made that year much more bearable. It’s the little things, the 1

day jobs, turned around immediately which really make life easy.

Away from labs? Well, that’d just be self-indulgent, wouldn’t it?

i

The Effect of Magnetic Fields on Autocatalytic Chemical Reactions

A Thesis Submitted for the Degree of Doctor of Philosophy

Robert Evans Worcester College Trinity Term 2007

ABSTRACT This thesis describes an experimental study into the effect of static magnetic fields on chemical reactions that display feedback and autocatalysis. Magnetic field effects have been observed in a variety of chemical systems. However, their small magnitudes (typically only a few percent) have caused justified scepticism about the likelihood of any such effects occurring in vivo. However it has been suggested that if any magnetic field effect could be amplified by non-linear kinetics, then magnetic field effects might indeed govern biological magnetic field effects such as the avian magnetic compass. It is the aim of this thesis to identify and study autocatalytic reactions that exhibit magnetic field dependence and investigate any effects observed in more detail. In the introductory chapter the different mechanisms by which a magnetic field can interact with a chemical system are introduced, such as the Lorentz force and the radical pair mechanism (RPM). A discussion as to why non-linear kinetics present in a reaction could amplify a smaller effect is also introduced. Part I of the thesis details the investigation of a travelling wave reaction manipulated by applied inhomogeneous magnetic fields. Magnetic resonance imaging techniques are used to follow the progress of the wave in a vertical tube. Magnetic field gradients of different geometries are applied to the reaction and the wavefront can be accelerated, decelerated and manipulated. The magnetic field effect can be understood by considering all of the magnetic fields and field gradients present. At the end of the section, there is discussion of potential future research on the topic. Part II focuses on the oscillating Belousov-Zhabotinsky reaction. The existence of a magnetic field effect on this reaction has been disputed in the literature and previously published data is inconclusive. Apparatus was designed and built specifically for the study of this reaction. Series of oscillations of the reaction catalysed by ferroin and cerium were produced. However, no magnetic field effect on the reaction was observed. The findings are discussed in the framework of the RPM. In the concluding section, Part III, the changes in magnetic susceptibility that occur as the reactions studied above proceed are used to investigate rather than manipulate the reactions. For the first time, SQUID magnetometry is used successfully to follow a liquid-phase chemical reaction. Applications of the technique, such as in observing magnetic field effects, are discussed.

ii

Physical Constants

Avogadro constant, NA 6.022 × 1023 mol−1

Planck constant, h 6.626 × 10−34 J s

2πh

=h

Boltzmann constant, k 1.381 × 10−23 J K−1

Vacuum permeability, 0μ 4π × 10−7 H m−1

Bohr magneton Bμ 9.274 × 10−24 J T−1

iii

Glossary

NMR Nuclear Magnetic Resonance

MRI

SQUID

rf

Magnetic Resonance Imaging

Superconducting Quantum Interference Device

Radiofrequency

Co(II)EDTA2−

Co(III)EDTA−

EDTA

(ethylenediaminetetraacetato)cobalt(II)

(ethylenediaminetetraacetato)cobalt(III)

Ethylenediaminetetraacetic acid (HO2CCH2)2NCH2CH2N(CH2CO2H)2

Ferroin

Ferriin

Iron(II) 1, 10 – phenanthroline

Iron(III) 1, 10 – phenanthroline

Phenanthroline

BZ

MA

CPMG

Belousov-Zhabotinsky

Malonic acid

Carr-Purcell-Meiboom-Gill sequence

O

iv

O

OH

N

O

N

HO

O OH

OH

N N

Chapter 1: Introduction

1

1: INTRODUCTION

The effects of magnetic fields on biological systems have been investigated since the early

seventies. The possibility of a detrimental effect to human health from a magnetic field has

driven this research. A link between childhood leukaemia and overhead power lines was

suggested by an early epidemiological survey of the problem1. A recent 6 year study of

possible links between mobile phone use and cancer has concluded that there is a “hint” of

higher cancer risk in the long term2. Furthermore, it has been shown that the Earth’s

magnetic field (a magnitude of ~ 50 μT) has a role in aiding animal migration3. These

investigations have prompted research into the effects of magnetic fields on biological

systems by considering relevant model systems and chemical reactions as well as probable

mechanisms which might govern such effects.

One argument against the existence of magnetic field effects is based on the fact that the

thermodynamic effects of magnetic fields on chemical reactions are typically very much

smaller than the thermal energy of any system considered. The energy difference between

the two states of an electron in a 1 T magnetic field, 11 J mol−1, is over 200 times smaller

than kT at room temperature, 2500 J mol−1. However, in reactions that feature

ferromagnetic materials, the significantly larger changes in magnetic energy that occur can

indeed lead to magnetic field effects at very high magnetic fields (> 10 T)4. Still, for the

vast majority of reactions, a magnetic field is unlikely to have much effect on the position

of equilibrium of a chemical reaction.

Chapter 1: Introduction However, it has been convincingly shown both experimentally and theoretically that even

small magnetic fields can have a pronounced effect on the kinetics of certain chemical

reactions. The well-established radical pair mechanism (RPM)5 produces magnetic field

effects by altering the rates of recombination of radical pairs. In inhomogeneous systems,

forces arise from the presence of magnetic fields and their gradients and convective flow

can develop. This flow can interact with a chemical reaction, leading to some striking

magnetic field effects, such as that observed in the reaction between Co(II)EDTA2− and

H2O26.

In discussion of the role of the radical pair mechanism in magneto-reception in birds7, Ritz

et al. argue the need for an effect to be amplified as not only are the magnetic field effects

likely to be small but the size of the effects may be limited by the complicated, biological

nature of the system. Biological systems also provide several examples of mechanisms

where a small initiating effect leads to a larger response. The reception of only a handful of

photons on one receptor in the eye is amplified enough to produce a response in the

nervous system8. Negative feedback, or inhibition, is a common feature of biological

processes, such as in regulation of body temperature or hormone levels. Calcium waves,

observed upon the fertilisation of eggs9, are a biological example of positive feedback.

Simpler chemical reactions showing similar kinetics could be suitable models for these

effects observed in biological systems.

The work presented in this thesis investigates simple chemical systems that involve some

form of feedback in their kinetics and could show magnetic field effects. Mechanisms for

the interaction between a magnetic field and a chemical reaction exist and are well known.

2

Chapter 1: Introduction Feedback is also a well-known phenomenon, observed in both chemical and biological

systems. Reactions which exhibit chemical feedback and could be manipulated by an

applied field can be identified. A range of experimental techniques could then be used to

determine if a magnetic field has an effect on a particular reaction and how that reaction,

and its non-linear kinetics, interacts with an applied magnetic field.

The following sections detail the magnetic properties of materials and the origins of

possible magnetic field effects. Non-linear kinetics, such as autocatalysis, are introduced at

the end of the section and the possibility of amplification is introduced.

1.1 Magnetic Fields

Although the properties of magnetic fields and materials have been observed throughout

history, study of the various phenomena was slow until the link between electricity and

magnetism was observed in 1819 by Oersted. Ampére, Biot and Savart expanded on this

discovery with experiments concerning magnetic forces acting between current carrying

wires10. Magnetic fields are produced by electric currents, from currents in wires, as first

observed in the 19th century, to those in atoms and molecules. A loop of current has a

magnetic dipole moment, μ (units of A m2), associated with it, and this magnetic dipole

interacts with a magnetic field of flux density, B (N A−1 m−1), in much the same way as an

electric dipole would interact with an electric field. A torque acts on the dipole to turn it

into the field, and a translational force acts on it in a magnetic field gradient. The properties

of materials in a magnetic field are determined by the interaction of microscopic magnetic

dipoles with an applied magnetic field.

3


1.1.1 Bulk Properties

When a material is placed within a magnetic field, the flux density, B, within it changes

relative to that in a vacuum. The extent of this change is indicated by the magnetisation, M,

induced in the material and determined by its magnetic susceptibility, χ, which is either

positive or negative. The magnetic flux density within the material is comprised of

contributions from the magnetic field strength, H, and the magnetisation, M, where:

)+(= 0 ΜΗB μ (1)

M is also defined as the magnetic dipole moment per unit volume, μ/V. For simple

materials, the magnetisation is proportional to the magnetic field strength:

(2) HM χ=

χ is the volume magnetic susceptibility, a dimensionless value. The mass magnetic

susceptibility, χw, and the molar magnetic susceptibility, χmol, are closely related. The

magnetisation is a response of the material to an applied magnetic field. There are two

contributions to the magnetic susceptibility of a simple material. For a material at a

temperature, T, the molar susceptibility is given by:

4


⎟⎟⎠

⎞⎜⎜⎝

⎛+=

3kTξ-μNχ

2

0Amolμ (3)

ξ is the induced diamagnetic magnetic moment and μ is the permanent magnetic dipole of

the material. The induced diamagnetic magnetic moment is found in all materials, as a

small magnetisation is directed against any applied magnetic field. Paramagnetism is

observed in materials that contain unpaired electrons and is the simplest form of

magnetisation. Unpaired electrons give rise to permanent dipole moments in atoms and

molecules. These dipoles will orientate with an applied magnetic field to give a positive

magnetisation. The diamagnetism of a material is considerably smaller than magnetism

arising from a permanent magnetic dipole. Both paramagnetism and diamagnetism are

small effects, with ~10−10 and ~10−8 m3 mol−1. Other types of magnetism,

such as ferromagnetism ( ~10−1 m3 mol−1) and antiferromagnetism ( ~10−9 m3

mol−1), occur in ordered materials due to the interactions between magnetic dipoles in the

material and are not considered here.

dia mol,χ para mol,χ

molχ molχ

1.1.2 Microscopic Properties

The bulk properties described above arise from the interactions of particles possessing spin

with magnetic fields. Spin is a quantum mechanical phenomenon and a measure of the

intrinsic angular momentum of a particle. Electrons, protons and therefore some nuclei

possess non-zero spin.

5

Chapter 1: Introduction A particle of spin quantum number, s, has a spin angular momentum, s, of magnitude.

h1)s(s +=s (4)

The particle has 2s + 1 magnetic substates determined and described by the spin projection

quantum number, =s, s−1, ..., −s. The component of this angular momentum along a

given direction is given by

sm

zs

(5) hsz ms =

For an electron, s = ½ and = ± ½, producing two possible states, designated as ‘up’ and

‘down’ or α and β. For systems with many electrons, a total angular momentum, S, can be

calculated. In the case of weak spin-orbit coupling, this can be obtained using a Clebsch-

Gordon series so that S = s1+s2, s1 + s2 −1, ... , s1 − s2. This has magnitude and projection

given by

sm

S and . zS

h1)S(S +=S (6)

hsz MS = , where = S, S−1, ..., −S (7) sm

The intrinsic spin of a charged particle produces a magnetic moment for that particle.

6


Sμ ⎟⎠

⎞⎜⎝

⎛−=h

Bs

μg (8)

g is the g-factor, approximately equal to 2 for an electron (ge for a free electron = 2.0023).

In the absence of an applied magnetic field, the different substates are degenerate.

However, this degeneracy is lifted by the application of a magnetic field, B, with the energy

of a magnetic dipole, μ, in the field, given by:

sM

(9) Bμ ⋅−=E

The energy of an electron in the magnetic field is then calculated from the projection of the

electron magnetic dipole onto the magnetic field.

(10) zBs ΒμgmE −=

For an electron, the two spin states give rise to two spin energy levels in a magnetic field.

The difference in energy levels for an electron is given as:

(11) zBΒgμE −=Δ

Absorption of a photon that has the same energy as the energy gap between the two states

will cause a transition between the two states. Given the relationship between the energy of

a photon and its wavelength, the resonance or Larmor frequency of the proton, Lν is found.

7


LhE ν=Δ

h

BgμhE zB

L =Δ

=ν (12)

This equation is important for resonance spectroscopy, such as NMR and ESR, as well as

the radical pair mechanism, described later in this section.

So how does the existence of spin give rise to properties such as paramagnetism? In the

absence of a magnetic field, the magnetic dipoles that make up the material are randomly

aligned and cancel each other. However, with an applied field, they become orientated and

the magnetic field within the material is now greater than that outside. The orientation is

limited by the effect of thermal noise, giving the paramagnetism inverse temperature

dependence. For a simple system, where spins are the only contribution to the

paramagnetism, a spin-only formula for the molar magnetic susceptibility can be produced.

3kTμN

3kTξ-μNχ

20A

2

0Amolμμ

=⎟⎟⎠

⎞⎜⎜⎝

⎛+=

3kT

1))(S(SμgμN3kT

μgμN 2B

2e0A

22

B2e0A +

=⎟⎠

⎞⎜⎝

⎛

=S

h (13)

Hence, the paramagnetism of a substance is directly related to the number of unpaired

electrons present per atom. The situation is complicated when there are contributions to the

angular momentum from electronic orbitals. This can be included in the expression for the

8

Chapter 1: Introduction magnetic moment, by considering the magnetic moment due to the orbital angular

momentum.

Lμ ⎟⎠

⎞⎜⎝

⎛−=h

Bo

μ (14)

( SLμμμ gμBos +⎟

⎠

⎞⎜⎝

⎛−=+=h

) (15)

There are contributions to the magnetic moment from both sources of angular momentum.

For heavier atoms, the situation gets further complicated by the effects of spin-orbit

coupling.

Analogous formulae to those given for electrons can be constructed for other particles with

intrinsic spin, such as nuclei with nuclear spin, I, and nuclear angular momentum, I. Many

important nuclei have I > 0, such as hydrogen and carbon-13 (both I = ½). As with

electronic spin, nuclear spin has magnitude and projection given by I and . zI

h1)I(I +=I (16)

hIz mI = , where = I, I−1, ..., −I (17) Im

The magnetic moments of magnetic nuclei can be derived in the same manner as for an

electron.

9


IIμ NN

N γμg =⎟⎠⎞

⎜⎝⎛=h

(18)

In Eqn. 18, and are the nuclear g-factor and nuclear magneton for the nucleus in

question. Much more commonly used is , the gyromagnetic ratio of the nuclei. This is

the ratio of its magnetic dipole moment to its angular momentum and is a property of a

given nuclei. It becomes important in magnetic resonance techniques, described in Part I.

Ng Nμ

Nγ

1.2 Origins of Magnetic Field Effects

There are several ways by which magnetic fields can interact with chemical reactions. The

effects can arise from the interaction of the bulk properties of the reagents and products

with an applied magnetic field, especially in inhomogeneous systems. They can also arise

from the interactions between electrons in reactive intermediates of a chemical reaction,

leading to a change in the kinetics of the reaction.

1.2.1 Lorentz Force

The movement of charged particles within a magnetic field exerts a force, FL, on a particle

with charge, q, moving with velocity, v, perpendicular to the magnetic field, B.

(19) BvF qL ×=

Chemical reactions often include ions. A flow of ions in the reaction would be affected by

this force. The force is proportional to B and, acting perpendicular to the direction of

10

Chapter 1: Introduction motion, induces rotational motion in affected particles. In solution, where ions and charged

particles collide with the solvent and other solutes, this leads to convection. The effects

produced by this force, known as magnetohydrodynamics11, tend to occur in

electrochemical systems where there exists a flow of current from an electrode into a bulk

solution. Reactions on solid-liquid interfaces give rise to some impressive magnetic field

effects. Helical crystals of silicates have been grown in magnetic fields12 and the precession

of silver dendrites as they precipitate out of solution onto a zinc surface can be observed13.

1.2.2 Magnetic Force

The forces acting on an electric or magnetic dipole in an electric or magnetic field can be

derived using the energy of a dipole, U, in the relevant field10.

(20) Ep ⋅−=EU

Bμ ⋅−=MU (21)

p is the electric dipole moment (units of C m) and E is the electric field strength (J C−1 or

more conventionally, V m−1). Pairs of analogous relationships can be produced, such as for

the torque of a dipole in a uniform field.

(22) EpT ×=E

BμT ×=M (23)

11

Chapter 1: Introduction Formulae for the force acting on a dipole in a non-uniform field can also be produced, by

calculating the gradient of the energy.

)(E EpF ⋅∇= (24)

)(M BμF ⋅∇= (25)

∇ is the vector differential operator. If the force is calculated by considering an electric

dipole, p, comprised of two equal but opposite charges, ±q, separated by a distance, l, in a

non-uniform electric field, a different expression is obtained.

EpF )(E ∇⋅= (26)

This is different to that obtained by the method described above, but the two expressions

are identical if , which is true in the absence of a magnetic field. However, a

magnetic dipole does not exist as a pair of magnetic monopolesI, but as a minute loop of

current. By considering the interaction of non-uniform magnetic fields on sections of the

current loop, an expression for the force acting on a magnetic dipole can be derived. It

requires that in order for the analogous force expression to be obtained.

0=×∇ E

0=× B∇

BμF )(M ∇⋅= (27)

12

Chapter 1: Introduction A force acting on a dipole can then be scaled up to a body of volume, V, and magnetisation,

M, as μ = MV. χ is assumed to be small enough that the field is not changed by the

presence of the body and an expression for force can then be obtained

BBF )(μ

Vχ

0

vM ∇⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛= (28)

The equation is a simplification of one of Maxwell’s equations (Eqn. 1.31 from

the set of four equations below). This set of equations can be used to describe the various

relationships between magnetic fields, electric fields, charge and current.

0=×∇ B

t∂∂

−=×∇BE (29)

0ερ

=⋅∇ E (30)

t

εμε 000 ∂∂

+=×∇EJB (31)

(32) 0=⋅∇ B

J is the current density and is the electric charge density of the material. ρ

Other derivations for this magnetic force exist14. For example, the magnetic energy, U, of a

body in a magnetic field which has acquired a magnetic dipole moment of m in being

brought from infinity to a point where the magnetic field has the initial value, B, is

–m.B/2. The dipole moment is the integral of the magnetisation, M, over the volume of the

13

Chapter 1: Introduction body, V. We assume first that B and χ are constant across the body, and also that χ is small

enough that the field is not changed by the presence of the body. Given that M = χH, then

BHMm )Vχ/μVχV 0(=== and the energy is given as:

2

02μχVU B⎟⎟

⎠

⎞⎜⎜⎝

⎛−= (33)

The force acting on the body can be calculated from this expression, as F = −∇U.

)(2μχV 2

0

BF ∇⎟⎟⎠

⎞⎜⎜⎝

⎛= (34)

There is the possibility of a force that is dependent on the χ∇ term. The effect of this force

on a system and its existence has been discussed elsewhere15. There is also the possibility

of a magnetic torque forming for molecules which possess an anisotropic magnetic

susceptibility16. However, these forces are very unlikely to have much effect in the systems

studied in this thesis.

While the Lorentz force is proportional to the magnetic flux density, B, the magnetic force

is proportional to the product of the field and its gradient. Phenomena such as the levitation

of water and small animals in high magnetic fields, or the magneto-Archimedes effect17

result from the magnetic force. The force acting on a paramagnetic liquid can be used to

control convection in solution18. It can also move and separate transition metal ions

supported on a silica gel19.

14


1.2.3 The Radical Pair Mechanism

is well known that some chemical reactions proceed via the formation of radicals. When

pair of radicals is produced20. Such a pair can

igu illustratio bl the radical pair, depicted using

e vector mo . The spins precess around external field, Bz

state and the two electron spins

It

a chemical bond is broken homolytically, a

have two spin configurations, determined and described by the relative orientation of the

spins of the two radicals to one another. A radical pair can exist in a singlet state, where the

electron spins are arranged anti-parallel to one another so that the total spin quantum

number, S, is zero and the spin multiplicity is one, or a triplet state, where the electrons are

arranged parallel to one another with total spin quantum number, S, equal to one and spin

multiplicity of three (corresponding to the magnetic quantum numbers, ms = −1, 0, +1). The

possibilities can be described pictorially using a simple vector model, such as Fig. 1.1, with

arrows representing the two spins, s1 and s2, of the pair.

F re 1.1: A schematic n of the four possi e spin states of

th del the .

When a radical pair is generated with conservation of spin angular momentum from a

singlet molecular precursor, it will be formed in a singlet

T0

B z Bz Bz B z

s1 s1, s2

s1

s2 s1, s2s2

S T− T+

15

Chapter 1: Introduction are correlated. Once such a pair has formed, it might diffuse, to eventually react with other

species, or it might recombine. The pair is affected by any magnetic fields arising either

from the magnetic dipoles of nearby magnetic nuclei (see chapter 1.1.2) or any applied

magnetic fields. During the lifetime of the radical pair, it is possible for interconversion

between the singlet and triplet states (S-T mixing) to occur. Typically, only singlet radical

pairs can recombine. The fate of any radical pair is therefore dependent on its spin state and

any changes in this spin state. If an applied magnetic field can affect the proportions of

singlet and triplet radical pairs formed, and if these have different fates, then the reaction

might, under favourable circumstances, show a magnetic field effect (see Fig. 1.2, below).

Figure 1.2: A schematic overview of the fates of a radical pair in a reaction, and the basis of the radical

pair mechanism.

T

Diffusion Recombination products or diffusion

MAGNETIC FIELD DEPENDENT STEP

bond breaks

S

e.g. hυ

S-T mixing

16

Chapter 1: Introduction The radical pair is subject to several magnetic interactions, summarised below.

1: Dipole-dipole interaction

2: Exchange interaction

3: Hyperfine coupling

4: Zeeman splitting

The first two are inter-radical interactions. The dipole-dipole interaction arises from the

direct magnetic interaction between the two electron magnetic dipoles. It is an anisotropic

interaction can be assumed to average to zero in systems with rapid molecular motion. The

exchange interaction is a consequence of the Pauli Exclusion principle and arises from

fundamental differences between the singlet and triplet state. Overlap of the two

wavefunctions is forbidden in the triplet state, but not in the singlet state. The S and T

levels are not degenerate, even in the absence of an applied magnetic field. The energy gap

that exists between them is an ever-decreasing function of the separation of the two radicals

and becomes neglible at ~ 1 nm . Hence, there is no mixing of the singlet and triplet states

of the radical pair until the separation between the radicals is large enough for the exchange

interaction to be minimal.

The hyperfine interaction is intramolecular and occurs between the electron spin and any

magnetic nuclei (where I > 0) present in the radical. It can occur directly between the

magnetic dipoles (analogous to the dipole-dipole interaction described above) or through

bonds and electron spins, via the Fermi Contact interaction. The dipole-dipole interaction is

anisotropic and averages out through motion of the radical in solution, leaving the isotropic

21

17

Chapter 1: Introduction Fermi contact. The hyperfine coupling is the main driving force of S-T mixing in low to

moderate magnetic fields.

Zeeman splitting due to an applied magnetic field raises the degeneracy of the ms substates

of the radical pair. The size of the splitting is given by Eqn. 1.11. S and T0 states (ms = 0)

re unaffected by the applied field and the T+ and T− states (ms = +1 and −1, respectively)

igure 1.3: Representation of the Zeeman splitting of the triplet and singlet states of a radical pair in an

pplied magnetic field. Expressions for the splittings and the exchange interaction are included for

clarity.

a

raised and lowered, as shown in Fig. 1.3. The exchange interaction, J(r) is also included in

the figure.

T+

F

a

T0

S

T−

E

Applied magnetic field, B

2 J(r)

gμBB

gμBB

18

Chapter 1: Introduction The magnetic field that an unpaired electron experiences is affected by orbital contributions

from nearby nuclei. Hence, the local field experienced by the electron spin is not the same

as the applied magnetic field. A slightly shifted electron g-factor is produced, as used in the

figure above, which is a unique property of the radical (analogous to a chemical shift in

NMR).

(35) localBe

ΒμgE −=Δ

ΒgμΒ)μ-(1gE BBe =−=Δ σ (36)

ixing at different appl

mixing is the Δg mechanism, where the S and T0 states interconvert due to differences in

the electron g-factors of the two radicals. Fig. 1.1 shows that the difference between the S

and T0 states is simply a difference in the phase of the precession of π between the spins. As

the electron spins have different g values, they precess at slightly different frequencies. S-

T mixing occurs at a rate given by the difference in Larmor frequencies of the two

radicals.

Magnetic field effects in reactions that feature spin correlated radical pairs arise from

differences in S-T m ied magnetic fields. One mechanism of S-T

0

h

zBSTω

0= (37)

BΔgμ

his mechanism only occurs in the presence of an applied magnetic field, and a higher field

T

leads to a higher rate of S-T0 mixing.

19

Chapter 1: Introduction Even if the two radicals have the same g-value, their couplings to nearby magnetic nuclei,

agnetic dipoles of the radical and nearby magnetic

uclei are aligned with the field. The nuclei experience an additional field due to the

through the hyperfine interaction, can lead to different precession frequencies. In a large

applied magnetic field, B, both the m

n

presence of the magnetic moments of the nearby nuclei, giving a local field, Bloc.

Iloc amBB += (38)

h

BgμBST0

Δω = (39)

B is the difference i

hyperfine couplings, a, and nuclei the electron is coupled to. This results in a change in the

ion frequency. E I

r the radicals due to the interactions of the magnetic nuclei in the precursor molecule.

ied

eld changes with time and S-T± mixing is possible. A simplified picture of this effect is

Δ n magnetic field experienced by the two nuclei, determined by the

precess ven if two radicals are identical, the values of m could be different

fo

In a weaker magnetic field22, where the field is of a similar size to the hyperfine

interactions, the electron spins precess around a combination of the external and hyperfine

fields. The projection of the electron’s magnetic moment onto the direction of the appl

fi

shown in Fig. 1.4. The frame of reference is rotating with s2 and further interactions

between the electrons s1 and s2 are ignored. The applied field, B, and the hyperfine

component of the local field, A, are depicted by the thick black and blue arrows,

respectively. The electron and hyperfine magnetic moments couple and both precess around

their resultant (brown arrow) and the applied magnetic field.

20


Figure 1.4: S-T± mixing in a low field as a result of the hyperfine interactions. In a rotating frame with

xed s2, the hyperfine interaction, A, and electron spin, s1, precess about their resultant field and the

esses around the applied field.

The mechanisms of spin evolution described above are coherent, as there is a regular

d spin-spin (transverse) relaxation. Radical pairs

rmed with conservation of spin angular momentum will be in the singlet state, a non-

his interaction is not necessarily zero and there are large

uctuations in the local magnetic field experienced by the radical pair. Spin-lattice

fi

resultant prec

cycling of singlet and triplet states. There are also incoherent relaxation mechanisms: spin-

lattice (also known as longitudinal) an

fo

equilibrium population. The equilibrium, Boltzman population distribution is achieved by

relaxation of the radical pairs.

The interaction of nearby magnetic nuclei, such as paramagnetic transition metal ions, on

the radical pair tend to be averaged to zero over time by rapid molecular tumbling.

However, at a given instant, t

fl

relaxation is the process by which the equilibrium populations of the spins in a field are

obtained. Random, local fluctuating magnetic fields match the energy splittings of the

radicals resulting in transitions between their α and β states. Spin-spin relaxation is the

A s1 s2 s

s − 1T S B B A

2

21

Chapter 1: Introduction process by which the polarisation of the spins is lost. The radicals experience a range of

slightly different magnetic fields resulting in slightly different precession frequencies. In

both cases, it is fluctuations in the local magnetic field that lead to the spin mixing. If these

processes occur at fast enough rates compared to the coherent mechanisms of spin-mixing

then the spin system quickly attains thermal equilibrium. A magnetic field effect will not be

seen if the relaxation processes are faster than the processes of singlet-triplet mixing or

radical recombination of the pair.

If a reaction is to show a magnetic field effect by the radical pair mechanism then not only

must it have a step in the reaction which occurs via a radical pair intermediate, but there

must be a mechanism by which the two spin states can mix. Furthermore, the rate of

terconversion between the two states must be on a faster time scale than the rates of

their own production. This can be negative

positive feedback. In this latter case, the

a maximum rate at some later stage in the

in

reaction and relaxation of the two radicals and interactions between the radicals must be

small.

1.3 Feedback and Autocatalysis

Feedback arises in chemical reactions when the products of later steps in the reaction affect

earlier steps in the reaction and the rates of

feedback, where the reaction is self-inhibiting, or

rate of the reaction increases with time, with

reaction, and then falling to zero as the reaction approaches completion23. Autocatalysis is a

type of positive feedback, where the reaction product is itself the catalyst for the reaction.

22

Chapter 1: Introduction There are many examples of feedback in physical, chemical and biological systems. A fire

spreading through a dry field has heat as its autocatalyst – heating the fuel ahead of it until

it combusts and creates more heat. In solution phase reactions, the presence of autocatalysis

a reaction leads to the reaction behaving as a clock. Fig 1.5 illustrates this behaviour. The

onditions [A]0 = 1 M, [B]0 = 0.0001 M and reaction rate

onstant k = 0.5 M−1 s−1.

in

simple autocatalytic reaction:

A + B 2 B rate = k[A][B] (40)

was set up, with the initial c

c

0

0.2

0.4

0.6

0.8

1.2

1

0 5 10 15 20 25 30 35time/s

[A]/m

oldm

-3

Figure 1.5: The fall in [A] for the simple, quadratic autocatalytic reaction A + B 2 B.

[A]/m

oldm

-3

Time/s

23

Chapter 1: Introduction With a small amount of autocatalyst present at the start, the reaction rate is slow but

increases as more autocatalyst is produced by the reaction. After a certain amount of time,

the reaction rate reaches its peak before falling as the reagents are used up. This is seen by

the observer as a sharp change in the solution from one state to another.

When autocatalysis is coupled with diffusion, such as by initiation of the reaction with a

small amount of the autocatalyst in a shallow layer, chemical waves form24. The wave

travels at a constant velocity through the solution, with unreacted solution ahead of it and

fully reacted solution behind it. The boundary between the two regions, the wavefront, is a

narrow region where the reaction is occurring.

If the reaction features a mechanism by which the clock is reset, then oscillations in the

tions is the

elousov-Zhabotinsky reaction, studied in this thesis, but there are many other examples of

eroxidise-oxidase reaction27). Magnetic field effects have also been observed in the

waves forms. More exotic behaviour, such

solution are possible. One of the most famous oscillating chemical reac

B

reactions of this type, such as the Bray-Liebhafsky reaction25 (iodate catalysed

disproportionation of H2O2). Oscillations are not limited to solution-phase reactions, with

the behaviour observed in combustion reactions (oxidation of CO, oxidation of simple

hydrocarbon fuels26) and also in biological systems (for example, the horseradish

p

oscillations of the peroxidise-oxidase reaction28.

Complex behaviour arises when these oscillations couple with diffusion in unstirred

shallow layers. Instead of the simple front described above, a single wave, with both a

wave front and a wave back or a series of such

24

Chapter 1: Introduction as chaos, is also possible29. Such reactions can also exhibit excitability where the system

art I details the investigation of a magnetic field effect in a travelling wave reaction and

elousov-

habotinsky reaction is an attractive reaction for this study as there have been some reports

to this, behaviour similar to

has a stable steady state that when perturbed by a small amount quickly returns to its initial

concentrations30. When the perturbation exceeds a certain threshold, a single wave is

generated before the system returns to its original state. This amplification of a small effect

is a common phenomenon in this class of reactions, with small changes in the starting

concentrations often having large effects on the behaviour observed in a reaction.

The work presented in this thesis investigates magnetic field effects in chemical reactions

which display feedback. This thesis is split into three sections.

P

the use of magnetic resonance imaging techniques to study the effect. From a magnetic

field effect readily observed in a bench-top reaction using a Petri-dish and a horseshoe

magnet, the reaction was investigated in increasingly more detail, with magnetic resonance

imaging techniques used to study the effect of different geometry magnetic fields on the

reaction and the role of chemical fingering in the magnetic field effect.

The second section (Part II) details attempts to observe a magnetic field effect in an

oscillating reaction. The kinetics that give rise to wave reactions, as investigated in Part I of

this thesis, also give rise to oscillations, as described in chapter 1.3. The B

Z

of MFEs occurring in the reaction and the mechanism of the reaction suggests that the

reaction might show some magnetic field dependence. Further

25


26

ld be used for this

urpose, it was shown that the magnetometer could follow the changes in magnetic

that observed in this reaction has also seen in many biological systems, making the reaction

a possible model for biological oscillations and feedback.

The last section outlines an investigation into the use of SQUID magnetometers in

following chemical reactions, with an aim of using the high sensitivity of the technique in

observing magnetic field effects. In order to test that the SQUID cou

p

susceptibility of a solution phase chemical reactions. The clock behaviour of the

autocatalytic reactions was more than suitable for this study, as the important features such

as the rapid change in metal oxidation state occur some after the reaction has been initiated.

Part I: MAGNETIC FIELD EFFECTS ON THE

TRAVELLING WAVE REACTION BETWEEN CO(II)EDTA2− AND H2O2

Part I Chapter 2: Introduction

28

2. INTRODUCTION

The travelling wave reaction between Co(II)EDTA2−, and hydrogen peroxide, H2O2,

exhibits a change of colour, with pink Co(II)EDTA2− oxidised at ~ pH 4 to dark blue

Co(III)EDTA−. It also displays a striking visual magnetic field effect when performed in a

shallow layer in a Petri-dish1. The reaction can be initiated by a small amount of sodium

hydroxide solution and a wave moves out isotropically from the initiation site. However,

with only a small horseshoe magnet placed under the dish, the dark blue region forms a

dumbbell shape (Fig 2.1). No effect is seen if a non-magnetic blank is used instead of the

horseshoe magnet.

(a) (b)

Figure 2.1: Photographs of the reaction of Co(II)EDTA2− with H2O2 in a shallow layer in a Petri-dish in

the absence (a) and in the presence (b) of an applied inhomogeneous magnetic field. The position of the

poles of the horseshow magnet is shown by black lines in (b). The Petri dishes have a diameter of 90

mm, and the gap between magnet poles was 20 mm. Light, pink regions are areas of unreacted solution

and dark, blue regions are areas of reacted solution.


The reacting solution used in Fig. 2.1 is a 9:1 by volume mixture of 0.02 M Co(II)EDTA2−

and 35 % H2O2, initiated with a small droplet of 0.016 M NaOH. A possible net reaction

mechanism, suggested by He et al.1, is shown here:

Co(II)EDTA2− + H2O2 → Co(II)EDTA. HO23− + H+ (1)

Co(II)EDTA. HO23− + Co(II)EDTA2− + H2O → 2 Co(III)EDTA− + 3 −OH

(2)

Hydroxide ions catalyse the reaction through the penetration of the peroxo-ligand into the

inner coordination sphere of the Co(II)EDTA2−. Dissociation of the first EDTA dentate site

is usually slow, but −OH ions readily penetrate this sphere, displacing one of the dentate

sites. This labilizes the chelate ring, facilitating further substitution1. The Co(II)EDTA2−

complex subsequently reacts with the H2O2. Since −OH is a product of the full reaction, the

reaction is autocatalytic. There is also formation of oxygen, observable after the reaction

has clocked. This results from the disproportionation of excess H2O2 in the alkaline,

Co(III)EDTA− product solution.

Accompanying the reaction is a change in magnetic susceptibility of the solution. The

Co(II) in the Co(II)EDTA2− complex has a d7 high spin electronic configuration, giving it

three unpaired electrons and making the ion paramagnetic. The product of the reaction,

Co(III)EDTA−, has a d6 low spin configuration, due to the increased charge on the cobalt

atom, and possesses no unpaired electrons. This ion is diamagnetic. This change in

magnetic property across the reaction wave front is the most probable cause of the

29


sensitivity of this reaction to magnetic field gradients. He et al. suggests that the effect

observed occurs due to the different behaviours of Co(II)EDTA2− and Co(III)EDTA− in

inhomogeneous magnetic fields. The Co(II)EDTA2− ions are attracted up the magnetic field

gradient, where they react, and the diamagnetic Co(III)EDTA− ions formed are repelled

down the magnetic field gradient. A related reaction, the Co(II)-catalysed autoxidation of

benzaldehyde2, shows very similar behaviour suggesting that the magnetic field is acting on

the transport of the various solutions involved rather than on a specific part of the chemistry

of the reaction.

The Petri dish experiments give a clear illustration of the magnetic field effect but they are

not suitable for a quantitative analysis of the reaction. In order to get a better idea of the

nature of the magnetic field effect, a series of preliminary studies were undertaken. A

simplified apparatus was designed and built to study the movement of a reaction wavefront

in a shallow trough up or down a known magnetic field gradient. Subsequently, the reaction

was investigated in vertical tubes using both visual and magnetic resonance imaging (MRI)

techniques to follow the wave. These experiments allowed well-defined magnetic fields and

field gradients to be applied to the reaction. All experiments involving this reaction were

strongly affected by free convection around the boundary between the reacted and

unreacted solutions. This convection has an important role in explaining the origin and

magnitude of the magnetic field effect.

30


2.1 Magnetic Resonance Imaging

The conversion of paramagnetic to diamagnetic ions across the reaction front allows a

study of the reaction using magnetic resonance imaging (MRI) techniques. The protons in

the water surrounding the Co(II)EDTA2− and Co(III)EDTA− ions show different relaxation

characteristics, due to the presence of unpaired electron spins in the Co(II)EDTA2− ions .

This difference can be exploited to produce relaxation contrast images of the travelling

wave. Not only do MRI techniques allow accurate measurement of the wave velocity, but

any pattern formation can be studied in terms of concentrations3. Furthermore, study is not

limited to contrast images. A variety of other techniques can be used to follow the wave.

Those that image the velocity profile of fluid flow in the sample are of particular interest.

The gradient coils used in imaging the wave can also be used to create linear, homogeneous

magnetic field gradients which can then be used to manipulate the wave.

2.1.1 Basics of Magnetic Resonance

Nuclear magnetic resonance (NMR)4 methods enable information about systems with

magnetic nuclei to be obtained by probing the energy splittings between nuclear spin states

in the presence of applied magnetic fields. In 1.1.2, a series of equations were produced that

describe the energy levels of electrons in an applied magnetic field. It was also shown that

nuclei with nuclear spin, I, form analogous systems. The equations are listed below, as a

reminder.

h1)I(I +=I (3)

, where = I, I−1, ..., −I (4) hIz mI = Im

31


IIμ NN

N γμ

g =⎟⎠

⎞⎜⎝

⎛=h

(5)

(6) Bμ ⋅−=E

The gyromagnetic ratio, , has the value 4.258 × 107 T−1 s−1 for 1H nuclei. In the presence

of a strong magnetic field, B, along the z-axis, the expression of the energy of a state with

magnetic quantum number mI is therefore:

Nγ

(7) zI γBmE h−=

For a proton, I = ½, the two values are +½ and –½. Transitions between the energy

levels are subject to the selection rule = ±1, and in the case of a proton, this gives an

energy gap of:

Im

IΔm

(8) γBΔE h=

Absorption of a photon that has the same energy as the energy gap between the two states

will cause a transition between the two states. Given the relationship between the energy of

a photon and its wavelength, the resonance or Larmor frequency of the proton, , is found. Lν

(9) LhνE =Δ

2πγB

hEνL =

Δ= (10)

32


However, protons do not typically resonate at the determined by the applied magnetic

field. Small variations in the field experienced by the nuclei due to the local magnetic and,

therefore, chemical environment lead to range of resonant frequencies of the protons in the

sample (for example, protons in an organic molecule). Chemical shifts can be produced by

comparing these resonant frequencies with those from a known standard.

Lν

The principle underlying both NMR and MRI is that the resonance frequency of a spin is

proportional to the magnetic field it is experiencing. By applying magnetic field gradients

across a sample, the spins experience a field that is now also dependent on their position

within the sample as well as their chemical environment. This is key to MRI.

2.1.2 Spin Relaxation

Chemical shifts are not the only information that can be extracted from an NMR signal.

Differences in the relaxation of the induced magnetisation of the proton spins occur due to

the different environments, chemical and magnetic, experienced by the magnetic nuclei.

In an applied magnetic field, at thermal equilibrium, there is a Boltzmann distribution of

nuclear spins between the higher energy state ( = − ½ (β)) and the lower energy state

( = + ½ (α)):

Im

Im

⎟⎠⎞

⎜⎝⎛ Δ

=kT

E-expNN

α

β (11)

33


Nα and are the populations of the two states and T is the temperature. In this case, ΔE

for 1H is 3.143 × 10−26 J at a magnetic field of 7.0 T at 300 K and corresponds to a

difference of three or four spins in one million. This net alignment of the magnetic dipoles

in the magnetic field leads to a macroscopic magnetisation of the bulk sample, M0. The

applied magnetic field in the spectrometer is the static magnetic field due to the

superconducting magnet of the NMR spectrometer and directed along the z-axis. At

equilibrium, there is only magnetisation along the z-axis, Mz.

βN

By applying a radiofrequency (rf) pulse of frequency equal to the Larmor frequency, spins

can undergo transitions between their α and β states. The macroscopic magnetisation tilts

away from the direction of the applied field. The duration of the pulse determines the flip

angle of the macroscopic magnetization. In addition to the loss of magnetisation along the

z-axis, the magnetisation is focused in the phase of the applied rf pulse with a

corresponding increase in the magnetisation in the xy plane (transverse magnetisation Mxy).

After the excitation of the sample, the populations will return to equilibrium. In other forms

of spectroscopy, spontaneous emission, where the nuclei spontaneously drop from a higher

energy level to a lower one, occurs. In NMR this is too slow to have any effect.

Furthermore because the nuclear spins interact weakly with most external influences, they

are effectively decoupled from molecular motions and remain aligned with any applied

magnetic field. However the excited spins are not isolated from other spins in the system or

their surroundings and energy can be exchanged with both through magnetic interactions.

34


There are two processes of relaxation, spin-lattice and spin-spin relaxation, which are

governed by the time constants T1 and T2 respectively. Spin-lattice relaxation is a process

by which nuclear spins flip between their excited state and their ground state, non-

radiatively. Energy is lost to the system as the Boltzmann distribution is regained. This is

an enthalpic process. Immediately after the pulse is applied, Mz starts to return to its

equilibrium value. The rate at which Mz returns to its equilibrium value M0 is governed by

the time constant T1 according to the equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=

1z,0z T

t-exp1MM (12)

Spin-spin relaxation is the process by which spins lose their coherence over time. It is an

entropic process. The transverse magnetisation starts to dephase because the individual

spins experience slightly different magnetic fields due to the presence of other spins in the

sample, such as other protons in a water sample. This gives rise to a range of different

precession frequencies. The rate at which falls towards 0 is governed by the time

constant, T2, according to the equation:

xyM

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

2xy,0xy T

t-expMM (13)

As the spins move around in the solution, there are a number of temporary, random

interactions with the other spins in the sample and these have a cumulative effect. Any

35


magnetic interaction can lead to relaxation and the presence of paramagnetic ions in the

sample further increase the rate of the dephasing due to their magnetic dipole moments.

There is a further contribution to spin-spin relaxation that arises from magnetic field

inhomogeneity. This leads to faster spin-spin relaxation than would be expected, with the

time constant replaced by . 2T *2T

(inhomo)T

1T1

T1

22*2

+= (14)

(inhomo)T2 is the relaxation time due to inhomogeneity of the magnetic field. The

dephasing of the spin that occurs due to this inhomogeneity can be refocused by a 180°

pulse.

2.1.3 Magnetic Resonance Imaging

To obtain an image of a sample, magnetic field gradients are applied. The Larmor

precession is now spatially dependent4.

(15) r)G(r)γ(Bω(r) 0 ⋅+=

G(r) is the applied magnetic field gradient and is the Larmor frequency at a given

position, r, within the sample. A 2-D image of a slice of a given sample is obtained by

applying three mutually perpendicular sets of magnetic field gradients.

ω(r)

36


By acquiring the signal in the presence of a magnetic field gradient, the frequency of the

spins will depend on their positions along the direction of the field gradient, according to

Eqn. 2.15. This is known as frequency encoding. The acquired signal will contain a

combination of contributions from across the sample and Fourier transform (FT) techniques

are needed to obtain information from the signal. In the absence of other magnetic field

gradients, the FT of the signal is a 1-D projection profile of the sample. Fig. 2.2 shows a

schematic of frequency encoding by applying a magnetic field gradient, Gx, to a sample. A

position dependent magnetic field leads directly to a position dependent frequency for the

spins.

x

y

Proton at x has frequency:

xG2πγωω x0 +=

Position of spins in x-direction is encoded into frequency of the spins

Magnetic field

gradient, Gx

Figure 2.2: Schematic diagram showing the principles of frequency encoding in magnetic resonance

imaging techniques.

37


To obtain an image in 2 dimensions, a second magnetic field gradient must be applied, but

applying two gradients while the signal is being acquired would merely change the

direction of the resultant gradient. Instead the magnetic field gradient is applied to the

sample before any signal is acquired. This gradient is only applied for a short period of time

and changes the precession frequency of the spins. Once the gradient is removed, the spins

return to their original frequency but with a change in the phase of the spins across the

sample. This is known as phase encoding. Fig. 2.3 shows a schematic of phase encoding.

Assuming a homogenous sample, the spins precess at the same frequency (shown in the

figure by the arrows pointing in the same direction). A magnetic field gradient varying

along the z-axis is applied. The frequency of the spins is changed depending on their

position within the tube as shown in the figure. Once the magnetic field gradient is turned

off, the spins return to their original precession frequency with a difference in phase

introduced along the z-axis.

Magnetic field gradient, Gz

Figure 2.3: A schematic diagram showing the principles of phase encoding in magnetic resonance

imaging techniques.

38


With the two sets of gradients applied so far, the image would be a 2-D profile of the whole

sample. Slices of the sample can be selected by applying a third magnetic field gradient. A

particular slice of the sample is selected by using a frequency selective rf pulse and a

magnetic field gradient. Only spins with the frequency of the selective pulse are excited.

This will correspond to a slice of the sample.

The imaging sequences used in these experiments are based on spin-echo images, as

depicted in Fig. 2.4. The 180o pulse used in this experiment refocuses the spins and

eliminates the effect of field inhomogeneities and chemical shifts. A 90o rf pulse produces

magnetisation in the xy plane, which dephases at a rate governed by the spin-spin relaxation

time, , of the spins in the sample. After a time delay, τ, an 180o pulse is applied and the

magnetisation flips and starts to rephase. This produces an echo at a time 2τ after the initial

pulse that has T2 dependence in its signal intensity.

*2T

39


(a)

90o rf pulse time delay, τ

(b)

time delay, τ

90o rf pulse echo

180o rf pulse

180o rf pulse

τ τ

Figure 2.4: A simple spin-echo experiment. (a) shows the changes in magnetisation in the rotating

frame. Magnetisation starts aligned along z-axis, then a 90o rf pulse along x rotates it into the xy-plane.

Over a period of time, τ, the magnetisation dephases. A 180o rf pulse along x flips the magnetisation,

causing it to rephase and refocus after another time interval, τ. This produces the spin−echo. (b) is a

schematic of the timings, the rf pulses applied and the echoI produced.

Other quantities can be used to introduce contrast into an image, such as spin density and

molecular motion. For the system studied here, there is a pronounced change in relaxation

time across the reaction wavefront and this is exploited.

40


T2 relaxation times can be measured using a Carr-Purcell-Meiboom-Gill (CPMG)

sequence5, based on the spin-echo techniques described above. A 90o RF pulse is applied to

the sample and aligns magnetisation into the XY plane, which dephases at a rate governed

by the relaxation time, (see Eqn. 2.1.14), of the spins in the sample. After a certain time

delay, τ, an 180o pulse is applied, and the magnetisation flips and starts to rephase. The

inhomogeneity of the magnetic field is refocused by this pulse. This produces an echo at a

time 2τ after the initial pulse that has T2 dependence in its signal intensity. After a further

time delay, τ, the magnetisation has dephased again, and a further 180o pulse is applied,

producing another echo. This process is repeated again and again, to obtain a series of

echoes, at intervals 2τ, that display T2 dependence.

*2T

Figure 10.1: Schematic of the pulse sequences and timings of the CPMG sequenceII.

To create a full image of the sample, the whole sequence is repeated with different phase

gradients applied. The number of different phase encoding gradients used determines the

number of pixels in the image. The experiment time is determined by the repetition time of

90o rf pulse echo 180o rf pulse 180o rf pulse echo

Repeated step

τ τ τ τ

41


the experiment and the number of phase encoding gradients used to produce the image.

This could be as long as a couple of minutes. For the imaging of a moving wave, a faster

imaging technique had to be used.

The imaging sequence used to obtain the images in this chapter was the fast imaging,

multiple spin-echo sequence Rapid Acquisition with Relaxation Enhancement, RARE6. A

single 90o excitation pulse is used to excite the spins in a sample. As with the basic spin-

echo imaging sequence (Fig. 2.4), a 180o pulse is applied. Once the echo is acquired, the

magnetisation is refocused and a different phase encoding gradient is applied. For each

excitation, multiple echoes are collected so the experiment time is a few hundred

milliseconds. T2 contrast is possible with this imaging sequence, where regions of longer T2

appear brighter than regions of shorter T2. The sampling time for the experiment is

comparable with the T2 relaxation time of the imaged solution, so there is a degree of

blurring, but this is not significant. Fig. 2.5 shows a schematic of the pulse sequence, with

frequency-encoding gradients, phase-encoding gradients, slice selection and the spin-echo

imaging technique all combining to produce the imaging sequence.

42


Gslice

r.f. 90o

τ τ

180o

Gphase

Gread

echo

signal

Repeat step

Figure 2.5: A schematic of the timings, the rf pulses, magnetic field gradients applied and the echoesI

produced for the RARE imaging sequence. In this figure, Gslice refers to the slice selection gradients,

Gphase to the phase-encoding gradients and Gread to the frequency encoding gradients.

In any one imaging experiment, Gphase is changed for each repetition of the spin-echo

sequence. This is shown in Fig. 2.5 by having the gradients superimposed on each other.

2.2 Convective Effects and Chemical Fingering

There is always the possibility of convection while studying any travelling wave reaction,

due to density differences across the reaction boundary. This behaviour has been observed

in a number of travelling wave reactions7 and was also present in the system studied here.

As a chemical wave moves through a solution, the reacted solution behind the wave has

both a different temperature and composition compared to the unreacted solution ahead of

43


the wave. Buoyant forces associated with these density differences will lead to fluid flow,

or free convection. A change in temperature of the solution will lead to a change in its

density. The change in density, ΔρT, due to the enthalpy change of the reaction is given by:

ΔρT = αρ0ΔT (16)

ΔT is the change in temperature in the reaction, α is the thermal expansion coefficient of

water, −(1/ρ)(∂ρ/∂T)P, and ρ0 is the initial density of the solution. There may also be a

change in density, ΔρC, due to the change in composition of the solution, if the partial molal

volumes of the products differ from those of the reactants. This is given by:

ΔρC = βρ0ΔC (17)

ΔρC is the change in density due to a given species, ΔC is the change in concentration of the

species being considered, β is the expansion coefficient of the solution for the species,

(1/ρ)(∂ρ/∂C) and ρ0 is the initial density of the solution. The overall change in density can

be related to a measured change in volume, ΔV, in a solution of initial volume V by:

Δρ = − (ΔV/V0)ρ0 (18)

The total change in density is the combination of the two different contributions.

Δρ = ΔρT + ΔρC (19)

44


If the reaction is exothermic (and most travelling wave reactions are7) and there is an

isothermal increase in volume during the reaction, then the total density change is negative

and the reacted solution is less dense than the unreacted solution. If a reaction is initiated in

a tube, from the top, a descending wave front will form. In this example, Δρ is negative and

the wave front, with less dense reacted solution above a denser unreacted solution is stable.

Convection does not arise and the wave front formed is flat, independent of the width of the

tube. If the wave is initiated from the bottom of the tube, however, the wave front could be

unstable to distortion due to free convection.

If ΔρT and ΔρC are of opposite signs, then the two contributions to the change in density act

in different directions. A reaction wave front that appears, at first glance, to have a stable

density gradient can still distort under free convection. Imagine an exothermic travelling

wave reaction that also features an increase in density as it reacts, so ΔρT < 0 and ΔρC > 0.

A small perturbation to the wave front leaves a small amount of warm, reacted solution in

the unreacted solution. The diffusivity of heat is larger than the diffusivity of any of the

species in the reacted parcel, so the solution in the perturbated volume rapidly cools,

becomes denser than the surrounding solution and sinks. As there is also reaction occurring

across all interfaces between the solutions, this behaviour is seen as a finger of reacted

solution moving down from the reacted solution through the unreacted solution. This

convection is known as ‘double−diffusive’ convection and produces chemical fingers7. If

the reaction is performed horizontally, such as in a trough or in a Petri dish, there is always

the possibility of convection around the wavefront, as the stable configuration of the two

solutions will always be horizontal and the boundary is vertical7.

45


46

It appears likely that the magnetic field effect observed will be associated with free

convection around the wave front. Free convection arises due to changes in the force acting

on the fluid, due to changes in density of the fluid. The magnetic force acting on the fluid is

simply be another force acting on the system.

Part I Chapter 3: Methods and Materials

47

3 METHODS AND MATERIALS

3.1 Materials

Sodium hydroxide, EDTA, cobalt chloride and hydrogen peroxide (35 % by volume) all of

ACS grade were obtained from Aldrich and used without further purification. A 0.02 M

Co(II)EDTA2− solution was made by dissolving a slight excess of EDTA with CoCl2 in de-

ionised water and then adjusting the pH to 4. The reacting solution used in the experiments

was made from the 0.02 M Co(II)EDTA2− and the hydrogen peroxide in a 9:1 ratio. The

H2O2 was stored in a fridge until needed.

3.2 Methods

3.2.1 Preliminary Experiments

The reaction was studied in a shallow trough held between the poles of an electromagnet.

Shaped pole pieces had been designed and built for a previous, preliminary study with

dimensions chosen so that the magnetic field generated had a constant magnetic field

gradient8. Fig. 3.1 shows the dimensions of the two steel pole pieces.


12 mm 42 mm 69 mm

93 mm

30 mm 64 mm

52 mm40 mm

80 mm

Figure 3.1: Shaped pole pieces used to generate a constant magnetic field gradient. Dimensions of the

pieces are shown in the figure. There was a distance of 80 mm between the two poles.

Different magnetic fields and magnetic field gradients could be produced by changing the

size of the current passing through the poles. For the preliminary experiments, the largest

possible current, 65 A through both sets of coils, was used. Using the pole pieces shown in

Fig. 3.1 produces a magnetic field which has a product of magnetic field and magnetic field

gradient that fell linearly from 0.27 T2 m−1 at the convex pole to 0.18 T2 m−1 at the concave

pole. This magnetic field, and product of field and gradient, was measured using a Gauss

54 mm 28 mm

48

Part I Chapter 3: Methods and Materials meter clamped in place at regular intervals between the poles of the electromagnet and is

shown in Figure 3.2.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 10 20 30 40 50 60 70 80

Distance from convex pole/mm

Mag

netic

fiel

d/T

.

0

0.05

0.1

0.15

0.2

0.25

0.3

|Mag

netic

fiel

d ×

mag

netic

fiel

d gr

adie

nt|

. / T

2 m

-1

Magnetic field

Product of magnetic field and field gradient

Distance from convex pole / mm

Figure 3.2: Graph showing how the magnetic field, and the product of magnetic field and its gradient,

changes with distance from the convex pole for the electromagnet and shaped pole pieces with 65 A

through the electromagnet’s coils.

The reaction was studied in a 2 mm layer of the reaction mixture, described in 3.1, in a

PTFE trough 80 mm long with a 5 mm wide channel and was initiated with a small droplet

of NaOH. The wave could be initiated at either end of the trough and the magnetic field

could be switched on or off. The progress of the wave was measured at regular time

intervals and its velocity at given distance intervals calculated. The trough was held flat

49

Part I Chapter 3: Methods and Materials between the poles of the magnet. A photograph of the complete apparatus is shown in Fig.

3.3. The results of these experiments are detailed in chapter 4.1.2.

Power supply

Electromagnet

Trough, held in place

Shaped pole pieces

Figure 3.3: Photo of the complete apparatus used for studying the reaction in a horizontal trough

Experiments were also conducted in vertical NMR tubes using the same reaction mixture as

described in 3.1 and initiated from above by a small amount of aqueous NaOH solution. A

range of different concentrations of NaOH were used. In some experiments, the NMR tube

was stoppered with a syringe cap, inverted and the reaction initiated by injection of NaOH

solution into the bottom of the sample. The progress of the reaction was followed by eye

and by camera in all of these preliminary experiments. The results of these experiments are

detailed in chapter 4.1.3.

50

Part I Chapter 3: Methods and Materials To confirm the differences in susceptibility between the reagents and the products of the

reaction, the magnetic susceptibilities of the Co(II)EDTA2− and Co(III)EDTA− were

measured using a Gouy balance. Co(II)EDTA2− solutions of concentrations 0.05, 0.04,

0.03, 0.02 and 0.01 M were prepared and measured. From these five solutions, a series of

9:1 by volume reacting mixtures with H2O2 were made up and left to react for ~ 24 hours.

These reacted solutions were measured in the Gouy balance. The Gouy balance

measurements gave a mass susceptibility in cgs units which needed conversion into SI units

and then into volume or molar susceptibilities. These measurements can be found in

chapter 4.1.1.

3.2.2 MRI Experiments

MRI experiments were conducted in Cambridge in collaboration with Dr. Melanie Britton

on a Bruker DMX-300 spectrometer equipped with a 7.0 T superconducting magnet

operating at a proton resonance frequency of 300 MHz. The reaction was studied in 5 mm

NMR tubes, using a 25 mm radiofrequency coil, with a maximum vertical observation

region of 30 mm.

Images were obtained using the fast-imaging, multiple echo sequence RARE. In the first set

of MRI experiments, described later in Chapter 4.2.1, the horizontal and vertical fields of

view were 10 mm and 50 mm, respectively, and comprised of a 256 × 64 pixel array. This

gave a pixel size of 195 μm (horizontal) by 156 μm (vertical). In the second set of MRI

experiments, described later in Chapter 4.2.2, the horizontal field of view was 13.5 mm

with a corresponding pixel size of 195 μm by 195 μm. Both vertical (in the zy plane) and

51

Part I Chapter 3: Methods and Materials horizontal (in the xy plane) RARE images were obtained. The vertical images had a slice

thickness of 1 mm and were positioned in the centre of the tube. Horizontal images were

acquired as a set of either six or ten xy slices, with the whole set of slices acquired

simultaneously. Each slice had a thickness of 1mm and a separation distance between the

centres of the slices of 1.2 mm. The field of view of the images was 5 mm in both

directions, comprised of a 64 × 64 pixel array. The positions of both the sets of xy slices

and the zy slices are shown in Fig. 3.4.

Figure 3.4: Schematic figure indicating both image orientation and fields-of-view for (a) a set of six xy

slices and (b) a zy slice. In both diagrams the white slices represents the field-of-view of the image.

Image reproduced from Evans et al9.

The T2 relaxation time of the Co(III)EDTA− solution was sufficiently long that an image

could be obtained from a single signal acquisition. The imaging time was 1 s for the zy

images and 3 s for the xy multiple slice images.

To follow the effect of the magnetic field gradients on the travelling wave, trains of

gradient pulses were applied between image acquisitions. Gradient trains were generated

52

Part I Chapter 3: Methods and Materials using the imaging gradients of the spectrometer and comprised of a sequence where the

magnetic field gradient was switched on for 2 ms and off for 1 ms, cycled 2000 times with

an amplitude of +0.2 T m−1 or −0.2 T m−1. This produced an average gradient of ±0.133

T m−1 over a period of 6 s. Constant gradients were not applied, as the gradient coils could

be damaged. Three sets of gradient trains were applied, at 5 s intervals, between imaging

experiments. Relatively long time intervals between imaging experiments were chosen to

minimize the influence on the wave from the magnetic field gradients associated with the

imaging sequences (typically 0.03 to 0.04 T m−1 for duration of ~350 ms). The timings of

the imaging sequences for the experiments shown in 4.2 are shown in the schematic Fig.

3.5. Heating of the sample due to the imaging sequences and gradient pulses was

negligible.

Imaging sequence

τI s

5 s 5 sτ s Gradient train

6 s

Gradient train

6 s

Gradient train

6 s

τ s

Δ s

n

Figure 3.5: Schematic representing the timings between imaging sequences and gradient sequences for

the experiments detailed throughout 4.2. For each experiment, this sequence is repeated n times.

For the experiments where vertical slices were acquired, τI = 1 s and τ = 11 s, giving a total

experiment time, Δ, = 51 s. For experiments where horizontal slices were acquired, τI = 3 s

and τ = 30 s, giving Δ = 91 s. In a small number of experiments, combinations of the two

types of slice were acquired, with horizontal slices and then vertical slices acquired before

53

Part I Chapter 3: Methods and Materials the sets of magnetic field gradients. For these experiments, the total imaging time was 15 s

and τ = 11 s.

The magnetic field gradients applied were x/Bz ∂∂ , y/Bz ∂∂ and z/Bz ∂∂ . Fig. 3.6 illustrates

the geometries of the magnetic fields for positive and negative z/Bz ∂∂ and y/Bz ∂∂ , with

the larger arrows indicating a region of higher magnetic field. Fig. 3.6.a shows the change

in magnetic fields when a positive or negative z/zB ∂∂ is applied, while Fig. 3.6.b shows

the changes in magnetic fields for a positive or negative y/Bz ∂∂ . Analogous patterns are

obtained upon application of magnetic field gradients x/Bz ∂∂ .

Figure 3.6: Schematic illustrating the changes in magnetic field when magnetic field gradients are

applied to a sample. Larger arrows relate to areas of higher magnetic field.

z z z z

y y y

a) b)

+

y

z/Bz ∂∂ + − − y/Bz∂ ∂

54


In some experiments, combinations of magnetic field gradients x/Bz ∂∂ and y/Bz ∂∂ were

used. In these experiments, the gradients were chosen so that there was a resultant magnetic

field gradient of magnitude 0.2 T m−1 angled at γ° to an arbitrary axis. The magnetic field

gradient = + 0.2 T m−1 was assigned to be at γ = 0. Fig. 3.7.a depicts the magnetic

field gradient with = + 0.2 T m−1 applied to the sample, while Fig. 3.7.b depicts the

magnetic field gradient with

y/Bz ∂∂

y/Bz ∂∂

x/Bz ∂∂ = + 0.128 T m−1 and y/Bz ∂∂ = + 0.152 T m−1 applied

to the sample. This produces a magnetic field gradient with magnitude +0.2 T m−1, with γ =

40.

Figure 3.7: Schematic showing the geometry of combinations of applied magnetic field gradients

applied to the sample. Fig. 3.7.a shows the resultant magnetic field when a gradient, ∂Bz/∂y = + 0.2

T m−1 was applied and Fig. 3.7.b shows the resultant magnetic field gradient when a combination of

magnetic fields were applied, defining the angle γ.

Transverse relaxation times, T2, for the water protons were measured for Co(II)EDTA2− and

Co(III)EDTA− solutions using CPMG experiments. A selection of relevant T2 times for

a) b) xx

∂Bz/∂y = + 0.2 T m-1

γ

∂Bz/∂y= + 0.152 Tm-1 ∂Bz/∂x= + 0.128 Tm-1

y y

55

Part I Chapter 3: Methods and Materials solutions used in these experiments is presented in Table 1. The Co(II)EDTA2− relaxation

times were measured using the 9:1 reacting solutions described in 3.1. The difference

between the relaxation times for the Co(II) and Co(III) solutions was large enough to

achieve the required contrast.

Solution

T2/ms

0.09 M Co(II)EDTA2−

7 ± 1


33 ± 1


71 ± 2

0.018 M Co(III)EDTA−

398 ± 3

Table 1: A selection of relevant T2 relaxation times.

The reaction was initiated inside the spectrometer magnet, ensuring that the wavefront was

not moved through the large stray field and field gradients associated with the 7.0 T

magnet. A simple delivery device was constructed by threading thin PTFE tubing through a

thicker 5 mm I.D. piece of tubing and sliding the thicker piece into the top of the NMR

tube. A small syringe was attached to the end of the thinner tubing. This reproducibly

layered a small amount of the sodium hydroxide solution on top of the Co(II)EDTA2−. The

NaOH solution used was less dense than the Co(II)EDTA2− solution and so initiated the

reaction at the boundary between the two solutions without immediately initiating any

convection due to density differences.

56


57

To observe any effect of reducing convective flow, experiments were conducted in a porous

medium. A 7.5 mm I.D. tube was used for these experiments. Glass balls of various sizes

were used initially as a porous medium, but the reaction initiated on the surface of the balls.

Ion exchange resin interacted with the reacting solution and the reaction no longer initiated.

Packing foam proved not to initiate or interfere with the reaction, and plugs of it were cut

out of a strip and forced into the tube. Standard 5 mm I.D. tubes proved to be too thin. The

wider tube was filled with reacting solution and initiated in the same way as the

experiments in 5 mm I.D. NMR tubes.

Part I Chapter 4: Results

4. RESULTS

4.1 Preliminary Results

4.1.1 Magnetic Susceptibility Measurements

Fig. 4.1 shows the measured volume magnetic susceptibilities of the two solutions used in

the experiments, measured using a Gouy balance, and linear graphs from which

susceptibilities for other concentrations can be obtained.

-12.0

-10.0

-8.0

-6.0

-4.0

-2.0

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Concentration of Co solution/ mol dm-3

Vol

ume

mag

netic

susc

eptib

ility

× 1

0-6 (S

I uni

ts)

Figure 4.1: Volume magnetic susceptibilities of the Co(II)EDTA2− and Co(III)EDTA− solutions in the

reaction studied. Pink line represents Co(II)EDTA2− data and the dark blue line represents the

Co(III)EDTA− data.

58


As expected, the Co(II)EDTA2− solution is more paramagnetic than the Co(III)EDTA−

solution. The magnetic susceptibilities of both solutions are negative for this range and

dominated by the contribution to the susceptibility from diamagnetic H2O (χv = − 9.05 ×

10−6).

4.1.2 Magnetic Field Effect

The reaction was studied by following the wave in the PTFE trough held between the poles

of the large electromagnet (described in Chapter 3.2.1). The progress of the wave was

measured at regular time intervals and its velocity at given distance intervals then

calculated. The results of these experiments are shown in Fig. 4.2.

These experiments give a good indication of the nature of the magnetic field effect. There

was an increase in the velocity of the wave moving from high to low field compared with

the two other reaction conditions. The velocity of the wave travelling from high field into

low field also depended on the position of the wave between the poles of the magnet and,

hence, the product of magnetic field and magnetic field gradient (see Fig. 3.2). There was

also a small deceleration of the wave when moving from low field into high field compared

with the wave velocities where no magnetic field was applied.

59


0

0.02

0.04

0.06

0.08

0.1

0.12

0 10 20 30 40 50 60 70 8

Distance from convex pole/mm

Spee

d of

wav

efro

nt/m

m s

-1

0

Wave travelling fromhigh to low field

No field

Wave travelling fromlow to high field

Figure 4.2: The effect of an applied magnetic field gradient on the velocities of the wavefront in a

shallow trough.

The wave front in these experiments was observed to be flat, in contrast to the distorted

wave front found in the accelerated waves. This apparatus makes the magnetic field effect

easy to observe but there were problems involving convection. A vertical boundary

between two horizontal layers will always be unstable if there is any density difference

between the reacted and unreacted solutions6.

60


4.1.3 Changes in Density and its Effect

The boundary between reacted and unreacted solution is unstable to distortion by chemical

fingering. Fig. 4.3 shows a typical finger forming from a previously flat wave, initiated in a

vertical tube. Note that the NaOH solution used in these experiments is less dense than the

Co(II)EDTA2− solution.

(a) (b) (c)

Figure 4.3: A series of photographs of chemical fingering in the travelling wave reaction between

Co(II)EDTA2− and H2O2 in a vertical tube, at room temperature. The reaction has been initiated at the

top of the tube, forming dark blue Co(III)EDTA−.

A 9:1 by volume mixture of Co(II)EDTA2− and H2O2 was initiated from above by a small

amount of 0.1 M NaOH, and the fingering distortion occurred almost immediately, as seen

in Fig. 4.3.a. Fig. 4.3.b shows the distortion ~ 2 minutes later, with fingers formed around

61


the edge of the tube. These have pooled into a single larger finger which has started to

move down the tube. Note that the ‘head’ of the tendril is larger than the tail. Fig. 4.3.c

shows the finger ~ 5 minutes after the initiation of the wave. The head of the finger is still

larger than the tail and the whole finger has grown, due to reaction occurring across the

whole interface of the reacted solution.

4.1.3.1: Distortion of the Wavefront

When NaOH solutions which were much less dense than the Co(II)EDTA2− solution were

used to initiate the wave, the flat wave front still distorted in the same manner. Even

organic bases, such as ethylamine, that layered immiscibly on top of the Co(II)EDTA2−

solution produced a wave front that ultimately distorted to produce a finger. Using NaOH

made denser with addition of NaCl, the reaction could be initiated at the bottom of the

sample. In these experiments, flat wave fronts developed which did not distort. However,

there was distortion of the wavefront by O2 bubbles rising up from the reacted solution. The

bubbles drag reacted Co(III)EDTA− and –OH with them as they moved through the

unreacted solution. This is unrelated to chemical fingering.

4.1.3.2: Dilatometer Measurements

Following the change in density against time by measuring the mass of the reacting

solution in density bottles of a known volume at regular time intervals indicated that the

reacting mixture decreased in density as the reaction proceeded. A simple dilatometer was

constructed with a large stock of solution in a stoppered conical flask with a thin tube

inserted to measure changes in volume through changes in height of the column of fluid

62


and a temperature sensor to measure changes in temperature. Measurement of the change in

density against time using this method was complicated by the formation of O2 by the

reaction of excess H2O2 with alkaline Co(III)EDTA− solution (around pH 9II). A typical set

of data from the dilatometer is shown in Fig. 4.4. A 9:1 by volume mixture of

Co(II)EDTA2− and H2O2 at pH 4.0 was used. The dilatometer had an initial volume of 325

cm3. The pink line shows the height of the column of fluid in a 1.0 mm I.D. tube and the

black line the temperature recorded by a small electronic thermometer.

Both measurements showed clock behaviour with an induction period preceding a larger

change in the quantities measured. The moment the reaction clocked, O2 formation would

occur in the bulk of the solution. Bubble formation was observed throughout the sample,

forcing the column of reacting solution up and out of the tube, limiting the amount of

information that could be gained from this method.

63


0

5

10

15

20

25

0 10 20 30 40 50 60

Time/min

Hei

ght o

f col

umn/

mm

19.9

20

20.1

20.2

20.3

20.4

20.5

20.6

20.7

Tem

pera

ture

/o C

Drop in column height

Column HeightTemperature

Figure 4.4: A typical set of results from the dilatometer. A 9:1 by volume mixture of Co(II)EDTA and

H2O2 at pH 4 was used, with regular measurements of both the height of the column of fluid (pink line)

and temperature (black line).

The most important feature was the sudden drop in volume just before the formation of O2,

while the temperature of the solution kept rising. This corresponds to an increase in the

density due to the changes in composition accompanying a fall in density due to the

exothermicity of the reaction. The dip and the clock behaviour of the temperature and

column height were reproduced in every experiment using this apparatus, as was the

formation of O2 that hindered any attempts to record further data.

64


Reasonable estimates of the sizes of the two contributions can also be made, before the O2

formation dominates the changes in height. There was a fall in the height of the column of

approximately 2 mm just before the reaction clocked. From Eqn. 2.18, this gives an

estimate for Δρ of ~ + 0.006 kg m−3. From Eqn. 2.16, ΔρT at this point can be estimated as ~

− 0.06 kg m−3. ΔρC is then given as ~ + 0.066 kg m−3. The different contributions to the

change in density can be seen though, with ΔρC > 0 and ΔρT < 0, conditions that can lead to

chemical fingering.

4.2 MRI Experiments

4.2.1 Application of Magnetic Field Gradients, z/Bz ∂∂

The preliminary work in the shallow trough was aimed at studying the effect of a linear

magnetic field gradient on the travelling wave reaction. The first MRI experiments used

magnetic field gradients of a similar geometry to the magnetic fields used in the

experiments detailed in 4.1.2 and were intended to investigate the effect of magnetic field

gradients parallel to the direction of the magnetic field, i.e. and zB z/Bz ∂∂ . The static field

of the superconducting magnet was 7 T and magnetic field gradients, = ± 0.2 T

m−1, were applied to the reaction. Fig. 3.6.a showed a schematic of the geometry of the

magnetic fields, with a positive gradient increasing the magnetic field from the bottom to

the top of the sample.

z/z ∂B∂

65


4.2.1.1 Flat Wave Fronts

After initiation of the reaction with 0.016 M NaOH, a flat wave front formed at the top of

the tube. The wave front then moved down the tube at a constant velocity. Fig. 4.5 shows a

set of typical images of the flat wave, with no magnetic field gradients applied, except for

those required for the imaging sequence. The first image, Fig. 4.5.a, shows the reaction

shortly after initiation, with further images at 102 s and 204 s respectively. Similar sets of

images were found for experiments where gradients, z/Bz ∂∂ = ± 0.2 T m−1, were applied

between images. The progress of the wave was followed by taking a series of images. By

following the position of the edge of the wave in this series, the velocity of the wave was

determined.

(a) (b) (c)

Figure 4.5: A series of 3 MRI images of a travelling wave formed in the reaction of Co(II)EDTA2− with

H2O2, showing the progress of the wave down the tube. Signal intensity is high (bright regions of the

image) where Co(III)EDTA− ions predominate and low (dark regions of the image) where

Co(II)EDTA2− ions predominate. Images depicted were acquired at 102 s intervals.

66


In these experiments, the wave front velocities were small, ~ 8 x 10−6 m s−1, and constant

while the wave is flat. There was no dependence of the wave velocity on the sign or

presence of an applied magnetic field gradient.

Magnetic Field Gradient Strength/ T m−1

Wave velocity/

10−6 m s−1

− 0.2

8.5 ± 1.3

0

8.0 ± 0.9

+ 0.2

8.3 ± 0.5

Table 4.1: Summary of the wave velocities of the reaction, where the wave is flat and undistorted. 4.2.1.2 Distorted Wave Fronts The flat wave that formed after initiation of the reaction wave front eventually distorted. A

small perturbation of the wavefront occurred which then developed into a finger. This

distortion of the wave front typically occurred 5 - 10 minutes after the initiation of the

reaction. The development of the finger was then followed by acquisition of consecutive

images of the finger until it propagated out of the observable region of the image. The

position of the leading edge of the finger was measured in the same way as with the flat

wave, and its velocity calculated in the same way. Fig. 4.6 shows a typical set of images

showing the fingering distortion. The image 4.6.a was acquired as the fingering distortion

became large, and then images were acquired at 51 s intervals, with alternate images

depicted in Fig. 4.6. No magnetic fields were applied between the images except for those

67


involved with the imaging sequence. Similar sets of images were produced for experiments

where magnetic field gradients, z/Bz ∂∂ = ± 0.2 T m−1 were applied.

(a) (b) (c) (d)


H2O2, after the development of fingering. Images depicted were acquired at 102 s intervals. No

magnetic field gradients were applied in between the images.

Once the finger formed, its velocity was constant. The velocities were greater for the finger

than for the flat interface. There was also a magnetic field effect observed. The velocity of

the finger was larger when a negative gradient was applied and slightly smaller when a

positive gradient was applied.

68


Magnetic Field Gradient

Strength/ T m−1

Wave velocity/

10−6 m s−1

− 0.2

173.2 ± 17.7

0

135.1 ± 3.3

+ 0.2

125.8 ± 3.6

Table 4.2: Summary of the wave velocities of the reaction, where the wave has distorted into a finger.

4.2.1.3 Waves in a Porous Medium I

By introducing the reaction into a porous medium, the effect of convection on the reaction

can be reduced. The system was optically opaque and so could only be observed using MRI

techniques. Fig. 4.7 shows a typical series of MRI images following the progress of the

wave through the porous medium. Fig. 4.7.a was acquired shortly after the reaction was

initiated. Figs. 4.7.b and 4.7.c were acquired 153 and 306 s afterwards. No magnetic field

gradients were applied between images. Similar sets of images were found for experiments

where gradients of + 0.2 T m−1 and − 0.2 T m−1 were applied between images. The

velocity of the wave was followed in the same way as in 4.2.1.1 and 4.2.1.2.

z/Bz ∂∂

69


(a) (b) (c)


H2O2, with the reaction performed in a porous foam. Images depicted were acquired at 153 s intervals.

No magnetic field gradients were applied between images.

No fingering of the wave was observed and the velocities of the waves, ~ 8 x 10−6 m s−1,

were comparable with those of the flat waves. There was no dependence of the wave

velocity on the sign, or presence, of the applied magnetic field.

4.2.2 Application of Magnetic Field Gradients x/Bz ∂∂ and y/Bz ∂∂

An advantage of using the MRI spectrometer to follow the wave is that well-defined

magnetic field gradients can be applied to the system and that these gradients are not

limited to those along the z-axis. Gradients of the magnetic field, Bz, along the x- and y-

axes can be generated by the gradients coils used for imaging. These gradients were applied

to the travelling wave in exactly the same way as described in the previous chapters. Using

these gradients, a magnetic field is obtained where the direction of the magnetic field and

the direction of the magnetic field gradient are perpendicular to one another.

70


4.2.2.1 Formation of a Chemical Finger

As described in section 4.2.1, when the wave was initiated by a small amount of 0.016 M

NaOH, the initial wave front was horizontal and flat. After some time, the wave front

distorted and a finger formed. In the experiments where no magnetic field gradients other

than those used for imaging were applied, the position on the front at which the finger

develops was found to be around the edge of the tube, with the finger pooling into the

centre of the tube. Frequently, more than one finger would form. In order to follow the

movement of the wave out of the zy plane, horizontal images in the xy plane were obtained.

These imaging sequences apply a larger number of gradient pulses associated with the

imaging of the reaction, as gradients are needed for positioning in both the xy plane and in

the z axis. A smaller number of image slices were taken to limit the effect of these magnetic

fields on the reaction. Only a limited region of the tube could therefore be imaged at any

one time. Hence, the sets of images were moved down the tube with time following the

progress of the wave down the tube. All of the images in a set of horizontal images are

acquired simultaneously.

Fig. 4.8 depicts a wave which has distorted and a combination of vertical and horizontal

images showing the position of the fingering distortion in the tube. Note that the vertical

image was acquired after the series of horizontal images, so the tip of the finger has moved

down into the last slice between acquisitions of the two images. The figure shows the

formation of two fingers and also a distortion of the wave around the edge of the tube.

71


(a) (b)

Figure 4.8: MRI images of a travelling wave formed in the reaction of Co(II)EDTA2− with H2O2,

showing the fingering distortion of the wave front. Figure 4.8.a shows a series of xy images taken 333 s

after initiation of the wave. Figure 4.8.b shows a zy slice of the wave, acquired 342 s after the initiation

of the wave. Positions of the horizontal xy slices are overlaid onto this image.

However, by application of the magnetic field gradients, y/Bz ∂∂ = ± 0.2 T m−1, not only

was a finger formed from a previously flat wave front, but the position of formation of the

finger in the vertical slice could be controlled. With the NaOH solution used in these

experiments to initiate the reaction and in the absence of applied magnetic field gradients,

fingering of the wavefront did not occur until ~ 300 s after initiation of the wave. Fig. 4.9

shows a typical series of zy images where magnetic field gradients, = + 0.2 T m−1,

were applied between the imaging experiments. Fig. 4.9.a was acquired shortly after the

initiation of the reaction and before any magnetic field gradients were applied to the

sample. Further images were acquired at 51 s intervals, with gradients applied between

images. Fig. 4.9 depicts a series of zy images, acquired at 102 s intervals, with the

intermediate images not shown. The distortion of the wave front can be clearly seen, with a

y/Bz ∂∂

72


finger formed from a previously flat wave and this finger moving down the side of the

NMR tube.

(a) (b) (c) (d)


H2O2. Image 4.9.a was acquired shortly after the initiation of the reaction by NaOH introduced onto the

top of the Co(II)EDTA2− solution. Images 4.9.b, 4.9.c and 4.9.d were acquired 102, 204 and 306 s

afterwards, respectively. Magnetic field gradients, ∂Bz/∂y, = + 0.2 T m−1 were applied, with geometry as

described in 3.2.2.

Application of magnetic field gradients, y/Bz ∂∂ = − 0.2 T m−1, lead to the formation of a

finger on the opposite side of the tube. Fig. 4.10 shows a typical series of zy images where

magnetic field gradients, y/Bz ∂∂ = − 0.2 T m−1, were applied between the imaging

experiments. Fig. 4.10.a was acquired shortly after the initiation of the reaction and before

any magnetic field gradients were applied to the sample. Further images were acquired at

51 s intervals, with gradients applied between images. Fig. 4.10 depicts a series of alternate

images, at 102 s intervals. With the sign and, therefore, direction of the magnetic field

73


gradient reversed, the finger formed on the other side of the NMR tube, from a previously

flat wave.

(a) (b) (c) (d)


H2O2. Magnetic field gradients, ∂Bz/∂y, = − 0.2 T m−1 were applied to the reaction. Some intermediate

images have been omitted.

The position of finger formation was reproducible and dependent only on the direction of

the applied magnetic field gradient. With repeated application of the magnetic field

gradients ( , = − 0.2 T m−1), additional fingers did not develop on the other side of

the tube in contrast to the experiments where no gradients were applied.

y/Bz ∂∂

To further demonstrate that the finger developed in a fixed position, and that there were no

fingers formed outside of the field of view of the zy slice, horizontal images of the wave

were acquired. Fig. 4.11.a shows a flat wave front shortly after initiation. Several sets of

magnetic field gradients, y/Bz ∂∂ = − 0.2 T m−1, were applied between 4.11.a and 4.11.b

with a finger forming down the left hand side of the tube, as expected. Intermediate images

74


of the finger formation have been omitted. Fig. 4.11.b is an image of the finger, acquired

198 s after 4.11a, and Fig. 4.11.c is a set of xy slices acquired 214 s after Fig. 4.11.a. The

last image, Fig. 4.11.d, was acquired 51 s after the set of horizontal images. The position of

the finger tight up against the side of the tube is clear from these images.

(a) (b) (c) (d)

Figure 4.11: A set of vertical images showing the position of the chemical finger formed by the

application of magnetic fields, ∂Bz/∂y = − 0.2 T m−1, on the wave. Images depicting the formation of the

finger in 4.11.b have been omitted. Figure 4.11.c is a series of xy slices acquired between figures 4.11.b

and 4.11.d.

4.2.2.2 Manipulation of a Chemical Finger

Once a finger has formed, its position could be controlled by further application of

magnetic field gradients. Fig. 4.12 shows a chemical wave with a finger formed by

application of a magnetic field gradient, y/Bz ∂∂ = + 0.2 T m−1. Fig. 4.12.a shows a flat

wave shortly after initiation of the reaction. Three sets of magnetic field gradients,

= + 0.2 T m−1, were applied between Figs. 4.12.a and 4.12.b, with the intermediate

images omitted from Fig. 4.12. With the chemical finger formed (as seen in Fig. 4.12.b,

y/Bz ∂∂

75


acquired 153 s after Fig. 4.12.a), magnetic field gradients, y/Bz ∂∂ = − 0.2 T m−1, were then

applied to the reaction. The position of the finger then clearly switched across the tube and

the finger moved down the other side of the tube. Figures 4.12.c and 4.12.d were acquired

204 and 255 s after 4.12.a respectively.

(a) (b) (c) (d)


H2O2 with magnetic field gradients, ∂Bz/∂y, = + 0.2 T m−1 were applied to the reaction between figures

4.12.a and 4.12.b and then magnetic field gradients, ∂Bz/∂y, = − 0.2 T m−1 applied afterwards.

Only the tip of the wave was manipulated by the applied magnetic field gradient. The part

of the finger that had already reacted was not manipulated by the magnetic field gradients.

A second finger, on the opposite side of the tube to the first, also started to form from the

interface at the top of the tube (see Figs. 4.12.c and 4.12.d). The situation was simply

reversed when the finger was formed with the magnetic field gradient, = − 0.2

T m−1, and subsequently manipulated with the magnetic field gradient, = + 0.2

T m−1, as shown in Fig. 4.13. Fig. 4.13.a shows a flat wave shortly after initiation of the

y/Bz ∂∂

y/Bz ∂∂

76


reaction. Three sets of magnetic field gradients, y/Bz ∂∂ = − 0.2 T m−1, were applied

between 4.13.a and 4.13.b, with the intermediate images omitted. With the chemical finger

formed (as seen in Fig. 4.13.b, acquired 153 s after Fig. 4.13.a), the direction of the

magnetic field gradients was switched, and magnetic field gradients, = + 0.2 T m−1,

were applied to the reaction. The position of the finger then clearly switched across the tube

and the finger moved down the other side of the tube. Figs. 4.13.c and 4.13.d were acquired

204 and 255 s after 4.13.a respectively.

y/Bz ∂∂

(a) (b) (c) (d)


H2O2 with magnetic field gradients, ∂Bz/∂y = − 0.2 T m−1, applied to the reaction between figures 4.13.a

and 4.13.b and magnetic field gradients, ∂Bz/∂y, = + 0.2 T m−1, applied to the reaction between figures

4.13.b, 4.13.c and 4.13.d.

Horizontal images were used to further illustrate the movement of the finger across the

tube, as shown in Fig. 4.14. A finger was formed by application of magnetic field gradients,

, = − 0.2 T m−1, with Fig. 4.14.a acquired ~ 300 s after the reaction was initiated, y/Bz ∂∂

77


and clearly showing the developed finger. Fig. 4.14.b was acquired 15 s after Fig. 4.14.a,

showing the finger’s position down the side of the tube. Between Fig. 4.14.b and 4.14.c, the

direction of the applied magnetic field gradients was switched and magnetic field gradients,

, = + 0.2 Tm−1, were applied to the reaction. The vertical image, 4.14.c, acquired

51 s after Fig. 4.14.b, shows the finger moving across the tube. The accompanying set of

horizontal images, Fig. 4.14.d, also shows the manipulation of the finger. The set of xy

slices shown in Fig. 4.14.b is 5 mm higher up the tube than the set of xy slices shown in

4.14.d.

y/Bz ∂∂

(a) (b) (c) (d)

Figure 4.14: A set of MRI images showing the manipulation of a chemical finger by application of

magnetic field gradients, ∂Bz/∂y = + 0.2 T m−1, after the wave has been formed by magnetic field

gradients ∂Bz/∂y = − 0.2 T m−1, using both zy slices (Figs. 4.18.a and 4.18.c) and sets of xy slices (Figs.

4.14.b and 4.14.d). Magnetic field gradients, ∂Bz/∂y = + 0.2 T m−1, were applied between images 4.18.b

and 4.18.c, with no gradients applied between vertical images and sets of horizontal images.

These magnetic field gradients are not limited to simply y/Bz ∂∂ = ± 0.2 T m−1.

Combinations of magnetic field gradients y/Bz ∂∂ and x/Bz ∂∂ can be applied. As described

78


in 3.2.2, the magnetic field gradients were chosen so that the resultant magnetic field

gradient has a magnitude of 0.2 T m−1, directed at an angle, γ, to the zy plane.

Figure 4.15 shows the manipulation of the wave around the xy plane by the application of

combined magnetic field gradients. Magnetic field gradients, y/Bz ∂∂ = + 0.2 T m−1, were

applied to produce a finger on the right hand side of the tube, as expected. Horizontal slices

through this finger are shown in Fig. 4.15.a. Between each set of horizontal images,

acquired at 91 s intervals, γ was increased in 30° increments from 0° (Fig. 4.15.a) up to 90°

(Fig. 4.15.d). Sets of horizontal slices were acquired after each set of applied magnetic field

gradients.

(a) (b) (c) (d)

Figure 4.15: A series of 4 sets of horizontal MRI images of a travelling wave formed in the reaction of

Co(II)EDTA2− with H2O2. Magnetic field gradients, ∂Bz/∂y, = + 0.2 T m−1, were applied to the reaction

to form a finger, shown in Fig. 4.15.a. Between each set of images, magnetic field gradients of

magnititude 0.2 T m−1 and at an angle γ° were applied to the sample, with γ increased in 30°

increments. Images were acquired at 91 s intervals.

79


In the previous experiments, only the reacting part of the wave front was manipulated, so

the sets of xy slices depicted in Fig. 4.15 are not at the same vertical displacement, but

shifted downwards so that the manipulation of the finger can be observed. The first image

in Fig. 4.15.b is 2 mm further down than the first image in Fig. 4.15.a while Figs. 4.15.c

and Figs. 4.15.d start 8 mm and 13 mm further down, respectively.

Figure 4.16 shows a second set of experiments where the application of combined magnetic

field gradients manipulated the wave around the xy plane. Sets of 10 xy slices were acquired

in this set of experiments, imaging a larger region of the reacting solution. Magnetic field

gradients, = + 0.2 T m−1, were applied to produce a finger on the right hand side of

the tube, as expected. This finger is shown in Fig. 4.16.a. Between each set of xy images,

acquired at 91 s intervals, γ was increased in 45° increments, from 0° (Fig. 4.16.a) up to

135° (Fig. 4.16.d), with sets of horizontal slices acquired after each set of applied magnetic

field gradients. As with the previous sets of xy slices, the sets of slices are not all at the

same vertical displacement but moved down the tube to follow the wave’s progress. The

first image in Fig. 4.15.b is 4 mm further down than the first image in Fig. 4.15.a while

Figs. 4.15.c and Figs. 4.15.d start 8 mm and 18 mm further down, respectively.

y/Bz ∂∂

80


(a) (b) (c) (d)

Figure 4.16: A series of 4 sets of horizontal MRI images of a travelling wave formed in the reaction of

Co(II)EDTA2− with H2O2. Magnetic field gradients, ∂Bz/∂y, = + 0.2 T m−1, were applied to the reaction

to form a finger, shown in Fig. 4.16.a. Between each set of images, magnetic field gradients of

magnititude 0.2 T m−1 and at an angle γ were applied to the sample, with γ increased in 45° increments.

81


4.2.2.3 Waves in a Porous Medium II

In analogy to the experiments described in 4.2.1.3, the reaction was introduced into a

porous medium, reducing the effect of convection on the reaction. A series of experiments

were carried out with the solution in porous foam in a 7.5 mm I.D. tube. The system was

optically opaque and so could only be observed using MRI techniques. Fig. 4.17 shows a

typical series of zy images where magnetic field gradients, y/Bz ∂∂ = + 0.2 T m−1, were

applied between the imaging experiments. Fig. 4.17.a was acquired shortly after the

initiation of the reaction and before any magnetic field gradients were applied to the

sample. Further images were acquired at 51 s intervals with magnetic field gradients,

= + 0.2 T m−1, applied between images. The figure depicts a series of zy images,

acquired at 102 s intervals.

y/Bz ∂∂

(a) (b) (c) (d)


H2O2, with the reaction performed in a porous foam. Magnetic field gradients, ∂Bz/∂y = + 0.2 T m−1,

were applied to the reaction. The images shown were acquired at 102 s intervals.

Although there was some distortion of the wave in Figs. 4.17, comparison with Fig. 4.9

shows that the finger was much more developed in the earlier experiments than in the

experiments in the porous medium.

82


As with the experiments in the 5 mm NMR tubes, the direction of the gradients was

reversed. Figure 4.18 shows a typical series of zy images for these experiments. Fig. 4.18.a

was acquired shortly after the initiation of the reaction and before any magnetic field

gradients were applied to the sample. Further images were acquired at 51 s intervals, with

magnetic field gradients, = − 0.2 T m−1, applied between images. The figure depicts

a series of zy images acquired at 102 s intervals.

y/Bz ∂∂

(a) (b) (c) (d)


H2O2, with the reaction performed in a porous foam. Magnetic field gradients, ∂Bz/∂y = − 0.2 T m−1,

were applied to the reaction. The images shown were acquired at 102 s intervals.

As with Fig. 4.17, there was some distortion of the wave and, as with Fig. 4.17, the finger

developed much slower in the porous medium than it did in the experiments in the 5 mm

NMR tube (see Figs. 4.10.). It is also worth noting that in both sets of experiments in the

porous medium the distortion was not quite up against the wall of the tube and there was a

comparable amount of distortion in the two sets of experiments. Fig. 4.18.d also shows the

reaction initiating away from the wavefront, about halfway down the image.

83

Part I Chapter 5: Discussion

5. DISCUSSION

5.1 The origin of the effect

The application of various combinations of magnetic field and magnetic field gradients on

the travelling wave reaction clearly has a large effect. The simple Petri dish reaction,

depicted in Fig. 2.1. shows that even a small magnet can produce a large effect.

The sensitivity of the reaction to applied magnetic fields should arise from the change in

magnetic susceptibility across the reaction wave front and the magnetic force acting on this

but the Lorentz force (Eqn 1.19) could also be acting on the reaction. However, this force

can soon be excluded as it has little effect. The Lorentz force acts in a different manner to

the magnetic force, operating at right angles to both the magnetic field and any flow of

ions. In simulations by Kinouchi et al.10 the Lorentz force acted to inhibit the diffusion of a

species similar to that present in these experiments. This would lead to a homogeneous

magnetic field possibly slowing down the wave’s velocity due to a smaller effective

diffusion constant. Further to the effect being one which would not speed up the reaction,

the fields as high as 106 T were required to have a significant effect on the diffusion

constants of the species involved in the reaction. The magnetic fields used in these

experiments ranged between 7 T for the MRI experiments and around 1 T, and lower, for

the Petri dish experiments. Hence, the Lorentz force does not drive the observed effects.

The preliminary results shown in Fig. 4.2 showed a strong dependence of the field effect on

the product of magnetic field and magnetic field gradient, when the wave is travelling from

84


high to low field. While this does not necessarily exclude the effect of the Lorentz force,

the data suggests that the dominant force is the magnetic force. Previous work focused on

the manipulation of droplets of solutions of paramagnetic ions through a surrounding

diamagnetic solution7. This transport of paramagnetic ions also showed a strong

dependence on the product of the magnetic field and its gradient, as well as on the magnetic

susceptibilities of the fluids involved. Crucially, the magnetic field acted to move the

neutral radical 2,2,6,6-tetramethylpiperidine-1-oxy (TEMPO), so the Lorentz force could

not be acting in these experiments.

The magnetic force could affect the reaction in two possible ways. First, there is the

movement of paramagnetic solution through a diamagnetic solution or, in this case, a finger

of diamagnetic solution through a paramagnetic one. This would occur in the absence of

any reactions, as seen in previous work. There is also the possibility of mixing of the

solutions through convection of the paramagnetic solution into the diamagnetic solution,

where Co(II)EDTA2− comes into contact with the autocatalytic −OH ions, hence, increasing

the reaction rate and wavefront velocity.

The magnetic force is given as:

BBF )(μ

Vχ

0

vM ∇⋅= (20)

This force can be considered as the product of two factors. First, there is a magnetic field-

dependent term proportional to BB )( ∇⋅ which, when expanded, can be written as:

85


( )

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

∂∂

+∂∂

+∂∂

∂

∂+

∂

∂+

∂

∂∂∂

+∂∂

+∂∂

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+∂∂

=∇⋅

zBB

yBB

xBB

zB

By

BB

xB

B

zBB

yBB

xBB

BBB

zB

yB

xB

zz

zy

zx

yz

yy

yx

xz

xy

xx

z

y

x

zyxBB

(21)

Clearly, it is certain combinations of magnetic field and magnetic field gradient that lead to

magnetic forces in a given direction.

The force acting on any droplet or finger of solution is also proportional to the magnetic

susceptibility of the species and the amount of it present. There is a change in magnetic

susceptibility across the reaction wavefront in the MRI experiments where the wave is

initiated at the top of the tube and moves down through the tube. Both solutions are actually

diamagnetic, with a large contribution to the overall magnetic susceptibility from the water

solvent. However, the Co(II)EDTA2− solution is less diamagnetic than the Co(III)EDTA−

solution above it. The difference in the susceptibility across the boundary is the important

quantity as it leads to a resultant force acting on the solution across the boundary.

For the experiments where the magnetic field gradients, z/Bz ∂∂ = ± 0.2 T m−1, were applied

to the reaction, the sample inside the spectrometer is in the magnetic field:

zBzBB z

0z,z ∂∂

+= (22)

86


0z,B =7.0 T is the homogeneous magnetic field produced by the vertical superconducting

magnet of the MRI spectrometer, z/Bz ∂∂ = ± 0.2 T m−1, is the magnetic field gradient

produced by the imaging coils and z is the distance along the z−axis from the centre of the

RF coil (0 - ~ 0.0125) m. Maxwell’s equation 0=⋅∇ B shows that a magnetic field gradient

cannot be produced independently and that the magnetic field gradients z∂/Bz∂ y/By ∂∂ and

must also be produced. These give rise to distance dependent magnetic fields

and .

x∂/Bx∂

xB yB

0z

By

Bx

B zyx =∂∂

+∂

∂+

∂∂

=⋅∇ B (23)

For the period that the magnetic field gradients are applied, the magnetic force acting on the

reaction is:

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

∂∂

⎟⎠

⎞⎜⎝

⎛∂∂

+

∂

∂⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂+

∂∂

⎟⎠

⎞⎜⎝

⎛∂∂

+

=

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

∂∂∂

∂∂∂

=∇⋅=

zB

zz

BB

yB

yy

BB

xB

xx

BB

μVχ

zBB

yB

B

xBB

μVχ

)(μ

Vχ

zz,0z

yyy,0

xxx,0

0

V

zz

yy

xx

0

V

0

VM BBF (24)

It is clear that there are distance dependent forces acting in the x- and y-direction, from the

terms and . However, these are small compared to the force acting in

the z-direction, due to the small distances (~ 0.0025 m) across the tube, and the absence of

x/BB xx ∂∂ y/BB yy ∂∂

87


either or . With =7.0 T and 0xB , 0yB, 0z,B z/Bz ∂∂ = ± 0.2 T m−1 substituted in, an

expression for the force is obtained.

( )⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

+

⎟⎟⎠

⎞∂

⎟⎠

⎞∂

4y

Bx

B

2y

2x

±

⎜⎜⎝

⎛ ∂

⎜⎝

⎛ ∂

=

0.04z1

y

x

μVχ

0

V

.

MF (25)

The size of the forces in the x- and y- directions are no larger than 1 × 10−4 T2 m−1. The z-

dependent term in the z- direction is no larger than 5 × 10−4 T2 m−1. Both of these terms are

much smaller than the ± 1.4 T2 m−1 term and can be safely ignored.

In control experiments, no gradients are applied and the product of magnetic field and

magnetic field gradient is zero, and no magnetic force acts on any of the sample. In the

other experiments, the dominant term in the magnetic force is ± 1.4 T2 m−1, depending on

the sign of the magnetic field gradient. This is a value that changes sign when the sign of

the applied magnetic fields is changed and is effectively constant over the area of the

reaction imaged.

With a magnetic field gradient, = − 0.2 T m−1, the magnetic field is higher at the top of the

tube than at the bottom. In much the same way as with the experiments in the shallow layer,

when the wave is travelling from high field to low, there is increased mixing of the

reagents. The diamagnetic reacted solution is forced away from the high field region and

88


more paramagnetic unreacted solution is pulled up the magnetic field gradient, into contact

with the reacted solution and a higher [−OH]. The magnetic force could also act to simply

move the finger down through the solution. This leads to the greater wave velocity

observed.

When the magnetic field gradient is reversed, z/Bz ∂∂ = + 0.2 T m−1 and the magnetic field

is lower at the top of the tube. With the travelling wave moving down the tube, the wave

moves from low field to high, with the reacted solution always in a lower field region than

the more paramagnetic unreacted solution. This would mean that the force acting on the

reaction would keep the two regions separated, limiting the amount of mixing around the

wave front.

With application of the magnetic field gradients x/Bz ∂∂ and y/Bz ∂∂ , the z-component of

the magnetic field, , is given by: zB

yB

yx

BxBB zz

z,0z ∂∂

+∂∂

+= (26)

As with the previous experiments, these magnetic field gradients cannot be produced in

isolation. In the absence of electric currents in the sample or time dependent electric fields,

Maxwell’s equation (Eqn. 1.31) simplifies to 0=×∇ B and the magnetic field gradients are

related by:

89


x

By

B yx

∂

∂=

∂∂ (27a)

yB

zB zy

∂∂

=∂

∂ (27b)

zB

xB xz

∂∂

=∂∂ (27c)

So there are concomitant magnetic field gradients produced11 and the magnetic field now

has components in the x- and y- direction, as well as that in the z-direction.

z

BzBB xx,0x ∂

∂+= (28a)

z

BzBB y

y,0y ∂

∂+= (28b)

yBy

xBxBB zz

z,0z ∂∂

+∂∂

+= (28c)

x,0B and are both 0 T and the full form of the magnetic force gives: y,0B

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂+

∂∂

⎟⎠

⎞⎜⎝

⎛∂∂

∂

∂⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+

=

yB

zB

zx

Bz

Bz

zB

yB

yx

BxB

zB

yBy

xBxB

μVχ

zyzx

yzzz,0

xzzz,0

0

VMF (29)

90


When magnetic field gradients y/Bz ∂∂ = ± 0.2 T m−1 are applied, the equation for the force

becomes:

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

++±=

z040y04041

0

μVχ

0

VM

...F (30)

As with the case described earlier, the two smaller, distance dependent terms can be

considered insignificant. The values of z would be ~ 0.0125 m and the value of y ~ 0.0025

m at most, which would produce distance dependent forces in the region of 10−5 T2 m−1,

leaving a dominant force in the y-direction that changes direction with the changed sign of

the magnetic field gradient and is nearly constant over the NMR tube.

In the experiments, the magnetic field gradient, y/Bz ∂∂ = + 0.2 T m−1, increases the

magnetic field from left to right in the images presented. The magnetic field increases from

right to left for = − 0.2 T m−1. In the experiments described in 4.2.2 where the

finger was formed from a previously flat wave front by application of one set of gradients,

the finger always forms on the low field side of the NMR tube. Throughout all of the

experiments in 4.2.2, the finger is found to move to the low field part of the NMR tube.

When combinations of magnetic field gradients,

y/Bz ∂∂

x/Bz ∂∂ and y/Bz ∂∂ , are applied to the

reaction, the equation for the force, ignoring any small distance dependent terms, is:

91


⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

∂

∂∂∂

=

0z

BB

zBB

μVχ y

z,0

xz,0

0

VMF (31)

The angle between the resultant magnetic force acting on the paramagnetic solution in the

reaction is then given by the angle between the gradients x/Bz ∂∂ and , exactly what

is observed in the experiments. This provides further evidence that the force producing the

magnetic field effect is the magnetic force.

y/Bz ∂∂

As the finger of reacted solution is composed of mostly diamagnetic Co(III)EDTA−, it is

not surprising that the finger is always found in the area of lowest magnetic field in the

NMR tube. However, only the part of the finger that reacts while the magnetic field is

being applied appears to be moved. If the magnetic field was only acting to move the

diamagnetic finger through a surrounding paramagnetic solution, then surely any

diamagnetic fluid present would be affected and the whole finger would be moved by the

magnetic field gradient. This suggests that the effect is not as simple as the magnetic force

suggests. The fact that a reaction is occurring in the solution appears to be critical to the

observed behaviour.

The role of convection and mass transport in the magnetic field effect is important. In the

experiments with a flat wave, there would be very little velocity around the interface

between the reacted and unreacted solutions and there would be little mixing of the

92


unreacted solution and the reacted solution. In these experiments, the magnetic force

appeared to only act on a convective flow that was already present. With the reaction

performed in a porous medium, similar results were observed. No dependence on the

applied magnetic field was seen when magnetic field gradients were applied and the wave

velocities were of a similar size to those measured with a flat wave. This suggests that the

velocity of the wavefront is determined by reaction and diffusion only in these two cases.

The experiments described in this section start to quantify the magnetic field effects seen

previously. Well-defined magnetic field gradients are applied to the reaction. The reaction

can be sped up and slowed down by the application of magnetic field gradients z/Bz ∂∂

y/Bz

and

the magnetic field effect is highly dependent on the possibility of free convection around

the reaction wave front. The application of magnetic field gradients ∂∂ and

had a more striking effect, as chemical fingering could be induced in a previously

flat wave and then manipulated by the further application of magnetic fields. It was also

found that the wave front could not be driven upwards by a magnetic field gradient, as the

coupling of reaction and diffusion alone ensured that it would propagate away from the

point of initiation.

x/Bz ∂∂

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5.2 Future Work and Applications

With the results reasonably well understood in terms of the magnetic force acting on the

travelling wave reaction, where else can this work go? Not everything has been explained.

Two main questions remain unanswered: first, why is only the part of the finger that forms

while the magnetic field is being applied manipulated by the field and secondly, why do the

magnetic field gradients y/Bz ∂∂ and x/Bz ∂∂ produce a distortion in the wavefront

while needs a distortion in the wavefront to have an effect? Are there any

experiments or models that can give further insight into the difference in behaviour? Also,

is the phenomenon observed here restricted to this reaction, or can other reactions show

similar magnetic field dependence? Can this magnetic field dependence be put to any

practical use? This chapter aims to start answering those questions, or, at least, highlight

how these questions could be answered.

z/Bz ∂∂

5.2.1 Modelling

Modelling the travelling wave and the finger phenomena observed gives an insight into the

nature of the flow around the wavefront. Even if a full, accurate model of the reaction is not

developed, analysing the forces acting on the system and the convective flow they produce

in the reaction would certainly aid understanding of the magnetic field effect and how it

arises. The relationship between the reaction, velocities around the wave front and the

magnetic field effect seen can then be analysed. Even a simplistic model could give

important insight into the nature of chemical fingering and the magnetic field effect. The

aim of this section is to introduce some methods that could be used to model the reaction

and to show some preliminary simulations. The reaction and travelling wave could be

94


modelled using a range of techniques, such as pseudospectral methods12 and computational

fluid dynamics (CFD). The latter technique formed the basis of a series of preliminary

studies modelling the effect of the magnetic field on the wave using the commercial

packages Femlab and CFD-ACE. In both programs, compressible Navier-Stokes flow was

coupled with changes in density of the fluid due to the autocatalytic reaction as a model of

the chemical fingering. It is the intention here to guide further, more theoretical, studies in

this area whilst a full investigation of the observed phenomena is beyond the scope of this

thesis.

In this series of simulations, a 2-D strip, scaled so that the width of the strip equalled the

diameter of the NMR tubes, was the geometry used throughout. A grid was added to the 2-

D strip, splitting the geometry up into a series of small cells. CFD-ACE uses a Finite

Volume AnalysisIII method to solve the equations. Time-dependent solutions were

obtained. Models in CFD-ACE could be made increasingly more complex by adding

different sub-routines modelling changes in different variables, increasing the complexity

of the reactions taking place and adding extra forces, if needed. Instead of starting with all

of the equations, the model was built up in a series of steps, increasing in complexity to

create an increasingly more accurate and realistic model.

A simple autocatalytic reaction can be easily modelled. A travelling wave is produced if an

autocatalytic reaction is coupled to diffusion of the species present in the reaction.

95


Diffusion:

ii2

iii )c(cDR

tc

∇⋅−∇+=∂∂ u (32)

Reaction:

A + B 2 B rate constant = k M−1 s−1

BAA

BAB ckc

tc

,ckct

c−=

∂∂

+=∂∂ (33)

ci is the concentration of a given species, i, and Di is the diffusion constant for that species.

Ri represents the rate of production or removal of a given species, i, due to reaction and u is

a velocity vector. Fig. 5.1 shows the initial conditions for the model. The results of this

simulation are shown in Fig. 5.2. The colour scale is such that where cA =1, the cells are red

and where cA = 0, the cells are blue, with white regions intermediate.

cA=1, cthrough cA=0, cB=1

at boundary

B=0 out

DA = DB = 10−9 m2 s−1

k = 0.25 M−1 s−1

Figure 5.1: A schematic showing the initial conditions for the model of a simple travelling wave using

CFD-ACE.

96


a) b) c) d) e) f)

Figure 5.2: A series of simulations, calculated at 100 s intervals, showing the propagation of the

travelling wave. Details of the model are shown in Fig. 5.1. The model is shown at 50 s intervals, with

the first figure at 0 s. Blue regions correspond to cA = 1, red regions correspond to cB =1.

As expected a wave of B travelling through A is produced and travels from the top

downwards at a constant velocity, as shown by Fig. 5.2. A simple reaction was used first,

because it ensured that an autocatalytic reaction that worked was modelled. The reaction

can be made increasingly more complicated after the physics of the system have been

modelled.

Changes in the density of the solution as the reaction occurs can then be included and these

changes in density will lead to free convection in the sample. To model this, the Navier-

Stokes equation, which models the flow of fluid, is introduced.

97


Navier-Stokes:

( )[ ] Fuuuuu=∇+∇+∇+∇⋅∇−

∂∂ p).ρ()()(η

tρ T (34a)

( ) 0ρtρ

=⋅∇+∂∂ u (34b)

where ρ is the density of the solution, dependent on the composition and the temperature of

the solution and η is the viscosity of the solution, p is the pressure of the solution and F is a

sum of all of the forces acting on the solution, such as gravity. A derivation of this equation

can be found in Appendix II. Eqn. 35 is based on equations featured in chapter 2.2.

Density:

ρ = ρ0 [1 + αΔT + βiΔci + ... ] (35)

ρ0 is the density of the solution at a given temperature and composition (T0, cA,0, cB,0). α

and βi were defined in chapter 2.2. In this first, simplest model, the only force acting on the

system is gravity. Changes in temperature were not modelled. Fig. 5.3 shows the initial

conditions for the model. Boundary conditions now become important. In these

simulations, u = 0 for all of the boundaries.

98


cA=1, cthrough cA=0, cB=1

at boundary

B=0 out

DA = DB = 10−9 m2 s−1

k = 0.25 M−1 s−1

Figure 5.3: A schematic showing the initial conditions for the model of a travelling wave coupled with

density differences, using CFD-ACE.

Two configurations are possible: one where the more dense solution is beneath a less dense

reacted solution (reacted solution has density = 1000.05 kg m−3, unreacted 1000 kg m−3)

and one where the more dense solution lies above a less dense solution (unreacted solution

has density = 1000 kg m−3). The first configuration shows no change from the wave with no

convection added, as would be expected. The propagation of the wave through the solution

was the same as that seen in the first, simplest model. The configuration where the denser

solution lies above a lighter one is unstable with respect to convective distortion. Figure 5.4

shows the development of the distortion over a series of images. The colour scale is such

that where cA =1, the cells are red and where cA = 0, the cells are blue, with intermediate

regions white.

99


a) b) c) d) e) f)

Figure 5.4: A series of images showing the model of the travelling wave, and the distortion due to

convection. Details of the model are shown in Fig. 5.3. The model is shown at 50 s intervals, with the

first figure at 0 s. Blue regions correspond to cA = 1, red regions correspond to cB =1.

The fingering is a reasonable first approximation of the fingering seen in the MRI

experiments. The distortion starts by the walls and then moves down, with reaction

occurring at every interface causing the finger to increase in size as it moves down the tube.

The wave also moves down the tube at a constant velocity, as seen in the MRI experiments.

Images of the velocities around the wavefront can also be produced. Fig. 5.5 and Fig. 5.6

show two pairs of velocity plots. The first pair, 5.5.a and 5.5.b, correspond to Fig. 5.4.c,

and show the x- and y- components of the fluid velocity respectively. Colour scales are

provided for each figure. A positive x-velocity corresponds to one moving from left to

right, while a positive y-velocity is one going upwards.

100


1.05 × 10−4 m s−1

−1.05 × 10−4 m s−1 −2.16 × 10−4 m s−1

9.68 × 10−5 m s−1

0 m s−1

0 m s−1

Figure 5.5: A pair of images showing the fluid velocities near the travelling wave. Details of the model

are shown in Fig. 5.3. Figures were acquired after 100 s. See Fig. 5.4.c for an image of the wavefront at

this time.

The travelling wave in Fig. 5.4.c does not yet show any distortion, but there is already some

flow around the wavefront. Fig. 5.6 shows the x- and y- components of the velocity for the

wave after 200 s, corresponding to Fig. 5.4.e.

101


1.05 × 10−4 m s−1

−1.05 × 10−4 m s−1

9.68 × 10−5 m s−1

−2.16 × 10−4 m s−1 a) b)

0 m s−1

0 m s−1

Figure 5.6: A pair of images showing the fluid velocities near the travelling wave. Details of the model

are shown in Fig. 5.3. Figures were acquired after 200 s. See Fig. 5.4.e for an image of the wavefront at

this time.

The magnitude of the velocity of the flow has not changed, but the region in which there is

convective flow has grown, moving out into the middle of the tube and down away from

the top of the tube. This is reflected in the finger moving down the tube at a constant

velocity. The velocity of the wavefront moving down through the solution has two

components: the wave velocity due to the coupling of reaction and diffusion and the

velocity due to the advection of the species on the fluid flow.

To model the effect of the magnetic field, a second force term can be added, representing

the magnetic force acting on the travelling wave. In order to simplify the problem, the

magnetic force used was an approximation of that given in Eqn. 20:

me)(cell_voluκcBmag =F (36)

102


κ is a constant and cell_volume is the volume of one cell formed by the grid. The force is

calculated on a cell by cell basis at the start of each time step. This expression was chosen

as all of the important details of the original force could be included while it was simple

enough so that reasonable results could be obtained, quickly. The constant, κ, contains the

constant of proportionality between volume susceptibility and concentration, the product of

magnetic field and gradient (assumed to be constant) and μ0. In this expression, the force

was to act only on cB, rather than cA. This should make no difference to the model as a

force acting to drive the reacted solution down should be equal to one acting to drive the

unreacted solution up the tube.

Fig. 5.7 shows the initial conditions for the model. Some results of these simulations are

shown in Fig. 5.8.

cA=0, cB=1 at boundarycA=1, cB=0

throughout

DA = DB = 10−9 m2 s−1

k = 0.25

βA = 1 ×10−6 βB = 5 ×10−5 κ = ± 0.5

Figure 5.7: A schematic showing the initial conditions for the model of a travelling wave coupled with

density differences and with an extra force applied to the reaction, solved using CFD-ACE.

103


Two possible configurations were modelled: one where the force acted alongside gravity (κ

−’ve) and one where it acted opposite to gravity (κ +’ve). For both simulations, the initial

conditions were set up with a denser solution propagating into a less dense solution. Fig.

5.8 shows some of the results of the simulation. Fig. 5.8.a shows the starting conditions for

the simulation and Fig. 5.8.b and Fig. 5.8.c contrast the different effects of the two applied

forces. In Fig. 5.8.b, the force was acting with gravity down the tube, and the travelling

wave was accelerated, while in Fig. 5.8.c, the force acted against gravity, so the distortion

of the wave was limited, leading to a flat wave and a slower wavefront velocity.

a) b) c)

Fmag F g ma

Figure 5.8: A set of images illustrating the effect of the additional force on the travelling wave. Image

5.8.a shows the initial conditions of the simulation. Both images 5.8.b and 5.8.c are of the wave 150 s

afterwards, but 5.8.b has a downwards magnetic force applied and 5.8.c has an upwards one applied.

Details of the model are shown in Fig. 5.7. Blue regions correspond to cA = 1, red regions correspond to

cB =1.

104


It is immediately clear that these simulations do not model the behaviour observed in the

reaction that well. The finger is accelerated but a comparison with Fig. 4.6.b or 4.6.c shows

that the experimentally observed finger has a more well-defined shape.

One key difference between the models and experiments is that the experiments feature

short pulses of magnetic field with no extra force acting on the wave for most of the

experimental time. The expression for the force was simplified, with the smaller terms

ignored and κ estimated, so that some effect would be seen. As described earlier, the aim

was to make a model that worked and then gradually make it more accurate, so the

magnitude of the force could be made more precise in later simulations.

The effect of temperature changes need to be considered in order to fully model the

fingering. In this reaction, the fingering distortion only formed when the wave was

travelling downwards, suggesting that the change in density due to changes in composition

of the reaction dominate in the long term. In light of this, the addition of heat transfer to the

model was held off until a later stage. Heat would be modelled by using the Heat Transfer

option of CFD-ACE, which solved equations based on the conservation of energy.

Preliminary heat simulations including heat production and transfer produced

unsatisfactory results.

It was the aim of this short section to point the way towards potential simulations of this

highly complicated system using available software packages. These initial models do

provide some insight into the forces acting on the reaction, the flow of the fluid they

produce and how the wave distorts, without giving detailed answers. It does however

105


provide a suitable platform for further work modelling both the phenomena of chemical

fingering and the effect of the magnetic force on the fingering.

5.2.2 Velocity Imaging

All of the images presented in Part I of the thesis were RARE images, contrasting the two

regions of the reacting system by exploiting the change of oxidation state across the

reaction wavefront. Variations on this technique exist, allowing the imaging of any velocity

flow in the sample. In the previous section, the simulations showed how convective flow

could interact with the travelling wave. By imaging the velocity of the solution in the

sample, detailed information about the mass transport around the wave front can be

obtained. The aim of this section is to briefly describe some techniques that could have

been used to image the velocity of fluid flow during the reaction, to show examples of the

images produced and what they show about the reaction and to discuss their use and,

ultimately, why they were not used.

The DANTE sequence13 overlays a grid of selective excitement before the image is

acquired and the image produced features a grid, distorted by any flow occurring in the

sample. An example of a DANTE image is shown in Fig. 5.9, with the grid clearly visible.

The image was acquired ~ 300 s after the initiation of the wave without magnetic field

gradients applied. The wave has distorted with fingers formed on both sides of the slice, but

the grid is only distorted close to the surface of the reaction.

106


Figure 5.9: An example of a DANTE image showing the fingering of the Co(II)EDTA2−/H2O2 wave and

the grid used to illustrate any velocity in the sample.

Better techniques at imaging the velocity of flow, such as fast velocity imaging, have been

developed exploiting changes in phase to obtain the velocity profile4. Figure 5.10 shows a

series of images of the Co(II)EDTA2−/H2O2 wave, with a well-developed fingering

distortion, acquired with a fast velocity imaging sequence, designed by Dr A. Sederman.

Two RARE images showing how the wave has developed are included, so that the velocity

image can be compared with the position of the finger. The first two images show the

formation of the finger and its movement down from the wave front. The last image, and

accompanying velocity scale, shows the velocity of the fluid flow in the finger. Only the

fluid associated with the finger is moving.

107


0.7 mm s-1

a) b) c)

0 mm s-1

Figure 5.10: A series of images of a fingering distortion of the Co(II)EDTA2−/H2O2 reaction. Figs. 5.10.a

and 5.10.b are RARE images, with 51 s between the images. Fig 5.10.c is a velocity image of the same

finger, acquired 11 s after 5.10.b, with a colour scale showing the relevant velocities. Note that only

areas which have some signal intensity for the RARE image give information about their velocity.

In both sets of images, the velocity can only be measured in regions that produce a signal in

a RARE image. In these experiments, this means that only the velocity of regions of reacted

Co(III)EDTA− can be measured. The fast velocity imaging sequence also applied more

magnetic field gradients than the standard RARE imaging sequence and these gradients

manipulated the wave to a much greater extent. This limits the suitability of the technique

for analysis of the wave front but it still can be used to illustrate the velocities of flow in the

finger. Used in conjunction with the simulations described in the previous chapter, velocity

imaging could be a useful tool in observing and understanding the interactions between the

reaction, convective flow and the observed MFE. However, due to the increased

manipulation of the finger, a detailed study of the reaction using the technique was not

attempted.

108


5.2.3 Other Reactions

The effects of inhomogeneous magnetic fields applied to travelling wave reactions should

not be limited to the reaction studied here. Any travelling wave reaction containing species

that exhibit a change in oxidation state and, hence, magnetic susceptibility across the

reaction wave front should show similar effects. MRI techniques used here can also be used

to image the reactions. Some reactions that have potential for further, similar, work are

briefly discussed here.

The Belousov-Zhabotinsky reaction would appear to be a prime candidate with waves of

changes in metal oxidation state being observed in an unstirred solution14. The change in

metal oxidation state also means that the reaction can be imaged by MRI techniques15,

although contrast between the oxidised and reduced forms of the catalyst might not always

be achieved, depending on the metal catalyst used16. There are also modifications of the

reaction, such as uncatalysed bromate oscillators that have been imaged using MRI

techniques17.

The reaction of iron(II) with concentrated nitric acid, the basis of the brown-ring test for

nitrates in qualitative analysis, can also produce a travelling wave18. The overall

stoichiometry of the reaction is given as:

3 Fe2+ + 4 H+ + NO3− 3 Fe3+ + 2 H2O + NO (37)

109


HNO2 is the autocatalytic species for the reaction. There is a change in metal oxidation

state across the wave front, which could both be imaged and manipulated. This reaction

shows a large dependence of wave velocity on whether the wave is travelling up or down19,

suggesting that convection plays an important role in the propagation of the wave.

Radical chain polymerisation reactions are a further possibility. In these reactions, the

autocatalyst is not a chemical species but heat. Free-radical polymerisation reactions are

highly exothermic and thermal fronts, analogous to the chemical waves, can form20. The

changing concentrations of radicals in the reaction lead to changes in magnetic

susceptibility. It is also possible that large changes in viscosity could lead to better control

of the magnetic field effect and allow more dramatic manipulation of any wave.

Travelling waves are also found in biological systems. One possible system that exhibits

travelling wave behaviour and also contains paramagnetic species is the Ca2+ waves

observed in sea urchin eggs upon fertilisation. Importantly, the radical species NO is

involved in the signalling process21, with NO possibly acting as an autocatalytic species.

There has been some preliminary work investigating a possible magnetic field effect in this

system, but no magnetic field effect was seen and no further work has been attempted22.

The possibilities for further work on this reaction are not limited to this small section, with

better and different modelling techniques, a large range of possible, similar reactions and

velocity imaging techniques allowing more detailed investigation of the magnetic field

effect. This section should serve to act as an initial guide to any further work.

110


111

At the start of the section, the magnetic field effect was introduced as a reaction in a

shallow layer in a Petri dish, with the magnetic field applied produced by a horseshoe

magnet placed underneath the dish. This effect can be quantitatively explained by

considering the magnetic field gradients around the magnet, with the wave accelerated out

from parallel to the sides of poles, but slowed down when travelling towards them. But the

work detailed here has developed from that initial problem. MRI experiments have shown a

wider range of behaviours, with different geometries of magnetic field having different

effects on the travelling wave. The mechanism by which the field interacts with the

travelling wave has also been investigated. Although not every detail of the magnetic field

effect is worked out and understood, this body of work goes a long way to understanding it

and opens up some interesting ideas for further research.

Part II: AN EXPERIMENTAL STUDY OF THE EFFECTS OF MAGNETIC FIELDS ON

THE OSCILLATIONS OF THE BELOUSOV-ZHABOTINSKY

REACTION

Part II Chapter 6: Introduction

113

6. INTRODUCTION

In Part I, the effect of an inhomogeneous magnetic field on an autocatalytic wave

reaction was observed, identified and investigated. In this section, the possibility that

the kinetics of a reaction could amplify a magnetic field effect is studied. The Belousov-

Zhabotinsky reaction between malonic acid and acidified bromate ions, catalysed by

metal ions, exhibits homogeneous oscillations in solution. A small body of work exists

suggesting that an applied magnetic field has an effect on the reaction, although there is

some doubt on the matter. Could the inherent autocatalysis of the reaction amplify any

magnetic field effect into one observable in the oscillations of the reaction? The sharp

changes in colour of the reacting solution allow for easy observation of the reaction, and

any potential effect on the reaction. The reaction also serves as a potential model of

biological systems as many of the features seen in this reaction are also observed in far

more complex systems.

6.1 A Brief History of the Belousov-Zhabotinsky Reaction

The Belousov-Zhabotinsky (BZ) reaction arose from attempts to replicate the Krebs

cycle using citric acid, a cerium salt and acidified bromate in 19511. The yellow colour

of the Ce4+ salt vanished, as expected, but then oscillations in the colour of the solution

between yellow and colourless were observed. These oscillations lasted for up to an

hour. And yet, even with recipes, photographs and an easily reproducible phenomenon,

referees refused to publish his results, saying that his “supposedly discovered

discovery”2 was impossible.


There is a long history behind oscillating reactions, with oscillations in the combustion

of phosphorous observed by Boyle in the 1600s, but by the 1900s, it was assumed that

any oscillating reaction would pass through equilibrium on each oscillation and that the

Gibbs free energy of the system would decrease and then increase as the reaction took

place. The Bray reaction, a reaction between iodate and hydrogen peroxide3, first

attracted many more papers attempting to debunk the oscillations reported than trying to

explain their existence4. The BZ reaction was famously denied publication for several

years. It took further work by Zhabotinsky5 and theoretical work to show that the

reaction did not necessarily break the Second Law of Thermodynamics6. It was shown

that the oscillations are not of the reagents or products but of intermediate species such

as Br−, HBrO2 and the metal catalyst. Field, Körös and Noyes then produced a

mechanism for the reaction (the classic FKN mechanism7), which reproduced many of

the features of the reaction in particular its oscillations.

The BZ reaction shows a wide range of behaviour, from simple oscillations in a well-

stirred batch reaction, to series of wave trains when left unstirred, with more

complicated behaviour such as spiral patterns8 and chaotic oscillations9 also possible.

The reaction can be modified with a range of different metal catalysts and organic

substrates to provide an even greater range of behaviour. With the ruthenium salt

Ru(bipy)32+ as a catalyst, for example, oscillations in luminescence are observed under

ultraviolet irradiation10. This catalyst is also photosensitive, allowing manipulation of

the reaction using light11. Ce(III), Mn(II), Np(V) and ferroin (a complex of iron(II) and

1, 10 - phenanthroline) have all been investigated as catalysts of the reaction. The

organic substrate can also be modified. The first BZ reaction used citric acid, but

malonic acid is now more commonly used. Methyl-malonic acid and gallic acid have

114


also been used in the reaction. More interesting is the use of compounds such as 1, 4-

cyclohexadione, which give rise to systems that do not need the metal catalyst12.

The change in colour of the metal catalyst provides an easy way to monitor the changes

in the state of the reaction but oscillations may also be observed in the redox potential

of the solution, determined by the ratio of metal in its oxidised and reduced forms, and

in the bromide ion concentration.

6.2 Mechanism of the BZ Reaction

The FKN mechanism, developed in 19727, was a key point in the history of the reaction.

It proposed a detailed mechanism for the reaction and gives a framework for

understanding the various phenomenon observed. It has been constantly updated, as

further experimental evidence has become available.

The overall reaction is driven by the oxidation of malonic acid by acidified bromate, but

the direct reaction between the two is slow.

3 BrO3− + 5 CH2(COOH)2 + 3 H+ → 3 BrCH(COOH)2 + HCOOH

+ 4 CO2 + 5 H2O (1)

The FKN mechanism is split into three sections: process A, the removal of bromide, an

inhibitor of the reaction, from the system, process B, the autocatalytic reaction that

oxidises the metal catalyst and process C, the regeneration of bromide and reduced form

of the metal catalyst by reaction with organic substrate. Processes A and B form the

115


clock part of the reaction, with an induction period followed by a rapid autocatalytic

reaction. HBrO2 is the autocatalytic species in process B. Process C resets the clock.

A summary of the key parts of the mechanism is shown below. The reaction labels are

those used by the FKN mechanism.

Process A

HOBr + Br− + H+ ⇌ Br2 + H2O (FKN 1)

HBrO2 + Br−+ H+ ⇌ 2 HOBr (FKN 2)

BrO3− + Br− + 2 H+ ⇌ HBrO2 + HOBr (FKN 3)

Process B

BrO3− + HBrO2 + H+ ⇌ 2 BrO2

. + H2O (FKN 5)

BrO3− + HBrO2 + H+ ⇌ Br2O4 + H2O (FKN 5a)

Br2O4 ⇌ 2 BrO2. (FKN 5b)

BrO2. + Mred + H+ ⇌ HBrO2 + Mox (FKN 6)

Process C

MA + Br2 → BrMA + H+ + Br− (2)

2 Mox + MA + BrMA → 2 Mred + f Br− + organic products (3)

2 HBrO2 ⇌ HBrO3 + HOBr (FKN 4)

116


f is a stoichiometric factor that can be adjusted to allow for different types of behaviour.

MA represents malonic acid and Mox and Mred are the oxidised and reduced forms of the

metal catalyst used in the reaction. The step shown here is a simplification of a large

series of reactions. The full mechanism for this process is radical in nature, consisting of

many reactions and further intermediates and products, such as oxalic acid, mesoxalic

acid, tartronic acid, brominated species and radical species13,I.

An idea of the scale and complexity of this organic step is given by the GTF model13

which has 26 reacting species and 80 reaction steps, of which 66 involve the formation,

removal or reaction of radical species. Not all of the 80 reaction steps are vital for

oscillations to occur14. However, this model still features the inorganic spine, shown

above. There have been successful attempts to simplify and model the FKN mechanism,

with the Oregonator, a simplified, reduced model15, widely used.

A + Y → X + P (O1)

X + Y→ 2 P (O2)

A + X → 2 X + 2 Z (O3)

2 X → A + P (O4)

B + Z → ½ f Y (O5)

In this model, A, B and P are the reagants and products, BrO3−, organic species such as

MA and HOBr, while X, Y and Z are the reaction intermediates: HBrO2, Br− and Mox.

The Oregonator can be simplified down to two or three variables. Key features of the

behaviour of the reaction can be reproduced using the model.

117


Fig. 6.1 shows some typical oscillations in Br− and cerium concentration for the reaction

to illustrate the behaviour of the reaction and to link the changes in concentration shown

in the figure to the reaction scheme shown above. These are usually recorded using a

platinum electrode, or absorption of light for the metal ion concentration and a bromide-

ion specific electrode for the Br−II.

[Ce(III)]

[Ce(IV)]

[Br−] A

B

C

D

a) b) A

Time Time

Figure 6.1: Typical changes in the concentrations of a) metal catalyst (cerium, in this case) and b)

Br− for two oscillations in the BZ reaction. Letters A, B, C and D refer to distinct sections of the

reaction and are explained in the text.

Fig. 6.1.a shows the changes in the metal catalyst, with a sharp increase in the oxidised

form of the metal catalyst followed by a more gradual return to the reduced form. This

behaviour can be observed as colour changes of the reaction. Fig. 6.1.b depicts the more

complex changes in the concentration of bromide. AB is a period of slow bromide

118


consumption, corresponding to process A (FKN 1-3), where Br− reacts with BrO3− and

HBrO2. When Br− falls to a certain, critical value, reaction FKN 2 is too slow to prevent

the reaction of HBrO2 with BrO3− and the autocatalytic FKN 5 dominates, with a large,

rapid increase in HBrO2. The section BC in Fig. 6.1.b corresponds to the sharp increase

in [Ce(IV)] in Fig. 6.1.a. The remaining small amount of Br− is rapidly consumed by the

rapidly increasing [HBrO2] and FKN 2. DA is a phase of rapid bromide production,

where the oxidised form of the metal catalyst reacts with BrMA to form Br−. The

reduced metal catalyst is regenerated, as seen in Fig. 6.1.a, and HBrO2 is removed by

reaction with Br− (FKN 2) and by disproportionation (FKN 4). A period of slow

bromide production, CD in Fig. 6.1.b, can appear in solutions with low concentrations

of MA present. Br2, produced in FKN 1, is removed by MA at too slow a rate and

accumulates, rather than reacting with the enol form of the MA to form Br−.

The original mechanism proposed by Field, Körös and Noyes7 has undergone some

revision since its publication. A revision of rate constants occurred as calculations

showed that some of the original set of rate constants were in error by several orders of

magnitude. These rate constants were calculated using the minimum amount of

thermodynamic and kinetic data, and as more information on the system was collected,

more accurate rate constants were produced. The key issue arose from estimating the

pK of HBrO2. A value of 2 can be assigned, based on the Pauling model of the strength

of oxyacids, but a value of ~ 4.9 was found to be more accurate16. A second set of rate

constants was developed, based on this change. The role of Br− in controlling the

reaction has also been put under some scrutiny. Addition of silver should suppress

oscillations as the formation of AgBr (solubility product at 25°C = 5 × 10−13 mol2 dm−6)

would quickly remove the Br− from the system. However, oscillations persisted, with no

119


oscillations of Br− recorded by a bromide ion specific electrode17. This raised the

possibility of radicals, such as MA., being the control intermediate.

The inorganic oxybromine chemistry that makes up the backbone of the reaction has

remained essentially unchanged from its first formulation. The revised set of rate

constants developed in the years following the publication of the original FKN

mechanism are summarised in Table 1. Values in table obtained from Field et al18.

FKN step

Forward rate constant

k+

Reverse rate constant

k−

1

8 × 109 M−2 s−1

110 s−1

2

3 × 106 M−2 s−1

2 × 10−5 M−1 s−1

3

2 M−3 s−1

3.2 M−1 s−1

4

3 × 103 M−1 s−1

1 × 10−8 M−2 s−1

5a

42 M−2 s−1

2.2 × 103 s−1

5b

7.4 × 104 M−2 s−1

1.4 × 109 M−1 s−1

6

8 × 104 M−2 s−1

8.9 × 103 M−1 s−1

Table 1: Summary of the rate constants of FKN mechanism for the cerium-catalysed BZ reaction in

aqueous solution.

120


Ferroin was used throughout the preliminary work to give an easy visual check on

whether oscillations were occurring. However, by changing the catalyst from cerium to

ferroin, several things are altered. In the experiments performed here, the key change is

that the BrO2. radical reacts with a different metal catalyst and this dramatically changes

the forward rate constant of that reaction18.

BrO2. + Ce(III) + H+ ⇌ Ce(IV) + HBrO2 (FKN 6)

k6+ = 8 × 104 M−2 s−1

BrO2. + ferroin + H+ ⇌ ferriin + HBrO2 (FKN 6*)

k6*+ = 1.9 × 109 M−2 s−1

There are other changes to the chemistry as the oxidised forms of the two metals react

with malonic acid in different ways. For the ferroin-catalysed reaction, this process is

very complicated19 and believed to feature radicals, due to the reaction

ferriin + MA ⇌ ferroin + MA. (4)

The BZ reaction is also sensitive to the addition of certain species which can interfere

with the oxybromine chemistry, leading to changes in the periods and even resulting in

the suppression of the oscillations. For example, Cl− ions interfere with the oxybromine

chemistry, by forming chlorous acid which reduces Ce(III) back to Ce(IV), to such an

extent that oscillations rapidly stop20. The addition of Ag+ has already been mentioned.

The low solubility product of AgBr means that Br− is precipitated out of the solution.

121


This, in turn, means that process A is ‘short-circuited’ and the autocatalytic process B

occurs almost immediately as [Br−] falls rapidly below its critical level.

Irradiation of the reaction with light over a range of wavelengths has been observed to

have an effect on the reaction. The effect of visible light on the ferroin-catalysed

reaction has been studied, with the period and amplitude of the oscillations both

increasing, with suppression of the oscillations observed above a given intensity of

light21. However, irradiation using a laser flash at 632.8 nm has been shown to initiate

waves in a shallow layer22. The photosensitivity of the Ru(bipy)32+ catalysed reaction is

thought to be based on the formation of an excited species, *Ru(bipy)32+, which has a

significantly lower standard reduction potential than the ground state23. The question

now arises as to whether a similar effect could be observed with the reaction studied

here. Whatever effect irradiation of the reaction has depends on the wavelength and

intensity of the light used, the metal catalyst used and the particular state of the reaction,

due to the constantly changing concentrations of reagents as the reaction proceeds.

However, it could be an interesting method of perturbing the reaction without adding

extra solution into the cell. There is also a practical reason for investigating the effect of

light on the reaction. If the reaction is light sensitive then the light used to follow the

reaction could also be perturbing the reaction. These experiments can be used to check

whether the monitoring light used to follow the reaction is having any effect on its

oscillations.

In a shallow layer, the surface of the reaction does not feature any oscillations24.

Oxygen is known to be an inhibitor of the BZ reaction, although the precise effect

depends on the conditions of the reaction. Various methods of dealing with the presence

122


of oxygen have been suggested, adjusting various sections of the Oregonator model.

Predictions of its effect on the reaction can be made by considering the oxygen to be

involved only in the organic part of the reaction (section C of the FKN mechanism)

interfering with the reaction of malonic acid with the oxidised form of the metal catalyst

by forming peroxyl radicals. Reacting solutions that minimise the effect of oxygen on

the reaction can be prepared25. In practical terms, flowing nitrogen through a degassed

solution throughout the experiment would ensure that the reaction is not affected by

oxygen.

6.3 Possibility of a Magnetic Field Effect

There exists a small body of published work detailing the effect of magnetic fields on

the BZ reaction. It is certainly an attractive system for such a study as the feedback

mechanism could allow for the amplification of any small effect. However, the work

published is contradictory as some papers report magnetic field effects in these systems

whilst others show no such effects.

No magnetic field effects were observed in the work of McLauchlan26, who expected

any change in the rate of the constituent reactions to have an amplified effect on the

period of the oscillations. However, several Russian researchers have reported a range

of effects, with static and oscillating fields used to reduce the wavelength of the

travelling waves in a shallow layer27, accelerate the rate of autocatalytic period of the

reaction, when performed as a clock with malonic acid absent28 and increase the

amplitude of the reaction29.

123


More recently, Blank and Soo reported an acceleration of the ferroin-catalysed BZ

reaction when a weak oscillating electromagnetic field (ranging from 0 – 80 μT and 0 –

600 Hz) was applied to the reaction30. A small acceleration of the reaction (up to 10 %),

seen as a decreasing period of oscillation, was observed. This effect fell as the rate of

the reaction increased. The frequency dependence showed that a broad maximum effect

was observed around fields of frequency 250 Hz (for 5 μT fields). These experiments

were then used as a model for more complicated biological systems such as cytochrome

oxidase and Na, K-ATPase. Sontag, however, failed to reproduce the results seen in the

previous work, applying a range of magnetic fields at different field strengths and

frequencies (5 – 2700 μT, 10-250 Hz) to the reaction31. None of the experiments

showed a significant effect on the period of the reaction. Both of these sets of results

were performed in batch reactions.

So could this reaction exhibit a magnetic field effect? The first indication that a reaction

could be magnetic field dependent is the presence of a radical pair in the mechanism of

the reaction. The BZ reaction features many steps that involve radicals, mostly in the

reaction of the oxidised metal catalyst with the organic species present in the reaction.

However, one well-characterised step produces a pair of radicals with two possible

reaction fates – recombination to form the dimer or further reaction with the metal

species. Furthermore, the radicals form from a single precursor, Br2O4, so they should

be spin-correlated. There is also a potential spin selectivity of the radical pair, as the

singlet pair is capable of both recombination reaction or reaction with the metal, while

the triplet is only able to react with the metal species. The potential radical pair is

highlighted in the reaction scheme below.

124


BrO3− + HBrO2 + H+ ⇌ 2 BrO2

. + H2O (FKN 5)

BrO3− + HBrO2 + H+ ⇌ Br2O4 + H2O (FKN 5a)

Br2O4 ⇌ 2 BrO2. (FKN 5b)

BrO2. + Mred + H+ ⇌ HBrO2 + Mox (FKN 6)

Importantly the radical pair highlighted above, 2 BrO2., is formed in the autocatalytic

step of the reaction, suggesting that even small changes in the reaction rates involved

could lead to an amplified effect on the period of the oscillations. It has to be pointed

out that this possible radical pair does not ensure that the whole reaction is magnetic

field dependent but its presence, particularly in the autocatalytic steps of the reaction, is

promising. It is possible that there are other reaction steps that feature radical pairs. For

the rest of this investigation though, discussion will focus on the radical pair identified

here and its properties.

The most likely mechanism by which S-T mixing occurs is through the hyperfine

coupling. With the identical pair of radicals predicted by this mechanism, the Δg

mechanism would have no effect on their spin evolution. Hyperfine constants for the

BrO2. molecule in solution can be estimated from the ESR of the species in an irradiated

K79BrO4 crystal32, which produces an average hyperfine coupling of 99 MHz. This

coupling corresponds to a magnetic field of 3.55 mT. The change in ‘solvent’ from the

solid state to aqueous solution could change the coupling, as any anisotropic

contributions to the hyperfine interaction would be averaged to zero leaving an isotropic

term. Both stable isotopes of bromine (79Br, 81Br) have magnetic nuclear spin quantum

number of 3/2, and are present in nearly equal proportions. Differences in the hyperfine

125


126

couplings of the electron due to the different isotopes could occur, although they should

be small.

A field exceeding a few hundred mT should have a significant effect on a radical pair

with such hyperfine couplings, assuming that there are favourable conditions for

exhibition of a magnetic field effect. Slow relaxation, weak radical-radical interactions

and favourable diffusion increase the likelihood of an effect being observed. If an effect

was seen by a large field, then it is likely that the radical pair formed during the reaction

is being affected by the magnetic field, according to the RPM. If this first study reveals

any effect, further experiments can then be performed, using lower fields and oscillating

fields.

Part II Chapter 7: Methods and Materials

127

7. METHODS AND MATERIALS

7.1 Methods

7.1.1 Continuously-flowed Stirred Tank Reactor (CSTR)

The impact of a magnetic field on the rates of reaction can be studied using the most

obvious feature of the BZ reaction: the change in colour associated with any change in

metal oxidation state. Preliminary experiments were performed in the absence of

malonic acid and the clock behaviour observed using the changing absorption of light as

the reaction proceeds. However, it was very hard to perform the reaction reproducibly

as a single-shot clock as the timings and details of the reaction were observed to vary

hugely. Inhomogeneities such as defects on the cell wall can initiate the reaction and

cause the reaction to act as a wave rather than as a homogenous clock. Even without

such waves forming in the cell, the induction period was still found to be highly

variable, due to minute variations in the starting reaction mixture33.

Given that the full B-Z reaction resets itself by reaction of the organic species with the

oxidised form of the metal catalyst, a series of oscillations could be used to see if some

change to the system has an effect. Batch reactions can be studied but, even though the

oscillations produced can last for several hours, the oscillations eventually die out as the

reagents are consumed. There are also slight differences between consecutive

oscillations as the reaction proceeds, slowly but surely, towards equilibrium. If fresh

reagents are flowed into the cell, then a steady state can be reached where the loss of

reagents due to reaction is balanced by the inflow of reagents into the cell. The contents

of the cell have to be continuously stirred in order to prevent the formation of


inhomogeneities and concentration gradients in the cell. This apparatus is known as a

continuous-flow stirred tank reactor (CSTR)

Although more complicated behaviour can be observed using a CSTR to study the

reactionIII, the main reason for their use in this investigation is that a reacting mixture

can be maintained so that series of oscillations with periods that should not increase or

decrease with time can be produced. Once a series of oscillations is set up, any effect an

external perturbation has on the system can be studied via any observed changes in the

period, amplitude or shape of the oscillations.

A simple apparatus was designed and constructed in PTFE (polytetrafluoroethylene).

PTFE had to be used for two reasons: it is resistant to the highly acidic reacting

solution, unlike other plastics and metals, and also it is not magnetic. Fig. 7.1 shows two

diagrams of the apparatus, one from the front and one from the side. A pump to flow the

reacting solutions through the cell was also built. Two plastic syringes were pumped at

the same rate by a small electric motor attached to a gear box and rack and pinion gears,

with PTFE tubing connecting the two syringes to the cell holder. The overflow tube was

also a length of PTFE tubing, leading away from the cell holder. The reaction was

followed by absorption of light from an Oriel 66011 300 W lamp, with appropriate

filters used to select wavelengths of light. Light guides were used to direct the light into

and out of the cell to a photomultiplier tube (PMT), through a pair of aligned holes in

the cell holder (see Fig. 7.1).

128


Clamp

Inflow pipe

Figure 7.1: Schematic diagrams of the cell holder, built out of PTFE. Top figure shows a front view

of the apparatus, and its position between the two steel poles of the magnet. The bottom figure

shows a slice through the cell holder.

Stirrer

LIGHT IN LIGHT OUT

Direction of flow of reacting solution

Tube cut into PTFE

Cell

PTFE

Flat steel poles of magnet

Clamp OverflowCell volume = 16.7 ml

220 mm 80 mm Holes for light guides

Holes for light guides

129


The lamp and PMT could be placed at a distance from the magnetic field so changes in

the magnetic field would have no effect on the voltage output of the PMT. The signal

produced by the PMT was recorded directly by a PCI 9112 data acquisition card using a

program written in Labview (see appendix IIIa). The oscillations were detected by

changes in the intensity of light passing through the cell, which can be related to

changes in the concentration of the metal catalyst.

Figs. 7.3 and 7.4 show the absorption spectra for the oxidised and reduced forms of

0.0025 M solutions of both ferroin and cerium solutions recorded in a cell with a path

length of 1 mm using a Unicam UV-2 UV/vis spectrometer. In both cases, the oxidised

form was produced by reacting 0.0025 M solution of the reduced metal solution with

0.35 M NaBrO3 and leaving overnight. For the ferroin experiments, a 510 nm filter was

used for the monitoring light and for the cerium experiments; a 380 nm filter was used.

Neither the bromate nor malonic acid used in the experiments absorbed at these

wavelengths.

130


0

0.5

1

1.5

2

2.5

3

3.5

350 400 450 500 550 600 650

Wavelength/nm

Abs

orpt

ion

Broad peak centred ~ 580 nm Absorption ~ 0.04 (See insert)

ferroin

0.02

0.025

0.03

0.035

0.04

450 500 550 600 650 700

ferriin

Figure 7.2: Absorption spectra of aqueous 0.0025 M ferroin and ferriin solutions.

0

0.5

1

1.5

2

350 400 450 500 550 600 650

Wavelength/nm

Abs

orpt

ion

cerium (IV)

cerium (III)

Figure 7.3: Absorption spectra of aqueous 0.0025 M cerium(III) and cerium (IV) solutions.

131


The static magnetic field was generated by a large electromagnet with flat steel pole

pieces designed to produce a homogeneous field. The maximum field strength of the

magnet was 0.14 T and this was used in all of the magnetic field experiments. The cell

holder was designed to hold the cell in between the two flat poles, in middle of the

homogeneous region.

The BZ reaction is very sensitive to both changes in temperature and in stirring rate.

The period of oscillation can depend in a complex way on the stirring rate. Amongst

possible explanations are changes in the interaction between the gaseous and liquid

phases34 and incomplete mixing of the inflow of reagents into the CSTR leading to an

increased inhomogeneity within the reactor35. Any interaction between the stirring rate

and the reaction is going to be complicated. For the CSTR used in these experiments, a

fall in stirring rate lead to both a fall in amplitude and increasing period of oscillation.

Hence, it was crucial that the large static magnetic field would not affect the stirring

apparatus. The motor for the stirrer was placed in a μ-metal box. The arm of the stirrer

was long enough for the stirrer motor to be held away from the cell holder and the high

magnetic field produced by the flat magnetic poles. It was then shown in preliminary

experiments that the applied magnetic field had no effect on the stirring rate of the

stirrer.

The BZ reaction (and its derivatives) is sensitive to changes in temperature, with

increasing temperature leading to both reduced induction periods and periods of

oscillation36. A cell holder built from PTFE does not easily allow for the heating or

cooling of the mixture as the reaction proceeds. Instead, the temperature within the cell

was followed using a calibrated Pt100 and the changes in temperature as the reaction

132


itself proceeded were small, around 1° C. They also fell with time towards a steady

temperature in the cell, achieved after only a few minutes. The change in oscillation

period due to a change of 1° C was less than 1-2 s. The periods of oscillations observed

in the experiments ranged between 100 and 200 s, so the changes in period due to

changes in temperature would be no more than 1-2 % of the period.

Several experiments were performed to calibrate the apparatus. First, series of

oscillations were produced showing that the apparatus functioned as intended and that

oscillations in the metal catalysts could be observed. Subsequently, different

perturbations to the system were applied showing that changes in these oscillations

could be observed by the apparatus. For these experiments, Br− and UV light were used.

Addition of Br− was achieved by briefly removing the stirrer and pipetting 1 cm3 of

AgNO3 solution into the cell. For the irradiation experiments, a second lamp would be

used to irradiate the cell through the higher light guide hole, shown in Fig. 7.1. Finally,

the magnetic field would be applied, and any effect of this on the reaction could then be

determined.

7.1.2 Analysis

The experiments were conducted by flowing the reagent solutions through the apparatus

and obtaining a series of oscillations. After a number of oscillations, the magnetic field

would be turned on and further oscillations recorded before the magnetic field was

turned off. A small number of oscillations with no field applied were then recorded.

To analyse the period of the oscillations, a simple peak detection program was written

in Labview (see Appendix IIIb). This took the data recorded from the PMT and

133


calculated the first and second derivatives with respect to time. Negative peaks of the

second derivative under a certain threshold amount were then picked out and the period

of oscillation calculated by the difference in time between the two peaks. This is shown

in Fig. 7.4, with the red lines showing the raw PMT data of the oscillations, the blue

lines the first derivative with time of this data and the green lines the second derivative.

-5000

0

5000

10000

15000

20000

25000

30000

1020 1040 1060 1080 1100 1120 1140 1160 1180 1200

Time/s

PMT

outp

ut in

to c

ompu

ter

50

60

70

80

90

100

110

120

130

140

150

Osc

illat

ion

perio

d/s

.

raw PMT data

first derivative wrt time

second derivative wrt time

Period data point

Figure 7.4: Diagram showing the raw data, and first and second derivatives, for a pair of

oscillations in the ferroin-catalysed BZ reaction. The period of the oscillation is calculated and

shown as a black square between the two peaks. All data presented in Chapter 8 will consist of

series of oscillations recorded from the PMT and the periods of these oscillations in the same figure

(see Fig. 8.1 for an example).

To determine if a change had occurred, and if that change was statistically significant,

Student’s t-test was used to test if the results were statistically different from each other.

134


It was then proposed that if an effect was observed using the highest field possible using

the magnet, further experiments would be performed using lower fields and oscillating

fields to start to quantify any effect.

7.2 Materials

Sodium bromate, sulphuric acid, silver nitrate and malonic acid, of A.C.S. grade, were

obtained from Aldrich and used without further purification.

A stock ferroin solution was produced by dissolving iron sulphate (FeSO4.7H2O) and 1,

10 – phenanthroline in Analar water to produce a 0.025 M solution. Both the iron

sulphate and 1, 10 – phenanthroline were obtained from Aldrich and used without

further purification. Cerium (IV) ammonium nitrate (Ce(NH4)2(NO3)6) was obtained

from Aldrich and used without further purification.

Table 2 summarises the reacting solutions used in the experiments. A second set of

concentrations for the cerium-catalysed reaction were prepared to eliminate the effect of

oxygen on the reaction25. The original reaction mixture is based on one detailed in

Scott’s “Oscillations, Waves, and Chaos in Chemical Kinetics”.

135


Reaction

(also solution name)

Solution 1

Solution 2

Ferroin-catalysed BZ

0.347 M NaBrO3

0.08 M

H+

0.154 M

MA

0.0025 M

ferroin

Cerium-catalysed BZ

(original)

0.347 M NaBrO3

0.08 M

H+

0.154 M

MA

0.0025 M

cerium(IV)

Cerium-catalysed BZ

(alternate)

0.400 M NaBrO3

0.4 M

H+

0.100 M

MA

0.0025 M

cerium(IV)

Table 2: Summary of the reacting solutions used in the BZ experiments. In order to further

distinguish between the sets of data in the results chapter, a colour code was also used with the data

in the figures drawn using the colours shown above.

The pumping rate for all experiments was 0.0052 ml s−1, with equal flow into the cell

from two syringes. Faster pumping rates were possible but not used.

For the irradiation experiments, a second Oriel 66011 300 W lamp was used. Ultraviolet

light was produced using a filter with a broad peak around 300 nm and Comar filters at

380 nm, 510 nm and 590 nm, with bandwidths of 10 nm, were also available. The light

was directed into the cell using a light guide through a higher hole in the cell holder

(shown in Fig. 7.1). Fig 7.5 shows the % of light transmitted through the filters for the

four filters and the cell used in all of the experiments.

136


0

10

20

30

40

50

60

70

80

90

100

200 300 400 500 600 700 800

wavelength/nm

% tr

ansm

issi

on

.

cell UV filter

590 nm 510nm

380 nm

Wavelength/nm

Figure 7.5: % of light transmitted for the 380, 510 and 590 nm filters, UV filter and cell used in the

experiments detailed in this section. Refer back to Figs. 7.2 and 7.3 for absorption spectra of the

relevant metal catalysts used in the experiments.

In order to minimise the amount of light passing through from the cell to the PMT in the

UV irradiation experiments, a green filter was fixed in place in front of the PMT. This

complemented the UV filter, so very little of the light produced by the second lamp

would pass through the cell and reach the PMT. Increases in light passing through to the

PMT would lead to a higher signal recorded by the data acquisition program. This could

lead to the signal exceeding the maximum that the data acquisition card can read. Large

changes in PMT signal occurring in a short space of time can be interpreted by the peak

detection program as peaks.

137


138

A 0.0167 M AgNO3 solution was made for experiments where silver ions interfered

with the oxybromine chemistry of the reaction. 1 ml of this was pipetted into the middle

of the cell when required giving a concentration of Ag+ in the cell of 0.001 M.

Part II Chapter 8: Results

139

8. RESULTS

8.1: Oscillations

Oscillations were recorded by the apparatus without any change to the reaction

conditions during the experiment. Fig. 8.1 depicts a typical series of oscillations for the

ferroin-catalysed BZ reaction in the CSTR.

0

5000

10000

15000

20000

25000

30000

0 500 1000 1500 2000 2500

Time/s

PMT

outp

ut

50

60

70

80

90

100

110

120

130

140

150

Osc

illat

ion

perio

d/s

.

Figure 8.1: A typical series of oscillations of the ferroin-catalysed BZ reaction in the CSTR.

Reaction solutions are as described in 7.2.

When the PMT output signal is high, the absorbance of the sample at the monitored

wavelength (510 nm) is low and this corresponds to a solution with a high ferriin

concentration. When the PMT output is low, the absorbance of the sample at the

monitored wavelength is high, so the solution has a high concentration of ferroin (see


Fig. 7.4 for relevant absorption spectra). For the typical set of data depicted in Fig. 8.1,

the average period was 113.4 s with a standard deviation of ± 2.0 s. Similar sets of data

were produced, with the standard deviation of the data varying between 2 and 6 s. This

set of results is an indication that the apparatus could be used to follow any changes in

the period of oscillations of a reaction, as long as they are greater than the inherent noise

of our design (~ 5 s).

There is a small amount of noise in the period of oscillation but, given that it is not a

general trend (i.e. an increasing or decreasing period), it must arise from small and

random fluctuations in the temperature or flow rate of the reaction or transient

formation of small areas of inhomogeneity in the cell. These result in small changes in

the concentrations of the reagents inside the cell so that each oscillation is not quite be

the same as the one preceding it. A small fluctuation in the period of oscillation is

introduced. As long as this is only a random variation around a constant period, rather

than a drift in the period, the CSTR can be considered to be working well enough to

detect the effects of applying a magnetic field to the oscillations. An error of the size

observed is unlikely to arise from the peak detection program. A small error could arise

in the location where the peak detection program picks the peak of the second

derivative. However, this should not be more than the time between points (~ 0.4 s).

The difference in period of oscillation between sets of experiments was found to be

greater than the difference in period during an experiment. The BZ reaction is

notoriously sensitive to its initial conditions33, with slight changes in the autocatalyst

(HBrO2) and inhibitor (Br−) concentrations causing large differences in oscillation and

induction period. Other factors such as small differences in stirring rate, temperature

140


and inhomogeneities on the cell wall can cause differences between experiments. As

explained previously, the nature of our apparatus made changing the temperature of the

solutions within it difficult, but once the reaction was running and the solutions flowing,

the temperature remained stable. Another factor that can influence the oscillations is the

presence of trace impurities. Attempts to remove them were taken by using the purest

water available, Analar water, and the chemicals of the purest grade possible. The

apparatus was thoroughly cleaned between experiments with concentrated nitric acid

and rinsed with Analar water.

Fig. 8.2 shows a typical series of oscillations for the cerium-catalysed BZ reaction in the

CSTR, obtained 2500 s into the reaction.

0

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2500 3000 3500 4000 4500 5000 5500 6000Time/s

PMT

outp

ut

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125

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175

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Osc

illat

ion

perio

d/s

.

Figure 8.2: A typical series of oscillations of the cerium-catalysed BZ reaction in the CSTR, using

the reacting solution, cerium-catalysed BZ I, as described in 7.2.

141


Light of wavelength 380 nm was used to monitor the reaction. For this experiment, the

PMT output is high when the reacting solution has a high Ce(III) concentration, and the

PMT output is low when the reacting solution has a high Ce(IV) concentration (see Fig.

7.4 for relevant absorption spectra).

The same issues of reproducibility that affected the ferroin-catalysed reaction also

affected the cerium-catalysed one. For the typical set of data shown in the figure, the

average period of oscillation was 178.5 s with a standard deviation of ± 4.9 s. Similar

sets of data were produced with similar standard deviations in the period data. As with

the ferroin catalysed reaction, the difference in period of oscillation between sets of

experiments was found to be greater than the difference in period during an experiment.

The oscillations seen in both sets of experiments are as expected for the reaction

(compare with Fig. 6.1.a), with rapid production of the oxidised metal catalyst and a

more gradual return to the reduced form. The difference in period between the ferroin-

catalysed and cerium-catalysed reactions can be assigned to the large differences in rate

constant that arise when the catalyst is changed, such as in R6 (see discussion in chapter

6.2). Fig. 8.3 compares single oscillations from the two sets of data, drawn on the same

time-scale for clarity.

142


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15000

20000

25000

30000

0 10 20 30 40 50 60 70 80

Ferroin-catalysed reaction

PMT

outp

ut . Cerium-catalysed

reaction

time/sT ime/s

Figure 8.3: A comparison of two typical oscillations in the ferroin-catalysed and cerium-catalysed

BZ reaction in the CSTR. Reaction solutions are as described in 7.2. The time scale is chosen so

both oscillations start to clock at the same time.

The heights of the two peaks are not directly comparable due to different solutions

being used with different absorptions and different filters used to monitor the two

reactions at the different wavelengths. The PMT outputs in this figure have not been

altered. However, two large differences are immediately obvious, with a much slower

increase in the concentration of cerium(IV), compared with ferriin, observed as the

reaction clocks. The cerium catalysed reaction also exhibits a longer slower period after

the initial fast reaction. As expected, series of oscillations with little change in the

period of the oscillations were produced for both experiments. As a comparison, Figs.

8.4 and 8.5 show examples of the BZ reaction, catalysed by ferroin and cerium

respectively, in a CSTR with no flow of fresh solution into the cell.

143


0

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15000

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0 200 400 600 800 1000 1200

PMT

outp

ut

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150

llatio

ns/s

.pe

riod

of o

scill

atio

ns/s

.O

scill

atio

n pe

riod

/s

time/sTime/s

Figure 8.4: A sample from a typical series of oscillations of the ferroin-catalysed BZ reaction in the

CSTR, but with no flow of solution through the cell. Reaction solutions are as described in 7.2.



In both sets of experiments shown here, the period of the oscillation changed as the

reaction proceeded. These changes were much greater than the small differences

observed in the series of oscillations shown in Figs. 8.1 and 8.2, with changes in the

period of oscillation of 40 - 50 s in both cases. There was a definite trend to the periods

in the latter two experiments, with the oscillations either increasing or decreasing with

time. Fig. 8.4 shows the oscillations dying out after ~ 20 minutes, tending towards a

solution of ferriin rather than ferroin. There was also an increase in the ‘base-line’ of the

oscillations, showing that subsequent oscillations were not returning to the same

concentrations as those preceding them.

In both sets of experiments shown here, the period of the oscillation changed as the

reaction proceeded. These changes were much greater than the small differences

observed in the series of oscillations shown in Figs. 8.1 and 8.2, with changes in the

period of oscillation of 40 - 50 s in both cases. There was a definite trend to the periods

in the latter two experiments, with the oscillations either increasing or decreasing with

time. Fig. 8.4 shows the oscillations dying out after ~ 20 minutes, tending towards a

solution of ferriin rather than ferroin. There was also an increase in the ‘base-line’ of the

oscillations, showing that subsequent oscillations were not returning to the same

concentrations as those preceding them.

144


0

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30000

710 910 1110 1310 1510 1710

time/s

PMT

outp

ut

.

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125

150

175

200

..O

scill

atio

n Pe

riod

Pe

riod

O

scill

atio

n pe

riod/

s

Time/s

Figure 8.5: A sample from a typical series of oscillations of the cerium-catalysed BZ reaction in the




Fig. 8.5, on the other hand, shows the period of the oscillations growing with time.

These oscillations also, eventually, died out with time. With the CSTR apparatus

producing series of oscillations that changed little with time, the experiments could now

move on to studying the effect of known perturbations on the oscillating reaction.

Fig. 8.5, on the other hand, shows the period of the oscillations growing with time.

These oscillations also, eventually, died out with time. With the CSTR apparatus

producing series of oscillations that changed little with time, the experiments could now

move on to studying the effect of known perturbations on the oscillating reaction.

8.2: Preliminary Results 8.2: Preliminary Results

With the apparatus producing suitable series of oscillations, it needed to be tested as to

whether changes in the period could be observed. Known perturbations on the reaction,

such as irradiation and the addition of certain chemicals, were used to further test the

experiment.

With the apparatus producing suitable series of oscillations, it needed to be tested as to

whether changes in the period could be observed. Known perturbations on the reaction,

such as irradiation and the addition of certain chemicals, were used to further test the

experiment.

145


8.2.1: Addition of Ag+ ions

As described in Chapter 6.2, the addition of Ag+ to a reacting BZ solution can result in

the suppression of oscillations. With any Br− present removed by the Ag+, there should

be a sudden switch to a solution of Mox. Once all of the Br− is removed, then a

combination of the BZ reaction releasing Br− from brominated organic species and

reactions of other oxybromine species and the inflow of new solution increases the

concentration of Br− in the cell and oscillations resume.

For the experiments where AgNO3 solution was added to the system, the stirrer was

briefly removed and 1 cm3 of solution was pipetted into the bottom of the cell, before

the stirrer was replaced. A small series of preliminary experiments were performed,

showing that there was no effect on the reaction from removing the stirrer for a short

period of time, or from inserting a pipette into the solution. Fig. 8.6 shows the effect of

adding silver ions to the BZ reaction.

146


0

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20000

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30000

0 500 1000 1500 2000 2500 3000 3500 4000 4500

PMT

outp

ut

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150

170

190

210

230

250

Osc

illat

ion

perio

d/s

.

[Ag+]cell = 0.001 M

time/sTime/s


CSTR, with AgNO3(aq) added at ~ 1950 s. Reaction solutions are as described in 7.2.

Immediately upon adding the silver ions (shown for clarity by the dashed grey line in

Fig. 8.6), the reaction switched to the oxidised state, as expected. There was a gradual

decay, much slower than that observed in a normal oscillation before the oscillations

gradually built up again. The lower intensity of the oscillations recorded after the

addition of AgBr could be due to the presence of the AgBr precipitate in the cell,

scattering light or due to the changes in the reacting mixture after the precipitation of

the Br− by the silver ions. The longer period of oscillations seen as they return to a

steady state is due to the different reacting solution found in the cell, diluted by the

addition of the Ag+ solution. Experiments were performed where 1 cm3 of water was

added to the reacting cell in the same manner as the AgNO3 solution here. The period of

147


the oscillations was seen to increase. The residence time of the cell in this reaction was

~3200 s, so it is not surprising that the oscillations are starting to fall to a steady state

after a delay of a similar period.

Fig. 8.7 shows the effect of Ag+ ions on the cerium-catalysed reaction.

0

5000

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20000

25000

30000

0 1000 2000 3000 4000 5000 6000 7000Time/s

PMT

outp

ut

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150

170

190

210

230

250

Osc

illat

ion

perio

d/s

.

[Ag+]cell = 0.001 M


CSTR, with AgNO3(aq) added at ~ 1950 s. Reaction solutions are as described in 7.2.

The addition of the silver ions has a very similar effect, except that the PMT output

drops rapidly upon addition of the AgNO3, further than the lowest point observed

during the oscillations. This could be due to the formation of the AgBr(s) in the cell,

scattering light and preventing it from reaching the PMT. As with the ferroin catalysed

reaction, the oscillations do start again over time with a decrease in the maximum PMT

148


output, possibly due to the presence of the precipitate in the cell. After a delay of around

3000 s, the oscillations have started to return to a steady state. This is probably due to

the concentration of Br− returning to a value that can support oscillations due to

formation by reaction of brominated organic species in the solution and reaction of

other oxybromine compounds in the cell, as well as inflow of fresh reagents.

Both sets of data show that large changes in the oscillations could be observed, through

changes in the height of the oscillations and in their periods. The amount of quantitative

information that can be obtained from these sets of data does look limited, with only the

qualitative effects of the perturbation easily obtained.

8.2.2: Irradiation of Reaction

The second method of perturbing the reaction was to irradiate the sample with light. The

effect of light on the BZ reaction is highly dependent on not only the metal catalyst used

but also on the state of the reaction when the light is applied. The oscillations mean that

the concentration of the reagents is constantly changing with time. In all of the

experiments carried out, the light was applied at the same point, at the peak of any

oscillation, so that the effects could be easily compared from experiment to experiment.

It was also applied continuously for several oscillations, so that all of the reaction was

irradiated.

149


Fig. 8.8 shows the effect of irradiation with UV light using the wide-band filter

described in 7.2.

0

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1490 1990 2490 2990 3490 3990Times/s

PMT

outp

ut

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75

100

125

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175

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Osc

illat

ion

perio

d/s

.

Light off

Light off

Light on


CSTR, with irradiation of sample by UV light indicated by blue lines. Reaction solutions are as

described in 7.2, transmission profile of the UV filter shown in Fig. 7.5.

Irradiation of the reaction with UV light has a large effect on the reaction, with a

reduction in the period of the oscillations (~ 33 % in the data shown). The period then

starts to grow back at a fairly constant rate.

Irradiation of the ferroin catalysed reaction at 510 nm (peak of ferroin absorption) and

590 nm (peak of ferriin absorption) was also attempted but neither showed any effect on

the period of oscillation. The cerium-catalysed reaction was also irradiated, but no

effect was observed using any of the ultra-violet, 380 nm, 510 nm and 590 nm filters.

150


These wavelengths of light were chosen as they correspond to absorption bands in both

metal catalysts used. If an effect is seen at one wavelength, or if an effect is seen in one

reaction but not when the catalyst has been changed, then it can be related to the

differences in absorption of the metal species. The absence of any effect observed when

the other filters were used could be due to the limited amount of light passing through

the cell when these narrow-band filters are used (see Fig. 7.4 for a comparison of the %

transmission spectra for the filters used).

Considering the effect of light on Ru(bipy)32+ in related reactions and proposed

mechanisms could give some insight into what effect irradiation has on the ferroin-

catalysed reactions studied here. The excited catalyst, *Ru(bipy)32+, is formed upon

irradiation with ultraviolet light and this can react directly with BrO3− to form the

BrO2.11.

Ru(bipy)32+ + hυ *Ru(bipy)3

2+

*Ru(bipy)32+ + BrO3

− + 2 H+ Ru(bipy)33+ + BrO2

. + H2O

The net result of this is a second mechanism by which the metal is oxidised, releasing

bromine dioxide radicals. These, in turn, react with any Ru(bipy)32+ that remains in the

cell, accelerating the autocatalytic part of the reaction. A similar effect could be

observed in the ferroin-catalysed reaction,

A second possibility is that visible light of ~ 630 nm is believed to catalyse the

reduction of ferriin to ferroin22. The second, high wavelength peak of transmission of

the filter used here is at ~ 720 nm (as shown in Fig. 7.5). This could also be a factor in

151


the reduction of the period of oscillation, with two routes by which the concentration of

ferroin could be returned to its previous level. However, this mechanism would not

release Br− by reaction of ferriin with the brominated organic species. Both methods

would act to reduce the period of the oscillations, by either speeding up the autocatalytic

process or speeding up the regeneration of the metal catalyst after the autocatalytic

process.

UV light of 300 – 350 nm is ionising and there is the possibility of other radical species,

such as Br. and MA. forming in the cell. The role of MA. as a second control

intermediate in the reaction has already been discussed briefly in chapter 6.2. However,

the absence of any observable effect on the cerium-catalysed reaction suggests that the

effect arises due to an interaction between the light and the metal catalysts used, rather

than an interaction between the light and the oxybromine chemistry or the organic

species in the reaction.

The full effect of light on the reaction could be analysed by modification of a model of

the reaction and adding the relevant equations for irradiation by light, such as in both

Kadar et al.11. and Tóth et al.22. In this thesis, the irradiation of light was used as a

method of checking whether changes in the period of oscillation could be observed by

the CSTR and whether the light used to monitor the reaction was having any effect on

the reaction. There is an effect when UV light at ~ 350 nm was used to irradiate the

reaction. This can be explained qualitatively by considering the species in the reaction

and also similar light-sensitive BZ reactions. Furthermore, as there was no effect on the

reaction when irradiating with either 510 nm light (in the ferroin-catalysed case) or 380

nm (in the cerium-catalysed case), it could be safely assumed that the monitoring light,

152


which was also at a lower intensity than the irradiating light, would not have an effect

on the reaction.

8.3 Application of Magnetic Field

The previous experiments showed that the apparatus could show changes in the

oscillations of the reactions. Experiments where a magnetic field of strength 0.14 T was

applied to the reaction were now performed. In Figs. 8.9, 8.10 and 8.11, the red lines

indicate that the magnetic field has been turned on and the black lines indicate that it

has been turned off. Several repeats of the experiments were performed producing

similarly shaped oscillations. Fig. 8.9 shows one typical series of oscillations, obtained

with the ferroin-catalysed BZ reaction.

0

5000

10000

15000

20000

25000

30000

250 750 1250 1750 2250 2750Time/s

PMT

outp

ut

50

60

70

80

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100

110

120

130

140

150

Osc

illat

ion

perio

d/s

.


CSTR, with magnetic field turned on and off as shown by the dashed lines.

153


No significant change in the period of oscillation appears to occur when the magnet is

switched on or when it is switched back off again. For the typical set of data depicted in

Fig. 8.9, the average period was 121.1 s, with a standard deviation of ± 3.4 s. Similar

sets of data were produced, with the standard deviation of the data ranging between 2

and 8 s. A full analysis of the data shown in this chapter, and any possible magnetic

field effect, is detailed in Chapter 8.4.

Fig. 8.10 shows a series of oscillations with the cerium-catalysed BZ reaction, with 0.14

T magnetic field applied during the experiment, as shown by red dashed line. Several

similar experiments were also performed, with similar series of oscillations obtained.

0

5000

10000

15000

20000

25000

30000

750 1750 2750 3750 4750 5750Time/s

PMT

outp

ut

,

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Osc

illat

ion

perio

d/s

Figure 8.10: A sample from a typical series of oscillations of the cerium-catalysed BZ I reaction in

the CSTR, with magnetic field turned on and off as shown by the dashed lines.

154


As with the ferroin-catalysed reaction, any changes were hard to determine by merely

looking at the period data. However, the analysis of these experiments was further

hindered by a tendency for the period of oscillation to gradually increase as the reaction

proceeded. The alternative cerium-catalysed BZ reaction recipe was then used as it

showed no such increases in period with time. Fig. 8.11 shows a typical series of

oscillations for this system. Note that the oscillations are reversed in this figure. This is

because the output is inverted, 33400 – PMT, rather than PMT, recorded.

0

5000

10000

15000

20000

25000

30000

1500 2000 2500 3000 3500 4000 4500 5000

Time/s

PMT

outp

ut

50

60

70

80

90

100

110

120

130

140

150

Osc

illat

ion

perio

d/s

.

Figure 8.11: A sample from a typical series of oscillations of the alternative cerium-catalysed BZ

reaction in the CSTR, with magnetic fields applied as shown by the dashed vertical lines.

Several experiments were also performed, producing similar series of oscillations. In

these experiments, as with the previous experiments, any changes in the period of

oscillation were too small to be seen by eye. For the typical set of data depicted in Fig.

8.11, the average period was 101.6 s, with a standard deviation of ± 2.9 s. Several

155


similar sets of data were produced, with the standard deviation of the data ranging

between 3 and 10 s.

The periods of oscillation in Fig. 8.11 are shorter than in those shown in Fig. 8.10, so

the alternate cerium catalysed reaction could have reached a steady state faster than the

original cerium catalysed reaction mixture. Further to this, the reaction was designed to

limit the effect of dissolved oxygen. This could also be a key reason for the changes

observed in the first cerium-catalysed experiments, with changes in the oxygen

concentration having an effect on the oscillation period. However, a similar effect

should have been observed in the ferroin-catalysed reaction.

8.4 Is there an effect?

The main question raised at the end of this study is “Is there a magnetic field effect on

the reaction?” The effects reported in other work was small – changes of a few seconds

within period of ~ 100s – so large differences in period were not expected. There does

appear to be very little effect of a magnetic field on the oscillations shown here.

Although a Student’s T-test could be performed on a single set of data, every oscillation

needs to be considered when trying to determine if the applied magnetic field had had

an effect or not. For each set of data (a series of oscillations, as shown in the figures

presented above), each period was recorded as a % difference from the mean value for

that particular set of data. All of the periods, recorded as % differences, for each field in

the set (i.e. field on or field off) were collated together, producing a mean % difference

and its standard deviation for field on or field off for each set of data. The means and

standard deviations can then be compared. To see if there is a significant effect, a T-test

156


that includes all the data for a given reaction condition (i.e. ferroin or cerium-catalysed,

field on or field off) has to be performed. All of the % differences from the mean values

have to be included to give a mean % difference and standard deviation of these

differences for all of the data.

8.4.1 Ferroin Catalysed Reaction

In Fig. 8.12, the different means and standard deviations are compared visually. For

each experiment, two mean % differences are produced, one where a magnetic field was

applied and one where it was not applied, with standard deviations also calculated. The

two means are separated slightly, for clarity, with red points signifying that the field

was applied and black points signifying that no field was applied. The ten experiments

performed are shown here.

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9 10

Experiment number

% d

iffer

ence

from

mea

n

Field on Field off

Fig. 8.12: A summary of the data collected for the ferroin-catalysed BZ reaction.

157


This figure highlights the nature of the small differences between the two possible field

conditions. No one condition accelerated the reaction and the differences are all less

than 5 %, with standard deviations usually around 5 %.

8.4.2 Cerium Catalysed Reaction

Fig. 8.13 is produced using the same method as Fig. 8.12, with nine rather than ten

experiments shown.

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Experiment number

% d

iffer

ence

from

mea

n

Field on

Field off

Fig. 8.13: A summary of the data collected for the alternate cerium-catalysed BZ reaction.

This figure again highlights the nature of the differences between the two possible field

conditions. No one condition accelerated the reaction and the differences are larger for

these reactions, but still all less than 5 %, with standard deviations usually around 5 %.

158


Fig. 8.14 combines all of the information shown in the previous two figures and

contrasts the differences between the oscillations in reaction with field off and field on

for the two different catalysts. The red data points represent the ferroin-catalysed

reaction and the yellow represent the cerium-catalysed reaction.

-10

-8

-6

-4

-2

0

2

4

6

8

10

% d

iffer

ence

from

mea

n .

Ferroin catalysed

Cerium catalysed

Field Off Field On

Fig. 8.14: A summary of all of the data collected for the BZ reaction, comparing field off and field

on for the two catalysts.

This figure clearly shows that there is no effect of a magnetic field for the data recorded

in this section. When all of the data is collated, the differences between field off and

field on tend towards zero, as expected if the magnetic field was having no effect on the

reaction. The error bars give a good estimation of the error of the experiments. Figs.

159


160

8.12, 8.13 and 8.14 indicate that an effect of > 5-6 % on the period of oscillations would

be needed in order for it to be observed using this apparatus.

To confirm that there is no statistically significant difference between the having the

field on and having the field off, a t-test is performed on the data. Student’s T-test was

used. The relevant data is summarised in Table 3, with the results of the Student’s T-test

included. The P-values produced indicate that the changes in period are not significant,

to a significance level of 5 %.

Reaction

Ferroin-catalysed BZ

Cerium-catalysed BZ

Magnetic field

ON

OFF

ON

OFF

% difference

−0.62

+0.44

+0.19

−0.19

Standard deviation

4.44

5.32

6.62

6.13

P-value

0.26

0.59

Table 3: A summary of the data shown in Fig. 8.14, and the result of a Student’s T-test on each set

of data.

Part II Chapter 9: Discussion

161

9. DISCUSSION

The results presented here show that there is no statistically significant magnetic field

effect on the BZ reaction when a static field of 0.14 T was applied to the reaction. The

standard deviation produced in Fig. 8.14 gives an indication of the size of effect that

would need to be present in order for it to be observed by the apparatus. For the

apparatus used in these experiments, an effect of < 5-6 % on the period of the

oscillations would simply not be observed by the apparatus. One other problem with

this CSTR is that, because it was hard to reproduce the period of oscillations between

experiments, it could only be used to monitor changes in period within a series of

oscillations.

So why is no effect seen? First, assuming that there is some magnetic field

dependence, the effect could, simply, be too small to be observed by the apparatus. As

said earlier, an effect of less than 5 % on the period of oscillation would not be seen

by this apparatus. This error compares well with similar work conducted by Sontag31,

who also failed to see any effect on the reaction. If the apparatus was improved to

reduce the error between oscillations to only one or two percent, the error reported by

Blank and Soo, then a smaller effect could be more easily observed. But Figs. 8.11

and 8.12 show that neither “field on” nor “field off” consistently speds up or slowed

down the reaction. If one condition did accelerate the reaction, then there might be

some justification for trying to improve the accuracy of the apparatus in order to

better characterise the extent of this acceleration. However, that neither condition did

suggests strongly that there is no effect.


It could also be possible that there was an effect on some individual rate constants but

the kinetics of the whole system act to minimise the effect. This behaviour was

possibly observed in Fig. 8.8, with the effect of irradiation of the reaction with UV

radiation decreased after an initial large fall in oscillation period. Similar behaviour is

also observed in a shallow layer when a perturbation that does not reach a certain

threshold does not produce a wave while one over that threshold does37. If this was

the case, then there could be some change in the rate of the autocatalytic part of the

reaction which is then compensated by changes in the rate of the regeneration of the

metal catalyst. Individual peaks could be compared but perhaps an easier method is to

show the first derivative with respect to time of the data plotted against time, as

shown in Fig. 9.1.

162


-3000

-1000

1000

3000

5000

7000

9000

11000

13000

15000

250 750 1250 1750 2250 2750

Time/ s

Firs

t der

ivat

ive

of P

MT

outp

ut w

rt tim

e

.

Figure 9.1: The first derivative with respect to time of the series of oscillations shown in Fig. 8. 9,

with magnetic field turned on and off as shown by the red and black dashed lines. The data set

used is that shown in Fig. 8.9.

If the magnetic field was having an effect, and the kinetics did act as described above,

then there should be changes in the heights of the peaks of the data upon turning the

magnetic field on and also corresponding increases in the depths of the troughs that

follow each peak. The data shown has a similar level of noise (in the height of the

peaks) as the original data set. Importantly, there are no large changes in the

derivative of the data upon changing the magnetic field. If the data in Fig. 9.1 showed

any features consistent with an acceleration of one step compensated by a deceleration

in another part of the reaction, then a full analysis of the first derivative data for all of

the magnetic field experiments would have been performed.

163


It is also possible that there was no effect on the reaction at this magnetic field

strength. Six criteria have been listed as necessary conditions for the observation of a

magnetic field dependent enzymatic reaction38. Although the BZ reaction is not an

enzymatic reaction, these criteria provide some insight into the likelihood of there

being a magnetic field effect. The six criteria are summarised below:

1) One reaction step must proceed via a radical-pair intermediate.

2) The radicals in the radical pair must be weakly coupled.

3) There must be a mechanism by which the singlet and triplet states of

the radical pair can mix.

4) The rate of the reaction must be sensitive to the concentration of the

radical pair.

5) The radical pair must be sufficiently long lived for significant

interconversion of the two states to occur.

6) The reaction step preceding the formation of the radical pair must be

reversible.

What criteria are fulfilled for the possible radical pair identified earlier? Certainly, the

formation of a pair of radicals in a known reversible step of the reaction, as suggested

by the FKN mechanism and identified earlier as a potentially magnetic field

dependent step, would meet criteria 1, 4 and 6. The remaining criteria can be dealt

with in turn.

Whether the radical can show interconversion between S and T states has been

discussed in Chapter 6.3, where coupling of the radical to Br nuclei, through the

164


hyperfine interaction, allows mixing of the two states and can result in a magnetic

field effect. ‘Weak coupling’ of the radical pair refers to the exchange interaction and

its role in S-T mixing. At small separations, the singlet and triplet wavefunctions of

the radical pair cannot overlap, so the radical pair has to separate, by diffusion, until

the exchange interaction falls to a neglible amount, and then S-T mixing can occur

between the pair. The radical pair must then recombine.

The lifetime of a radical pair is perhaps the most important factor in determining

whether a magnetic field has an effect. If the reactions of the BrO2. radical, either with

another radical or with the metal catalyst occur at a faster rate than any spin-mixing, a

magnetic field effect will simply not have the time to occur. The reaction will not be

magnetic field dependent. There is only a build up of the radical during the

autocatalytic clocking section of the oscillation. This is backed up by data shown in

Försterling et al. and related papers 39. For the radical pair identified as potentially

important in this reaction, the isotropic hyperfine couplings are ~ 4 mT, leading to a

spin mixing on the timescale of nanoseconds while the references above suggest that

the radicals have a lifetime as long as seconds. These very different timescales of

reaction and S-T mixing may contribute to the absence of a magnetic field effect,

although an effect is only ruled out if the radical recombines on a faster rate than the

S-T mixing.

A large difference in rate constants of the reaction of the radical with the metal

catalyst that occurs when cerium is substituted with ferroin was identified in chapter

6.2, with the ferroin reacting with the radical at a rate 105 times faster than cerium.

The result of this is that, in the ferroin-catalysed reaction, any BrO2. formed reacts

165


faster with the ferroin than it would react with another bromine dioxide molecule to

recombine. As the radical pair is no longer formed in a reversible reaction, any MFE

in this system is unlikely. In the cerium catalysed reaction, the rates of reaction with

metal catalyst and of recombination are similar18. An example of the lifetimes of the

bromine dioxide radical in solutions of metal ions typically used in the BZ reaction

can be found in Field et al.40 where BrO2. was formed by the radiolysis of solutions of

bromate. Although the experiments were performed in a different solution (neutral

solutions, no MA present, different metal catalysts), they show a marked difference in

the lifetimes of the radicals depending on the metal used. The reaction rate of BrO2.

with Fe(CN)64− is comparable with that of ferroin and the data presented by Field et

al. clearly shows how much faster the radical reacts with the metal catalyst than with

other radicals in recombination reactions.

The diffusion of the radicals is likely to be a key factor in whether a magnetic field

effect is observed. If the radical pair forms and then diffuses apart without a chance to

recombine then no magnetic field effect is ever going to be seen. The radical pair

consists of neutral radicals, so there is no coulombic attraction holding them together.

If a reacting solution could be prepared in a more viscous solution, then similar

experiments to those conducted here could easily be performed to check if there is

still no magnetic field effect observed.

There is also another mechanism which would remove any magnetic field effect. For

the system that was studied here, incoherent mixing must be having some effect on

the radical pair present produced. The presence of paramagnetic transition metals has

a large effect on the relaxation times of electron spins of radical pairs. A further effect

166


is that of the bromine atom on the radical pair. This atom has large electric

quadropolar coupling41 and it is possible that the nucleus does not precess around the

applied field but a resultant of the applied field and this quadropole. This precession

may be affected by the rotation of the molecule but should be capable of inducing

incoherent S-T+ and S-T− transitions for the radical. These two relaxation processes

occur on a similar (or faster) timescale than the rate of reaction due to cerium or

recombination, so any coherence will be lost by the time the radical reacts with either

the metal or recombines. There could also be a spin-orbit coupling effect. In a

photolysis experiment, magnetic field effects observed in the reactions of dibenzyl

ketone were removed when Br was substituted into one of the aromatic rings42. In

these experiments, spin-orbit coupling was proposed to be dominating the mixing of

the singlet and triplet states of the radical pair. Given radicals formed in the radical

pair being considered here are bromine-centred, it is likely that there is also very fast

relaxation of the electron spins through this mechanism. No magnetic field effect is

observed because the rates of incoherent mixing, by a range of mechanisms, occur on

a faster time scale than the rates of reaction of the radical.

One key point is whether there are any other reactions in the mechanism that could be

magnetic field dependent. In chapter 6.3, a particular sequence of reactions was

identified as the most likely step to give rise to any magnetic field dependence.

Discussion of the results has focussed on one particular section of the reaction.

However, there could be other radical pairs formed, especially in the reactions

involving the organic species present. Looking at the GTF model12, there are 8

reactions that produce radicals, but 5 of these are reactions of Ce4+ with an organic

167


species. The remaining 3 all produce bromine centred radicals, which are unlikely to

given any magnetic field effect for reasons given above.

Admittedly, this work is only concerned with the effect of a large static field on the

oscillating reaction, whereas some of the previous work had considered small,

oscillating magnetic fields. But in terms of the radical pair mechanism theory

considered here, an oscillating magnetic field effect can only be observed in a system

where there is already a known static magnetic field effect. The frequency of the

oscillating magnetic field would have to be the same size as the hyperfine couplings

in order for it to have an effect, so a MHz field would have to be used. The fields used

in the Blank and Soo experiments were in the Hz – kHz range30. This does raise the

question of whether there are other mechanisms by which an oscillating magnetic

field can influence a chemical reaction. Although there are other mechanisms by

which a magnetic field could interact with a chemical reaction29, only the RPM is well

accepted.

Modelling of the reaction could give more insight into what size an effect could be

expected and whether a reasonable change to key reaction rate constants, such as

those identified earlier, will lead to an observable effect in the reaction as a whole. If a

reasonable change in the rate constants or behaviour of key reactions does not produce

an observable effect in the overall reaction, then no effect on the whole reaction can

be expected. Various attempts to model the reaction and the effects observed in this

thesis were made with simulations42 based on the FKN model, the Oregonator and

sub-sets of the reaction, such as the autocatalytic clock taken in isolation. The larger

models added little to the problem due to difficulties in getting them to produce

168


169

suitable sets of oscillations while the smaller sub-sections were limited by their very

nature, concentrating on one or two reactions and ignoring the changes in

concentration that occur during each oscillation. Theoretical work of this nature has

been conducted by Baxter43 who analysed the Brusselator model of the BZ reaction.

Some striking changes in behaviour of the simulated oscillations were produced. That

work gives further details into the sensitive kinetics of the reaction and also shows

how the whole reaction could be affected by changes in relevant rate constants.

However, the Brusselator is a much reduced version of the model, consisting of four

reactions. It could be used as a starting block for a more thorough investigation of the

kinetics. Given that no effect was observed in the experimental section and that the

absence of an effect can be explained by considering relaxation of the electron spins

due to both transition metals and the bromine atoms, a full kinetic analysis was not

attempted here.

The experimental evidence convincingly shows that no magnetic field effect was

present in the experiments conducted and the absence of any effect can be explained

using a well-established theory that describes magnetic field effects. The BZ reaction

remains an interesting reaction to investigate due to the wide range of phenomena

observed.

Part III: USING SQUID MAGNETOMETRY TO

FOLLOW CHEMICAL REACTIONS.

Part III Chapter 10: Introduction

171

10. INTRODUCTION

The change in magnetic susceptibility of a reaction, which was used in Part I to

manipulate a reaction, can also be used to monitor its progress. One potential

application utilising this change in susceptibility could be in following reactions which

proceed via a radical pair mechanism. The formation of the radical pair can be observed

by a range of methods such as UV/vis spectrophotometry1, fluorescence spectroscopy2

and time-resolved infrared spectroscopy3. However, there are some limitations to these

techniques. For example, the species involved might not be fluorescent or the spectra of

the precursor and the radical pair might overlap. Any changes in susceptibility will be a

direct result of any changes in the concentration of radicals, with no dependence on the

absorption or fluorescence properties of the radical molecule, making the technique

more universal. Using a suitably precise magnetometer, such as a superconducting

quantum interference device (SQUID), to measure the changes in magnetic

susceptibility could prove to be a further method available for the study of such

systems.

The technique could also be used to follow the progress of other suitable reactions with

time. The reaction between Co(II)EDTA2− and H2O2 at ~ pH 4 displays wave behaviour

when initiated locally by a small amount of NaOH solution (see Part I for more details),

but also displays clock behaviour when mixed, well-stirred and then left to stand4. The

reaction can be followed in a number of ways, with the striking change in colour and the

increase in the autocatalyst concentration, −OH, two main indicators of the reaction’s

progress. There is also a change in the magnetic susceptibility of the reacting solution,

as shown by the susceptibility data recorded using a Gouy balance in Fig. 4.1.1. It


should be possible to follow the progress of the reaction by measuring this change in

magnetic susceptibility with respect to time.

In this chapter, SQUID magnetometry is used, for the first time, to measure the progress

of a solution phase reaction. The results acquired can then be compared and contrasted

with data collected using other methods such as absorption spectroscopy and previous

research to give further information on the reaction and on the presence and nature of

any intermediates formed during the reaction. The study is not limited to just the

Co(II)EDTA2−/H2O2 reaction described above. There are number of other reactions,

such as the Belousov-Zhabotinsky reaction (studied in detail in Part II), that could

possibly be followed using the technique introduced here. These are discussed in

Chapter 12.2. The work that follows is intended to show that the SQUID magnetometry

can be used to follow liquid phase reactions. The reactions chosen for the study have

relatively large changes in magnetic susceptibility and should be easily measured by the

SQUID magnetometer. If the SQUID can be used to follow these reactions, then it

could be used in the study of radical pair reactions and this section acts as a proof of

principle that the SQUID can be used to study solution phase reactions.

10.1 Methods of Measuring Magnetic Properties

There are various ways of measuring the magnetic properties of materials5. One can

measure the force acting on a sample of material in an inhomogeneous magnetic field.

The Gouy balance is an example of this method. There is a change in energy of a

material with magnetic moment, μ, as it is placed in a magnetic field of strength, H (see

Chapter 1.2.2). With an inhomogeneous magnetic field, there a force is generated on the

172


sample. The change in weight due to this force can then be measured by a sensitive

balance.

(1) Hμ χV=

)(2χVμ 20 HF ∇⎟

⎠

⎞⎜⎝

⎛= (2)

One can also measure the net magnetic moment of the sample. The induction of a

current in a coil by a magnetic moment can be used to measure the size of the magnetic

moment. This is the basis of the vibrating sample magnetometer and similar techniques.

SQUID magnetometers are the most sensitive devices for measuring magnetic fields.

Conventionally, they are used to characterise the magnetic properties of solid materials,

particularly those with ordering of magnetic domains, looking at changes in magnetic

susceptibility as functions of temperature or applied magnetic field6. Other possible uses

include the measurement of minute magnetic fields in a range of applications, such as in

the brain, the heart, occurring during the corrosion of metals and geological magnetic

fields7.

The sensitivity of these devices arises from the use of superconducting materials, which

can conduct current without developing a potential difference across the material, and,

specifically, Josephson junctions, where superconducting material is separated by a thin

(~ 1 nm) layer of insulating material. With a sufficiently thin barrier, tunnelling occurs

and the wavefunctions of the two superconducting materials can interact across the

barrier. Appendix IV is a brief overview of how the sensitivity of a SQUID is obtained.

173


This effect was predicted in 19628, with the first junction built in 19639 and the first

SQUIDs were built in the following years. Several superconducting components feature

in the magnetometer used: a superconducting magnet to produce large magnetic fields, a

set of superconducting detection coils through which the sample passes and a SQUID

connected to the superconducting detection coils. The SQUID used here has one

Josephson junction in the current path of a closed superconducting loop (a

radiofrequency (rf) SQUID). Properly calibrated, a SQUID magnetometer can be

capable of detecting a change in a magnetic field approaching 10−15 T.

The SQUID device in the magnetometer used in these experiments does not directly

detect the magnetic field from the sample. The junction is too small and too fragile for

this purpose. Instead, a sample moves through a set of superconducting coils which are

connected to the SQUID in a superconducting loop. Any change in magnetic flux

passing through the detection coils produces a proportional change in the persistent

current in the coils. This current is inductively coupled to a Josephson junction, which

acts as a highly sensitive flux-to-voltage converterI.

Measurements are made by moving the sample through the detection coils. The change

in the sample’s position changes the flux within the superconducting coil, changing the

current in the complete superconducting circuit. As the circuit is superconducting, the

current does not decay and produces a voltage output from the SQUID. The sample is

passed through the coils in a series of steps, which produces a series of voltage

measurements, from which the magnetic moment of the sample can be calculated by

reference to a calibration of the SQUID with a known mass of a material of a known

susceptibility.

174


This technique is used in conjunction with other spectroscopic techniques, such as

uv/vis absorption spectrophotometry, NMR techniques and pH electrodes, to both

follow the reaction and, by comparing the various techniques, identify any intermediates

in the reaction.

10.2 Other Methods of Following Chemical Reactions

The results obtained using the SQUID magnetometer are supported by data acquired

using a range of other techniques. Hydroxide ions are known to be the autocatalyst in

the Co(II)EDTA2−/H2O2 reaction (see Chapter 2 and Eqns 2.1 and 2.2), so following the

reaction with a calibrated pH electrode was an obvious method. Other methods

employed probe changes in the oxidation state of the metal ions, allowing comparison

with the SQUID data.

10.2.1 Absorption Spectroscopy

The absorption spectra of solutions give information as to the electronic spectra of the

ions in the solution and changes in the intensity of light absorbed by a solution can be

used to follow changes in the concentrations of species in the solution. The Beer-

Lambert law shows the relationship between the intensity of light transmitted, I, and the

concentration of the sample, c, its molar absorption coefficient, ε, the incident light

intensity, I0, and the path length of the lightthrough the sample, l:

I = I010−(εcl) (3)

175


176

The product of the three terms, ε, c and l, is the absorbance of the sample, A.

0IA=εcl=logI

⎛⎜⎝ ⎠

⎞⎟ (4)

The absorbance can be measured by the spectrometer, calculated from the light intensity

that passes through the sample. There is often a striking change in colour in reactions

where transition metal ions change oxidation states. In the Co(II)EDTA2−/H2O2 reaction

pink Co(II)EDTA2− is oxidised to dark blue Co(III)EDTA−. In the Belousov-

Zhabotinsky reaction, the colour change is determined by the catalyst used, with red to

blue oscillations observed for the ferroin-catalysed reaction. By following the changes

in absorbance of light at specific wavelengths passing through a sample, the changing

concentrations of the coloured metal ions in the solution can be followed.

10.2.2 Nuclear Magnetic Resonance

The changes in metal oxidation state can also be measured by magnetic resonance

techniques. Chapter 2.1.2 described how the presence of transition metal ions caused a

drop in the spin-spin relaxation time of protons in water. A Carr-Purcell-Meiboom-Gill

(CPMG) sequence is used to measure T2 times of protons in solution10.

Part III Chapter 11: Methods and Materials

177

11. METHODS AND MATERIALS

11.1 Materials

Sodium hydroxide, EDTA, cobalt chloride and hydrogen peroxide (35 % by volume),

all of ACS grade, were obtained from Aldrich and used without further purification. A

0.02 M Co(II)EDTA2− solution was made by dissolving equimolar quantities of EDTA

and CoCl2 in de-ionised water and then adjusting the pH to ~ 4. The reacting solution

used in all of the Cobalt experiments in Chapter 12 was a 9:1 by volume mixture of 0.02

M Co(II)EDTA2− at pH 3.9 and 35 % H2O2 solution.

Sodium bromate, sulphuric acid, silver nitrate and malonic acid, of A.C.S. grade, were

obtained from Aldrich and used without further purification. A stock ferroin solution

was produced by dissolving iron sulphate (FeSO4.7H2O) and 1, 10 – phenanthroline in

Analar water to produce a 0.025 M solution. Both the iron sulphate and 1, 10 –

phenanthroline were obtained from Aldrich and used without further purification.

Cerium (IV) ammonium nitrate (Ce(NH4)2(NO3)6) was obtained from Aldrich and used

without further purification. Concentrations of the reacting solutions for the BZ

reactions in Chapter 12.5 are described in the text. Ammonium metavanadate and

hydrochloric acid were obtained from Aldrich and used without further purification.

Any dilute acid solutions were made from concentrated stock solutions.


11.2 Methods

11.2.1 pH Electrode Experiments

A pH electrode was connected directly to a computer using a PCI 9112 data acquisition

card. A simple data acquisition program was written in Labview (see Appendix IIIa)

and the pH meter calibrated using buffer solutions (pH 4, 7 and 10). The measurement

of pH was taken from 50 ml of reacting mixture in a small flask, with measurements of

pH taken every 100 ms. The reacting mixtures were thermostatted at 22 oC using a

water bath.

11.2.2 Absorption Spectroscopy Experiments

Ultraviolet/visible light absorption spectra were obtained for the reacting mixture in a

Unicam UV-2 spectrometer. A thin path length (1 mm) cell was used as the absorption

of the Co(III)EDTA− product was too high for the spectrometer to record accurately

with longer path lengths. The clock reaction was followed in the spectrometer with full

spectra of the solution in a 1 mm path length cell from 350 to 700 nm acquired at 2

minute intervals, and the absorption of the solution at given wavelengths against time

taken from the full scans. The spectrometer could also record spectra at a given

wavelength by recording the absorption at that wavelength every 125 ms. No

temperature control of the reacting solutions was possible in the spectrometer.

11.2.3 NMR Experiments

MRI experiments were conducted on a Bruker DMX-300 spectrometer equipped with a

7.0 T superconducting magnet, operating at a proton resonance of 300 MHz, and at 295

K. The reacting solution was prepared outside of the magnet and a 5 mm ID NMR tube

178


was filled to a depth of a few centimetres of the reacting solution. The CPMG sequence

recorded 64 echoes with a τ of 2 ms. CPMG measurements of the reacting sample were

obtained at 30 s intervals. A small number of experiments were performed by acquiring

RARE images instead of using the CPMG sequence. As described in 2.1.3, the RARE

imaging sequence uses the difference in relaxation time to obtain contrast. These

experiments acquired RARE images of the clock reaction at 30 s intervals.

11.2.4 SQUID Experiments

The magnetic moment of the sample was measured using a Quantum Design MPMS5

magnetometer at 300 K. The SQUID magnetometer uses cgs units with the applied field

measured in oersteds, rather than tesla, and the moment in emu, as opposed to A m2 (see

Appendix I for a discussion of the different systems and units). A field of 50000 Oe was

used for all of the experiments in this chapter, and was converted into the equivalent SI

unit, A m−1, for calculations (see flow chart, Fig. 11.2). Other magnetic fields could be

produced by the superconducting magnet but this highest field possible was chosen. The

reaction was initiated outside of the SQUID magnetometer and a small, known mass

(around 100 mg) of the reacting solution placed inside a 5 mm NMR tube which was

then sealed. This sealed sample was loaded into a thin plastic tube and held in place

with empty gelatine capsules lodged into position. A typical sample tube is shown in

Fig. 11. 1. These prevent the sample from moving while it is passed through the coils.

179


(a)

Empty capsule, wrapped with tape and lodged into place 100 mm

170 mm

Sample tube, 5 mm diameter

Empty capsule, lodged into place

Empty capsules

Figure 11.1: Image of the sample tube. For a description of the internal mechanism of the SQUID

see 10.1 and appendix IV.

The loaded tube was then put in the SQUID magnetometer. Before a measurement

could be taken, the sample had to be centred within the coils of the SQUID

magnetometer. This process would usually take at least 5 to 7 minutes. A single SQUID

measurement consists of the sample being passed, in a series of discrete steps, through

the superconducting coils and inducing a response in the SQUID magnetometer. The

SQUID magnetometer was programmed to take measurements at 1 s delays, with each

measurement taking ~ 15 s. For the Co(II)EDTA2−/H2O2 experiments, four

measurements were taken and averaged for each data point. For the later experiments on

the BZ and similar systems (detailed in Chapter 12.2), only one measurement was taken

at a time, allowing more measurements to be taken at a faster rate.

By assuming that the only change in moment is due to the change in the oxidation state

of the metal, a maximum or minimum value can be subtracted to give a change in

magnetic moment due to the reaction. As the diamagnetic susceptibility is related to the

180


atomic number of an atom11, the change in moment due to any change in metal

oxidation state can be assumed to be a result of changes in the number of unpaired

electrons. The next steps are conversion to SI units to give a moment in A m2 and then

division by the volume of material, in m3, present to give a volume magnetisation in A

m-1. The volume magnetic susceptibility is then calculated by dividing the volume

magnetisation by the magnetic field applied. Volume, mass and molar susceptibilities

can be interconverted using the density and concentrations of the material, and from the

molar susceptibility, the number of unpaired electrons per metal atom can be estimated

from the spin-only formula for magnetic susceptibility, Eqn. 1.13. A flow chart showing

the series of calculations required is depicted in Fig. 11.2.

181


magneticmoment (emu)

recorded by magnetometer

Change in moment(emu)

Change in moment(A m )2

Cha ge in volume magnetisation

(A m )

n

-1

Change in volume magnetic

susceptibility

Change in molar magnetic

susceptibility(m mol )3 -1

Change in massmagnetic

susceptibility(m kg )3 -1

Concentration(mol m )-3Density (kg m )-3

÷ magnetic field (in SI units)

÷ volume/ m3

conversion to SI units 1× ×10−3

Subtract maximum/minimum

Magnetic field /Oe

Magnetic field /A m-1

×(1/4π)×103

Figure 11.2: Flow chart detailing the calculations required to convert magnetic data recorded by

SQUID into a measurement of magnetic susceptibility.

182


11.2.5 Analysis

In order to compare the various methods of following the reaction described above,

some methods of quantifying the features of the reaction are needed. One of the

distinctive features of autocatalysis in a reaction is a period of slow reaction rate

(sometimes known as the ‘induction period’) followed by one where the reaction rate

increases to a maximum value before slowing down again. This behaviour is

colloquially known as ‘clocking’, given that the reaction changes rapidly from

unreacted to reacted after a period of time. Fig. 1.5 is reproduced here, with the rate of

reaction added, in order to illustrate the behaviour and terms used.

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30Time/s

[A]/m

oldm

-3

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

d[A

]/d t

/ m

oldm

-3s-1

Induction period ?

Clocking time

Unreacted solution

Reacted solution

Figure 11.3: The fall in [A] for the simple, quadratic autocatalytic reaction A + B 2 B. Figure is

based on a reproduction of Fig. 1.5.

183


184

Various features of the reaction could be chosen to be the indicator required, as long as

its use is consistent. The induction period is not a well-defined measure as it can be hard

to determine the state of the reaction and whether the reaction is slow or not. Likewise,

there is rarely a clear point when the reaction can be said to be finished. A first

derivative of the data with respect to time will show when the reaction reaches its

maximum rate, as shown in Fig. 11.3. This is the parameter used in this work to

quantify the clock reactions depicted in the next chapter and will be referred to as the

‘clocking time’ in this thesis. This measurement can also be used for every set of data.

Assigning the clocking time to some maximum or minimum value of the data may work

for some methods but not all methods produce convenient sets of data. Certainly, in the

experiments depicted in Chapter 12, the end of the reaction is often not clear as there are

further reactions of hydrogen peroxide in an alkali transition metal solution, as well as

the presence of an intermediate species. The maximum value of the first derivative

should correspond to the same point for all of the experimental methods used.

The values of this clocking time should not differ much between the methods, as the

same reaction is being observed in all cases. There will be slight variations in the

reaction conditions for each method used to follow reaction leading to small variations

in the clocking time of the reaction. What is interesting is how reproducible the clocking

time is for a particular method.

Part III Chapter 12: Results

185

12. RESULTS

12.1 Study of the Co(II)EDTA2−/H2O2 Reaction

12.1.1 pH Electrode Experiments

The clock behaviour of the reaction is clearly shown in Fig. 12.1. The reaction starts at

pH 4, where the rate of reaction is slow. However, as the reaction proceeds, both the pH

and the rate of reaction increase. The reaction rate reaches a peak before slowing down

as the reacting species are rapidly used up. The final pH of the solution is ~ 9, with the

solution changing from acidic to basic as the reaction proceeds. The data gives no clues

as to the presence or absence of any intermediates in the reaction.

3

4

5

6

7

8

9

10

0 500 1000 1500 2000 2500 3000 3500time/s

pH

2 Co(II)EDTA2− + H2O2 → 2 Co(III)EDTA− + 2 −OH

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

2450 2550 2650 2750

Time/s

dpH

/dt

.

Figure 12.1: Results from a typical experiment showing the change in pH against time for the clock

reaction for a 9:1 by volume mixture of 0.018 M Co(II)EDTA2− and 35 % H2O2. Insert shows the

rate of change of pH with respect to time. Arrow used to illustrate clocking time.


The rate data, shown in the insert, clearly shows when the reaction is fastest, with a

clocking time of this typical reaction = 2655 s. Similar sets of pH data were acquired

with differences in the clocking time of no more than 60 s. The changing concentrations

of [−OH] can be extracted from the pH data using the relationships:

pX = −log[X] (5)

pH + pOH = 14 (6)

and a plot of [−OH] against time, such as in Fig. 12.2, gives a much better indication of

when the reaction switches from its slow period (induction time) to its fast period

(where the reaction clocks).

3

4

5

6

7

8

9

10

0 500 1000 1500 2000 2500 3000 3500Time/s

pH

-0.5

0

0.5

1

1.5

2

2.5

3

[−O

H]/m

oldm

−3

[−O

H] ×

106 /m

ol d

m−3

Original pH data [−OH]

Clocking time

2655 s

Figure 12.2: A graph showing the change in [−OH] against time for the pH data shown in Fig. 12.1.

Fig. 12.1 is reproduced here so that a comparison between the two sets of data can be made.

186


This data shows the difference between the slow period and the fast period much more

clearly than the pH data, giving a clearer moment when the reaction ‘clocked’, but

shows little else. The period immediately after the reaction has clocked is not included

in the figure as not only is signal to noise (S/N) poor for this region, the change in

behaviour from slow to fast is more interesting. The transformation of the pH data into

[−OH] produced a data set with a poor S/N at higher pH as small differences in pH are

highly exaggerated by the calculation. The reactions of H2O2 with the basic, transition

metal after the reaction has clocked mean that there are still changes in pH after all of

the Co(II)EDTA2− has reacted.

12.1.2 Absorption Spectroscopy Experiments

Fig 12.3 shows absorption spectra for 0.018 M solutions of Co(II)EDTA2− and

Co(III)EDTA− between 350 nm and 700 nm. The Co(III)EDTA− solution was

produced by letting a 9:1 by volume mixture of Co(II)EDTA2− and H2O2 react

overnight. To check that the reaction has proceeded to completion, two spectra were

recorded several minutes apart, showing no change in the absorption of the solution.

187


0

0.2

0.4

0.6

0.8

1

350 400 450 500 550 600 650 700Wavelength/ nm

Abs

orpt

ion/

nm

.

Co(II)EDTA2−

Co(III)EDTA−

Figure 12.3: absorption spectra from 350 nm to 700 nm for 0.018 M Co(II)EDTA2− and 0.018 M

Co(III)EDTA− solutions. Pink line shows the Co(II)EDTA2− solution and the blue line shows the

absorption of the Co(III)EDTA− solution.

There is large difference in absorption between the Co(II)EDTA2− and Co(III)EDTA−

solutions across all of the wavelengths, reflected in the large difference in colour

between the two solutions. The Co(II)EDTA2− solution has a broad peak at around 500

nm, while Co(III)EDTA− has two peaks of greater intensity, one at about 380 nm and

one at about 550 nm. Fig. 12.4 shows the changes in the absorption of the reacting

solution over the range of wavelengths, 300 nm to 700 nm, during the reaction. The

spectra are shown at 4 minute intervals. An initial Co(II)EDTA2− solution with no H2O2

added is shown here as the first spectrum. The oxidation of Co(II)EDTA2− to

Co(III)EDTA− is clear. The peak at 550 nm develops slowly at first, then quickly as the

reaction clocks. There is also a build up of absorption between 300 and 400 nm that

188


forms rapidly then decays to leave a peak at ~ 380 nm. The spectrometer had difficulty

recording absorption values over 3, due to the minute amount of light passing through

the sample, so these are not included in the figure.

300350

400450

500550

600650

700

0

0.5

1

1.5

2

2.5

3

Abs

orpt

ion

Wavelength/ nm

Fi

gure 12.4: Spectra showing the changes in absorption for a typical clock reaction between

Co(II)EDTA2− and H2O2 between 300 nm and 700 nm. Spectrum of starting solution (line at lowest

absorption) added at the start. First spectrum recorded 1 minute after initiation of reaction and

subsequent spectra shown at 4 minute intervals.

Time

The behaviour of the reaction can be more easily observed by following the absorption

at specific wavelengths. Fig. 12.5. shows the change in absorption for this data at both

350 nm and 550 nm, with clock behaviour observed in both cases. Each data point on

the graph corresponds to a spectrum shown in Fig. 12.4. At low wavelengths such as

350 nm, the large growth in absorbance is clearly seen. The broad peak at around 580

189


nm, observed in Fig. 12.4, forms at the same time as the absorption in the ultra-violet

but does not decay as markedly as the absorption in the ultraviolet region. It does shift

slightly, both increasing in absorption and moving to a wavelength approximately 10

nm lower. The small change in absorption can be seen in the 550 nm time profile

depicted in Fig. 12.5.

0

0.5

1

1.5

2

0 500 1000 1500 2000 2500 3000 3500 4000time

350 nm

550 nm

550 nm 350 nm

Abs

orpt

ion/

arbi

tary

uni

ts

/sTime/s

Figure 12.5: The time–dependent absorptions of the reaction described in Fig. 12. 3. at 350 nm and

550 nm.

This is convincing evidence that there is an intermediate formed during the reaction

which then decays to form the final product. The formation of the large peak at ~ 550

nm at the same time as the absorption in the ultra-violet suggests that the species formed

is a Co(III) species. As the intermediate decays to form the final product, the large peak

shifts slightly. This is due to changes in the ligand field around the central metal atom.

The strong absorption in the ultra-violet region of the spectrum is evidence of a ligand-

190


to-metal charge transfer band and such strong absorptions are found in peroxo-dicobalt

species12. This work is in agreement with data by Yalman4.

These spectra can be used to follow the concentrations of Co(II) and Co(III) species.

The total absorption measured at a given wavelength, λ, would be given by:

Atot, λ = (εCo(II)EDTA,λ×[Co(II)] + εCo(III)EDTA,λ×[Co(III)]) (7)

ε are absorption coefficients for the given species at a given wavelength. The path

length is constant throughout and can be ignored. The wavelength chosen is the

isosbestic point of the two Co(III) species involved, 578 nm, so that the formation of the

intermediate does not complicate matters. The calculation is made simpler by

considering that the total cobalt concentration, [Co(III)EDTA−] + [Co(II)EDTA2−], is

constant throughout. The change in the contribution of H2O2 to the absorption has been

neglected, given that it is a clear, colourless solution. However, the addition of peroxide

clearly has some effect on the solution, with an increase in absorption across all

wavelengths, and especially at lower wavelengths. To correct for this, the first point,

recorded 1 minute after the initiation of the reaction is corrected to give an absorption of

0 at 574 nm. Fig. 12.6 shows the results of this calculation.

191


0

0.002

0.004

0.006

0.008

0.01

0.012

0.016

0.018

0.02

0 500 1000 1500 2000 2500 3000 3500 4000Time/s

[Co(

III)

]

Clocking time 2520s

-10123456789

10

0 1000 2000 3000 4000d[C

o(III

)]/d

t ×10

5 / m

oldm

−3

/mol

dm−3

0.014

Figure 12.6: Time-dependent changes in the concentration of Cobalt(III) species, calculated from

the absorption data shown in Fig. 12. 4. Insert shows the rate of change of concentration of cobalt

with clocking time identified.

The clock behaviour is quite clearly observed. The clocking time, 2520 s is easily

observed in the rate data although the precision of the value is limited entirely by the

time taken to take an individual spectrum.

It was also possible for the spectrometer to record the absorptions at one given

wavelength every 625 ms. Fig. 12.7 shows one such measurement, following the

reaction at 600 nm. As with all of the UV/vis spectroscopy, the clock behaviour of the

reaction is reproduced.

192


0

0.5

1

1.5

2

2.5

3

3.5

0 500 1000 1500 2000 2500 3000Time/s

Abs

orpt

ion

at 6

00 n

m

.

-0.05

0

0.05

0.1

0.15

0.2

2400 2420 2440 2460 2480 2500d[

Abs

]/dt

2478 s

Clocking time

Figure 12.7: The time–dependent absorption for a typical reaction of Co(II)EDTA with H2O2 at 600

nm. Measurements of absorption taken every 625 ms. The inset highlights the rate of change in

absorption for the time period 2400 to 2500 s after initiation of the reaction, with clocking time

identified.

The last two figures, Figs 12.6 and 12.7 illustrate the reproducibility of the experiments

performed in the UV/vis spectrometer, with only a 42 s difference between the two

clocking times shown in the two figures. This technique proved to be reliable in

reproducing both the details of the peaks, such as that assigned to an intermediate and

the timings of the Co(II)EDTA2−/H2O2 reaction, with the difference between clocking

times exhibited by the two absorption curves here typical for the method.

193


12.1.3 NMR Experiments

Similar clock behaviour is observed when measuring the relaxation time of the reacting

solution using the CPMG pulse sequence. Two distinct types of behaviour were

observed for the reaction, as shown in Fig. 12.8. In the majority of cases, the relaxation

times show the time dependence reflected by the black line, with a trough just before

the steep increase in relaxation time. Sometimes, this trough is absent but the rapid

increase in relaxation is not nearly as steep, depicted by the red line in Fig. 12.8. This

second behaviour was seen much less often than that with the trough.

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500 3000 3500time/ s

T 2/ m

s

Time/s

Figure 12.8: Changes in transverse relaxation time for the clock reaction between Co(II)EDTA2−

and H2O2, with the two lines showing the two different results obtained.

A possible explanation for the lack of the hump in some of the experiments is that

sometimes a chemical wave initiated randomly in the tube and propagated throughout

194


the whole sample, seen in RARE images of the clock reaction. This would have the

effect of smearing out any details in the spectrum. How this wave initiates is unknown,

but it could be due to any inhomogeneity in the reaction sample, such as a defect in the

NMR tube or a speck of dirt or dust.

1H relaxation times can be related to the concentrations of paramagnetic species13, with

increasing concentration of paramagnetic ions such as Co(II)EDTA2− reducing the

relaxation time of the protons. They are also dependent on other factors such as the

packing of the solvent around the complex and size of the complex, through changes in

its rotational behaviour and interaction with the solvent molecules. For example, the

addition of H2O2 to Co(II)EDTA2− had a marked effect on the relaxation times, with T2

falling from 259 ms for a 0.018 M Co(II)EDTA2− solution with no H2O2 present to 30

ms for the typical 9:1 by volume reacting solution, with 1.44 M peroxide in the solution.

Measurements of the magnetic susceptibility of these solutions were made, showing no

increase in the magnetic susceptibility of the solutions. It is also worth pointing out that

the relaxation times of Co(II)EDTA2− solutions with no peroxide present are not short

enough to obtain a suitable contrast across the reaction wavefront (see Part I).

The changes in relaxation time due to the presence of hydrogen peroxide make it hard to

relate the changes in relaxation time as the reaction proceeds to changes in the

concentration of the species involved in the reaction. No attempt to calculate the rates of

change of the relaxation time was made, due to the different behaviour observed and the

presence of the hump. The reproducibility of the technique is shown in Fig. 12.8 where

both experiments reach their maximum within a few seconds of each other. The

presence of the hump does indicate that the reaction is proceeding via some

195


intermediate, as also suggested by the UV/vis spectra. An intermediate that leads to an

increase in the paramagnetism of the solution, explaining the fall in 1H relaxation time,

would be readily observed using the SQUID magnetometer.

12.1.4 SQUID Experiments

The SQUID magnetometer records the raw data as a current induced in a set of coils

and this is converted to a magnetic moment (in the cgs unit, emu) by the device. The

reacting solution for all of the experiments presented here was a 9:1 by volume mixture

of 0.02 M Co(II)EDTA2− and 35 % H2O2. Figure 12.9 shows the raw SQUID magnetic

moment data for the Co(II)EDTA2−/H2O2 reaction at 298 K.

-3.8

-3.7

-3.6

-3.5

-3.4

-3.3

-3.2

-3.10 500 1000 1500 2000 2500 3000 3500

time/sTime/s

mag

netis

atio

n ×

103 /e

mu

Figure 12.9: A typical set of raw data acquired from the SQUID magnetometer for the clock

reaction between Co(II)EDTA2− and H2O2 showing the change in magnetic moment of the sample

with time. The weight of the sample was 0.0896 g. Insert depicts the rate of change of magnetic

moment, with the clocking time identified.

Δm = 5.5×10−4

Δm = 5.8×10−5

Clocking time

2335 s

-7

-6

-5

-4

-3

-2

-1

0

1

2000 2200 2400

dmag

/dt 1

06 / em

u s1

Mag

netic

mom

ent ×

103 /

emu

196


Only the clock behaviour of the reaction is observed, although there is a rise in

magnetic moment of the sample after it has clocked. The change observed for this

experiment is 5.50 × 10−4 emu. The errors in individual measurements are around 1 ×

10−7 emu. From the data in Fig. 12.9, a clocking time of 2335 s can be found. The

precision of this value is limited by the time taken to acquire a measurement of

magnetic moment. The minimum value of magnetisation could be used as another

measure of the clocking time of the reaction. Compare Fig. 12.1 with Fig. 12.9 and it is

clear that not every method produces a clear maximum/minimum value of the data.

The change in the number of unpaired spins can be calculated from the flow chart (Fig.

11.1), and the results are summarised below:.

Δmagnetic moment/emu = 5.50 × 10−4

Δmagnetic moment/A m2 = 5.50 × 10−7

Δvolume magnetisation/A m−1 = 6.14

Δvolume magnetic susceptibility = 1.54 × 10−6

Δmolar magnetic susceptibility/m3 mol−1 = 8.57 × 10−8

From this change in molar susceptibility, the number of unpaired spins can be estimated

from the spin-only formula for susceptibility.

3kT

1))(S(SμμgNχ

2B0

2eA

m+

= (8)

For the data presented in Fig. 12.8, the change in the number of unpaired spins = 3.15,

slightly higher than the expected value of 3, but an error of only 5%. It is likely that

197


there is some contribution to the susceptibility of the Co(II)EDTA2− solution due to

orbital contributions that arise from the d7( ) configuration of the ion. These

effects are largest when there is an unoccupied orbital of a similar energy to a singly

occupied orbital present in the ion (such as d1 and d2 configurations). The electron

configuration here should have an orbital magnetic contribution and such contributions

has been observed in some Co(II) complexes14. The Co(II)EDTA2− complex is likely to

have a higher magnetic moment than predicted by a simple spin-only model, so the

change in susceptibility as it reacts to form the Co(III)EDTA− complex

( configuration so no orbital contribution) should be larger than predicted.

52gt 2

ge

62gt

The later rise in recorded magnetic moment is probably due to the formation of

paramagnetic O2 from the disproportionation of excess H2O2 in the final reacted

solution:

2 H2O2 2 H2O + O2 (9)

This reaction is catalysed by transition metals and is also more rapid in solutions where

pH > 7. The maximum amount of O2 produced by the reaction can be estimated by

considering the amount of H2O2 present in a small reacting sample, and assuming that

all of it decomposes to form O2. For a typical reacting sample of 0.1 ml, there are 1.4 ×

10−4 moles present in the sample, and this will decompose to form 7 × 10−5 moles of

oxygen. The volume one mole of the gas will take can be estimated, using the molar

volume of a gas, approximately 2.4 × 10−2 m3 mol−1, to give a volume of 1.7 × 10−6 m3.

There might be small differences in the molar volume, due to an increasing pressure

from produced gas, but this gives an answer in the range of cubic centimetres. With a

198


suitably large space above the reacting solution, there should be no danger in the

pressure building up too much and breaking the tube.

Is this gas responsible for the rise in magnetic moment of the sample after the reaction

has clocked? Assuming that all of the gas remains in the sample space, the magnetic

moment of this volume of O2 can be calculated using the volume susceptibility of the

gas, 1.83 × 10−6 15. This gives a potential rise in magnetic moment, in emu, at 50 kOe of

8.74 × 10−3. This is far larger than that seen in Fig. 12.9. However, the formation of

bubbles shows clearly that not all of the gas does remain in the sample. The saturation

concentration of oxygen in water is ~ 0.2 × 10−3 mol dm−3. Given a molar susceptibility

of O2 of 4.3 × 10−8 m3 mol−1, this gives rise to an increase in the magnetic moment of

the 0.1 ml sample of reacting solution, in a field of 50 kOe, of 6.84 × 10−6 emu,

approximately a power of ten smaller than that seen in the figure. The higher value

observed soon after the reaction has clocked could be due to a rapid production of O2 as

the reaction clocks then as the gas escapes from the solution and out of the measured

region of the sample, the magnetic moment of the sample falls towards that expected of

a saturated O2 solution. Not all of the oxygen that can be produced from the reactions of

H2O2 will be released at once. Bubbles of gas are observed in the reaction many hours

after the Co(II)EDTA2−/H2O2 has finished. Also, as the pressure in the sealed tube

increases, the saturation concentration of oxygen will increase, increasing the

contribution from the dissolved oxygen. Could the change in magnetic moment after the

reaction has clocked be related to the formation of the complex, as observed in the

UV/vis spectroscopy? In the UV/vis experiments, an intermediate formed which

decayed to form the final product. The SQUID experiments showed a rise in the

magnetic moment which is then followed by a subsequent fall. This is reproduced in all

199


four experiments depicted in Fig. 12.10. This rise then fall is not consistent with the

simple decay of the intermediate, as seen in Fig. 12.5.

The reproducibility of the reaction in the SQUID magnetometer needs to be considered.

In earlier experiments with this reaction, a larger amount (0.3182 g) of reacting solution

was measured, and the clock times were in the order of hours, rather than the expected

40 minutes. With smaller samples (< 0.1 g), the timings were much closer to those

obtained using the more traditional methods. However, the reproducibility between

experiments was still worse than that observed in all three previous methods. This is

highlighted in Figure 12.10, which shows a set of four experiments, all observed in the

SQUID magnetometer on the same day.

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 500 1000 1500 2000 2500 3000 3500 4000

Time/s

Vol

ume

susc

eptib

ility

×10

-6

.

/ 6

Vol

ume

susc

eptib

ility

× 1

0

Figure 12.10: A collection of typical clock reactions, showing changes in volume susceptibility, from

one typical day’s work. The only differences are small differences in mass of the sample (sample

masses range between 0.08 to 0.10 g).

200


The measured moment has been converted into volume susceptibilities to enable easier

comparison of the data.

The four sets of data all show the same details – a slow induction period, which

gradually speeds up into a fast period before reaching a minimum of volume

susceptibility and then a smaller rise after the reaction has clocked. It is reassuring that

the smaller increases are similar in height for three of the four sets of data. As with the

data presented in 12.9, the clocking time is limited by the resolution of the technique

and there is little difference between the sets shown here. However, there is clearly a

difference in the clocking times of the reactions – for this set of data, the average

clocking time was 2400 s, similar to the clocking times observed in all of the techniques

shown, but, more importantly, the standard deviation was 340 s, almost 15 % of the

clocking time. This is larger than that seen in any of the previous experimental

techniques.

Further proof that the SQUID has followed the reaction can be obtained by comparing

typical sets of the SQUID and the electronic absorption data. Both techniques follow the

changes of the metal species in the reaction, and should produce very similar results.

201


0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.02

0 1000 2000 3000 4000Time/s

[Co(

III)

]/mol

dm -3

uv/vis data SQUID data 0.016

0.018

Figure 12.11: A comparison of [Co(III)EDTA−] data obtained from typical absorption spectroscopy

(black squares) and SQUID magnetometry (red squares and line) experiments.

Only a small portion of the SQUID data was included as the technique tends to over-

estimate the number of spins per atom (as seen in the calculation earlier in the section

and subsequent discussion). The minimum value recorded was set as 0.018 M

Co(III)EDTA. This allowed some comparison of the two techniques, such as the time

scale of the fast period of the reaction and, although not exactly the same, the two sets

of data are very similar.

202


12.2 Other Reactions

The clock reaction between Co(II)EDTA2− and H2O2 is not the only reaction that can be

followed using SQUID magnetometry. In theory, any reaction that displays a change in

magnetic susceptibility could be followed using a SQUID magnetometer. Reactions

involving the transition metals that feature changes in the oxidation state of the metal

species are particularly attractive candidates for such a study. There are further

considerations that limit the number of potential reactions for study. The time taken

between initiation of the reaction (which, at present, has to occur outside the SQUID as

the sample tube must be sealed before being placed inside the SQUID) and the first

measurement of the sample limits possible reactions to those which are slow, or those

which are slow at the start of the reaction. Autocatalysis, such as that observed in the

Co(II)EDTA2− reaction, leads to kinetics where the reaction is slow at initiation.

Important details of the reaction, such as the clocking time, occur much later on and

make these reactions suitable for observation by SQUID magnetometry.

12.2.1 Belousov-Zhabotinsky Reaction and Derivatives

One group of reactions that could be suitable for this technique are those based on the

Belousov-Zhabotinsky (BZ) reactionIII. This reaction features the autocatalytic

oxidation of a metal ion, such as Mn(II), Ce(III) or ferroin (iron(II) phenanthroline) by

acidified bromate, with the regeneration of the original metal ion by the reaction of the

oxidised ion with an organic species, such as malonic acid. A more detailed description

of this reaction can be found in Part II. With the organic species present, the reaction

displays oscillations while a clock reaction can be prepared by removing the organic

species. As this reaction exhibits both a change in oxidation state and an induction

period due to the autocatalytic nature of the reaction, it should be suitable for the

203


technique. The cerium-catalysed BZ reaction exhibits both an induction time and

oscillations between Ce(III) and Ce(IV), making study of that reaction a very attractive

option.

12.2.1.1 Cerium-catalysed Belousov-Zhabotinsky Reaction

Fig. 12.12 shows a typical set of oscillations found in the cerium-cataysed BZ reaction,

with the reaction followed by absorption of light at 310 nm in a sealed 1 mm path length

cell in a Unicam UV-2 spectrometer.

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0 500 1000 1500 2000 2500 3000time/s

abso

rptio

nA

bsor

ptio

n

Time/s

Fig 12.12: A typical set of oscillations for the cerium-catalysed BZ reaction, followed by the

absorption of light at 310 nm. Reagent concentrations are specified in the text.

204


The reacting solution was made from a 1:1 by volume mix of 0.347 M NaBrO3 and

0.0025 M Ce(NH4)2(NO3)6 in 0.08 M H+ with 0.154 M malonic acid mixed then placed

in the cell. In order to attempt to replicate the conditions in the SQUID sample, the cell

was sealed shut with a plastic stopper.

There is an induction period with little change in the absorption of light which precedes

a series of oscillations that can last tens of minutes with only a small change in

amplitude and period. These changes occur because, as the reaction proceeds towards

equilibrium, small amounts of the reagents (BrO3−, MA) are consumed and each

oscillation takes place in a slightly different reacting solution. The period of the

oscillations is reproducible, although, as also noted elsewhere16, the induction time of

the reaction is much less reproducible.

For this reaction, the metal oscillates between colourless Ce(III) (electronic

configuration 4f1) and yellow Ce(IV) (electronic configuration 4f0). The lack of

unpaired electrons in Ce(IV) makes analysis simple. Oscillations between the two

oxidation states would be observed in the magnetometer as changes between a

paramagnetic solution and a diamagnetic one.

Compare the oscillations in Fig. 12.1 with those in Fig. 12.2, which shows a typical set

of oscillations observed in a ferroin-catalysed BZ reaction. The reaction was followed at

510 nm in a 1 mm path length cell, using a 1:1 by volume reaction mixture of 0.347 M

NaBrO3 in 0.08 M H+ mixed with 0.154 M malonic acid and 0.0025 M ferroin. In this

set of oscillations, there is no induction period17 and both the period and the intensity of

the oscillations clearly change with time. Observation of the reaction in an NMR tube

showed that the reaction tended to react as a series of waves travelling through the

205


solution rather than as a series of oscillations of the whole solution. Over time, there is

no homogeneous change of the bulk solution as a whole. For this reaction, the metal

oscillates between red ferroin (Fe(II)) (d6, low spin, diamagnetic)) and blue ferriin

(Fe(III)) (electronic configuration (d5, low spin, one unpaired electron, paramagnetic)).

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 200 400 600 800 1000 1200 1400 1600 1800 2000time/s

abso

rptio

nA

bsor

ptio

n

Time/s

Fig 12.13: a typical set of oscillations for the ferroin-catalysed BZ reaction, followed by the

absorption of light at 510 nm. Reagent concentrations described in text.

The cerium-catalysed reaction showed real potential for study using SQUID

magnetometry, with oscillations of a long enough period for the SQUID magnetometer

to resolve and an induction period long enough for the sample to be loaded into the

SQUID before oscillations commence. The same reacting mixture as the earlier

absorption experiments was used and samples weighing between 0.06 and 0.1 g were

measured in the SQUID magnetometer. However, the SQUID magnetometer failed to

206


record data that showed any of the features of the absorption work. Often, the SQUID

recorded a magnet moment that simply fell gradually with time. This could have been a

result of the SQUID failing to correctly centre on the sample, perhaps due to its low

initial value. The SQUID also measured how well the data recorded fit an ideal point

magnetic moment. The graphs of this measure against time also showed it falling with

time, in much the same way as the magnetic data did. Attempts to use larger samples of

reacting solution (> 0.1 g) were not successful in recording any oscillations.

There were two further possible problems with this reaction that were not tested by this

SQUID work but are worth considering. First, the reaction sample, both in the SQUID

magnetometer and in the absorption work, is not stirred. In an unstirred vessel, the

reaction mixture does not remain homogeneous and travelling waves can form. The

motion of the sample as a measurement is made could mix the solution to some extent

but it is not vigorous to ensure that the solution is homogeneous. In this case, the bulk of

the mixture does not change oxidation state. The SQUID might also have problems with

a sample with magnetic susceptibility gradients present within it18.

The BZ reaction, like the Co(II)EDTA2−/H2O2 reaction, also produces gas: Br2 through

the reactions of oxybromine species in acidified aqueous solution and CO2 through the

reactions of malonic acid. This could be a problem in the sealed SQUID sample but, as

with the Co(II)EDTA2−/H2O2 reaction, the amount of gas can be calculated and the

space above the solution can be maximised. If the sample tube were to break within the

cryometer at the heart of the SQUID, further experiments using the apparatus would be

limited. Br2 is produced but is consumed by the malonic acid to produce bromomalonic

acid19, so the production of that should not be a problem.

207


HOBr + Br− + H+ ⇌ Br2 + H2O (10)

Br2 + CH2(COOH)2 → BrCH(COOH)2 + Br− + H+ (11)

The overall reactions for the reaction of malonic acid with Ce(IV)17 are:

CH2(COOH)2 + 6 Ce(IV) + 2 H2O → HCOOH + 6 Ce(III) + 2 CO2 + 6 H+

(12)

BrCH(COOH)2 + 4 Ce(IV) + 2 H2O → Br− + 4 Ce(III) + HCOOH + 2 CO2 +

5 H+

(13)

Every mole of malonic acid that reacts will produce 2 moles of CO2 gas. In the SQUID

experiments, [MA] = 0.076 M and the sample volume was ~ 0.1 ml so there would be ~

7.6 × 10−6 moles of malonic acid in the sample. This would produce 1.52 × 10−5 moles

of CO2 gas. The volume of this gas can then be estimated, assuming that the molar

volume of a gas is ~ 24 ×103 cm3mol−1, as 0.36 cm3 of gas. With a large enough space

above the solution, the production of gas should not be a problem. Also, the gas is

produced in small amounts throughout the series of oscillations. Observation of the

reaction in a sealed tube revealed that only small bubbles of gas formed, and only after a

long time after the reagents were brought together.

208


12.2.1.2 Ferroin Clock Reaction

An alternative reaction was the ferroin BZ reaction but without the malonic acid

present20. This reaction exhibited the autocatalytic oxidation of the ferroin to ferriin

without the regeneration of the metal catalyst. The reaction could be catalysed by an

alternative metal catalyst such as cerium or manganese, but, for a first attempt at

looking at the reaction, the change from red to blue exhibited by the ferroin-catalysed

reaction made its progress easily observable in NMR tubes outside of the SQUID.

The ferroin-catalysed reaction shows different reaction mechanisms depending on

different relative concentrations of ferroin and bromate ions. At concentrations of

ferroin, so that [ferroin] < [BrO3−], the key step is the autocatalytic oxidation of ferroin.

However, as the concentration of ferroin is increased, a second reaction pathway, the

dissociation of ferroin, becomes increasingly important. This change in behaviour could

be used to check whether the reaction was being followed or not by the SQUID

magnetometer.

The overall stoichiometry of the reaction is:

4 ferroin + BrO3− + 5 H+ → 4 ferriin + HOBr + 2 H2O (14)

While this does not look autocatalytic, the key sequence of steps in the reaction is the

same as for the BZ reaction. It assumed that there are small concentrations of HBrO2

and Br− present in the reaction mixture.

HBrO2 + BrO3− + H+ ⇌ Br2O4 + H2O (15)

209


Br2O4 ⇌ 2 BrO2. (16)

BrO2. + Mn+ + H+ ⇌ M(n+1)+ + HBrO2 (17)

This set of reactions show that a autocatalytic species, HBrO2, is present. There is

autocatalytic oxidation of the metal ion in the same manner as observed in the BZ

reaction. When the ratio, [ferroin]/[BrO3−] reaches a certain value, a second pathway

becomes important20.

[Fe(phen)3]2+ ⇌ [Fe(phen)2]2+ + phen (18)

[Fe(phen)2]2+ → products (19)

Körös et al. observed this change in pathway as a change in behaviour of the reaction.

The reaction would start with normal, autocatalytic behaviour, but then switch to a first

order oxidation of ferroin. This change in behaviour provides a second method by

which the SQUID results can be checked, alongside the calculation of what the change

in magnetic moment corresponds to in terms of numbers of unpaired electrons per atom.

UV/vis studies of the reaction were attempted but, as with similar experiments

described in Part II, spectra of the reaction were difficult to obtain. Absorption spectra

of the reaction were measured in a 1 mm path length cell but the study was significantly

hindered by the tendency for the reaction to initiate somewhere in the sample and a

travelling wave to form and propagate through the reacting solution. Similar behaviour

was observed in reactions performed in NMR tubes. Barkin et al. noted in their work on

the cerium catalysed clock reaction that the induction time depended strongly on the

210


pH, with a small increase in pH leading to a much longer induction time. The solutions

used in these experiments were of a higher pH than the BZ solutions used in Part II in

order to lengthen the induction period of the reaction.

Figure 12.14 shows the magnetic moment data for the reaction of ferroin with acidified

bromate, with 1.875 × 10−3 M ferroin and 5.2 × 10−3 M NaBrO3 at pH 2.1. 0.2353 g of

reacting solution was used at 300 K.

-6.74

-6.73

-6.72

-6.71

-6.70

-6.69

-6.680 200 400 600 800 1000 1200 1400 1600

time/sTime/s

mag

netis

atio

n

10-3

em

uM

agne

tic m

omen

t × 1

03 / em

u

Δm = 3.5 × 10−5 emu

Figure 12.14: A typical set of raw magnetic moment data acquired from the SQUID magnetometer

for the clock reaction between ferroin and acidified BrO3−. Concentrations and conditions specified

in the text.

The clock reaction is observable in the SQUID magnetometer. The change in magnetic

moment, shown by the black arrow in Fig. 12.13 is 3.5 × 10−5 emu.

211


Δmagnetic moment/emu = 3.50 × 10−5

Δmagnetic moment/A m2 = 5.50 × 10−8

Δvolume magnetisation/A m−1 = 0.149

Δvolume magnetic susceptibility = 3.74 × 10−8

Δmolar magnetic susceptibility/m3 mol−1 = 1.99 × 10−8

The molar magnetic susceptibility can be related to the amount of unpaired spin per

metal atom in the same way as the cobalt reaction. For the data presented in Fig. 12.15,

the change in the number of unpaired spins = 1.17. This is approximately the same as

that expected for the oxidation of ferroin to ferriin. A larger magnetic moment of the

oxidised complex, ferriin, is expected given that there is an orbital contribution from the

ground state14. There is also a change in behaviour as [ferroin] is increased,

further evidence that the SQUID magnetometer is measuring the reaction. Figure 12.15

shows the change in magnetic moment for the clock reaction with 1.875 × 10−2 M

ferroin and 5.2 × 10−3 M NaBrO3 at pH 2.1. 0.2290 g of reacting solution was used at

300 K.

0g

52get

212


-6.70

-6.65

-6.60

-6.55

-6.50

-6.450 1000 2000 5000 6000 70003000 4000

time/sTime/s

Mag

netis

atio

n

10

em-3

uM

agne

tic m

omen

t × 1

03 / em

u

Dissociation of ferroin dominates

Δm = 1.44×10−4 emu

Δm = 8.39×10−5 emu Autocatalytic kinetics

Figure 12.15: A typical set of raw magnetic moment data acquired from the SQUID magnetometer

for the clock reaction between ferroin and acidified BrO3−. Ferroin is 10 times more concentrated

in this experiment than in Fig. 12. 14. Concentrations and conditions specified in the text.

The shape of the curve certainly suggests that the reaction is behaving as expected. The

first part of the curve resembles a clock, with an induction period and then a sharp rise

in the magnetic moment. After the ‘clock’ behaviour, there is still an increase. This

behaviour was as predicted by Körös et al.20. The reaction has not been followed to

completion, but the change observed can still used to give an idea of what has happened

during the reaction. The total change in magnetic moment, Δm = 2.28 × 10−4 emu,

corresponds to the change in 1 unpaired electron per atom in a 1.56 × 10−2 M solution,

which is only just short of the concentration of ferroin used in the reaction.

213


As with the Co(II)EDTA2−/H2O2 reaction, there were issues with the reproducibility of

the reaction. The difference in timings of the reactions was similar to that observed in

the Cobalt reactions detailed in 12.4 with two added problems. The first was that in

order to obtain a set of data that showed that the reaction was actually taking place a

larger mass of solution had to be used. Smaller samples (< 0.1 g) failed to show any

behaviour. It was observed early in studying the Co(II)EDTA2−/H2O2 reaction that a

larger mass of solution could lead to much longer reaction times, with the reaction

sometimes taking several hours to react. In order to obtain data that showed the clock,

accurate measurement of the kinetics had to be sacrificed. The second was that the

reaction itself was inherently noisy, with a tendency for the reaction to form of the

surface of the cell. It was hard to get a set of reactions to clock at about the same time

outside of the SQUID. Placing these reactions in the cryostat of the magnetometer

added to the difficulty. In addition to this, there were still problems with measuring the

reaction using the SQUID magnetometer with many failed experiments.

12.5.2 Vanadium Chemistry

Vanadium chemistry was also considered as several oxidation states can be reached

through reaction. The reaction of vanadate solution with zinc metal in hot acid displays

a range of colours as the reaction oxidises the reduces the vanadium from a yellow

VO2+ (V(V)) solution to blue VO2+ (V(IV)) via a green solution, a mixture of the two.

Further reduction of the vanadium occurs, with formation of a green V(III) solution and

then purple V(II) possible. A simplified chain of equations for the reaction is shown

below, showing the changes in vanadium oxidation state.

214


2 VO2+ + 4 H+ + Zn(s) 2 VO2+ + 2 H2O + Zn2+ (20)

VO2+ + 2 H+ + Zn(s) V3+ + H2O + Zn2+ (21)

2 V3+ + Zn(s) 2 V2+ + Zn2+ (22)

This sequence of reactions was confirmed by reaction of a 0.085 M V(V) solution at pH

1, reacting with 2-3 g of powdered zinc. However, the reaction conditions would be far

too vigorous for the SQUID magnetometer to cope with. To get the reaction to proceed

past the blue solution, it needed heating to ~ 40°C. The reverse reaction was also

considered, with an appropriate oxidising agent used to return the solution back up.

However, this was also not suitable, with the reaction quickly returning to higher

oxidation states in air, even upon transferring to another container. Hydrogen ions in

solution can oxidise the final V2+ solution back to V3+, producing hydrogen gas, and the

presence of air continues the oxidation of the vanadium ions.

The reaction of the VO2+ ion with d-fructose was another reaction that showed promise,

with work suggesting that the reaction showed suitable kinetics21. However, following

the reaction using absorption of light showed that the reaction was actually not suitable,

with no induction period observed. Fig 12.16 shows the change in absorption between

400 and 750 nm of a reacting solution. A 0.027 M solution of NH4VO3 at pH 1 was

mixed in a 1:1 by volume ratio with 0.26 M d-fructose solution. The original VO2+

solution was bright yellow/orange, which gradually turned green, then pale blue. The

first spectrum was acquired 30 s after initiation and subsequent spectra at 90 s intervals.

215


216

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

400 450 500 550 600 650 700 750

Wavelength/nm

Abs

orpt

ion

Figure 12.16: A series of absorption spectra from 400 to 750 nm showing the reaction of d-fructose

with a vanadium metavanadate solution. First spectrum (red) acquired 30 s after initiation of

reaction and subsequent spectra acquired at 90 s intervals. Arrows added to show decay and build

up of the two peaks.

Part III Chapter 13: Discussion

217

13. DISCUSSION

The aim of this work was to show that solution phase chemical reactions can be

monitored using a SQUID magnetometer. The clock behaviour of the

Co(II)EDTA2−/H2O2 reaction as Co(II)EDTA2− is oxidised to Co(III)EDTA− is

observed. Data recorded on the SQUID magnetometer can be compared with that

acquired using more traditional techniques, such as absorption spectroscopy.

Calculations based upon the changes in metal species in the reaction confirm that the

magnetometer is recording the changes in magnetic susceptibility due to the clock

reaction. The timings of the reaction are similar for all of the techniques suggesting that

the applied magnetic field of the SQUID has no effect on the Co(II)EDTA2−/H2O2

reaction. The clock reaction between ferroin and acidified BrO3− is also observed in the

magnetometer, with an expected change in behaviour of the reaction as the

concentration of ferroin is increased.

Taken in isolation, the SQUID data from the Co(II)EDTA2−/H2O2 reaction, like the pH

data from the reaction, only shows the clock behaviour of this reaction. The difference

between the two techniques is that they follow two different species, transition metal

complex and hydroxide ions, present in the reaction. However, it is in combination with

all of the data acquired that the SQUID data can give further insight into the reaction.

There is an intermediate present in the reaction, as suggested by Yalman4, and

confirmed here in the UV/vis spectra. As the peak at 550 nm forms at the same time as

the strong absorbance in the ultra-violet (see Fig. 12.5.), the intermediate would

probably be Co(III) centred with a ligand-to-metal charge transfer absorption, such as

that due to a peroxo-ligand. The small change in the wavelength of the peak at 550 nm


is then probably due to small changes in the ligand field as the peroxo-compound forms

and then decays. The magnetic resonance data adds more detail, with a fall in relaxation

time observed just before the reaction does clock. This fall in relaxation time could be

due to the change in oxidation state of the metal species. If this was the case, any

change in magnetic properties would be seen in the SQUID data. As the hump is absent

in the SQUID data, this fall in relaxation time must arise from some other change in the

complex. The T2 of a solution can depend on the ordering of the solvent around ions in

that solvent and, as there is some intermediate formed, this is a possible explanation for

the spectra seen. Further to this, the relaxation time of the Co(II)EDTA2− solution is

dependent on the presence of H2O2, so some interaction between these two species

could explain this. This data supports Yalman’s proposed intermediate – a peroxo-

dicobalt(III) species – as the SQUID data shows that the intermediate has the same

number of unpaired spins per atom as the final cobalt(III) product. A larger metal

complex formed with two metal centres bridged by a peroxo- group could also lead to

the change in relaxation time observed. Time-resolved electron spin resonance (ESR)

spectra of the reaction could give further information about the nature of the metal

complexes involved. A preliminary study has been attempted, with spectra of frozen

samples of the reacting solution acquired at known intervals, however further work is

required.

The use of SQUID magnetometry in following the ferroin-bromate clock fails to add

any further details to the reaction, but confirms that a clock reaction does occur and, as

the concentration of ferroin is increased, there is a change in behaviour, confirming

previous research. What these experiments do is confirm the potential of using the

technique to follow a reaction other than the Co(II)EDTA2−/H2O2 clock.

218


As a method of following a reaction, the SQUID magnetometer has its uses but also its

limitations. As described in Chapter 12, there is a limitation as to what reactions can be

followed due to the time taken to load a sample into it and the limited number of

reactions that feature changes in magnetic properties. The kinetics of the reaction are an

important factor in the suitability of a reaction, with those exhibited by most

autocatalytic reactions suitable for study. The resolution of the technique is also a

limitation with a fastest possible speed of data acquisition of one measurement every ten

to fifteen seconds. With the reactions studied here, the changes in behaviour occur over

a similar time scale, but a faster reaction would not be able to be followed using the

reaction. There is the possibility of freezing the sample before placing it in the SQUID.

This can interfere with the reaction as ice crystals form inhomogeneities in the sample.

The ferroin clock reaction is observed to react completely upon freezing. If the samples

are frozen quick enough and the freezing does not interfere with the reaction, then the

SQUID can be used to follow a reaction by studying frozen samples taken at known

time intervals/reaction conditions. This approach has been used to characterise changes

in a Manganese-centred species22.

The reproducibility of the timings of the clock reaction in the SQUID reaction are worse

than the other techniques used to follow the reaction, as shown in Fig. 12.10. In

comparison, all the other techniques used give measurements to within 60 s of each

other, with the thermostatted pH measurement the most accurate method of following

the timing of the reaction. Although the reaction is thermostatted at the centre of the

SQUID coils, the sample has to pass through temperature gradients as it passes from the

outside into the superconducting magnet at the heart of the magnetometer. It may also

pass through temperature gradients as the sample is moved through the cryostat as the

219


magnetic moment is measured. A larger volume of solution is more likely to pass

outside of the thermostatted region of the cryostat and into colder regions of the

magnetometer. This leads to cooling of the sample. These problems with temperature

gradients are not relevant for the typical use of the SQUID in measuring magnetic

properties of solid state compounds. Only the temperature of the sample as these

measurements of magnetisation is made is important. However, when following a

reaction, cooling the reaction does affect the rate of the reaction, changing the clocking

time, for example.

There may also be heating of the sample as it is sealed, although this can be limited by

sealing the tube as far away from the solution as possible. The SQUID treats the sample

as a point source magnetic dipole, which might cause problems with a larger sample as

the magnetisation of the sample is calculated by comparison with an ideal sample. Both

of these effects can be minimised by using as small an amount of material as possible.

Similar problems with the timings of the reaction occur with studies of reactions based

on the BZ reaction, with larger samples needed so that measurements could be made,

even though this makes the reaction slower. All of these factors limit the usefulness of

the technique in analysing the kinetics of the reaction.

The SQUID is different to the other methods of the reaction in a number of other ways.

The reaction is sealed, in the dark and in a large applied static magnetic field. The effect

of these conditions on the Co(II)EDTA2−/H2O2 reaction was replicated outside of the

SQUID with the reactions performed in 5 mm I.D. NMR tubes. No large effects on the

reaction were observed on the rate of reaction for any of the conditions. The staccato

motion of the sample as a measurement is made was also replicated. Again, this had no

220


effect on the Co(II)EDTA2−/H2O2 reaction. However, it failed to mix the BZ and related

reactions enough to prevent the formation of waves dominating the changes in oxidation

state of the reaction. This raises an important point relevant to all of the techniques.

Inhomogeneities on the surface of the reaction vessel are known to initiate wave

reactions. The Co(II)EDTA2−/H2O2 reaction was a lot more robust than the BZ reaction,

with wave formation only observed in a small number of experiments performed in

NMR tubes (see 12.1.3). However, the BZ reaction was known, and observed, to be

very sensitive to inhomogeneities and waves formed on most glass surfaces. Reducing

the surface area relative to the volume of the solution could reduce the effect of these

waves on the reaction.

In spite of these caveats, this technique could be useful in systems where the reaction

proceeds with little change in either pH or absorption, such as in opaque solutions or

materials. It is non-invasive, so suitable for analysis of light- or air-sensitive materials.

It is a direct method of determining the concentration of any paramagnetic species

present during a reaction and very sensitive measurements of the species can be made.

The information obtained about a reaction can then be used in conjunction with other

spectra and data to produce a more detailed picture of the reaction and the presence (or

absence) of any intermediates and their nature. This study is the first time the SQUID

magnetometer has been used to follow the progress of a liquid phase chemical reaction.

The SQUID magnetometer lends itself to the study of magnetic field effects due to two

key aspects of the technique, and one modification. First, the magnetometer is contained

within a superconducting magnet, and the applied magnetic field within the

magnetometer can be easily, and quickly, changed from 0 up to 5 T. Second, there is the

221


222

inherent sensitivity of the technique, so even small changes in the concentrations of

radicals in the sample can be seen through the change in magnetisation observed. The

concentration of radical pairs in a typical flash photolysis experiment will be ~ 1 × 10−5

M23. In the ferroin clock experiments, the change of 1 unpaired electrons per mole in a

1.875 × 10−3 M solution was clearly seen, with a change in moment of 5.5 × 10−4 emu.

The changes in the radical pair will be ~ 100 times smaller than this change. This is on

the limit of the sensitivity of the SQUID, as the errors for most measurements were ~ 1

× 10−7 emu. A second problem arises from the transient nature of the radical pairs

formed. A radical pair can have a lifetime of only nanoseconds while it takes the

SQUID seconds to make a measurement. Importantly, the SQUID can be modified so

that a light guide can be attached and a sample continuously irradiated within the

magnetic field. The applied magnetic field can then be changed, so any magnetic field

dependence on the concentration of radicals in the sample could be observed. An

example of this modification of the SQUID is shown by the SQUID study of the

irradiation of 2,4,6-triazo-3,5-dichloropyridine crystals to form paramagnetic centres24.

A liquid phase radical pair, formed by the continuous irradiation of a sample, and

subjected to changing magnetic fields, is not too many steps removed from this

experiment and certainly a possibility avenue for further use of the technique.

14. SUMMARY AND CONCLUSIONS

This thesis is based on the possibility that autocatalysis in a reaction mechanism may

play a role in amplifying any magnetic field effect present in a reaction. The possibility

of the kinetics of a reaction amplifying a small effect, such as that of an applied

magnetic field, is certainly an interesting topic of research and one with many possible

applications such as in biological systems.

Two particular reactions were investigated: the reaction between Co(II)EDTA2− and

H2O2 and the Belousov-Zhabotinsky reaction. The key features of the reactions,

travelling waves and clock behaviour/oscillations, were used to observe the effects of

magnetic fields on the reactions.

An investigation of the travelling wave that forms when Co(II)EDTA2− reacts with H2O2

forms the first section of the thesis. A series of preliminary experiments started to

quantify the reaction in terms of the forces acting on the wave front. Magnetic

resonance imaging techniques produced a series of striking images of the fingering

distortion. Both vertical and horizontal slices were used to image the wave, so that

manipulation of it around the xy plane could be observed.

The different effect of different geometry magnetic fields was also observed, with a

magnetic field gradient needing some convection around the wavefront in order

for it to have an effect on the reaction, while magnetic field gradients and

had a large effect on previously flat waves, initiating a distortion in the wave.

This distortion could be manipulated by the application of further magnetic field

z/Bz ∂∂

x/Bz ∂∂

y/Bz ∂∂

Chapter 14: Summary and Conclusion

gradients. By performing the reaction in porous foam, the role of convection as a key

factor in the magnetic field effect was identified. While the work presented here shows

a visually impressive magnetic field effect and provides an explanation for the magnetic

field effect, there is also great potential for future work, as described in chapter 5.2.

The Belousov-Zhabotinsky reaction was identified as a reaction that could show a

magnetic field dependency. In contrast to the Co(II)EDTA2−/H2O2 experiments, the

reaction itself was thought to be magnetic field dependent and that autocatalysis would

amplify any effect. Research done by other groups suggested that a magnetic field effect

on the reaction could be observed.

Apparatus was designed and built to observe the oscillations of the reaction. Solution

was continuously flowed through the cell and stirred to remove any inhomogeneities

from the solution. Series of oscillations were obtained using both cerium and ferroin as

the catalyst for the reaction, showing that the apparatus worked. Perturbations, such as

the addition of silver ions, were applied to the reaction and showed that changes in the

period of oscillations could be observed using the apparatus. Qualitative analysis of

these perturbations was also carried out.

When a magnetic field was applied to the reaction, no effect was observed in either the

ferroin-catalysed or the cerium-catalysed reactions. This was confirmed by analysis of

the data using Student’s T-test. The absence of any effect was explained by considering

the factors needed for a reaction to be magnetic field dependent. The lifetimes of the

radicals in the reaction were shown to be many powers of ten different to the timescale

224

Chapter 14: Summary and Conclusion

225

of any mixing of the radical state, while the presence of paramagnetic metal ions and

bromine atoms would remove any coherent spin-mixing through relaxation processes.

The final section of the thesis concerned not the manipulation of the reactions but the

analysis of the reactions using their changes in magnetic properties. SQUID

magnetometry is the most sensitive method of measuring magnetic fields and this

sensitivity could be used to measure tiny changes in concentration of radical species.

The work in the thesis used the reactions described previously to determine how

suitable SQUID magnetometry was for following chemical reactions and what details

the technique could show about a chemical reaction. Both reactions were successfully

followed with the technique, with the changes in magnetic susceptibility observed. The

data collected for the Co(II)EDTA2−/H2O2 reaction was compared and contrasted with

that obtained by more traditional methods, such as NMR and UV/vis spectroscopy. This

gave more information about intermediates that formed during the course of the reaction.

SQUID magnetometry proved to be another possible technique that can be used to

follow chemical reactions. Modification of the magnetometer to make it suitable for the

study of magnetic fields arising from the radical pair mechanism was discussed.

This thesis has shown how magnetic fields can be used to both manipulate and

investigate autocatalytic chemical reactions. A range of experimental techniques have

been used in this thesis. In particular, MRI techniques illustrated how magnetic field

gradients can manipulate and control travelling waves and SQUID magnetometry was

shown to be a potentially useful tool in observing chemical reactions. This thesis opens

up possibilities for detailed theoretical work that can supplement and complement these

investigations and further experimental work to build on the progress made here.

Appendix I

I

APPENDIX I

I.1. Systems of Magnetic Units

One of the more confusing aspects of magnetic fields is the different units, what they

represent, and different systems of units. The modern system, SI (Systèmes Internationales

d’Unités), is based on kilograms, metres and seconds. Before this convention came into

place, the cgs (centimetres, grams, seconds) was commonly used. A further complication to

the cgs system is that there are two distinct sets of units when dealing with electrostatic

problems (esu) and when dealing with electromagnetic problems (emu) as well as a mixed

‘Gaussian’ system. Units based on this system can still be found, notably magnetic

susceptibility (the 80th edition of the CRC Handbook of Chemistry and Physics, for

example, gives the molar susceptibility data in cm3 mol−1).

Combined units provide an early problem, with 1 dyne = 1 × 10−5 newtons and 1 erg = 1 ×

10−7 joules, but these alternatives are rarely used now. The relevant issue for this thesis

arises in electromagnetism, as both conventions are regularly used alongside each other.

Taking the magnetic flux density, B, as a starting point, the force acting on a charge is

given by the Lorentz force (Eqn. 1).

(1) BvF ×= q

In the cgs system, a force of 1 dyne is generated on a charge of 10 coulombs moving

through a 1 gauss (G) field at 1 cm s−1, while in the SI system, 1 newton is generated on 1

Appendix I

coulomb moving through a 1 tesla (T) field at 1 ms−1 (where 1 tesla = 104 gauss). These

units are interchanged freely, as 1 T is a large magnetic field. Alongside B, there is also the

magnetic field strength, H and magnetisation M (see chapter 1.1.1). The SI system defines

the three quantities B, H and M by

)(μ 0 MHB += (2)

whereas in the cgs emu system

MHB π4+= (3)

This would not be a problem, but magnetic fields measured in oersteds (cgs unit of H) are

still used, such as in the SQUID magnetometer used in Part III. To convert from oersted to

the SI equivalent, A m−1, a conversion factor of 1/4π × 103 is required. One advantage of

the latter system is that B and H have the same dimensions. This factor of 4π arises again in

measurements of susceptibility. A molar susceptibility of cm3 mol−1 requires a conversion

of 4π × 10−6 rather than 1 × 10−6, as the units might suggest.

These differences arise from the fact that electricity and magnetisation are linked through

and the values of ε0 and μ0 cannot be independent. The different systems simply

introduced different values for the two constants. These competing systems can easily add

confusion to any problem, with different units being used in different areas by different

people . In this thesis, SI units have been used wherever possible. Although the SQUID

dQ/dtI =

II

Appendix I

III

magnetometer measures in the cgs emu system, the measurements were converted to those

in the SI system as soon as possible and then SI units were used wherever possible. If cgs

units are used, they will be appropriately labelled.

Appendix II

IV

APPENDIX II

II.1 Derivation of Navier-Stokes equations Towards the end of Part I, the Navier-Stokes equation was used in the simulation of the

fingering phenomena. A derivation of the two equations was not included at the time,

but a guide to its derivation is included here, for completeness. The flow module of

CFD-ACE computes the velocity and pressure field for the flow. It does this by first

computing the momentum equations in the x, y (and potentially z) directions and then

generates a pressure field. This is achieved by solving conservation laws for the flow.

The fluid is treated as a continuous material for the volume, and is described by density,

ρ, velocity, u, pressure, p, and temperature, T. These four variables are all functions of

displacement (r) and time.

Reynolds’ Transport Theorem

Consider a volume of fluid, that is convected by the fluid. This volume always consists

of the same group of particles. For any function, f(r, t) that is continuously

differentiable with repect to r and t, then:

).dV.(ftff.dV

dtd

V(t)V(t) u∇+∂∂

=∫ ∫ ∫∫ ∫ ∫

This is used in all of the following derivations.

Appendix II Conservation of mass

The rate of change of mass of a fluid in a volume is balanced by the net mass flow rate

into that volume. Consider the mass of fluid in a volume V(t) that flows with the fluid.

∫ ∫ ∫= ρ.dVM V(t)

As mass must be conserved, then

0dV.)(ρtρρ.dV

dtd

dtdM

V(t)V(t) =⎟⎠⎞

⎜⎝⎛ ⋅∇+∂∂

== ∫ ∫ ∫∫ ∫ ∫ u

This equation can be easily simplified.

( ) 0ρtρ

=⋅∇+∂∂ u

This equation can also be understood by considering the two terms. The first term is the

rate of change of the density of the fluid. The second term is the flow of density through

the boundaries of the volume.

V

Appendix II Conservation of momentum

For the conservation of momentum, Newton’s second law applies. The rate of change of

momentum equals the applied force acting on a volume of material. The momentum of

the fluid is given by:

∫ ∫ ∫= .dVρV(t) uP

This is balanced against the forces acting on the fluid.

totaldtd FP

=

.dVt

ρ.dV).(ρtρ.dVρ

dtd

V(t)V(t)V(t) ∫ ∫ ∫∫ ∫ ∫∫ ∫ ∫ ⎟⎠⎞

⎜⎝⎛ ∇+∂∂

=⎟⎠⎞

⎜⎝⎛ ∇+∂∂

= uu.uuuuu

The forces acting on the body can be split into two contributions. There are external

body forces, such as gravity, which contribute a net force on the fluid.

∫ ∫ ∫= .dVV(t)ext FF

There is also an internal force, acting on each volume of fluid by surrounding volumes

of fluid. There is a contribution due to the pressure, p, acting inwardly.

( ) ( )∫ ∫ ∫∫ ∫ ∇−=−= .dVp.dSp V(t)Vint nF δ

VI

Appendix II There is also a contribution due to the viscosity of the fluid. In order to include these

forces, assumptions must be made about the nature of the fluid. If it is assumed that

viscosity is neglible, then:

( ).dVpρgdV.t

ρ V(t)V(t) ∫ ∫ ∫∫ ∫ ∫ ∇−=⎟⎠⎞

⎜⎝⎛ ∇+∂∂ uu.u

0dVρg.-pt

ρV(t) =∇+⎟⎠⎞

⎜⎝⎛ ∇+∂∂

∫ ∫ ∫ uu.u

The integrand must also equal 0, and the equation of fluid flow for a zero-viscosity fluid

is obtained. The presence of viscosity, μ, results in stresses within the fluid. In order to

include this in the equations, certain assumptions about the fluid must be made. In order

to produce the equation 5.34a, the stress tensor was assumed to have the form:

uuu .λδrr

μT iji

j

j

iij ∇+⎟

⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂∂

=

The second term arises due to the presence of a second coefficient of viscosity, λ,

associated with changes in volume. This term is normally neglible. The remaining term

is included in the equation as T⋅∇ , giving the equation used.

VII

Appendix II Conservation of energy

Equations of motion can also be calculated by considering that energy must be

conserved for the solution. If heat is to be included in the equations, then it can be

included in the equations of motion by considering that energy must be conserved. The

kinetic energy of a volume of the fluid is given by:

dVρ21 2

V u∫∫∫

The thermal energy of the volume of fluid is given by

TdVρcvV∫∫∫

where cv is the specific heat of the solution. Energy sources and sinks also have to be

included in the model. The same technique used above can be used to produce a third

equation.

There are now three equations, but four unknowns (ρ, u, p and T). A fourth equation is

needed, to link pressure, density and temperature, such as:

ρRTp =

In the model shown in the thesis, the relationships between concentration, temperature

and density are the relevant equation.

VIII

Appendix II

IX

Finite Volume Analysis

The technique used by CFD-ACE is known as finite volume analysis. The governing

equations are solved on discrete control volumes. A recommended book on the topic is

“Computational Methods for Fluid Dynamics” by Ferziger and Peric, Springer.

Appendix III

X

APPENDIX III

III.1 Data acquisition program

In order to monitor the output from the PMT, a simple data acquisition program was

written in Labview. The following pages show the program and its various subroutines,

with a brief description of how the program works.

False, false: The program is not yet running.

True, true 1-1: This image shows the key part of the program. A suitably large array

filled with zeros is produced. The relevant data (PMT output, time) fills it up and a final

array can be saved. The program also plots the data on a graph so that the progress of

the experiment can be followed. A number of individual measurements can be averaged

to produce a data point.

The various subroutines shown deal with the timing of the data acquisition.

0 : Records the starting time of the experiment

1-0 : Records the time of the first measurement in any set of averages 1-1 : Measurement of the PMT signal for N measurements and summation of the

measurements 1-2 : Timing of the data point calculated. Output is the total

Appendix III

XI

False, False

Appendix III

XII

True, True, 1-1

Appendix III

Subroutine 1 – set as 0

XIII

Appendix III

XIV

Subroutine 1, 0

Appendix III

Subroutine: 1, 1

Subroutine: 1, 2

XV

Appendix III

XVI

III.2 Data analysis program A second program was written, also in Labview, to analyse the data. See section 7.1.2

for some description of the technique used.

The most important pages are Subroutine: 1, 1 and Subroutine: 3, 1. The other

sections deal with the loading of data into the program, production of graphs to show

the data and the analysis and saving the data produced.

Subroutine: 3, 1 produces a set of derivatives with respect to time for a set of signal

against time data loaded into the program. Both a graph of the three sets of data

against time and an array with three rows (data, first and second derivatives), time and

a row of zeros where the peak data go are produced. The small logic circuit stops the

program when both PMT signal and time are zero.

Subroutine: 1, 1 shows the peak detection program. Whether peaks or valleys are

detected, a required threshold and a required peak width can be selected here. The

repeated routine simply calculates the time between peaks (difference between two

successive peaks) and their timing (average of those successive peaks). This data is

added to the original data and its first two derivatives with respect to time to produce

an array which can be saved and a graph showing the analysis.

This program can be easily modified to run the peak detection routine on the original

data or the first derivative of the data depending on the nature of the data used.

Appendix III

Subroutine 1 (set as 0)

XVII

Appendix III

Subroutine: 1, 1

Subroutine 1 (set as 1)

Subroutine 2a (set as 1)

XVIII

Appendix III

Subroutine: 1, 0

XIX

Appendix III

Subroutine: 1, 2

XX

Appendix III

Subroutine: 2, 0

Subroutine 2b (set as 0)

XXI

Appendix III

Subroutine: 2, 1

Subroutine 2b (set as 0)

XXII

Appendix III

Subroutine: 3, 0

Subroutine 2c (set as 0)

XXIII

Appendix III

Subroutine: 3, 1

XXIV

Appendix III

XXV

Subroutine: 3, 2

Appendix IV

XXVI

APPENDIX IV

SQUID Magnetometry

The principles behind SQUID magnetometry are derived from the properties of

superconducting materials. This appendix is meant to serve as a brief guide explaining why

and how SQUIDs work as they do. For more detail, especially in terms of electronic

hardware and practical considerations, see Rev. Sci. Instrum., 77 (2006) 101101 and The

Squid Handbook, Wiley. Tinkham, M., Introduction to Superconductivity, McGraw-Hill is

a more detailed guide to all of the relevant theory of low-temperature/superconducting

physics.

Superconductivity

As certain materials approach absolute zero, their resistance can fall to practically zero.

This behaviour is theorised to be a result of weakly bound electron pairs (Cooper pairs).

The critical temperature, Tc, is a property of the material. There also exist critical current

densities (Jc) and critical magnetic fields (Hc), above which the superconducting behaviour

is lost. For example, mercury has a Tc = 4.153 K, Hc = 0.0412 T and can support a

current(Jc) of up to 108 A cm−2.

Another property of superconducing materials is the exclusion of magnetic fields from a

material held in a magnetic field as Tc is reached (Meissner effect). If the superconducting

material forms a ring and the applied magnetic field is turned off, then the flux becomes

trapped, threading through the ring. In a normal ring of material, this magnetic flux decays,

Appendix IV due to the resistance of the material. Howver, below Tc, there is no resistance and no decay

of the current or the magnetic flux. This current persists as long as the material stays below

Tc. One further, interesting property of this behaviour is that the flux contained within the

ring is quantised and only exists in multiples of Φ0 = 2.068 × 10−15 Wb.

Josephson Junctions

If a ring of superconducting material is interrupted, by a resistive region or even a

constriction in the ring, then it would be expected that the current would decay across the

gap and the persistent current would cease. However, tunnelling between the two regions

can occur, as predicted by Josephson and observed by Anderson and Powell. Below a

characteristic Ic for the junction, superconducting behaviour is observed. Above it, normal

current flow occurs with V = IR.

Superconducting State

Voltage

Ic Current

Fig. IV.1: The voltage-current (V-I) curve for a typical Josephson junction at a given T (T<Tc), showing

that a superconducting current can be maintained without applied voltage, until a certain critical

current flows. At this point, normal resistive behaviour occurs.

XXVII

Appendix IV

XXVIII

A SQUID uses the behaviour of the Josephson junction to measure extremely small

variations in magnetic flux. The general experimental set up is that a bias current is applied

to the junction, holding it at a point between superconducting and normal resistive

behaviour. Magnetic flux is inductively coupled into the loop. This changes Ic.

.

a) b)

Ic

V

I

V Φ0

Φ Fig. IV.2: Fig. IV.2.a shows V-I curve for a Josephson junction, showing the size of the biased current

locking the junction. Changes in current in the SQUID, due to applied field, correspond to changes in

the V-Φ curve, Fig. IV.2.b.

As the flux changes, there is a change in the voltage drop across the junction. External

feedback can be used to lock the SQUID at some unique point in the V-I curve (see Fig.

IV.2.a), usually the steepest part of the curve. The feedback current is then a measure of the

applied flux, and the SQUID can measure changes of a fraction of Φ0.

The precise nature of the SQUID depends on whether a dc (two junctions) or an rf (one

junction, SQUID coupled to a rf coil). However, the essential physics of the junction

remain unchanged.

References

I

REFERENCES AND NOTES

The references are listed by section of the thesis. If a reference appears in more than one

section, then it will be repeated in each relevant section of the references.

INTRODUCTION

NOTES:

I: Given the analogous behaviour observed between magnetic and electric dipoles, it is

tempting to extend the analogy to the structure of the dipoles. A magnetic dipole could

consist of two poles of equal and opposite strength, ± p, separated by a small distance, l.

However, magnetic monopoles have not been found, while dipoles, consisting of loops

of current, have. The Maxwell equation 0=⋅∇ B can be interpreted as a statement that

there can be no magnetic monopoles as it indicates that magnetic field lines must be

closed lines.

REFERENCES:

1: Werthheimer, N. and Leeper, E., Am. J. Epidemiol., 109 (1979) 273

2: UK Mobile Telecommunications and Health Research Programme, Report 2007. Articles based on the report can be found at:

http://news.bbc.co.uk/1/hi/health/6990958.stm and http://www.guardian.co.uk/science/2007/sep/13/mobilephones.health

3: Schlichte, H. J. and Koenig, K., Proc. Nat. Acad. Sci. USA, 69 (1972) 2446-2447

Keeton, W. T., Proc. Nat. Acad. Sci. USA, 68 (1971)102-106 4: see Chapter 4, Tanimoto, Y. and Yamaguchi, M., Magnetoscience – Magnetic Field

effects on Materials: Fundamentals and Applications, Kodansha.

http://news.bbc.co.uk/1/hi/health/6990958.stm

http://www.guardian.co.uk/science/2007/sep/13/mobilephones.health

References

Relevent papers include Yamaguchi, M., Nomura, H., Yamamoto, I., Ohta, T. and Goto, T., Phys. Lett. A, 126 (1987) 133-135 and a summary/theoretical analysis of the magnetic field effects Yamamoto, I. et al., Jpn. J. Appl. Phys., 41 (2002) 416-424.

5: Steiner, U. E. and Ulrich, T., Chem. Rev., 89 (1989) 51-147 6: He, X., Kustin, K., Nagypál, I. and Peintler, G., Inorg. Chem., 33 (1994) 2077-2078 7: Ritz, T., Adem, S. and Schulten, K., Biophysical Journal, 78 (2000) 707-718 8: Bialek, W., Ann. Rev. Biophys. Biophys. Chem., 16 (1987) 455-78

Chapter 16, Essential Cell Biology, Garland also features a small but useful section on amplification processes in the eye.

9: McDougall, A., Shearer, J. and Whitaker, M., Biol. Cell., 92 (2000) 205-214

10: Orchard, A. F., Magnetochemistry, Oxford Chemistry Primers 75, OUP is a good place to start for an overview of this topic and its history.

Duffin, W. J., Electricity and Magnetism (4th Ed), McGraw-Hill is another good text. 11: see Chapter 3, Tanimoto, Y. and Yamaguchi, M., Magnetoscience – Magnetic Field

effects on Materials: Fundamentals and Applications, Kodansha. 12: Katsuki, A and Tanimoto, Y., Chem. Lett., 34 (2005) 726-727 13: Uechi, I., Katsuki, A., Dunin-Barkovskiy, L. And Tanimoto, Y., J. Phys. Chem.,

108 (2004) 2527-2530 14: Boyer, T. H., Am. J. Phys., 56 (1988) 688-692 15:Coey, J. M. D., Rhen, F. M. F., Dunne, P. and McMurry, S., J. Solid State

Electrochem., 11 (2007) 711-717 16: see Chapter 5, Tanimoto, Y. and Yamaguchi, M., Magnetoscience – Magnetic Field

effects on Materials: Fundamentals and Applications, Kodansha. 17: Ikezoe, Y, Hirota, N, Nakagawa, J. and Kitazawa, K., Nature, 393 (1998) 749-750 18: Braithwaite, D., Beaugnon, E. and Tournier, R., Nature, 354 (1991) 134-135 An application of this can be found at: Tanimoto, Y., Sueda, K. and Irie, M., Bull.

Chem. Soc. Jpn., 80 (2007) 491-494 19: Fujiwara, M. Kodoi, D., Duan, W. and Tanimoto, Y., J. Phys. Chem. B., 105 (2001)

3343-3345 Further papers on the topic: Chie, K., Fujiwara, M., Fujiwara, Y. and Tanimoto, Y.,

J. Phys. Chem. B, 107 (2003) 14374-14377

II

References

Fujiwara, M., Chie, K., Sawai, J., Shimizu, D. and Tanimoto, Y., J. Phys. Chem. B, 108 (2004) 3531-3534

Fujiwara, M., Mitsuda, K. and Tanimoto, Y., J. Phys. Chem. B, 110 (2006) 13965-13969

20: Steiner and Ulrich’s review (reference 5) is comprehensive.

Further reviews of the topic that could be useful are Brocklehurst, B., Chem. Soc. Rev., 31 (2002) 301-311 and Timmel, C. R. and Henbest, K. B., Phil. Trans. R. Soc. Lond. A, 362 (2004) 2573-2589

As with most of this chapter, Tanimoto, Y. and Yamaguchi, M., Magnetoscience – Magnetic Field effects on Materials: Fundamentals and Applications, Kodansha is recommended. Chapter 6 deals with the radical pair mechanism.

21: O’Dea, A. R., Curtis, A. F., Green, N. J. B, Timmel, C. R. and Hore, P. J., J. Phys.

Chem. A, 109 (2005) 869-873 22: predicted by Brocklehurst, B., J. Chem. Soc. Faraday Trans., 72 (1976) 1869-1884

23: A good place to start reading on the topic of non-linear kinetics and related

phenomena is Scott S. K., Oscillations, Waves and Chaos in Chemical Kinetics, Oxford Chemistry Primers 18, OUP.

Epstein, I. R. and Showalter, K., J. Phys. Chem., 100 (1996) 13132-13147 and Sagués, F. and Epstein, I. R., Dalton. Trans., 7 (2003) 1201-1217 are two fairly comprehensive reviews of the same topic.

24: Scott, S. K. and Showalter, K., J. Phys. Chem., 96 (1992) 8702-8711 25: Bray, W.C. and Liebhafsky, H. A., J. Am. Chem. Soc., 53 (1931) 38 26: Scott, S. K., Oscillations, Waves and Chaos in Chemical Kinetics, Oxford

Chemistry Primers 18, OUP, chapter 6 See also: chapter 9, Scott, S. K., Chemical Chaos, OUP 27: Møller, A. C., Hauser, M. J. B. and Olsen, L. F., Biophysical Chemistry, 72 (1998)

63-72 28: Møller, A. C. and Olsen, L. F., J. Phys. Chem. B, 104 (2000) 140-146

Møller, A. C., Lunding, A. and Olsen, L. F., Phys. Chem. Chem. Phys., 2 (2000) 3443-3446

29: Scott, S. K., Chemical Chaos, OUP is the best place to start. Chaotic behaviour is a

feature of the reactions studied in this thesis but no attempt to investigate the behaviour was attempted.

30: Page 37 and following, Scott, S. K., Chemical Chaos, OUP

III

References

PART I

NOTES:

I: The echo depicted in this image is an schematic illustration of the Lorentzian spin-

echo.

II: See chapter 12.1 for an illustration of the pH changes of the Co(II)EDTA2−/H2O2.

III: A description of the method of finite volume analysis is too broad a topic to be

dealt with in this thesis, but a brief description of the technique and a helpful text can be

found in Appendix II.

REFERENCES:

1: He, X., Kustin, K., Nagypál, I. and Peintler, G., Inorg. Chem., 33 (1994) 2077-2078

2: Boga, E, Kadar, S., Peintler, G. and Nagypál, I., Nature, 347 (1990) 749

3: Britton, M. M., J. Phys. Chem. A, 110 (2006) 2579-2582 Britton, M. M., J. Phys. Chem. A, 110 (2006) 13209-13214

4: For a detailed overview of both NMR and MRI, see Callaghan, P. T., Principles of

Nuclear Magnetic Resonance Microscopy , OUP.

Hore, P. J., Nuclear Magnetic Resonance, Oxford Chemistry Primers 18, OUP was also found to be useful.

Mantle, M. and Sederman, A., Prog. Nuc. Magn. Res. Spec., 43 (2003) 3–60 reviews the techniques from a chemical engineering point of view.

5: Meiboom, S and Gill, D., Rev. Sci. Instrum., 29 (1958) 688-691

6: Hennig, J., Naureth, A. and Freidburg, H., Magn. Reson. Med., 3 (1986) 823-833

7: Nagypál, I., Bazsa, G. and Epstein, I., J. Am. Chem. Soc., 108 (1986) 3635-3640 Pojman, J. A. and Epstein, I., J. Phys. Chem., 94 (1990) 4966-4972 follows on from the previous paper.

IV

References

There is a further series of papers: Pojman, J. A., Epstein, I. R., MacManus, T. J. and Showalter, K., J. Phys. Chem., 95 (1990) 1299-1306 Pojman, J. A., Nagy, I. P. and Epstein, I. R., J. Phys. Chem., 95 (1990) 1306-1311

8: Harris, G., Part II Thesis, 2001 9: Evans, R., Timmel, C. R., Hore, P. J. and Britton, M. M., J. Am. Chem. Soc., 128

(2006) 7309-7314 10: Kinouchi, Y., Tanimoto, S., Ushita, T., Sato, K., Yamaguchi, H. and Miyamoto, H., Bioelectromagnetics, 9 (1988) 159-166

11: Norris, D. and Hutchison, J., Magn. Reson. Imaging, 8 (1990) 33 12: De Wit, A. and Homsy, G., Physics of Fluids, 11 (1999) 949 - 951 13: Morris, G. and Freeman, R., J. Magn. Reson., 29 (1978) 433-462 14: Mori, E., Schreiber, I. and Ross, J., J. Phys. Chem., 95 (1991) 9359-9366 15: Su, S., Menziger, M., Armstrong, R., Cross, A. and Lemaire, C., J. Phys. Chem.,

98 (1994) 2494-2498 16: Gao, Y., Cross, A. and Armstrong, R., J. Phys. Chem., 100 (1996) 10159-10164 17: Britton, M., J. Phys. Chem. A, 107 (2003) 5033-5041

Britton, M., J. Phys. Chem., 110 (2006) 5075-5080 Taylor, A. F. and Britton, M., Chaos, 16 (2006) 37103-37111 18: Bazsa, G and Epstein, I., J. Phys. Chem., 89 (1985) 3050-3053 Póta, G., Lengyel, I. and Bazsa, G., J. Phys. Chem., 95 (1991) 4379-4381 19: Pojman, J. A., Nagy, I. and Epstein, I., J. Phys. Chem., 95 (1991) 1306-1311 20: Pojman, J. A., Ilyashenko, V. M. and Khan, A. M., J. Chem. Soc., Faraday Trans.,

92 (1996) 2825-2837 A useful review: Epstein, I. R. and Pojman, J. A., Chaos, 9 (1999) 255-259

21: Wilmott, N. Sethi, K. Walseth, T. F., Lee, H. C., White, A. M. and Galione, A. J.

Biol. Chem., 271 (1996) 3699-3705 22: Baxter, E., Part II Thesis, 2001

V

References

PART II

NOTES:

I: Although not vitally important, the structures of malonic acid, tartronic acid, oxalic

acid and mesoxalic acid, are:

II: The data shown in fig. 6.1 is meant to be a representive set of oscillations of the BZ

reaction, and is not data collected in this thesis. Further, similar sets of oscillations can

be found in Field, R.J., Körös, E and Noyes, R. M., J. Am. Chem. Soc., 94 (1972) (for a

range of different reaction compositions), as well as S. K. Scott’s “Chemical Chaos”

(Page 196) or S. K. Scott’s “Oscillations, Waves and Chaos in Chemical Kinetics”

(Page 27)

O O

OHHO

O O

OH HO

OH Tartronic Acid Malonic Acid

O O

OHHO

O

OH

HO

O

Oxalic Acid

O

Mesoxalic Acid

VI

References

III: Examples of chaotic oscillations observed in a CSTR can be found in S. K. Scott’s

“Chemical Chaos” (Page 200 and following)

REFERENCES:

1: Belousov, B. P. (translated by Field, R. J. and Burger, M.), Oscillations and Travelling Waves in Chemical Reactions, Wiley Interscience, NY, 1984

2: Winfree, A. J., J. Chem. Ed., 61 (1984) 661-663

3: Bray, W. C., J. Am. Chem. Soc., 43 (1921) 1262-1267

4: Shaw, D. H. and Pritchard, H. O., J. Phys. Chem., 72 (1968) 1403-1404. Reply to this letter: Degn, H and Higgins, J., J. Phys. Chem., 72 (1968) 2692-2693

Further reply: Shaw, D. H. and Pritchard, H. O., J. Phys. Chem., 72 (1968) 2693 5: Zaikin, A. N. and Zhabotinsky, A. M., Nature, 225 (1970) 535-537

6: Prigogine, I. and Le Fever, R. J. Chem. Phys., 48 (1968) 1695-1700

7: Field, R. J., Körös, E and Noyes, R. M., J. Am. Chem. Soc., 94 (1972) 8649-8664

8: Winfree, A. T., Science, 175 (1972) 634

9: Györgi, L. and Field, R. J., Nature, 355 (1992) 808-810

10: Bolletta, F. and Balzani, V., J. Am. Chem. Soc., 104 (1982) 4250-4251

11: Kádár, S., Amemiya, T. and Showalter, K., J. Phys. Chem. A, 101 (1997) 8200-8206

12: Szalai, I. and Körös, E., J. Phys. Chem. A, 102 (1998) 6892-6897

13: Györgi, L., Turanyi, T. and Field, R. J., J. Phys. Chem., 94 (1990) 7162-7170

14: Turanyi, T., Györgi, L. and Field, R. J., J. Phys. Chem., 97 (1993) 1931-1941

15: Field, R. J. and Noyes, R. M., J. Chem. Phys., 60 (1974) 1877-84

16: Noyes, R. M., J. Phys. Chem., 90 (1986), 5407-5409

17: Noszticzius, Z., J. Am. Chem. Soc., 101 (13): 3660-3663 1979

Further discussion of the results: Noyes, R. M., Field, R. J., Försterling, H. D., Körös, E and Ruoff, P. J. Phys. Chem., 93 (1989) 270-274

18: Field, R. J. and Försterling, H. D., J. Phys. Chem., 90 (1986) 5400-5407

VII

References

Zhabotinsky, A. M., Buchholtz, F., Kiyatkin, A. B. and Epstein, I. R., J. Phys. Chem., 97 (1993) 7578-7584

19: Noyes, R. M., J. Am. Chem. Soc., 102 (1980) 4644-4649 Further discussion and work: Rovinsky, A. B., J. Phys. Chem., 88 (1984) 4-5

Chou, Y-C, Lin, H-P, Sun, S. S. and Jwo, J-J, J. Phys. Chem., 97 (1993) 8450-8457 Ungvarai, J. Nagy-Ungvarai, Z, Enderlein, J. and Müller, S. C., J. Chem. Soc., Faraday Trans., 93 (1997) 69-71

20: Jacobs, S. S. and Epstein, I. R., J. Am. Chem. Soc., 98 (1976) 1721-1725

21: Gaspar, V., Bazsa, G. and Beck, M., Z. Phys. Chem. (Leipzig), 264 (1983) 43

22: Tóth, R., Gaspar, V., Belmonte, A., O’Connell, M. C., Taylor, A. and Scott, S. K., Phys. Chem. Chem. Phys., 2 (2000) 413-416 23: Ram Reddy, M. K., Szlavik, Z., Nagy-Ungvarai, Z. and Miller, S. C., J. Phys.

Chem., 99 (1995) 15081-15085 24: Taylor, A. F., Johnson, B. R. and Scott, S. K., J. Chem. Soc., Faraday Trans., 94

(1998) 1029-1033 25: Steinbock, O., Hamik, C. T. and Steinbock, B., J. Phys. Chem., 104 (2000) 6411-

6415 26: Broomhead, E. J. and McLauchlan, K. A., J. Chem. Soc., Faraday Trans., 74 (1978)

775-781 27: Kovalenko, A. S., Lugina, L. N., Andreev, E. A. and Tikhona, L. P., Teor. Eksp.

Khimiya, 25 (1989) 647-652 28: Agulova, L. P., Opalinskaya, A. M. and Kiryanov, V. S., Teor. Eksp. Khimiya, 26

(1990) 624-627 29: Agulova, L. P., Opalinskaya, A. M., Zhurnal Fizicheskoi Khimii, 59 (1985) 1513-

1516 30: Blank, M. and Soo, L., Bioelectrochemistry, 61 (2003) 93-97

31: Sontag, W., Bioelectromagnetics, 27 (2006) 314-319

32: Byberg, J. R. and Linderberg, J., Chem. Phys. Lett., 33 (1975) 612-615

33: Barkin, S., Bixon, M. Noyes, R. M. and Bar-Eli, K., Int. J. Chem. Kin., 11 (1977) 841-862 34: Menziger, M. and Jankowski, P., J. Phys. Chem., 94 (1990) 4123-4126

VIII

References

35: Schneider, F. W. and Münster, A. F., J. Phys. Chem., 95 (1991) 2130-2138 36:Dutt, A. K. and Müller, S. C., J. Phys. Chem., 97 (1993) 10059-10063

BZ with gallic acid: Dutt, A. K. and Menziger, M., J. Phys. Chem., 96 (1992) 8447-8449

37: Field, R. J. and Noyes, R. M, Faraday Symp. Chem. Soc., (1994) 21- 27

See also: Scott, S. K., Oscillations, Waves and Chaos in Chemical Kinetics (page 37)

38: Grissom, C. B., Chem. Rev., 95 (1995) 3-24 39: Försterling, H. D., Murányi, S. and Noszticzius, Z., React. Kinet. Catal. Lett., 42

(1990) 217 See also: Försterling, H. D., Murányi, S. and Noszticzius, Z., J. Phys. Chem., 94 (1990) 2915-2921

40: Field, R. J., Raghaven, N. V. and Brummer, J. G., J. Phys. Chem., 86 (1982) 2443-

2449 41: Symons, M. C. R., Free. Rad. Res., 32 (2000) 25-29

42: Turro, N. J., Chung, Ch-J, Jones, G and Becker, W. G., J. Phys. Chem., 86 (1982) 3677-3679

43: Modelling attempts used the Chemical Kinetics Simulator.

44: Baxter, E., Part II Thesis, 2001

IX

References

PART III

NOTES:

I: SQUID magnetometry is a practical application of quantum interference in

superconducting materials. A brief summary of the low-temperature solid state physics

that gives rise to the behaviour is described in Appendix IV. The SQUID was used

without modification, so a detailed understanding of the physics driving the phenomena

and the electronics used in the magnetometer was thought unnecessary. References for

further reading are also given.

II: As with the NMR/MRI sequences shown in Part I, the echo depicted in this image is

a schematic illustration of the Lorentzian. spin-echo.

REFERENCES:

1: Eveson, R.W. , Timmel, C. R., Brocklehurst, B., Hore P. J. and McLauchlan, K. A., Int. J. Rad. Biol., 76 (2000) 1509-1522.

See also: Thomas, P. G., DPhil Thesis, 2004 2: Henbest, K. B., Maeda, K., Athanassiades, E., Hore, P. J. and Timmel C. R., Chem.

Phys. Lett., 421 (2006) 571-576 See also: Norman, S. A., DPhil Thesis, 2006, Wedge, C., Part II Thesis, 2005.

Steiner, U. E. and Ulrich, T., Chem. Rev., 89 (1989) 51-147 is a comprehensive review, and features further examples of how reactions featuring radical pairs can be studied.

3: Vink, C. B. and Woodward, J. R., J. Am. Chem. Soc., 126 (2004) 16730-16731. 4: Yalman, R. G., J. Phys. Chem., 65 (1961) 556-560

5: Chapter 5.7, Blundell, S., Magnetism in Condensed Matter, OUP

6: Adkin, J. J. and Heyward, M. A., Chem. Mater., 19 (2007) 755-762

X

References

XI

7: An overview of the many applications of SQUIDs can be found in Fagaly, R. L., Rev. Sci. Instrum., 77 (2006) 101

Tinkham, M., Introduction to Superconductivity, McGraw-Hill is a more detailed guide to all of the relevant theory. See Appendix IV for a brief overview. Juzeliūnas, E. and Hinken, J. H., J. Electroanal. Chem., 477 (1999) 171-177

8: Josephson, B. D., Phys. Lett., 1 (1962) 251-253

9: Anderson, P. W. and Rowell, J. M., Phys Rev. Lett., 11 (1963) 230-232

10: Meiboom, S and Gill, D., Rev. Sci. Instrum., 29 (1958) 688-691

11: page 5, Orchard, A. F., Magnetochemistry, Oxford Chemistry Primers 75, OUP

12: Yalman, R. G. and Warga, M. B., J. Am. Chem. Soc., 80 (1958) 1011

13: Britton, M. M., J. Phys. Chem. A, 110 (2006) 13209-13214 14: Nicholls, D., Complexes and First Row Transition Elements, Macmillan

15: Handbook of Chemistry and Physics, 80th Edition, CRC Press

16: Barkin, S., Bixon, M. Noyes, R. M. and Bar-Eli, K., Int. J. Chem. Kin., 11 (1977) 841-862

17: Smoes M-L., J. Chem. Phys., 71 (1979) 4669-4679 18: McElfresh, M., Fundamentals of Magnetism and Magnetic Measurements ,

(Quantum Design’s guide to the SQUID magnetometer) 19: Field, R.J., Körös, E and Noyes, R. M., J. Am. Chem. Soc., 94 (1972) 8649-8664 20: Körös, E., Burger, M. and Kris, Á, React. Kinet. Catal. Lett., 1 (1974) 475-480

21: Khan, Z., Babu, P. S. S. and Kabir-ud-Din, Carbohydrate Research, 339 (2004) 133-140

22: Horner, O., Rivière, E., Blondin, G., Un, S., Rutherford, A. W., Girerd, J-J. and

Boussac, A., J. Am. Chem. Soc., 120 (1998) 7924-7928 23: Henbest, K. B. and Maeda, K., private communications 24: Morgunov, R. B., Berdinskii, V. L., Kirman, M. V., Tanimoto, Y. and Chapysev, S.

V., High Energy Chemistry, 41 (2007) 33-36

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