Ultraviolet/Visible Spectroelectrochemistry

Ultraviolet/Visible Spectroelectrochemistry

Daniel A. Scherson, Yuriy V. Tolmachev, and Ionel C. Stefan

inEncyclopedia of Analytical Chemistry

R.A. Meyers (Ed.)pp. 10172–10225

John Wiley & Sons Ltd, Chichester, 2000

ULTRAVIOLET/VISIBLE SPECTROELECTROCHEMISTRY 1

Ultraviolet/VisibleSpectroelectrochemistry

Daniel A. Scherson, Yuriy V. Tolmachev, andIonel C. StefanCase Western Reserve University, Cleveland, USA

1 Introduction 1

2 Theoretical Considerations 22.1 Optics 22.2 Mass Transport 3

3 Experimental Considerations 7

4 Applications 84.1 Transmission Thin-layer Spectro-

electrochemistry 94.2 Transmission Spectroelectrochem-

istry in Semi-infinite Media 174.3 Internal Reflection 184.4 External Reflection 204.5 Spatially Resolved Spectroelectro-

chemistry 304.6 Ultraviolet/Visible Spectroelec-

trochemistry in the Presence ofConvective Flow 34

4.7 Modulation Techniques 43

Concluding Remarks 50

Acknowledgments 51

Abbreviations and Acronyms 51

Related Article 51

References 51

This article reviews the field of solution-phase ultravio-let/visible (UV/VIS) absorption spectroelectrochemistryand its application to problems in thermodynamics,kinetics, and mass transport, with emphasis on both exper-imental and theoretical aspects. Examples are providedfor transmission in thin layer and semi-infinite media,using optically transparent electrodes, and external andinternal reflection in quiescent media. Also illustrated isthe coupling of UV/VIS spectroscopy to systems underforced convection, such as rotating disk and channelelectrodes, under steady state and transient conditions.Attention is also focused on spatially resolved spectro-electrochemistry for the imaging of diffusion and reactionlayers. The last section is devoted to the more complexand particularly powerful modulation techniques involv-ing diffraction, refraction and absorption in stagnant media

and in the presence of convective flow. Factors that limit thesensitivity and spatial and temporal resolution of UV/VISabsorption spectroelectrochemistry, as well as its futureprospects in analytical chemistry are briefly discussed.

1 INTRODUCTION

Light in the UV/VIS range, i.e. 190–700 nm, can promoteexcitation of electronic states in atomic and molecu-lar species in gas and solution phases, and also incondensed matter, including crystalline solids and pureliquids. As such, it represents a valuable probe of thestructure and properties of materials..1 – 3/ UV/VIS spec-troelectrochemistry refers collectively to a wide arrayof techniques that employ radiation in this frequencydomain for the study of the optical properties ofelectrodes and electrolyte solutions, particularly thoseinduced by changes in the applied potential across elec-trode–solution interfaces..4 – 8/ Implicit in this definitionis the fact that measurements are performed in situ,i.e. with the electrode immersed in the solution underpotential control. Particularly amenable to UV/VIS spec-troelectrochemical investigation are electrode processesthat generate soluble species that absorb radiation in thisspectral region, elicit spatial variations in the index ofrefraction, or modify the optical properties of interfaces.The dependence of the molar absorptivity on the wave-length of the probing beam, which is often specific to eachand every chromophore, provides an added dimensionfor the identification and monitoring of species involvedin electrochemical reactions as compared to simple cur-rent–potential relationships.

This article reviews the field of solution phase UV/VISabsorption spectroelectrochemistry and its application toproblems in kinetics, mechanisms and mass transport.Within this rather narrow scope, it excludes equallyimportant areas that rely on the analysis of light reflectedfrom the electrode surface, such as ellipsometry.9,10/

and electroreflectance,.11,12/ as well as simple refraction,notably probe beam deflection.13/ and interferometry,.14/

for the study of interfacial and bulk phenomena. As thevast majority of heterogeneous electron transfer reactionsinvolve generation or depletion of species in solution,diffusion plays an important role in controlling thecurrent that flows across the interface and, thus, the timeevolution of concentration profiles..15/ Hence, it is of keyimportance to highlight at the outset fundamental aspectsof the two most relevant physical phenomena, namely,the interaction of light and matter, and mass transport ofspecies in condensed media, to gain a full appreciationof the various factors associated with the design andinterpretation of spectroelectrochemical experiments.

Encyclopedia of Analytical ChemistryR.A. Meyers (Ed.) Copyright John Wiley & Sons Ltd

2 ELECTROANALYTICAL METHODS

2 THEORETICAL CONSIDERATIONS

2.1 Optics

2.1.1 Light Propagation through Single-phaseMaterials

The optical properties of an isotropic nonmagnetic mediaare defined in terms of its complex refractive indexOn D n� ik, or its complex dielectric function, Oe D e0 � ie00,where the index of refraction n and the extinctioncoefficient k are both functions of the wavelength l,and e0 D .n2 � k2/ and e00 D 2nk..16,17/ Modifications inthe composition of an otherwise homogeneous solu-tion, such as those derived from electrode processes,will often bring about variations in the local magni-tudes of n and k, so that the intensity, as well as thedirection of light propagating through the media maybe altered. These effects can be exploited to obtaintime- and space-resolved concentration profiles, allow-ing important aspects of electrochemical systems tobe investigated, including identification of products ofredox reactions, measurements of diffusion coefficients,elucidation of reaction mechanisms, and determinationof the rates of both heterogeneous and homogeneouselectron transfer reactions involving electrogeneratedspecies.

Correlations between n and k, and the concentra-tion of a single species in solution are usually linear,a factor that simplifies considerably the analysis of exper-imental data. Furthermore, if ionic migration in anelectric field is sufficiently minimized, for example byusing an excess of supporting electrolyte, mass transportunder either quiescent or laminar flow conditions canbe approximated by relatively simple differential equa-tions, allowing solutions to be expressed in terms ofcommon analytic functions. It is precisely the interac-tion of light with such spatially and temporally varyingconcentration fields that constitutes the basis for a rigor-ous mathematical treatment of spectroelectrochemicalexperiments that rely on absorption, refraction, anddiffraction of light. In view of the nature of the materialbeing reviewed, it seems appropriate to focus gen-eral attention on light absorption, and defer discussionof refraction and diffraction to those few specializedsections where methods based on these phenomena areintroduced.

2.1.2 Absorption

The instantaneous attenuation in the intensity I of acollimated light beam propagating along an axis y, �dI,through a media of thickness dy, containing, without lossof generality, a single absorbing species, is most oftenproportional to the intensity of the light incident on the

infinitesimal volume, dx dy dz, I.x, y, z, t/, to the localconcentration c.x, y, z, t/ and to the molar absorptivity ofthat species e.l/:

�dI.x, y, z, t/ D I.x, y, z, t/k.l/c.x, y, z, t/ dy .1/

In Equation (1) k.l/ D ke.l/, k D 2.303, and l is thewavelength of light at which the measurements are beingcarried out. The intensity of the light emerging from a cellof length d along y, I.x, d, z, t/, is given by Equation (2),

I.x, d, z, t/ D I.x, 0, z/ exp

{�∫ d

0k.l/c.x, y, z, t/ dy

}.2/

where, for simplicity, the intensity of the beam incidenton the cell, I.x, 0, z/ has been assumed independent oftime. Equation (2) can be integrated over the entire cross-sectional area of the beam xz, to yield Equation (3)∫

x

∫z

I.x, d, z, t/ dx dz D∫

x

∫z

I.x, 0, z/ exp

{�∫ d

0k.l/

ð c.x, y, z, t/ dy

}dx dz .3/

If absorption is weak,.18/ as is assumed throughout thisarticle, the exponential function can be approximated bythe first two terms in its Taylor’s series expansion. Onthis basis, the instantaneous absorbance A.t/, i.e. the log(base 10) of the ratio of the light intensity incident on, andthat emerging from the cell, is expressed by Equation (4):

A.t/ D

∫x

∫z

I.x, 0, z/

{e.l/

∫ d

0c.x, y, z, t/ dy

}dx dz∫

x

∫z

I.x, 0, z/ dx dz

.4/In cases in which the concentration is only a function

of y and t, A.t/ reduces to the much simpler Equation (5):

A.t/ D e

∫ d

0c.y, t/ dy .5/

where the explicit dependence of e on l will, hereafter,be omitted. This expression specifies that the intensity ofthe light emerging from the cell is proportional to theintegral of the concentration profile along y, and wouldbe applicable for measurements in which a beam of lightis incident normal to a semitransparent, planar electrodeplaced in the xz plane (Figure 1a). Alternatively, the beamcould propagate through the solution and reflect off thesurface of a highly polished electrode at an angle strictlysmaller than 90° (Figure 1b). This geometry will increasethe effective optical path compared to the transparent


Figure 1 Experimental arrangements for UV/VIS spectroelec-trochemical experiments: (a) optically transparent electrodetransmission; (b) external reflection; (c) parallel geometry;(d) internal reflection.

electrode, which will appear as a correction factor toEquation (5) (see section 4.4.1).

A far more powerful strategy involves the use of a well-collimated beam of monochromatic light of finite widthpropagating parallel to and very close to the surface ofa planar electrode (Figure 1c). This can then be imagedonto a photodiode array detector, for example, to yieldspatially resolved profiles of absorbing species.

It becomes evident from these arguments, that aquantitative analysis of dynamic spectroelectrochemi-cal experiments involving solution-phase chromophoresrequires time dependent concentration profiles to be cal-culated. Such problems are inextricably linked to findingsolutions of the equations that govern the mass trans-port of species in solution, subject to the appropriateboundary conditions, especially those prescribed at theelectrode surface..15/

2.1.3 Internal Reflection

Consider a beam of light propagating in the xy plane inphase 1 with index of refraction n1 impinging onto theplane xz that separates phase 1 from another phase 2 withdifferent index of refraction n2, at an angle of incidencefi with respect to the normal to the interface (Figure 1d).Classical optics predicts that fi is related to the anglethe transmitted light will make with respect to the sameplane, ft, through the familiar Snell’s law (Equation 6),

sinft D sinfi

n12.6/

where n12 D n2/n1. If n2 < n1 and sinfi > n12, ft becomesimaginary leading physically to a condition known astotal internal reflection..16/ Based on purely trigonometricarguments, Equation (6) can be rewritten as

cosft D ši

√sin2 fi

n212

� 1 .7/

Based on Equations (6) and (7), the amplitude of theelectric field, E, may be shown to be proportional toEquation (8):

e�iω.t�..x sin fi//.n12v2///e�..ωy//.v2//

(√.sin2 fi//.n2

12/�1

).8/

where ω D 2pvj/lj and vj and lj are the velocity andwavelength of light in medium j, respectively. Thisexpression represents a wave travelling along the x-axiswithin the interfacial plane, for which its intensitydecreases exponentially along the y-axis, i.e. normal to theplane. The distance at which the magnitude of the electricfield E decreases to 1/e of its value at the precise interfaceis known as the depth of penetration d (Equation 9):

Ed

EoD 1

eD e

�..ωd//.v2//

(√.sin2 fi//.n2

12/�1

).9/

Hence, in terms of ω D 2pvj/lj,

d D l2

2p

√sin2 fi

n212

� 1

D l1

2p√

sin2 fi � n212

.10/

where l1 D n12l2 in Equation (10).This evanescent wave can be used to probe species

present at, and in the near vicinity of the interface,as has been widely popularized in the infrared spectralregion under the acronym of attenuated total reflection(ATR)..19/ It thus follows from Equation (10) that l andd are of the same order of magnitude, i.e. a few hundrednanometers in the UV/VIS region.

2.2 Mass Transport

2.2.1 Quiescent Solutions

In the absence of complications derived from ionicmigration in an electric field, natural convection, andhomogeneous chemical reactions, mass transport instagnant solutions is governed to a good degree ofapproximation by Fick’s second law,.20/

@c@tD Dr2c .11/

where D is the diffusion coefficient of the species inquestion. The symbol r2 in Equation (11) represents the


Laplacian, which in cartesian coordinates is given byEquation (12):

r2 D @2

@x2C @2

@y2C @2

@z2.12/

For measurements performed over relatively shortperiods of time, as is often the case, the changes inconcentration of reactants and products are confined toa small volume of solution close to the electrode surface.Under these conditions, the composition of the mediafar away from the electrode may be assumed to remainunaltered during the entire data acquisition period, andthus the actual size of the container may be regarded asbeing arbitrarily large.

The theoretical treatment of a vast number of UV/VISspectroelectrochemical experiments involving planar,cylindrical and spherical electrodes reduces to findingsolutions of Equation (11) in one dimension under theinitial and boundary conditions specified in the leftcolumn of Table 1, where CR is the concentration of anelectroactive reactant R, and the superscript ‘o’ representsits bulk value. As will be illustrated for a few simple casesin this article, the Laplace transform method.21/ affordsa particularly powerful tool for solving problems of thistype..15,22/

It is convenient from a computational viewpoint todefine a dimensionless concentration, i.e.

qR.y, t/ D CoR � CR

CoR

.13/

Substitution of Equation (13) into Equation (11) ren-ders a similar differential equation subject to initial andboundary conditions shown in the center column inTable 1, which do not depend explicitly on the valueof Co

R.Subsequent application of the Laplace transform with

respect to t reduces the problem to solving a simple lineardifferential equation, as prescribed in the third columnin that same table, for which a solution can be easilyobtained to yield

NqR.y, s/ D NqR.0, s/e�.s/DR/1/2y .14/

In Equation (14) the bar above indicates that thefunction has been Laplace transformed, and NqR.0, s/ is theconcentration of the reactant at the boundary for t > 0 inLaplace space. As will be shown, the quantitative analysisof a variety of electrochemical techniques requires forNqR.0, s/ to be explicitly specified.

Many of the systems to be described in this articleinvolve simple reactions of the Equation (15) type:

R ��! P .15/

where, unless otherwise stated, both R and P are solutionphase species. A relationship between the concentrationprofiles of R and P can be obtained from conservation ofmass at the surface (Equation 16)

[email protected], t/

@y

∣∣∣∣yD0D �DP

@CP.y, t/@y

∣∣∣∣yD0

.16/

The terms on the right and left of this equationrepresent the fluxes of P and R through the electrode,respectively, bearing opposite signs, as required.

2.2.1.1 Chronocoulometry Consider a planar elec-trode embedded in the xz plane immersed in a quiescent,homogeneous solution containing an electrochemicallyactive species R, and assume a potential step is applied tothe electrode of a magnitude large enough to reduce CR

to zero at the surface. This experimental protocol consti-tutes the basis of chronocoulometry, an electrochemicaltechnique in which the current generated following thepotential step is monitored as a function of time. Thetime evolution of the concentration profile for R in thiscase may be obtained by setting qR.0, t/ D 1. Inserting itsLaplace transform, NqR.0, s/ D 1/s, in Equation (14) givesEquation (17),

NqR.y, s/ D 1s

e�.s/DR/1/2y .17/

which yields Equation (18) upon Laplace inversion:

CR D CoRerf

(y

2p

DRt

).18/

where erf(z) is the error function of argument z..23/

Table 1 Differential equations and boundary conditions for mass transport of speciesin quiescent media in real and Laplace spaces

Real space Laplace space

@CR.y, t/@t

D [email protected], t/

@y2

@qR.y, t/@t

D [email protected], t/

@y2DR

d2 NqR.y, s/dy2

D s NqR.y, s/

CR.y, 0/ D CoR qR.y, 0/ D 0 NqR.y, s/ D 0

CR.1, t/ D CoR qR.1, t/ D 0 NqR.1, s/ D 0


Figure 2 Time evolution of the concentration profile for areactant R following application of a potential step to a planarelectrode based on Equation (18) for DR D 10�5 cm2 s�1. Eachof the curves was calculated for the specified times in units ofseconds..73/

A series of CR/CoR versus y plots show that for fixed

values of t, the concentration near the surface is propor-tional to the distance from the electrode (Figure 2). Linearextrapolation to the bulk concentration, i.e. CR/Co

R D 1,as indicated in that figure defines an imaginary regionknown as the Nernst diffusion layer. This simple diffu-sional theory predicts that, as time elapses, the thicknessof this layer dN extends progressively into the bulk solu-tion. In practice, however, variations in concentrationgive rise to differences in the density of the media, andthus to the onset natural convection, a phenomenon notconsidered by Fick’s second law, leading ultimately to theformation of a rather static boundary layer..24/

If the product of the reaction P is not present at thebeginning of the experiment, its time-varying concen-tration profile can be calculated in a very similar wayby defining an appropriate dimensionless concentration(Equation 19),

qP.y, t/ D �CP

CoR

.19/

rendering a problem identical to that specified for R inTable 1. In Laplace space this gives Equation (20),

NqP.y, s/ D NqP.0, s/e�.s/DP/1/2y .20/

where NqP.0, s/ is the dimensionless concentration of Pat the electrode surface. The latter can be obtainedfrom Equation (16) in Laplace space, as the additionalboundary condition, which in terms of dimensionlessconcentrations reads

NqP.0, s/ D �NqR.0, s/(

DR

DP

)1/2

.21/

Insertion of Equation (21) into Equation (20) and replac-ing NqR.0, s/ by 1/s yields Equation (22),

NqP.y, s/ D �1s

(DR

DP

)1/2

e�.s/DP/1/2y .22/

which upon subsequent Laplace inversion gives the time-dependent concentration profile of P for a chronocoulo-metric-type experiment (Equation 23):

CP.y, t/ D(

DR

DP

)1/2

CoRerfc

(y

2p

DPt

).23/

where erfc.z/ D 1� erf.z/ is the complementary errorfunction of argument z..23/

An explicit expression for the flux of P at the surfacecan be obtained from Equation (20) as Equation (24),

�[email protected], s/

@y

∣∣∣∣∣xD0

D√

DPs NqP.0, s/ .24/

a quantity proportional to the charge that flows across theelectrode per unit time due to a heterogeneous electrontransfer reaction, or faradaic current.

The total amount of material produced by the electrodereaction up to time t is then proportional to the integralof the flux with respect to t, which in Laplace space isequivalent to simply dividing Equation (24) by s, to yielda quantity denoted as Q.s/.

Q.s/ D√

DP

sNqP.0, s/ .25/

Equation (25) is also obtained by integrating thedimensionless concentration profile along the entire y-axis, a quantity proportional to the absorbance (seeEquation 5), provided P is the only absorbing speciesin the media (Equation 26):∫ 1

0

NqP.y, s/ dy D∫ 1

0

NqP.0, s/e�.s/DR/1/2y dy

D√

DP

sNqP.0, s/ .26/

Such an identity should not be surprising, as the totalamount of solution-phase material produced by the elec-trode, is indeed directly proportional to that calculatedbased on the flux at the interface. However, no such rig-orous relationship exists involving the measured charge,as in many cases the current may contain nonfaradaiccontributions derived primarily from interfacial doublelayer capacitive effects.

2.2.1.2 Coupled Chemical Reactions Many elec-trochemical processes of fundamental and technolog-ical interest involve generation of species that are


either intrinsically unstable, i.e. undergo spontaneousdecomposition, or are capable of reacting with othersolution-phase species. The latter include redox-mediatedcatalysis in which reduction or oxidation of the reactantR at an electrode produces P (Equation 27), which in turnreacts with Q via homogeneous electron transfer to yielda desired product Z, regenerating R (Equation 28):

R ��! P .27/

PCQk��! ZCR .28/

A mathematical analysis of this reaction sequencerequires that the appropriate diffusion equations forR and P are solved simultaneously. Under conditionsin which there is great excess of Q in solution, thehomogeneous electron transfer reaction may be assumedto be pseudo first order in P. Furthermore, if both Q andZ are electrochemically inactive in the potential rangein which R is either oxidized or reduced, the system ofdifferential equations governing the overall process maybe shown to be given by Equations (29) and (30),

@CR

@tD DR

@2CR

@y2C b2CP .29/

@CP

@tD DP

@2CP

@y2� b2CP .30/

where b2 D kCQ is a pseudo-first-order rate constant.A solution to the concentration step problem for P inLaplace space, assuming DR D DP D D, may be obtainedby the same techniques introduced above,.25/ yieldingEquation (31):

NqP.y, s/ D e�.[sCb2]/D/1/2

y .31/

where NqP.y, s/ D CP/CoR and CP is the Laplace transform

of CP.

2.2.2 Diffusion in the Presence of Convective Flow

The relationship that governs convective diffusion ofsolution-phase species that do not participate in anyhomogeneous phase reactions may be written in generalas Equation (32):

@c@tD Dr2c� vrc .32/

where v is a vector that represents the fluid velocity.Considerable mathematical simplifications to this ratherformidable problem can be obtained provided that twoconditions are fulfilled:.26/

1. The thickness of the diffusion boundary layer must besmall compared to the thickness of the hydrodynamic

boundary layer, i.e. that region of the solutionin which velocity gradients occur, so that thevelocity components along the relevant axes canbe approximated by the first terms of their powerseries expansion along an axis normal to the electrodesurface.

2. Convection, rather than diffusion, is the predominantmode of mass transport along the axis parallel to theelectrode surface in the direction of fluid flow.

Under the same conditions specified for diffusion inquiescent media (section 2.2.1), the convective diffusionequations for a rotating disk (and ring-disk), channel-type, and tube-type geometries under steady state aregiven by Equations (33) in Table 2..27/ Solutions fortransient convective diffusion for rotating disk andchannel-type electrodes are discussed in section 4.

The dimensionless variables defined in Equa-tions (34–36) enable a single equation to be obtained thatis applicable to a reactant (and under certain conditionsto a product.27/) for all three electrode arrangements(see Equation 37), subject to the boundary conditionsspecified in Equations (38) and (39) in that same table.By taking the Laplace transform of Equations (37) and(39) with respect to X, denoted as LX , and using Equa-tion (38), yields Equations (40) and (41):

s Nq.s,Y/ D 1Y

@2 Nq.s,Y/@Y2

.40/

limY!1

Nq.s,Y/ D 0 .41/

where LXfq.X,Y/g D Nq.s,Y/The general solution to this problem may be written as

Equation (42),

Nq.s,Y/ D A1.s/Ai.s1/3Y/ .42/

where Ai(z) is the Airy function of argument z..23/

At Y D 0 Equation (43) holds

Nq.s, 0/ D A1.s/31/3.2/3/

.43/

Hence, A1.s/ D 32/3.2/3/ Nq.s, 0/, and therefore,

Nq.s,Y/ D 32/3

(23

)Nq.s, 0/Ai.s1/3Y/ .44/

From Equation (44), and recalling Equation (45),

@Ai.s1/3Y/@Y

∣∣∣∣YD0D � 3�1/3

.1/3/s1/3 .45/

the flux at the surface is given by

@Nq.s,Y/@Y

∣∣∣∣∣YD0

D �31/3.2/3/.1/3/

Nq.s, 0/s1/3 .46/


Table 2 Steady-state convective diffusion equations, dimensionless variables, boundary conditions anduniversal dimensionless differential equation for rotating disk, channel and tube electrodes

Rotating disk Channel Tube

Steady-state convective diffusion equation

ay�(�

n

)1/2{r@Ci

@r� y

@Ci

@y

}D Di

@2Ci

@y22vo

yh@Ci

@xD Di

@2Ci

@y22vo

(1� r

R

) @Ci

@xD Di

@2Ci

@r2(33)

Dimensionless variables

X D(

rr0

)3

D r3 X D xl

X D xl

(34)

Yi D(

rr0

)(3anDi

)(�

n

)1/2

y Yi D(

2voh2

Dil

)yh

Yi D(

2voR2

Dil

)(1� r

R

)(35)

i D R or P qR D CoR � CR

CoR

qP D KCP

CoR

(36)

Universal equation

Y@q

@XD @2q

@Y2(37)

Boundary conditionslim

X!1q.X,Y/ D 0 (38)

limY!1

q.X,Y/ D 0 (39)

Table 3 Fundamental relationships for concentrations and fluxes at the surface in Laplace and real spaces

Laplace space Real space

Nq.s,Y/ D 32/3.2/3/Ai.s1/3Y/ Nq.s, 0/ q.X,Y/ D Y32/3.1/3/

∫ X

0q.x, 0/.X � x/�4/3 exp

{� Y3

9.X � x/

}dx

Nq.s,Y/ D �31/3.1/3/Ai.s1/3Y/

s1/3

@Nq@Y

∣∣∣∣∣YD0

q.X,Y/ D �131/3.2/3/

∫ X

0

@q

@Y

∣∣∣∣YD0

.X � x/�2/3 exp{� Y3

9.X � x/

}dx

Nq.s, 0/ D �3�1/3.1/3/.2/3/

s�1/3 @Nq@Y

∣∣∣∣∣YD0

q.X, 0/ D �131/3.2/3/

∫ X

0

@q

@Y

∣∣∣∣YD0

.X � x/�2/3 dx

@Nq@Y

∣∣∣∣∣YD0

D �31/3.2/3/.1/3/

s1/3 Nq.s, 0/@q

@Y

∣∣∣∣YD0

D � 31/3

.1/3/

∫ X

0.X � x/�1/3 dq.x, 0/

Equation (46) can be rearranged as Equation (47)

Nq.s, 0/ D �3�1/3.1/3/.2/3/

@Nq.s,Y/@Y

∣∣∣∣∣YD0

s�1/3 .47/

and then replaced into Equation (44) to yield Equa-tion (48):

Nq.s,Y/ D �31/3.1/3/@Nq.s,Y/

@Y

∣∣∣∣∣YD0

s�1/3Ai.s1/3Y/

.48/Equations (44) and (46–48) and their corresponding

inverse Laplace transforms (see Table 3),.28/ provideuseful relationships between fluxes and concentrations,which can be used to solve a variety of complex problemsof electrochemical and spectroelectrochemical interest.

3 EXPERIMENTAL CONSIDERATIONS

Spectroelectrochemical experiments in the UV/VIS rangemay be broadly classified as transmission, external reflec-tion, and internal reflection (see Figure 1). This briefsection summarizes general aspects of these measure-ments with particular emphasis on factors that limit theircapabilities in terms of spatial and temporal resolution, aswell as detection sensitivity. More specialized issues arediscussed in the applications section.

With the exception of the thin layer technique inthe static mode, for which cells can be readily adaptedto fit in the sample compartment of commercial spec-trophotometers, implementation of all other UV/VISspectroelectrochemical methodologies requires the cus-tom assembly of optical components to bring radiation


into the cell and, after interaction with the electrolytesolution, redirect the beam to the detection stage.

The spatial resolution of profile images is governed pri-marily by diffraction limits imposed by the optics, whichset bounds to how small a volume can be reliably imaged,about 2–4 µm for this type of application, although insome cases the size of individual pixels or diodes in arraysmay become the limiting factor. Beam collimation, animportant aspect of this type of experiment, can be mostreadily achieved with lasers. However, wavelength tun-ability may at times be required and, in the absence ofexpensive instrumentation such as tunable solid-state anddye lasers, conventional optical components can be uti-lized to modify beams from arc or filament lamps intothe desired shape. Even when collimation is optimum,a beam traveling parallel and too close to the electrodesurface will undergo diffraction. Although analysis of thepattern generated is closely related to the profile itself,it has been difficult to obtain reliable quantitative spa-tial information using this approach. Advantage has beentaken, however, of the spatial specificity of the diffractedbeam to probe a small volume of solution, within less than10 µm from an electrode surface especially for transienttype measurements..29/

Technical advances in electronics have rendered elec-trochemistry (more precisely, the ability to establish aspecific working electrode potential over a short periodof time) as the factor that limits time-resolution, ratherthan data acquisition. Conventional potentiostats sufferfrom serious limitations, in that the powers required toachieve potential control are higher than the compliancelimits of regular operational amplifiers. For example, if a0.5 V step is applied to an electrode with a double layercapacity of 1 µF, over a period of 1 µs, the potentiostatmust supply a current of 0.5 A. If, in addition, the resis-tance due to the electrolyte is of about 0.5 k�, the voltagerequired to drive the system would be 250 V, or a peakpower of 125 W.

A means of overcoming some of these restrictions,implemented by Winograd,.30/ involves the use of acapacitor to inject charge into the double layer at veryfast rates, coupled to a potentiostat, to establish potentialcontrol at a later time. Further reductions in the timeconstant of the cell tcell, defined as the product of thecell resistance and the cell capacitance, can be achievedusing microelectrodes. Their size leads to smaller currentsand, thus, reduced power requirements. This strategyallows use of a two-electrode cell arrangement with acomparatively much larger counter electrode, so thatits potential may not be greatly affected followingthe potential step. Using this approach, charge canbe delivered to the working electrode over tens ofnanoseconds. It is indeed serendipitous that UV/VISspectroelectrochemical methods have played a key role

in verifying that potentials can indeed be controlled oversuch short periods of time..31/

Detection sensitivity is determined by the responseof the photomultiplier, photodiode or charge-coupleddevice (CCD), including their noise characteristics.Most often, signal averaging or modulation schemesare required to extract signals for systems involvingspecies displaying small molar absorptivities at low con-centrations, or cells with thin pathlengths. Althoughdouble-beam instruments have been used for UV/VISspectroelectrochemical studies,.12/ it is usually not possi-ble to employ a reference beam to normalize absorptionfrom the cell. Under such conditions, special efforts mustbe made to stabilize the single beam by using, for instance,a split beam in conjunction with its own photomultiplierto control the voltage at the primary photomultiplier.

A powerful experimental approach to enhancingsensitivity via signal averaging involves the use ofspectrophotometers capable of acquiring spectra overa wide wavelength region in times of the order ofmilliseconds. Some of these instruments are based onmechanical motion, such as the vibrating grating/mirrordeveloped by Harrick, the ingenious ScanDisk of OLIS’ssubtractive monochromator, or on the use of CCD suchas that described by Park..32,33/ Wavelength modulationprovides yet another viable means of extracting veryweak spectral signals..34/ This technique relies on theapplication of a periodic perturbation to the wavelengthby, for example, mechanically vibrating a grating or aslit..35/ Hence, using a conventional lock-in amplifierit becomes possible to measure a signal proportionalto the derivative of the response, which can then beintegrated to generate, within an additive constant, amore conventional spectrum. Another type of signalaveraging involves single wavelength measurements inwhich the same experiment is performed repetitively.Implementation of this methodology relies on returningthe system to its original state following each acquisitionover as short a time as possible. Such conditions aremost readily achieved by probing volumes of solutionvery close to the electrode surface using, for example,internal reflection or diffraction, which can be ‘‘filled’’and ‘‘dumped’’ by potential control.

Because of differences in the acquisition times andother considerations, it is difficult to assess absolutesensitivities of the various techniques developed to date.Nevertheless, a very useful semiquantitative comparisonof these methods has been provided by McCreery et al..29/

4 APPLICATIONS

This section presents experimental and theoretical aspectsof the techniques that constitute the foundations of


modern UV/VIS solution-phase spectroelectrochemistry.The intent has not been to review exhaustively theliterature in this area, but rather to provide illustrativeexamples that may be used as a basis for the designand execution of experiments and interpretation ofdata.

The material selected has been organized in increasingorder of complexity, which coincides, by and large, withtheir chronological development. In this spirit, the firstsubsection introduces the now classical thin-layer celltechnique in the static mode, a method that providesprimarily thermodynamic and kinetic information ofstrictly solution-phase reactions, followed by dynamicmeasurements in quiescent media involving opticallytransparent electrodes. Attention is then focused onthe monitoring of solution composition changes in theimmediate vicinity of the electrode by internal reflection,and of the entire diffusion layer by the more powerful andversatile specular reflection mode. This latter approachenhances the detection sensitivity by increasing theeffective optical path allowing, in addition, use of amuch wider variety of electrode materials. Illustrationsof reflection techniques are provided for a number ofelectrode geometries, including microelectrodes, understagnant and forced convection conditions. Describedin the subsequent section are imaging techniques toobtain detailed dynamic information regarding evolutionof concentration profiles using mostly multidiode arraydetectors. Owing to its own mathematical nuances, steadyand transient UV/VIS spectroelectrochemical methodsunder forced convection were grouped in a separatesubsection. Finally, the last subsection addresses methodsthat rely on potential modulation for the study of kineticsand mass transport phenomena associated with electron-transfer reactions.

Because of their unique spectroscopic and electrochem-ical properties, a few systems have been used as modelsfor the development of most of these techniques. Themost useful absorption features and the correspondingdiffusion coefficients of some of the most representativespecies involved are compiled in Table 4.

4.1 Transmission Thin-layer Spectroelectrochemistry

The simplest type of UV/VIS spectroelectrochemicalexperiment, both from experimental and theoreticalviewpoints, involves measurements of fully homogeneoussolutions that contain a single species that absorbs lightin this spectral region, either a redox-active reactantor a product generated directly or indirectly by anelectrochemical process. Such conditions can be achievedby using the electrode as a source or sink of electronsto convert reactants into products to the desired extent,rendering a solution for which the concentration of all

Table 4 Molar absorptivities at the specified wavelengths anddiffusion coefficients for selected chromophores commonlyused in spectroelectrochemical experiments

Chromophore e.M�1 cm�1/ D.cm2 s�1/ Ref.ð10�3.l.nm// ð106

CPZ cation 12 (520) 4.1a 36Orthodianisidine cation 22.7 (515) 4.4a 37Ferricyanide 1.0 (425) 6.32 38MB 56 (633) 4.1 39TAA cationb 11š 0.1.633/ 1.25 40Methyl promazine 5.46 (600) 2.83 41Methyl viologen cation 9.7 (632.8) 8.6a 42

a Values correspond to D of the parent neutral species.b TAA, tris(4-methoxyphenyl)amine; CPZ, chlorpromazine; MB,

methylene blue.

species is uniform within the thin layer cell and inequilibrium with the applied potential. On this basis,the absorbance may be interpreted in the same fashionas in conventional nonelectrochemical spectroscopicmeasurements.

Owing primarily to their ease of construction, highversatility and compatibility with commercial spectro-scopic instrumentation, thin-layer cells have becomea common tool for thermodynamic and also for cer-tain kinetic studies of redox-active materials containingUV/VIS chromophores..5,7/ In particular, the lack of spa-tial dependence allows conventional kinetic analyses fordetermination of rate constants and reaction orders andelucidation of mechanisms.

The archetypal UV/VIS thin-layer spectroelectrochem-ical cell is comprised of two flat plates made out of amaterial transparent in this wavelength range, such asfused silica or quartz, placed parallel to and at a smalldistance from each other (10–200 µm) forming a smallvolume cavity..8/ Either a thin metal, or a conductive oxidelayer, such as In-doped Sn oxide, deposited on one of theplates, or a thin self-standing open metal grid interposedbetween the plates is used as the optically transparentworking electrode. Structural integrity and isolation fromthe ambient atmosphere are achieved by means of adhe-sives, gaskets or mechanical compression. Depending onthe design, the cell can be filled by suction or by capillaryaction through an opening at the bottom in contact witha bulk solution reservoir, where the reference and aux-iliary electrodes are placed (Figure 3). Various types ofoptically transparent thin-layer electrode (OTTLE) cellshave been designed to fit in the sample compartment ofconventional spectrophotometers enabling transmissionspectroelectrochemical data to be acquired normal to theelectrode in a rather straightforward fashion..7/

Vast improvements in the spectral sensitivity of thinlayer cells can be obtained by placing the beam parallelas opposed to normal to the electrode surface, thereby


Figure 3 Optically transparent thin-layer electrochemical cell:(a) front view; (b) side view. A D point of solution suction;B D Teflon tape spacers; C D microscope slides; D D solution;E D gold minigrid electrode; F D optical path of spectrometer;G D reference and auxiliary electrodes; H D solution exit..5/

increasing the optical pathlength, a configuration thatalso allows the use of nontransparent electrodes. Atleast two versatile long optical pathlength thin-layer cells(LOPTLCs) have been described in the literature usingeither conventional windows.43/ (Figure 4) or arrays ofoptical fibers.44/ to bring the beam in and out of the cell.

Among its many advantages, transmission thin layerspectroelectrochemistry enables expedient and quantita-tive conversion of reactant into products, which in manycases may be difficult to synthesize, handle or stabilizeover long periods of time. In addition, the small areaof contact between the solution in the thin layer andthat in the bulk reservoir increases the time requiredto achieve chemical equilibration. In other words, thecomposition of the solution within the layer followingpolarization remains virtually unaltered after the elec-trode is open circuited for periods of time on the orderof minutes. As the electrolyte solutions are at all timeshomogeneous, the absorbance in Equation (5) reducesto the most familiar form of Beer’s law, allowing thespectral properties of electrogenerated species to bedetermined.

However, the thin character of the cell brings aboutlarge ohmic resistances. Consequently, the time requiredfor a uniform potential to be established within thecell can be relatively long, thereby restricting the rangeof accessible homogeneous rate constants that can bemeasured with this technique. In fact, about 30 s are often

Figure 4 (a) View of the LOPTLC: A D cell body; B D thick-ness spacers; C D quartz windows; D D solution contact chan-nels; WE D working electrode; RE D reference electrode;AE D auxiliary electrode. (b) Diagrams of the LOPTLC andthe interior of the cell cavity: 1 D base plate; 2 D cellmount; 3 D thumbscrew and mount; 4 D cell; 5 D auxiliaryelectrode chamber; 6 D pressure plate; 7 D working elec-trode; 8a D Teflon thickness spacer; 8b D silicone rubberseal; 9 D quartz window; 10 D reference electrode chamber;11 D solution inlet chamber.

required for complete electrolysis of material confinedwithin the OTTLE cell.

Despite these shortcomings, transmission UV/VISspectroelectrochemistry has become a well-establishedtool in inorganic chemistry and biologically oriented areasfor the characterization of redox-active species underequilibrium conditions, or for reactions that proceed viafast electrochemical steps followed by a relatively slowerchemical step. Examples of some of these applicationsare given below.

4.1.1 Thermodynamics

4.1.1.1 Determination of the Formal Reduction Poten-tial Eo0 and the Number of Electrons Transferred n forRedox Reactions Involving Stable Solution-phase SpeciesConsider a generalized reversible redox couple (Equa-tion 49)

RC ne� ��! �� P .49/

where both R and P represent stable solution phasespecies, for which the kinetics of electron transfer for


both the forward and reverse process are relatively fast.Under these conditions, the ratio of the concentrationsof R and P at the electrode–solution interface will bedetermined by the applied potential Eappl, via the Nernstequation. If the electrode is polarized at a fixed value ofEappl for a sufficiently long time, so that CR and CP becomeuniform throughout the region probed by the beam, anexplicit relationship can be obtained between Eappl andthe relative concentrations of R and P (Equation 50):

Eappl D Eo0 C(

RTnF

)ln(

CR

CP

).50/

where Eo0 is the formal reduction potential of the redoxcouple.

If it is further assumed that at least one of thesespecies displays one or more clearly defined features in theUV/VIS region, it becomes possible to determine CR/CP

as a function of Eappl directly from the spectroscopicdata, i.e.

CR

CPD Ai �AP

AR �Ai.51/

In Equation (51) AP and AR are the absorbances due to Pand R, respectively, at judiciously selected wavelengths,measured at potentials sufficiently positive or negative sothat only P or R are present in the solution, and Ai isthe corresponding absorbance at some intermediate Eappl

value. Combination of Equations (50) and (51) yieldsEquation (52)

Eappl D Eo0 C(

RTnF

)ln(

Ai �AP

AR �Ai

).52/

from which Eo0 and n can be determined, respec-tively, from the intercept and slope of Eappl versus.Ai �AP//.AR �Ai/, or Nernstian plots. The subsectionsto follow will show examples of application of theseprinciples.

Reversible Systems. Figure 5 shows in situ UV/VISspectra of a 2.0 mM K3[Fe(CN)6] aqueous solution in1 M KCl at different potentials recorded in a thin layercell..45/ As indicated, [Fe(CN)6]3� displays two ratherprominent bands centered at 213 and 420 nm, whichcan be used to construct Nernstian plots, such as thoseshown in the insert to Figure 5. Analysis of these datayielded values of Eo0 D 0.256š 0.001 V versus Ag/AgCland n D 0.965š 0.0015, in fairly good agreement withresults obtained by other means.

Quasireversible Systems. The virtual diffusionaldecoupling between the solution contained within thethin-layer cell and that in the bulk reservoir allowsspectroelectrochemical experiments to be conductedover periods of time long enough to investigate slow

Figure 5 UV/VIS absorption spectra of 2.0 mM K3Fe(CN)6in aqueous 1 M KCl at different potentials in the range C0.5(a) and 0.0 (h). The inset shows a plot of Eappl versus log.CR/CP/at (ž) l D 312 nm and (�) l D 420 nm obtained in a thin-layercell..45/

redox reactions. For example, vitamin B12, cyano-[CoIII]cobalamin, exhibits no cyclic voltammetric reduc-tion features at potentials positive to the observed two-electron reduction wave, (Figure 6), regardless of scanrate..46/ Clear evidence that this reaction proceeds via twoconsecutive one-electron transfer steps was obtained byMark et al..46,47/ in buffered solutions (pH D 6.86), usingan Hg�Au minigrid working electrode in an OTTLEcell. For these measurements, the potential was steppedto different values in the range �1.15 < E < �0.1 V ver-sus SCE (saturated calomel electrode) and the UV/VISspectrum recorded after equilibrium had been estab-lished. Two distinct absorption peaks were observedfor potentials in the range �0.58 < E < �0.75 V at311 and 361 nm (Figure 7a), and �0.77 < E < �0.95 Vversus SCE (Figure 7b) at 368 nm. Nernstian plots ofthe absorbance measured at these wavelengths yieldedfor the two one-electron transfer processes values ofE1/2 D �0.655 V and E1/2 D �0.88 V versus SCE.

Mediated Electron Transfer. The rates of heteroge-neous electron transfer of large redox-active molecules,


Figure 6 Cyclic voltammogram of 1 mM vitamin B12, BrittonRobinson buffer pH D 6.86, 0.5 M Na2SO4 obtained with anHg–Au minigrid in a thin-layer cell. Scan rate 2 mV s�1..46/

such as proteins, are very small, due at least in partto the insulating character of the chemical environmentsurrounding the redox site. A common strategy to over-come this difficulty, shown schematically in Scheme 1,is to employ an electron-transfer mediator M, eitherin solution or bound to the electrode surface, capableof exchanging electrons with such larger molecules insolution at much higher rates.

Mox

Mred

e−

Bred

BoxEle

ctro

de

e−

Scheme 1

Figure 7 UV/VIS spectra obtained in a thin-layer cell for(a) the one-electrode reduction of vitamin B12 under thesame conditions specified in the caption to Figure 6. Appliedpotentials: a D �0.550; b D �0.630; c D �0.660; d D �0.690;e D �0.720; f D �0.770 V versus SCE and (b) the sec-ond one-electron reduction. Applied potentials: a D �0.770;b D �0.820; c D �0.860; d D �0.880; e D �0.900; f D �0.920;g D �1.000 V versus SCE..46/

This approach enables spectra of redox-active proteinsor other large molecules to be recorded as a functionof Eappl, allowing values of Eo0 and n to be deter-mined by the same method described above. A classicexample of this principle is provided by cytochromec, a species that exhibits no clear voltammetric fea-tures on Au electrodes. However, large enhancementsin the electron transfer rates can be obtained by using2,6-dichlorophenolindophenol (DCIP) as a mediator, asshown in Scheme 2.

Cl

Cl

O N OH + 2H+ + 2e−

Cl

Cl

HO N OHH

DCIPox

DCIPred + 2 cytochrome c (ox) DCIPox + 2 cytochrome c (red)Solution:

Electrode:

Mred

Scheme 2


Figure 8 UV/VIS spectra of cytochrome c in 0.5 phosphatebuffer (pH D 7.0), obtained in a thin-layer cell in the presence of2,6-dichlorophenol– indophenol mediator–titrant, for a seriesof applied potentials versus SCE..48/

This mediated process was monitored spectroelectro-chemically in phosphate buffer (pH D 7), using a Auminigrid working electrode in an OTTLE cell, at poten-tials in the range �0.600 (fully reduced cytochrome c) to0.300 V (fully oxidized cytochrome c) (Figure 8)..48/ Nern-stian plots for absorbance measured at 520 and 550 nm,the characteristic absorption maxima for cytochromec(oxidized) and cytochrome c(reduced), yielded valuesof Eo0 D C0.264 V versus SHE and n D 1.

4.1.2 Coupled Chemical Reactions

Electrochemistry provides an expedient means of prepar-ing solutions of a given composition by controlling thecharge that flows through the interface over a certainperiod of time. It thus becomes possible to use thismethod to monitor rates of some chemical reactionsinvolving electrogenerated species under various initialconditions as a function of time. Application of this simplemethodology assumes that the total time of charge injec-tion is long enough for the concentration of all speciesto be uniform throughout the thin-layer cell before anysignificant bulk reaction occurs.

This approach has been exploited for studies of certaininorganic and biological processes that proceed viacomplex mechanisms, including chemical reactions thatprecede or follow an electron-transfer step (Scheme 3),for which one of the species involved absorbs light in theUV/VIS range.

R + ne− P

P Qk

Scheme 3

Three different techniques will be featured in thissection to illustrate the principles involved.

4.1.2.1 Single Potential Step Perhaps the simplesttransient spectroelectrochemical experiment of the typediscussed above involves monitoring the absorbance ofone or both of the redox species as a function of timefollowing a potential step. An excellent illustration ofthis technique is provided by the work of Owens andDryhurst,.49/ who studied the electrochemical oxidationof 5,6-diaminouracil in aqueous buffered solutions pH D4–6, for which the product, the corresponding diimine,undergoes hydrolysis, as depicted in Scheme 4. Thissystem may be regarded as a model for a variety ofbiologically fundamental redox processes, including theenzymatic oxidation of purines.

HN

N

O

O NH2

NH2

H

HN

N

O

O NH

NH

H

−2H+, −2e−

−2H+, +2e−

HN

N

O

O O

O

H

HN

N

O

O NH

O

H

H2Ok2

+ NH3

H2Ok1

Scheme 4

UV/VIS spectra obtained using an OTTLE cell incor-porating a Au minigrid electrode, recorded at differenttime intervals after the potential step was applied,revealed a broad band centered at 320 nm (not shownhere) attributed to the diimine intermediate. If it isassumed that the decomposition of diimine follows first-order kinetics, the time dependence of its decay can berelated to the change in absorbance via Equation (53):

ln.At �A1/ D �kt C ln.A0 �A1/ .53/

where A0, At and A1 are the absorbances at times 0, tand at the end of the experiment. A linear relationship


Figure 9 (a) Absorbance versus time recorded at l D 320 nmduring the electrooxidation of 10 mM 5,6-diaminouracil inMcIlvaine buffer (pH D 5) at 0.35 V in a thin-layer cell withan Au minigrid electrode. The arrow indicates the time at which5,6-diaminouracil was fully electrolyzed. (b) Plot of t versuslog.A�A1/ obtained from the data in (a) by setting t D 0, atthe point specified by the arrow..49/

was observed between t and ln.At �A1/ recorded atl D 320 nm (Figure 9), from which the rate constant k1

was calculated, yielding a value of 0.04 s�1 at pH D 4.

4.1.2.2 Double Potential Step A slight variation of themethod just described involves application of a secondpotential step, after allowing a period of time tR to elapsefollowing the initial potential step. Assume, for example,that a certain absorbing species produced during theinitial step, is then partially consumed via a first-orderchemical reaction as specified in Scheme 3 above. If apotential step is applied in precisely the opposite directionat tR, so as to convert all remaining P back to R, thedifference in the change in absorbance between the first,Af (proportional to the amount of P generated), andthe second step, Ab (proportional to the amount of Premaining in solution), provides a measure of the amountof product decomposed during tR. Based on informationcollected for various values of tR, the rate of chemicaldecomposition of the product can be determined fromEquation (54):

lnAf

AbD ktR .54/

This method was employed to determine kf for benzi-dine rearrangement.50/ in an aqueous acidic electrolyte, aprocess that proceeds via the electrochemical–chemical(EC) mechanism shown in Scheme 5, using an Au mini-grid electrode in an OTTLE cell.

For these experiments, azobenzene was first completelyreduced to hydrazobenzene during the first potentialstep from 0.0 to �0.6 V versus SCE, the potentialwas then maintained at �0.6 for a reaction timetR, and the remaining hydrazobenzene reoxidized toazobenzene during the second potential step to 0.3 V. Allspectroscopic data were acquired at l D 325 nm, a valueat which only azobenzene displays significant absorption.Typical optical response curves are shown in Figure 10,and the plot based on Equation (54 ) is given in Figure 11.

The advantage of the double-potential step versussingle-potential step method is that either P or R canbe monitored spectroscopically. However, the resultsobtained with this approach are less precise than for

N N

Azobenzene

+ 2e− + 2H+N N

Hydrazobenzene

H H

N N

Hydrazobenzene

H H

Diphenyline

kH+

H2N

NH2Benzidine

H2N NH2

+

Solution:

Electrode:

Scheme 5


Figure 10 Absorbance versus time curves obtained atl D 325 nm for a double-potential-step experiment performedin a thin-layer cell in 1 mM azobenzene, 0.100 M HCl, 0.150 MKCl, 44% ethanol aqueous solution. First step from C0.0 to�0.6 V and second step to C0.3 V versus SCE; tR D 50 (A),100 (B), 150 (C), 200 (D), and 300 s (E)..50/

Figure 11 Kinetic plot, ln.Af/Ab/ versus time based onthe absorbance versus time data for the double-potential-stepexperiment described in the caption to Figure 10..50/

single potential step, as tR has to be calculated graphically(dotted lines in Figure 10).

4.1.2.3 Single Potential Step Open Circuit RelaxationIn some cases, species P in Scheme 3 can yield uponsubsequent chemical reaction an electroactive speciesQ, which might be the original electroactive reactant Ritself, a factor that can complicate analysis of spectro-scopic data of the type introduced in previous sections.If k in Scheme 3 is sufficiently small, it becomes possibleto monitor the reaction progress by bringing the electro-chemical reaction to completion and then opening theelectrical circuit enabling P to undergo further chemicaltransformations. This technique, known as single poten-tial step open circuit relaxation, has been used to elucidatethe mechanism of oxidation of the psychoactive drugCPZ..51/ This material can be electrochemically oxidizedin strongly acidic media via two sequential one-electron

steps to produce first, a deep red cation radical chlorpro-mazine cation radical (CPZCž) (see Table 4), and, at morenegative potentials, a colorless sulfoxide-type derivative(CPZO). However, the cation radical undergoes dispro-portionation according to the reaction sequence shown inScheme 6.

Electrode:

Solution:

CPZ

CPZ + CPZO2 CPZ+

CPZ+ + e−

k

H2O•

•

Scheme 6

For this process, Q in Scheme 3, happens to beidentical to R. Evidence in support of this mechanism wasobtained by spectroelectrochemical experiments using anAu minigrid working electrode in an OTTLE cell in astrongly acidic solution. Figure 12 shows a series of spectrarecorded for a potential step from 0.250 V to 0.620 mVversus SCE. Curves a and b in this figure represent spectracollected before (CPZ) and after the step allowing 2.8 minfor equilibrium to be reached, whereas all other spectrawere recorded after the circuit was opened. The peaksat 262 and 525 nm, characteristic of CPZCž, decreasedduring open circuit, and new features appeared at 292 and337 nm, attributed to the final reaction product CPZO.

Plots of 1/C versus t for absorbance measured at 525and 337 nm were linear, and therefore consistent with a

Figure 12 UV/VIS spectra recorded during a thin-layerchronoabsorptometry experiment with open-circuit relaxationin a 4.8 mM CPZ in 3 M H2SO4: (a) spectrum of CPZ at 250 mV;(b) spectrum of CPZ at open circuit. Spectra were acquiredevery 2.8 min..51/


second order mechanism for CPZCž decomposition, withslopes of 8.6 M�1s�1 and 4.4 M�1s�1, i.e. a ratio of 2 : 1, inaccordance with the reaction stoichiometry.

4.1.3 Slow Scan Rate Cyclic Voltammetry

The small amount of electroactive material containedwithin a thin-layer cell allows changes in compositioninduced by the applied potential to occur within rathershort times, of the order of tens of seconds. Underthese conditions it becomes possible to follow opticallyelectrochemical processes involving absorbing species,by scanning the electrode potential linearly betweentwo prescribed limits, while monitoring the current, atechnique known as cyclic voltammetry. Analysis of thesemeasurements can be greatly simplified by scanning thepotential at slow enough rates to achieve at every instantquasi-equilibrium conditions throughout the cell.

Figure 13 Curve (a) is the absorption versus time plotrecorded during the cyclic voltammogram shown by curve (b)at l D 420 nm using a glassy carbon electrode in a 0.4 mMferricyanide in 0.5 M KCl solution at linear scan rates of ( )2 mV s�1 and (- - -) 1 mV s�1..43/

Figure 13 shows simultaneous absorbance and currentdata obtained on a glassy carbon electrode in the longpathlength thin layer cell (LPTLC) shown in Figure 4in a solution of 0.4 mM ferricyanide in 0.5 M KCl atl D 420 nm..43/ For this LPTLC, the absorbance change,following full reduction or subsequent oxidation, is abouttwo orders of magnitude larger than those observed forOTTLE cells described earlier.

4.1.4 Molecular Adsorption on Solid Electrodes

Advantage can be taken of the much enhanced sensitivityof LPTLC spectroelectrochemical cells and the possibilityof using flat opaque electrodes to measure minutechanges in concentration C, such as those derivedfrom adsorption of UV/VIS chromophores on electrodesurfaces, by monitoring the corresponding decrease inthe absorbance A. As may be inferred from simplearguments, these two quantities are related to the widthof the optical cell w and e.l/ (Equation 55):

C D Awe.l/

.55/

On this basis, material lost from the solution phase, asmeasured by spectroscopic means, may be assumed to beadsorbed on the electrode surface, and the coverage may be calculated from Equation (56),

D VCa

.56/

where V is the volume of the cell, and a is the areaof the electrode. The ability to measure accurately isthus determined by how small an absorbance change theinstrument is capable of detecting. Saturation coveragesof small size organic molecules on common metals areabout 10�10 mol cm�2; hence, assuming a cell volumeof 10 µL, the change in concentration associated withformation of a full monolayer would be 10�5 M. Minimumdetectable values of A are of the order of 0.002at a signal-to-noise ratio of 2; therefore, for e.l/ of1000 M�1cm�1, w D 1 and a D 1 cm2, C as small as2ð 10�6 M, and, thus, smaller that those correspondingto D 1 could be observed.

Measurements involving a series of heterocyclic aro-matics were performed by Kuwana et al. with the sameLPTLC spectroelectrochemical cell shown in Figure 4incorporating a Pt electrode..52/ Figure 14(a) showsabsorbance versus time plots obtained after inject-ing a solution 32.9 µM trans-1,2-bis-(4-pyridine)ethylene(PycDcPy) in buffered (pH D 7) 0.1 M NaClO4 (firstcurve) monitored at l D 299 nm with the Pt electrodepolarized at�0.1 V versus Ag/AgCl. The two other curveswere obtained after a second and third injection withoutremoving PycDcPy adsorbed on the Pt surface during the


Figure 14 (a) Plots of absorbance versus time recorded atl D 299 nm after the first, second, and third fillings of a thin-layercell with a solution 32.9 µM PyC-CPy (trans-1,2-bis(4-pyridine)-ethylene) in 0.1 M NaClO4 in 0.02 M phosphate buffer (pH D 7)using a Pt electrode polarized at �0.1 V versus Ag/AgClimmediately after each filling. Experiments began at point A.(b) Absorbance spectra acquired at E D �0.1 V after thecorresponding absorbance versus time response has reacheda steady state value for the 1st ( . . . ), 2nd (-Ð-Ð-Ð-) and 3rd ( )fillings..52/

first injection. Figure 14(b) shows the corresponding spec-tra of the solution phase recorded after the absorbancehad reached steady state following each injection. Thevery small differences observed between the second andthird injections indicate that the surface had attainedsaturation, i.e. D 1.

These data may be used to determine molecularpacking densities and from these to infer the mode ofbonding of species to the surface as thoroughly discussedby Soriaga and Hubbard..53/ Proposed orientations of fourof the species investigated by Kuwana et al. are shown inScheme 7..52/

N

Pt

N

Pt

N

N

Pt

N

N N

Pt

Scheme 7

4.2 Transmission Spectroelectrochemistry inSemi-infinite Media

Methods based on the dynamic monitoring of absorbancechanges induced by electrochemical perturbations canprovide kinetic information regarding rates of homoge-neous electron transfer rates involving electrogeneratedspecies, as well as mass transport phenomena, not acces-sible by the static techniques described in the previous

section. For simplicity, consider an OTE immersed in asolution containing a single, nonabsorbing solution-phasespecies R capable of undergoing heterogeneous electrontransfer to yield an absorbing solution phase product P(Equation 57):

RC ne� ��! P .57/

If CP is independent of x and z, the instantaneousabsorbance A.t/ in Equation (4) reduces to Equa-tion (58),

A.t/ D e

∫ d

0CP.y, t/ dy .58/

where d is the length of the optical cell along the axisof propagation of the light. Provided the measurementsare made over relatively shorts periods of time, so thatthe diffusion layer thickness is always smaller than d, themedia may be regarded as semi-infinite and A.t/ may berewritten as Equation (59),

A.t/ D e

∫ 10

CP.y, t/ dy .59/

or, in Laplace space (Equation 60), as

A.s/ D e

∫ 10

CP.y, s/ dy .60/

If it is further assumed the overall measurement timeis short so that no complications arise from naturalconvection, an explicit form for CP.y, s/ for a potentialstep experiment of the type described in section 2.2.2 maybe obtained from Equation (22):

CP.y, s/ D �CoR

s

(DR

DP

)1/2

e�.s/DP/1/2y .61/

Equation (61) can be substituted into Equation (60) toyield Equation (62),

A.s/ D eCoRD1/2

R

s3/2.62/

and inverse Laplace transformed to afford an expressionfor the time dependence of the absorbance due to P forsuch diffusion-controlled process (Equation 63):

A.t/ D eCoR

(4DRtp

)1/2

.63/

Based on the analysis of such chronoabsorptometric-type experiment, it becomes possible to determine DR ife is known or, conversely, e if DR is known.

A rather versatile cell design reported by Kuwanaet al..4/ suitable for this type of measurements incorpo-rates an OTE in a glass sandwich-type cell (Figure 15), in


Figure 15 Sandwich cell for transmission UV/VIS spectroelec-trochemical experiments..4/

which the light travels along the axis of the cylinder. Thesmall bent tube, known as a Luggin capillary, allows elec-trolytic contact between the main and reference electrodecompartments.

Potential step chronoabsorptometry at an opticallytransparent tin oxide electrode has been used.54/ to studythe oxidation of [Fe(CN)6]4� to [Fe(CN)6]3� in aqueouselectrolytes by monitoring A.t/ at l D 420 nm (Table 4).In accordance with theoretical predictions, plots of A.t/versus t1/2 (Figure 16) were found to be linear, yieldingvalues of D for [Fe(CN)6]4� determined from the slope,

Figure 16 Plot of A versus t1/2 for the chronoamperometricoxidation of [Fe(CN)6]4� at a tin oxide optically transparentelectrode..54/

of 6.5ð 10�6 cm2 s�1, in reasonable agreement with thoseobtained by other methods.

One of the advantages of using large-volume cells, asopposed to thin-layer cells, is the decrease in tcell, whichleads to improvements in transient response. However,the relatively low spectral sensitivity due to the very shortoptical paths associated with OTE, the restricted numberof electrode materials with suitable electronic and opticalcharacteristics, and the high resistance associated withthin films, severely limit the applicability of the techniquedescribed in this section. As explored in detail laterbelow, some of these difficulties can be overcome byimplementation of dynamic methods in both internal andexternal reflection modes.

4.3 Internal Reflection

As briefly discussed in section 2.1.3, light travelingthrough a media of high index of refraction, impinging ona planar interface with a media of smaller index of refrac-tion at a sufficiently large angle, will penetrate slightlyinto the adjacent phase and interact with species presenttherein. For spectroelectrochemical applications, the sur-face of the internal reflection element (IRE) is coatedwith a thin film of an electronically conducting material,such as a metal or a highly doped semiconductor, whichserves as the optically transparent working electrode. Thistechnique was pioneered by Kuwana, Winograd et al. inthe 1970s..4/

The volume of solution probed by the evanescent waveis of the same order of magnitude as the wavelengthof light, about 100–300 nm in the UV/VIS range, andtherefore the size of the cell becomes immaterial. Undersuch conditions, the time response of the cell is limitednot by the solution resistance, but by the thin characterof the electrode, as was the case with the OTE-basedtechniques described in the previous sections.

Owing to the very short optical path and the rela-tively low concentrations of chromophores often used,the extent to which the exponentially decaying evanes-cent wave in the solution is attenuated is very small,and therefore its spatial dependence may be regardedas unperturbed by the presence of absorbing mate-rial therein. Under these conditions, the instantaneousabsorbance is given by Equation (64),

A.t/ D eNeff

∫ 10

CP.y, t/ exp(�yd

)dy .64/

where d is the penetration depth (see Equation 10), andNeff is a sensitivity factor that depends on the geometryand electrode material.


Insertion of Equation (22) into Equation (64) inLaplace space and subsequent inversion, yields Equa-tion (65) for a chronoabsorptometric experiment:

A.t/ D edNeffCoR

(DR

DP

)1/2 [1� exp.b2t/erfc.bt1/2/

].65/

where b D D1/2R /d.

For d ¾ 100 nm, A.t/ reaches steady state in about 1 ms,which may be regarded as the time needed to fill the cell.If the potential is then returned to its original value byapplying a reverse step, the cell can be dumped over asshort a time, making it possible to perform numerousidentical experiments that can then be co-added andaveraged to improve signal detection.

A multiple reflection internal reflection spectroscopy(IRS) cell designed by Kuwana and Winograd.55,56/ isshown in Figure 17. In this optical arrangement two prismsare used to guide the beam into and out of the IRE,allowing five internal reflections to probe the solutionphase of the interface, thereby increasing the effectivepathlength.

Sensitivities better than one part in 105 with timeresolutions in the microsecond range have been obtainedfor systems in which Neff × 1, and long averaging times.This is illustrated in Figure 18 for MVCC reduction,for which the time resolution, using charge injectionto achieve fast potential control, was of the order

Figure 17 Cell for UV/VIS IRS measurements..59/

Figure 18 Absorbance versus time curves for the reductionof methyl viologen dication (MVCC) reduction, monitoredat l D 605 nm in the internal reflection mode. Curve (a)corresponds to the diffusion-limited reduction of MV2C to itscation radical. Curve (b) is for the reduction to MV0. Solid linesare theoretical transients; noisy curves are experimental..57/

of 4 µs..57/ Advantage was taken of the extraordinarycapabilities of this measurement scheme for kineticsstudies involving fast processes,.58/ such as the second-order catalytic mechanism (Scheme 8) for the reactionof cyanide with electrogenerated tri-p-anisylamine cationradical (TAACž) in acetonitrile.

TAA TAA+ + e−

TAA+ + CN− TAA + CN•k1

2 CN• k2 (CN)2

•

•

Scheme 8

Plots of absorbance versus time following a potentialstep recorded at l D 715 nm, a wavelength at whichTAACž exhibits a characteristic absorption band, wererecorded both in the presence and in the absenceof tetraethylammonium cyanide (TEACN; Figure 19).Analysis of these data yielded values for the k1 inScheme 8 of 2.7ð 105 M�1 s�1, in agreement with thoseobtained by other means.

IRS also lends itself to the study of homogeneouselectron-exchange reactions involving electrogeneratedspecies for values of k in Scheme 8 larger than 106 M�1 s�1.Under such conditions, the intermediate is formed in close


Figure 19 Absorbance versus time curves obtained atl D 715 nm in the internal reflection mode following a potentialstep for (a) 0.5 mM TAA and (b) 0.5 mM TAA with 15 mMTEACN added, in 0.3 M tetraethylammonium perchlorate(TEAP) in acrylonitrile (AN) using an optically transparentPt electrode for 800 repetitions. Neff D 15,

pD/d D 115..58/

proximity to the electrode surface and can, therefore, bedetected by the evanescent wave.

From a general perspective, quantitative analysis ofexperimental data can be pursued using digital sim-ulation techniques to predict, for a proposed mech-anism, time-dependent concentration profiles for allspecies involved,.59/ as illustrated for an electrochem-ical–electrochemical–chemical (EEC)-type process inFigure 20. Numerical values for the various parame-ters involved can then be calculated based on best fitsto the experimental curves. In fact, for the reductionof MVCC mentioned above, which has been found tofollow the mechanism in Scheme 6, a fit to the dataobtained by monitoring A.t/ at l D 605 nm, associatedwith the radical cation intermediate MVCž, yielded valuesof kf D 3ð 109 M�1 s�1..57/

More recently, Heineman et al..60 – 63/ have imple-mented the use of IRS to develop spectroelectro-chemical sensors with high selectivity and sensitivity.For this application, the IRE is covered first with athin conducting layer as before, and then with a filmdisplaying molecular specificity or selective film, asshown in Figure 21. This device allows three indepen-dent sensing techniques to be employed simultaneously,i.e. electrochemistry, spectroscopy, and selective par-titioning, thereby enhancing the degree of specificityfor chemical detection. As a means of illustration,Figure 22 shows results obtained with simultaneous opti-cal (panels a and b) and electrochemical techniques(panel c) for the detection of ferrocyanide partitionedinto a poly(dimethyldiallyl ammonium chloride)-SiO2

Figure 20 Concentration profiles obtained by digital simula-tion for an EEC mechanism with kfC D 102 s�1. The differ-ent curves are drawn for t D 1, 10, 100, and 500 ms, from(a) to (d)..59/

composite sol-gel film from an aqueous solutions at twodifferent concentrations.

4.4 External Reflection

The rather short effective pathlengths associated withtechniques based on OTEs limits their applicability tosystems involving strong chromophores, or long timesfor sufficient absorbing material to accumulate and bedetected. Although gains in sensitivity can indeed be


Figure 21 Simplified diagram of an internal reflection-based spectroelectrochemical sensor cell. ITO, indium-tin oxide..60/

Figure 22 Optical response at l D 420 nm of the sensor in Figure 20 to (a) potential step and (b) cyclic voltammetry for twoconcentrations of Fe(CN)6

4�. Panel 1, 0.025 mM; panel 2, 2.5 mM. Panels (c) show cyclic voltammograms recorded in those solutionsrecorded at a scan rate of 10 mV s�1. Potentials are referred to an Ag/AgCl reference electrode..60/


achieved by IRS using extensive signal averaging, theregion probed by the evanescent wave is very closeto the electrode surface. Hence, it is not possible tomonitor changes in composition at times longer thana few milliseconds. In addition, IRS is very sensitive towavelength and refractive index effects on the pathlength,compromising the analysis of spectral data, particularlywhen Neff is large.

Many of these problems can be minimized by exper-iments in which light propagating in the solution isreflected from, as opposed to transmitted through, theelectrode. This approach allows transient studies to beperformed under either quiescent or convective flowconditions, involving weakly absorbing and short-livedspecies. Such improvements are derived primarily, butnot exclusively, from increases in the optical pathlength,achieved for example by employing grazing incidence ormultiple reflection, better current distribution, and fromthe possibility of using microelectrodes.

Implementation of external reflection geometries oftenrequires custom assembly of components, including alight source, either a laser or a conventional arc lamp, amonochromator, a detector, and other optical elements,as prescribed by the specific application. A few opticalarrangements designed for this type of spectroelectro-chemical experiments are depicted in Figure 23..31/ Con-siderable care has been taken to develop electrochemicalcells displaying optimum optical and electrochemicalresponse. For example, Figure 24.39,64/ shows two cellsreported in the literature for (a) external reflection atconstant angle of incidence and (b) for multiple reflectionexperiments. One of the most interesting applicationsof external reflection, reported by McCreery et al.,.31/

Figure 23 (a) Optical arrangement and (b) schematic diagramof a cell for spectroelectrochemistry at a microdisk electrode..31/

Figure 24 (a) Spectroelectrochemical cell for chronoabsorpto-metric studies: (a) top view, (b) side view,.64/ (c) cross-sectionof a multiple specular reflection spectroelectrochemical cell..39/

exploits the advantages of the small currents associatedwith micro-electrodes to eliminate the need for a poten-tiostat and use instead a capacitor-based injection circuitto charge the double layer, coupled to a pulse generator.As shown by these workers, and discussed later in thischapter, such a strategy enables a fixed electrode poten-tial to be established following a step, within times shorterthan 35 ns, making it possible to follow the time evolutionof the absorbance from times as short as 0.15 µs.

Metals, even when optically polished are not perfectreflectors in the UV/VIS region; in addition, theirreflectance is often a function of the state of charge andcoverage of adsorbed species on the surface..12/ However,


it is possible to either minimize, or account for theseeffects, allowing quantitative information to be acquiredregarding the identity and reactivity of electrogeneratedsolution phase species produced at conventional solidelectrodes.

4.4.1 Planar Electrodes

The solution-phase absorbance measured with lightreflected from a planar electrode at an angle of incidencef(Figure 24a.64/) is 2/cosf larger than that observed, underotherwise identical conditions, using a beam normal toan OTE in the standard transmission configuration. Thefactor of 2 accounts for the beam crossing the diffusionlayer twice, whereas the divisor of cosf reflects theincrease in pathlength for a single crossing of the layer.This enhancement factor, denoted as h, arises purelyfrom geometric considerations, assuming the electrodesurface to be perfectly reflecting, and that the incident andreflected beams traverse a diffusion layer uniform alongan axis normal to the surface, i.e. possible edge effects areignored. Based on these considerations, h will range from2, for normal incidence, up to about 400 for f slightlyless than 89.7°. Comparisons between theoretical andexperimental data, as well as quantitative calculations ofedge effects, have been provided in the literature..38,42,65/

The higher absorbances achieved at glancing incidenceenable detection of short-lived electrogenerated chro-mophores with increased sensitivity, making it possibleto monitor, for example, species with small e, or stronglyabsorbing materials at lower concentrations. In addition,the higher electrical conductivity of massive, comparedto thin film electrodes, allows measurements to be per-formed with better time resolution. Some of these aspectsare discussed in more detail later in this section.

4.4.1.1 Identification of a Solution-phase CorrosionProduct Polarization of metals at sufficiently highpotentials may result in the formation of species derivedfrom the electrode displaying finite solubility in the elec-trolyte solution. An illustrative example of the use ofUV/VIS spectroscopy in the external reflectance modefor the identification of a metal corrosion product wasreported by Kolb et al..66/ for the case of Ru in acidsolutions. For these experiments, a Harrick rapid scanspectrophotomer was employed to collect spectra byreflecting light from an optically smooth Ru film electrodesputtered on glass as a function of the applied potential.Figure 25 shows the normalized reflectivity of Ru polar-ized at 1.17 V versus SCE in 0.5 M H2SO4 using thereflectance spectrum of pristine Ru at �0.1 V as a refer-ence. Based on a comparison of the features observed withthose of the genuine material (shown by the inset in thefigure), the corrosion product could be identified as RuO4.

Figure 25 Background-corrected differential reflectance spec-tra for an Ru electrode in 0.5 M H2SO4. ( . . . ) Result obtainedfollowing a potential step from �0.1 to C1.17 V versus SCE.The inset shows the molar extinction coefficient e versus l forRuO4..66/

4.4.1.2 Chronoabsorptometry

Glancing Incidence – Systems Involving a Single Absorb-ing Product. Some of the advantages associated withexternal reflection compared to transmission through anOTE may be illustrated using potential step chronoab-sorptometry (see section 4.1) as an example. Assumingthat the only optically absorbing species at the wave-length selected for the measurements (l) is the productP of the electrochemical reaction, and that the heteroge-neous electron transfer process is under strict diffusioncontrol, A.t/ is given by Equation (63) corrected for thedifference in optical path, i.e. h D 2/cosf, namely

A.t/ D ePCoR

2cosf

(4DRtp

)1/2

.66/

Equation (66) has been verified in a number oflaboratories for simple electrochemical processes. Inparticular, Figure 26(a).42/ shows absorbance versus timeand Figure 26(b) the corresponding absorbance versust1/2 plots calculated from these data for a bufferedsolution (pH D 7) of 0.59 mM MVCC. The potential inthis case was stepped from �0.3 to �0.8 V versus SCEusing an Au electrode with an He�Ne laser beam(l D 632.8 nm) incident on the sample at f D 88.52°.At this energy MVCž displays significant absorption.The straight line in the figure was calculated basedon values of eP and DR reported in the literature(see Table 4). It is evident from these results that theagreement between theory and experiment is excellentfor times longer than 10 ms. The discrepancies found at


Figure 26 (a) Absorption versus time and (b) absorptionversus t1/2 plots obtained in a solution 0.59 mM methyl viologenin 0.3 M phosphate buffer (pH D 7.0) for a potential step from�0.3 to �0.8 V versus SCE. The data represent the average ofthree runs..42/

shorter times were attributed to a variety of factors,a thorough discussion of which may be found inthe original literature..42/ Good quantitative agreement(<2%) was also observed between the theoretical andexperimental values of h for f in the range 88–89°,which corresponds to h values of about 50–100, forelectrolysis times of the order of 50 ms. However,deviations were detected at shorter times and smallerf. This technique has been successfully extended to theentire UV/VIS range by using a continuum light sourceand a well-collimated beam, augmenting significantly itsoverall versatility.

Glancing Incidence – Systems Involving an AbsorbingReactant and an Absorbing Product. In the case ofsystems in which both R and P in Equation (57) absorb atthe same wavelength l, Equation (66) must be modified

to Equation (67):

A.t/ D e.l/CoR

2cosf

(4DRtp

)1/2

.67/

wheree.l/ D eP.l/� eR.l/. Assume that after a certainperiod of time t, following application of the step,the electrode potential is stepped to a new value atwhich the reverse reaction occurs under diffusion control.Equation (68) presents this in mathematical terms (seesection 2.2.1),

CR.0, t/ D St where St D{

0, t � t1, t > t

, qR.0, t/ D 1� St,

and NqR.0, s/ D 1s� e�ts

s.68/

and, hence,

Q.s/ D(

DR

s

)1/2NqR.0, s/ D D1/2

R

s3/2�D1/2

Rets

s3/2.69/

After inversion of Equation (69) and substitution inEquation (25) the transient absorbance is given byEquation (70):

A.t/ D e.lo/CoR

2cosf

(4DR

p

)1/2

ð [t1/2 � St.t� t/1/2]

.70/

which reduces to Equation (54) for t � t, and, for thesecond step only Equation (71) holds:

A.t > t/ D A.t/�e.lo/CoR

2cosf

(4DR

p

)1/2

ð [t1/2 � t1/2 C .t� t/1/2]

.71/

An interesting application of this formalism wasdescribed by Jones and Hinman,.64/ who examined theredox properties of iron tetraphenylporphyrin chloride(FeTPPCl) in a nonaqueous solution, using the cellshown in Figure 24(a). Figure 27 shows a plot of Aversus t obtained for a 10.6 µM FeTPPCl solution in0.1 M tetra-n-butyl ammonium perchlorate (TBAP) inCH2Cl2 for an experiment in which the potential wasstepped from 0.9 V to 1.3 V versus SCE for 1 min, and thenstepped back to 0.9 V. A clear indication that the systembehaves in an ideal way was obtained from the linearcharacter of the plots of A versus t1/2, and A versust1/2 � t1/2 C .t� t/1/2 (Figure 28), which may be used asa criterion to ascertain that, within the timescale of themeasurements, the product of the reaction P is stable.As the spectrum of R is often known, measurements ofthis type at different values of l, allow the spectrum ofthe other species to be determined, yielding in this case


Figure 27 Plot of A versus t obtained at l D 410 nm in a10 µM FeTPPCl solution in CH2Cl2 containing 0.1 M TBAP dur-ing a double potential step chronoabsorptometric experiment.The data represent an average of 64 measurements..64/

Figure 28 Plots of (a) A versus t1/2 and (b) A versusj D t1/2 � t1/2 C .t� t/1/2 obtained from the data in Figure 27.The broken lines represent a linear least-squares fit..64/

Figure 29 UV/VIS spectrum of FeTPPCl ( ) and itsone-electron oxidation product ( ) calculated from chronoab-sorptometric data..64/

excellent agreement with that of the oxidized form ofFeTPPCl obtained by other means (Figure 29).

Multiple Reflection. A different approach.39/ toincreasing the pathlength is to introduce a well-collimatedbeam into a cell consisting of two working electrodesplaced parallel, and at close distance from each other, asshown schematically in Figure 24. Under these conditionsand assuming P is the only absorbing species, A.t/ for thismultiple reflection configuration is given to a good degreeof approximation by

A.t/ D ePCoR

2wT sinf

(4DRtp

)1/2

.72/

where w and T are the cell length and cell thickness,respectively. According to Equation (72) the furtherenhancement in absorbance derived from multiple,compared to single, reflection amounts to a factorL/.T tanf/. For systems in which the only absorbingspecies at l is the reactant R, the decrease in absorbanceafter a potential step will also be linear in t1/2, namely,

A.t/ D eRCoRL

sinf� 2L

T sinfeRCo

R

(4DRtp

)1/2

.73/

The leading term in Equation (73) represents the initialabsorbance of the solution, a factor which is independentof T, and L/ sinf represents the total pathlength.

Shown in Figure 30 are A versus t1/2 plots for thereduction of MB on Au in 0.1 M KCl solutions buffered(pH D 7) obtained with the cell shown in Figure 24(c),using an He�Ne laser, following a potential step as afunction of MB concentration. Excellent linearity wasobserved within the timescale of the measurements,except for the most concentrated solution, for whichthe electrogenerated radical undergoes precipitation.


Figure 30 Plots of A versus t1/2 for the reduction of MB atconcentrations in the range 0.5 to 10 µM..39/

Furthermore, the magnitude of A, based on e for MBat 632.8 nm (see Table 4), the geometry of the cell andthe angle of incidence, was in agreement with that foundexperimentally with f < 45° for about 330 reflections.

4.4.1.3 Determination of Rate Constants of HomogeneousElectron Transfer Reactions Involving ElectrogeneratedSpecies Consider a reaction involving exclusivelysolution-phase species, A, ACž, B and B0, in whichA is reduced at the electrode surface to yield ACž,which then reacts with B to yield B0 regenerating A(Equation 74):

2ACž C B ��! 2AC B0 .74/

Two simple reaction mechanisms consistent with thisstoichiometry may be envisaged as Equation (75) with(76), and Equation (75) with (77):

ACž C Bk2��! BCž CA .75/

ACž C BCžfast��! B0 CA .76/

2BCžfast��! BC B0 .77/

Assume further, that the rate-determining step isfirst order both in ACž and B, such as a collision

between these species, and that the equilibrium constantfor the overall reaction is large so that all reactionsfollowing the slow step will proceed to completion.Hence, if Equation (75) is slower than (76) and (77),then Equation (78) holds:

d[ACž]dt

D �2k2[ACž][B] .78/

If an electrode immersed in a homogeneous solutioncontaining A and B at known concentrations is stepped toa potential sufficiently positive to form the correspondingradical cation ACž under strict diffusion control diffusinginto the solution, then ACž will encounter and react with Bdiffusing toward the electrode in an electron transfer-typeprocess to yield BCž. As the amount of B at, and near thesurface is expected to be small, Equation (75) will proceeda distance away from the electrode. Analytic solutions ofthis rather complex problem do not exist in general;however, it is possible to generate concentration profilesof each of the species involved by digital simulationtechniques, provided that all the relevant parametersare specified and, from these, to predict the absorbanceassociated with the chromophores.

The power of UV/VIS spectroelectrochemistry as atool to determine rate constants of reactions betweenan electrogenerated radical with a species in solution,i.e. k2 in Equations (76) and (77), was demonstratedby McCreery et al.,.67/ who measured the rates ofCPZCž with a catecholamine, using, among other tech-niques, grazing incidence external reflection at a Ptelectrode.

Figure 31 shows the results of numerical simulations forthe reaction sequence shown above, as CCPZCž observedin the presence and in the absence of catecholamine,denoted as DA, as a function of distance, expressed interms of units of .Dt/1/2, for four different values ofkt assuming equal bulk concentrations for both CPZand DA. For simplicity, the diffusion coefficients ofall species involved were assumed to be the same.Figure 31(a) corresponds to a situation in which k2 D 0,i.e. no subsequent reaction involving CPZCž. For k2 finiteand t 6D 0, the concentrations of both CCPZCž and CDA at afixed distance from the electrode decrease, and thereforethe extent of overlap between the two profiles of the twospecies, also diminishes.

Based on arguments set forward in previous sections,the absorbance of a chromophore is proportional tothe integral of the concentration profile, enablingcomparisons to be made with experimental measure-ments. Figure 32 shows normalized absorbances, i.e.those obtained in the presence and in the absence ofequimolar amounts of DA, monitored at wavelengthsat which only DOQ, the oxidation product of DA(l D 400 nm, upper curve), and CPZCž (l D 525 nm, all


Figure 31 Simulated concentration versus distance profiles for the EE0C reaction sequence at various values of b and kt:(a) Co

CPZ D CoDA (b D 1); (b) Co

CPZ D 2CoDA (b D 2.0). In all cases the ordinate represents fractional concentration relative to the

CoCPZ value..67/ DOQ, dopamine quinone.

other curves) absorb, respectively. Also included in theseplots as solid lines are best-fit numerical simulations forb D CCPZ/CDA, of 0.5, 1, 2, and 5. 5, yielding k2 values of2.12š 0.25 M�1 s�1.

4.4.2 MicroelectrodesPlanar electrodes of dimensions larger than about 0.1 mmsuffer from relatively slow diffusional relaxation; hence,long times are required to recover the initial conditions


Figure 32 Normalized absorbance versus log.kCbt/ for variousvalues of b. The solid curves are theoretical plot for DOQmonitored at l D 400 nm (top curve) or CPZCž monitoredat l D 525 nm (remaining curves). Points are best fits toexperimental data..67/

and, thus, acquire sufficient measurements over reason-able times for efficient signal averaging. Considerableenhancements in mass transport in quiescent solutionscan be realized by using electrodes of micrometer dimen-sions, including disks and cylinders. Despite their size,the absorbance observed for such microelectrodes inthe external reflection mode is larger than that usingan OTE for similar electrolysis times. Because of theirsmall area, both capacitive and faradaic currents aresmall, placing lower demands on the potentiostat power,increased time averaging, higher duty cycle, low cell-time constants, more precise solution resistance and,most importantly, better conditions for studies of fastreactions.

4.4.2.1 Microcylinders An analytic expression forthe time-dependent concentration profile of a speciesP in a stagnant solution, produced at the circumfer-ence of a circular electrode of radius r0, via oxidationor reduction of R under chronocoulometric conditions,can be obtained by solving the appropriate Fick’slaw using the Laplace transform method. The solu-tion to this problem may be shown to be given byEquation (79):.37/

where J0.z/, and Y0.z/ are Bessel functions of order zero ofthe first and second kind of argument z, respectively..23/

Figure 33 shows a plot of Acyl/Apl where Acyl and Apl

represent the absorbances observed with a cylinder byintegration of Equation (79) along r, and with a planarelectrode (see Equation 64), respectively, as a functionof the dimensionless variable .DRt/1/2/r0. As would beexpected, Acyl/Apl is close to unity for dN < r0 (seeFigure 33), but deviates significantly at longer times forfixed r0.

Figure 34 shows average absorbance versus t1/2 plots inthe range 0.1–100 ms following a potential step from 0.3to 1.1 V versus SCE in solutions of 3.5 mM OD in 1 MH2SO4 using a Pt microcylinder with r0 D 12.5 µm. Theopen circles in this figure were obtained based on thetheory introduced above without adjustable parameters.Similar data over a much shorter timescale, down to4 µs, could be recorded using a Pt microcylinder withr0 D 5 µm in 2.2 mM OD in 1 M H2SO4 after 2700averages, under otherwise identical conditions. In thislatter case, deviations of only up to 5% could be observedat 1 ms. Both of these experiments involved the use ofa laser focused onto the cylinder wall as the radiationsource, and optical fibers to collect the reflected light ina two-electrode configuration (Figure 35). The primaryfactor that limits a quantitative analysis of data acquiredat longer times relates to thermal effects induced byheat dissipation within the electrode. Such phenomenarestrict the range of validity of the model to times atwhich dN is less than twice the electrode radius, i.e.

Figure 33 Ratio of absorbance for a cylindrical (cyl) and aplanar (pl) electrode as a function of the dimensionless variable(DRt/1/2/r0..37/

CP.r, t/ D CoR

1C 2p

∫ 10

J0

(rr0x

)Y0.x/� Y0

(rr0x

)J0.x/

J20.x/C Y2

0 .x/

(exp[.�DRt/r2

0/x2]

x

)dx

.79/


Figure 34 Absorbance versus t1/2 for a 12.5 µm radiusplatinum electrode in 1 M H2SO4 containing 3.5 mM OD(o-dianisidine): open circles D theoretically predicted response;solid line D experimental response for a conventional three-electrode arrangement, average of 100 runs; solid circles D res-ponse for a two-electrode configuration, average of 60 runs. Eapp

was stepped from 0.3 to 1.1 V versus SCE..37/

Figure 35 Experimental arrangement for UV/VIS spectro-electrochemical measurements involving a microcylinder elec-trode..37/

.Dt/1/2/r0 < 2. As discussed by these authors, both theIR drop, and the time constant of the cell increase asr0 decreases; hence, smaller-diameter electrodes will notallow access to measurements for times shorter than a

few microseconds. Nevertheless, it is possible to achievesubmicrosecond resolution by employing a microdiskelectrode, as described in the next subsection.

4.4.2.2 Microdisk Electrodes Unlike the case ofcylindrical electrodes, the solution resistance Rsol for amicrodisk is directly, as opposed to inversely, propor-tional to r0. As for a typical microdisk electrode, thecontribution of the capacity to tcell is very small com-pared to that ascribed to Rsol, decreasing r0 should leadto a better transient response. Indeed, chronoabsorpto-metric experiments involving the use of a coaxial Aumicrodisk electrode with r0 D 30 µm in a two-electrodecell configuration, allowed for absorbances associatedwith electrogenerated MVCž to be monitored in themillimeter range with an Xe arc lamp down to 150 nsfollowing extensive signal averaging (Figure 36)..31/ Thisimproved methodology enables measurements of second-order homogeneous rate constants of reactions involvingelectrochemically generated strong chromophores (k2

in Equation 75), of the order of 108 M�1 s�1, as illus-trated by the reaction of CPZ with DA at physiologicalpH. It should be emphasized that these values exceedthose achievable with more conventional stopped flowexperiments.

Shown in Figure 37 are absorbance versus time plotsfor generation of CPZCž both in the absence and inthe presence of DA. The solid lines in the lower curverepresent best digital simulation fits to the average of1120 runs, for which k2 for the reduction of the radical

Figure 36 Absorbance versus time curves for the generation ofMVCž from 5.6 mM MVCl2 in 2 M phosphate buffer, (pH D 7.0)recorded using a coaxial Au microdisk working electrode (30 µmradius) with an He�Ne laser at l D 632.8 nm. The dashed lineis an average of 60 000 runs covering 1–200 µs. The solid noisyline is a shorter transient at higher time resolution. The straightline is a least squares fit to all of the data, and has the same slopeas 5 ms runs..31/


Figure 37 Absorbance versus time curves for the generationof CPZCž in the presence (lower curve) and absence (uppercurve) of equimolar DA in 40% MeOH/H2O, containing 0.2 Mdimethylarsenate buffer (pH D 6.8) plus KCl for a total ionicstrength of 1.8 M. The noisy lines are averages of 1120 runs.The upper smooth curve was calculated for k D 0, the lowercurve for k D 6.2ð 107 M�1 s�1 for the reduction of the radicalby dopamine..31/

by DA is 6.2ð 107 M�1 s�1 (lower curve), whereas that inthe upper curves assumes k2 D 0.

4.5 Spatially Resolved Spectroelectrochemistry

Transmission and external reflection spectroelectrochem-ical methods afford information about integrated profilesof the species being monitored. Additional insight intomechanistic aspects of homogeneous-phase redox reac-tions and transport phenomena can be obtained from theconcentration profiles themselves. Not surprisingly, con-siderable effort has been devoted to monitor their tempo-ral and spatial evolution using both interferometry.14/ andtransmission spectroscopy. This section summarizes themost salient features of the latter of these two method-ologies and discusses with various illustrations its scopeof applicability.

The problems associated with the lack of selectivity andrather weak sensitivity of solution-phase imaging tech-niques based on interferometry so far reported can becircumvented to a significant extent by using absorption,as opposed to refraction, as the physical phenomenonbeing monitored. Although restricted to systems involv-ing one or more chromophores, absorption-imagingmethods have provided a wealth of high spatial resolu-tion information regarding the time evolution of diffusionprofiles induced by heterogeneous electron transfer reac-tions at electrode–solution interfaces approaching thelimits imposed by optical diffraction. Because of therather low concentrations of reactants often involvedin spectroelectrochemical experiments, distortions in

Figure 38 Diagrams of experimental arrangements for profileimaging using (a) a scanning slit.68/ and (b) a multidiode array..40/

the spatially resolved profiles measured by absorption,induced by changes in the index of refraction, can beneglected.

Two types of absorption-based profile imaging met-hods.40,68/ have been described in the literature, involvingin both cases weakly focused light propagating par-allel to the electrode surface. The first, depicted inFigure 38(a),.68/ employs a moving mechanical slit alignedalong an axis normal to the electrode, and a photomulti-plier to measure the extent of light attenuation throughsmall volumes of solution. The second approach.40,69/

(Figure 38b), relies on a photodiode array detector tocapture the magnified image of the beam producedeither by a laser or a lamp, after crossing the diffu-sion boundary layer, as a function of time. Analysisof the projection of an expanded image onto such anarray enables, within diffraction-limited resolution, con-struction of time-resolved and spatially resolved maps oflight intensities, which can then be related to a physicalvariable of the system being examined, such as concen-tration, as a function of distance normal to the probingbeam.


4.5.1 Imaging of Diffusion Layers

4.5.1.1 Potential Step

Planar Electrodes. Figure 39 shows a series ofCTAACž/Co

TAA versus y (the distance from the electrodesurface) plots obtained for single and double potentialstep experiments in 2.56 and 4.06 mM TAA in acetonitrilesolutions, respectively..40/ As shown in Table 4, thespecies TAACž exhibits a large e at l D 632.8 nm. Eachof the solid curves in (a) and (b) were acquired withan He�Ne laser at different times after application of apotential step from 0.0 to C0.8 V versus SCE, whereasthose in (c) and (d) were recorded at various times afterreturning the potential to 0 V, following polarization atC0.8 for 2 s (see caption). Excellent agreement was foundbetween the results of these experiments using valuesof e and D obtained independently, based on solutionsof Fick’s law (see Equation 23). Deviations observed attimes longer than 8 s in (a) and (b), are attributed to theonset of natural convection.

Modifications to the optical set-up.70/ in Figure 40, toinclude an Xe arc lamp instead of a laser, makes it possibleto gain access to a much wider spectral region and therebymonitor profiles of a more general class of chromophores.Using such an approach, direct verification of theoreticalpredictions for times up to 10 s could be obtained for thepotential step oxidation of ferrocyanide ion [Fe(CN)6]4�

to the corresponding ferric species.Overall, analysis of these type of data allows for D

for both R and P to be determined without specificknowledge of electrode areas, concentration, molarabsorptivity, absorbance, number of electrons transferredor current, as would be required by chronoamperometryand chronoabsorptometry.

Microelectrodes. Imaging techniques have also beenimplemented for the analysis of cylindrical diffusionfields around thin wires..71/ In this case, a parallelbeam of light of dimensions larger than the diameterof the wire is directed normal to the cylinder axis, as

Figure 39 (a and b) Plots of CTAACž relative to CoTAA as a function of y after various times following application of a single potential

step from 0.0 to 0.8 V versus SCE: (a) 0.05 s, (b) 0.1 s, (c) 0.3 s, (d) 0.5 s, (e) 1.0 s, (f) 2.0 s, (g) 4.0 s, (h) 8.0 s, (i) 16 s. Solid lines areexperimental profiles: points were calculated from Fick’s law and Beer’s law with pathlength D 0.015 cm and e D 11 000 M�1 cm�1;Co

TAA D 2.56 mM. (c) As for (a) following application of a subsequent step after 2 s at 0.8 V, back to 0.0 V versus SCE: (a) 0.1 s, (b)0.4 s, (c) 1.0 s, (d) 3 s. (d) Expanded profile of curve b in (c) above; Co

TAA D 4.06 mM..40/


Figure 40 Optical arrangement for profile imaging using an arc lamp and a photodiode array..70/

Figure 41 Orientation of microwire (cross-hatched) diffusionfield, and detector. Magnification was accomplished with atwo-element simple magnifier..71/

shown in Figure 41, and then magnified before strikingthe array detector. Concentration profiles based oninformation obtained from lateral absorbances can beobtained by a mathematical technique known as Abelinversion, a procedure readily amenable to computerimplementation. Experimental results in agreement withtheoretical predictions have been obtained for microwiresof radii 6–25 µm and electrolysis times ranging from 50 msto several seconds. Good agreement between theory andexperiments were obtained for C.r/ for various timesfollowing the potential step, as shown in Figure 42.

4.5.1.2 Cyclic Voltammetry The same experimen-tal approach enables images of concentration profilesto be obtained for planar electrodes during cyclicvoltammetry..40/ For example, Figure 43(a) shows pro-files recorded during the forward and Figure 43(b) reversesweeps for the TAA/TAACž redox system in acetonitrile.Also depicted in the insert to Figure 43(a) is a plot ofabsorbance versus potential obtained with a photomul-tiplier tube (PMT), instead of a diode array, through aslit (see Figure 38) illuminating the region 0.0š 0.2 µm,i.e. very close to the electrode surface, under the sameconditions. For scan rates up to ca. 80 mV s�1, these

Figure 42 Radial concentration profiles at a 6 µm radiusmicrowire, determined by Abel inversion. Dotted curves areexperimental; solid lines are simulated C.r/. From the bottom,electrolysis times are 0.2, 0.5, 1, 2, 4, 6, and 10 s; Co

CPZ D 4.2 mMin 1 M HClO4, 40% MeOH..71/

curves displayed virtually no hysteresis. At the half-wave potential, i.e. E1/2 D 0.54 V versus SCE, the surfaceconcentrations of TAA and TAACž are equal. Underthese conditions, the surface absorbance should thenbe half that of the maximum absorbance for full TAAoxidation, which can be measured at the most positivepotentials (see Figure 43). Furthermore, the overall mag-nitude and shapes of these curves are consistent withthe predicted Nernstian behavior for fast heterogeneouselectron transfer.

Although the concentration profiles of TAACž re-corded during the forward and reverse scans showcommon values for the surface concentration, largedifferences are observed away from the electrode (seeFigure 43). This is not surprising as TAACž accumulates


Figure 43 (a) Absorbance versus y, for the forward scan.(b) Same as (a) for the reverse scan during a cyclic voltam-mogram recorded at a scan rate of 80 mV s�1 in solution,Co

TAA D 3.6 mM (see text for details). The inset shows thepotentials at which the diode array was triggered to obtainthe absorbance profiles..40/

during the forward scan, diffusing away from theelectrode.

4.5.2 Imaging of Reaction Layers

The ability of measuring time-, and space-resolvedprofiles can be advantageous for the evaluation of rateconstants of homogeneous electron transfer reactionsinvolving electrogenerated species and the diagnosis ofreaction mechanisms.

4.5.2.1 Determination of Rate Constants Scheme 9represents a process in which a species S, produced by theoxidation of R, reacts with another electroactive speciesP to regenerate R and the oxidized form of P, denotedas Q. The equilibrium constant of the overall reaction isgiven by Equation (80):

[R]n2 [Q]n1

[S]n2 [P]n1D Keq .80/

R S + n1e−

P Q + n2e−

n2S + n1P n2R + n1Q

Scheme 9

The magnitude of Keq can be calculated directly fromthe values of the formal reduction potentials of the tworedox couples involved. As demonstrated by theoreticalcalculations, the concentration profiles of these speciesare very sensitive to the reaction parameters, includingstoichiometry (i.e. n2/n1), Co

P/CoR, Keq and the rate

constant, often expressed in terms of a dimensionlessquantity g D k1Co

Rt.An example of this type of mechanism.41,72/ is provided

by the oxidation of methoxypromazine (MPZ) by theelectrochemically generated CPZCž (DS) at potentialsat which MPZCž (DQ) is also produced as shown inScheme 10. Equation (81) gives the equilibrium constantfor the overall reaction:

Keq D k1

k�1D exp

[(nFRT

).E1 � E2/

]D 159 .81/

CPZ CPZ+ + e−

MPZ MPZ+ + e−

CPZ + MPZ+k1

k−1

CPZ+ + MPZ

E1 = +0.68 V versus SCE

E2 = +0.55 V versus SCE

•

•

• •

Scheme 10

For these studies, the He�Ne laser was replaced by anXe arc lamp, thereby allowing the beam to be tuned tothe specific absorption bands of the chromophores, i.e.CPZCž and MPZCž. The contributions due to MPZCž tothe absorbance at l D 520 nm, the absorption maxima ofCPZCž, can be determined from the results obtained at600 nm, a wavelength at which CPZCž, CPZ, and MPZdo not absorb. A comparison between experimentalresults (solid lines) and best fit simulations (dottedlines) in the form of C.y, t//Co

CZP versus y, where yis the distance normal from the electrode surface, forl D 600 nm and 520 nm, are given in Figure 44(a) and (b),respectively, for t D 1, 3 and 6 s, assuming Keq D 159,n1 D n2, g D k1Co

Rt D 1. The latter condition simplyimplies that the reaction rate is very large, i.e. no kineticinformation can be inferred from this analysis.

Equally large rate constants were found for the cross-reaction between triflupromazine hydrochloride (TPZ)and hydroquinone (H2Q) for which n2/n1 D 2. As forKeq, absolute values of n1 and n2, can be obtained usingconventional electrochemical techniques, or spatiallyresolved spectroelectrochemistry for the individual redoxcouples.


Figure 44 (a) Experimental ( ) and simulated ( . . .) con-centration profiles for the CPZCž/MPZ cross-reaction: curvesA–C are CPZCž, curves a–c are MPZžC. Simulations are fork1, g D 1, Keq D 159. Curves: (A, a) t D 2 s; (B, b) t D 3 s;(C, c) t D 6 s. Experimental profiles determined at l D 600 nmfor MPZCž, and at l D 520 nm for CPZCž, corrected forabsorption due to MPZžC. (b) Experimental ( ) and sim-ulated ( . . . ) absorbance profiles determined at l D 520 nm forthe CPZ/CPZCž cross-reaction. g, k1 D 1, Keq D 159. Curves:(a) 1 s; (b) 3 s; (c) 6 s..41/

Careful inspection of simulated profiles for the reactionmechanism in Scheme 10 reveals for large values of Keq

and infinitely large values of g, a rather linear regionextending from the electrode, at which the dimensionlessconcentration of S under the operating diffusion controlconditions is unity, into the solution. Extrapolation ofthis profile onto the abscissa may be used to definea dimensionless reaction layer thickness, denoted dr, aparameter that depends on n2/n1, and the relative bulkconcentrations of P and R.

4.5.2.2 Mechanistic Diagnosis Methods based onthe measurement of integrated profiles by absorptiontechniques yielded data consistent with at least twoproposed mechanisms for the oxidation of DA by CPZCž,already given in Equations (75–77). In other words, it wasnot possible to discern whether DACž reacts with CPZCž

or undergoes dismutation (see Equations 76 and 77) toyield the specified products. As evidenced by numericalsimulations,.36/ however, the spatial and temporal profilesof CPZCž do indeed show differences for these twomechanisms and, therefore, direct observation could helpidentify the preferred pathway.

Comparisons between experimental and theoreticaldata.36/ provided unambiguous proof that Equation (75)with (77) is not operative, thus favoring stepwise electrontransfer (Equations 75 and 76) as being the most likelymechanism. Moreover, analysis of the data obtainedwith a wire electrode revealed that under very acidicconditions the reaction between the neutral species CPZand DOQ cannot be neglected, i.e. the rate constant isindeed significant. Overall, there appears to be no othermethod available to date capable of providing this levelof detail regarding such a complex reaction.

4.6 Ultraviolet/Visible Spectroelectrochemistry in thePresence of Convective Flow

The specificity of spectroscopic techniques, together withthe well-defined mass transport characteristics of therotating disk electrode (RDE), the rotating ring-diskelectrode (RRDE), the channel electrode and, to a lesserextent tube electrodes,.73/ provide excellent experimentaltools for the quantitative analysis of complex electrodeprocesses. This section illustrates with representativeexamples, theoretical and experimental aspects of thecoupling of UV/VIS spectroscopy and forced convectionsystems, both under steady-state and transient conditions.

4.6.1 Steady-state Measurements

4.6.1.1 Near Normal Incidence Ultraviolet/Visible Reflec-tion–Absorption Spectroscopy at Rotating Disk Elec-trodes Optical access to the diffusion boundarylayer of an RDE under near-normal incidence condi-tions requires an experimental arrangement of the typedepicted in Figure 45..74/ The beam enters through awindow parallel to the electrode surface, travels alongthe axis of rotation of the disk, reflects off the elec-trode surface and, after emerging from the cell throughthe same window, is directed toward the detector. Caremust be exercised to set the distance between the elec-trode surface and the window (Figure 45) sufficientlylong to preserve the laminar fluid flow characteristicsundisturbed. The amount of product generated duringthe experiments will be assumed to be sufficiently smallso that the bulk solution composition remains unalteredduring data acquisition. Such requirements will be closelyfulfilled provided the currents are small, the experimentsshort and the volume of the solutions large. For smallincidence angles, such as those used in practice, the


Figure 45 Diagram of the experimental arrangement forreflection–absorption UV/VIS spectroscopy at a RDE at nearnormal incidence angle. The labels ‘In’ and ‘Out’ refer to theincoming and outgoing beams, respectively. Other componentshave been omitted for clarity..74/

errors introduced by assuming strict normal incidenceare relatively small and therefore will be neglected.

Simple Redox Reactions. Steady-state concentrationprofiles for a stable product P generated at a RDE alongthe rotation axis of the disk can be obtained by solvingEquation (33) in Table 2, assuming variations in the radialcoordinate can be ignored, to yield Equation (82):

CP.z/ D CsP

.4/3/

∫ 1ςP

exp.�u3/ du .82/

On this basis, the absorbance due to P is given byEquation (83):.74/

A.E/ D 1.62936en1/6D2/3R D�1/3

P ω�1/2 1� CsR.E/

CoR

.83/

where the superscript ‘s’ refers to the concentration atthe surface, and the potential E in this case is positive(or negative) enough for oxidation (or reduction) toensue. Shown in Figure 46 is a comparison of plotsof the current I versus E (dashed line, left ordinate)and A versus E (solid line, right ordinate) for an AuRDE in a 0.01 M Fe(CN)6

4� solution in aqueous 0.5 MK2SO4 recorded atω D 530 rpm.74/ using the arrangementshown in Figure 45. For these experiments, the opticalresponse was monitored while scanning E at relativelyhigh rates of 100 mV s�1 whereas the current was recordedat 2 mV s�1. At high scan rates, the concentration profilescannot achieve steady state; hence, the optical signal issmaller than that expected from the current. This effectis particularly pronounced for potentials at which thecurrent is below its diffusion-limited value ilim, i.e. Cs

R D 0.Nevertheless, as predicted by theory, a plot of absorbance

Figure 46 Combined plot of the current (dashed line) andA.E/�A.0.0 V/, as defined in Equation (81), as a function ofthe applied potential for the oxidation of 0.01 M [Fe(CN)6]4� in0.5 M K2SO4 aqueous solutions. These curves were recorded atω D 530 rpm and l D 420 nm. The optical and electrochemicaldata were recorded at scan rates of 100 and 2 mV s�1,respectively..74/

at the diffusion-limited current as a function of ω�1/2 wasfound to be linear, yielding values for e of [Fe(CN)6]3�

within about 1% of those reported in the literature.

Determination of Faradaic Efficiencies of Complex Pro-cesses. Electrosynthesis affords an expedient routefor the industrial production of a variety of high-valuedchemicals. In addition to cell design considerations andelectrode stability, the overall efficiency of these pro-cesses is often controlled by the kinetics of heterogeneouselectron transfer, as well as by the rates of precedingand subsequent chemical reactions. Of common occur-rence are situations in which materials, other than thedesired product, are generated during operation, therebydecreasing the specific faradaic efficiencies, i.e. the frac-tion of the total current (or charge) involved in thegeneration of a given product. Quantitative aspects ofthis phenomenon may be assessed by determining prod-uct distributions using conventional analytical techniquesexternal to the reactor or cell. A far more desirable strat-egy is to acquire such information in situ or on line, i.e.by probing directly the solution adjacent to the electrodesurface under well-defined conditions of mass transfer,especially when dealing with rather unstable products.

Within the Levich formalism, the flux jP of a non-adsorbing product P at the surface of a RDE, may beexpressed in terms of the partial current density due tothe formation of P (Equation 84):

DP

(dCP

dy

)0D �jP

nPF.84/

where nP is the number of electrons required to form onemolecule of P. This parameter is defined as negative or


positive depending on whether the process is a reductionor an oxidation, respectively. As is customary, the sign ofthe current is positive for an oxidation and negative for areduction.

In terms of the dimensionless variable zP D y/dP, wheredP D 1.805 D1/3

P n1/6ω�1/2 is the thickness of the diffusionboundary layer for P, Equation (84) can be rewritten asEquation (85): (

dCP

dzP

)0D �jPdP

nPFDP.85/

The solution for the profile of a stable product P, i.e.displaying no decomposition, along an axis normal to theelectrode surface at steady state may be expressed interms of the flux at the surface (Equation 86):.26/

CP.zP/ D �(

dCP

dzP

)0

∫ 1ςP

exp.�u3/ du

D �jPdP

nPFDP

∫ 1ςP

exp.�u3/ du .86/

For normal incidence reflection absorption experi-ments at an RDE, and assuming P is the only opticallyabsorbing species in the media, the absorbance A isgiven by

A D 2eP

∫ 10

CP.y/ dy D 2ePdP

∫ 10

CP.ςP/ dςP

D 2ePd2

P

DP

jPnPF

∫ 10

∫ 1ςP

exp.�u3/ du dςP .87/

The value of the double integral in the right-hand sideof Equation (87) is (2/3)/3, where (2/3) is the gammafunction of argument 2/3..23/ Hence, upon rearrangement,Equation (87) may be written as

AωjPD 2.9408

eP

nPF

(n

DP

)1/3

.88/

As the right-hand side of Equation (88) involvesparameters intrinsic either to the product (eP, nP,DP)or to the solution (n), the quantity Aω/jP is constant. Infact, the constancy of this ratio for different E, ω, andCR may be regarded as proof that the process indeedsatisfies the requirements of the model. Note that in thederivation of Equation (88), no restrictions were imposedon the nature of the step-limiting the values of jP, such asdiffusion, heterogeneous or homogeneous reactions, or acombination thereof.

The reduction of bisulfite in mildly acidic solutionsgenerates dithionite S2O4

2�, a material that displays ahigh e band centered at l D 316 nm, i.e. within a spectralregion that does not interfere with other species in themedia.

Figure 47 Current density j (solid line), partial current densityfor dithionite generation jP (points), and difference betweenthese two currents jres (dotted line), obtained with an Au disk(area 0.452 cm2) of an Au–Au RRDE assembly in 10 mMNa2SO3 in 0.50 M phosphate buffer solution (pH D 5.25), atdifferent rotation rates: A D 200, B D 400, C D 900, D D 1600,E D 2500, and F D 3600 rpm. Values of jP were calculatedfrom Equation (86) based on the absorbance measured inthe reflection absorption mode at near-normal incidence atl D 316 nm..92/

Plots of j versus E, known as polarization curves, wherej is the total current density, were recorded with an AuRDE in solutions of 10 mM Na2SO3 in 0.50 M NaH2PO4

adjusted to pH 5.25 with NaOH using the arrangementshown in Figure 45. At all rotation rates examined, thecurrents at the inflection (solid lines in Figure 47), weresignificantly smaller than the diffusion-limited currentdensities (jlim) for the two-electron oxidation of sulfite inthe same electrolyte at 1.00 V, e.g. jlim D 19.1 mA cm�2 at900 rpm.

Plots of A at 316 nm versus E recorded during acqui-sition of I versus E curves in Figure 47, were used toconstruct jP versus E plots using Equation (86), andare given in scattered form in the same figure. Forthese calculations, the constant Aω/jP was determinedbased on e of S2O4

2�, i.e. 7.3š 0.3ð 106 cm2 mol�1,and the diffusion coefficient of S2O4

2�, i.e. 9.1š 0.03ð10�6 cm2 s�1, respectively, n D 0.010 cm2 s�1, the kine-matic viscosity of water, and n D 2, yielding a value of9.9š 0.6 rpm cm2 mA�1. Also given in this figure are plotsof jres versus E, where jres is the contribution to the totalcurrent j due to processes other than bisulfite reductionto dithionite, jres D j� jP.

In the range�0.60 > E > �0.75 V, j and jP were foundto virtually coincide at jres about 0. This observationprovides convincing evidence that j and jP are not onlyproportional, but also that the specific faradaic efficiency(jP/j) for dithionite generation under these conditions is


Figure 48 Faradaic efficiency for dithionite generation, i.e. jP/j,as a function of the applied potential based on the data shownin Figure 47 for six different rotation rates: solid line D 200,diamonds D 400, solid circles D 900, open circles D 1600, solidtriangles D 2500, and open squares D 3600 rpm..92/

within experimental error about 100% (Figure 48). Thedecrease in the specific faradaic efficiency at more positivepotentials is probably caused by contributions to the totalcurrent due to the reduction of adventitious oxygen in thesolution. Furthermore, jP increased with ω over the entirepotential range, indicating that the reaction proceedsunder partial mass transport control. However, despitethe increase in j as the potential was made more negative,jP reached a maximum at about �0.80 V (jmax

P ) for all ω,and decreased steadily thereafter. In addition, plots ofjmaxP versus ω1/2 and 1/jmax

P versus 1/ω1/2 yielded straightlines with nonzero intercepts, and jres was found to beindependent of ω.

4.6.1.2 Rotating Disk Electrode with a Concentric Trans-parent Ring An interesting forced convection systemintroduced by Debrodt and Heusler,.75/ involves a con-ventional RRDE assembly in which the metal ringis replaced by a material transparent in the UV/VISregion. This device makes it possible to detect opti-cally absorbing species generated at the disk electrode(Figure 49). Although certain theoretical aspects of thisRRDE electrode have been analyzed by digital simula-tion techniques,.76/ analytical solutions can be obtainedfor simple reactions via the unified formalism given inTables 2 and 3..77/ Specifically, the dimensionless con-centration and flux of a reactant, or a product alongthe surface of an RDE are constant, and given byqD D f1C b�1g�1, and (@q/@z/jzD0 D �3qD/.1/3/, respec-tively, where b D [.1/3//3]k[3/.anD2

R/]1/3.n/�/1/2.

Based on the second equation for real space in Table 3,the concentration along an axis normal to the surfaceof an RDE beyond the electrode edge (1 < r, z) can be

Figure 49 Diagram of a transparent ring RRDE..75/ A, circularlight inlet; Q, quartz glass cover; C, optical fiber cable; R, ring;B, D, receivers built similarly; E, rotating disk with quartz ringand electrode; F, aperture; G, H, adjusting devices.

expressed as Equation (89),

D q

qDD 3

[.1/3/.2/3/

]�1 ∫ 1

0exp

[ �ς3

.1� r/r0/

]

ð[

1�(r

r0

)3]�2/3

r0 dr0 .89/

which at z D 0 reduces to Equation (90):

.r > 1, ς D 0/ D 34C√

34p ln

[1C g3

.1C g/3

]� 3

2p arctan [.2g� 1/

p3] .90/

where g D .r3 � 1/1/3. Concentration profiles along z forthree values of r are given in Figure 50.

The integrated profile along z, defined as I.r/ may bewritten as Equation (91):

I.r/ D∫ 1

0.r, ς/ dς D

[.1/3/.2/3/

]�1 ∫ 1

0r0.r3 � r03/�2/3

ð∫ 1

0exp

{ �ς3

1� .r0/r/3}

dς dr0 .91/

A plot of I.r/ versus r is shown in Figure 51(a).An explicit expression for the total amount of material

probed by the light beam, defined by a cylindrical shell


Figure 50 Plot of q.r, z/ versus z for three values of r, i.e. curvea D 1, b D 65.5/64.5, and c D 74.5/64.5..77/

Figure 51 Plots of (a) I.r/ versus r and (b) A.r/ versus r for atransparent ring RRDE..77/

with inner, and outer dimensionless radii, r1 D r1/r0 andr2 D r2/r0, respectively, can be shown to be given by

Equation (92):

Nvol D NoqD{

2∫ r2

r1

I.r; b/rdr}

D NoqD[A.r2/�A.r1/] .92/

where A.r/ is given by Equation (93),

A.r/ D 2∫ r

0I.r/rdr .93/

and No is the same as for the RDE..77/ A plot of A.r/versus r is shown in Figure 51(b).

4.6.1.3 Channel Electrodes

Profile Imaging Downstream from the Electrode Sur-face. The composition of a solution downstreamfrom a channel-type electrode depends, among otherfactors, on the rates of heterogeneous electron transferand homogeneous reactions involving electrogeneratedspecies, and their mass transport characteristics. Infor-mation regarding various aspects of these processes canbe obtained from the analysis of spectroscopic measure-ments in which a beam oriented normal to the electrodesurface is used to monitor the absorbance of the solutionalong an axis parallel to the fluid flow. A cell arrange-ment suitable for this type of measurements is shown inFigure 52..78/

Simple Electrode Reaction. In the case of uniformsurface concentration, the integrated concentrationsprofile of the absorbing product P, denoted as I, at adistance X from the downstream edge of the electrode(X > 1) along an axis normal to its surface may be shownto be given by Equation (94):

I.X > 1;1/ D∫ 1

0qP.X,Y/ dY D 1

31/3

(23

)ð∫ 1

0x�1/3.X � x/�1/3 dx .94/

Figure 52 Diagram of a channel cell for spectroelectrochemicalstudies..78/


where qP D .DP/DR/2/3.CP/CoR/. This requirement is

fulfilled when the reaction is reversible and, thus, CR

and CP are prescribed by the Nernst equation, or underdiffusion limited conditions.

Figure 53 shows plots of current and absorbance versusE obtained in a solution 0.01 M K4Fe(CN)6 in 0.25 MK2SO4 recorded simultaneously using a potential scanrate of 1 mV s�1 and a flow rate of 1.74 mL min�1,.79/

where the optical monitoring was performed at 1.1 cmfrom the downstream edge of the electrode. The ordinates

Figure 53 Combined plots of current (left ordinate, solidcircles) and absorbance (right ordinate, open circles) versus Efor a solution 0.01 M K4Fe(CN)6 in 0.25 M K2SO4 solution. Datawere collected simultaneously as E was scanned at 1 mV s�1 ata flow rate of 1.74 mL min�1. The ordinates of the two curveshave been scaled using an appropriate conversion factor..79/

of the two curves in this figure are scaled based on thevalues of A at ilim.

Experiments performed under diffusion-limited condi-tions.80/ showed that the absorbance as a function of Xfor X > 1 (solid squares in Figure 54), which may beregarded as an image of the integrated concentrationprofile, was in quantitative agreement with that predicted

Figure 54 Plot of the steady-state dimensionless integratedconcentration profile of [Fe(CN)6]3�, generated at the surfaceof an Au electrode by the oxidation of 0.01 M [Fe(CN)6]4� in0.25 M K2SO4, as a function of the dimensionless distancefrom the downstream edge of the electrode c2 D x2/l. Allmeasurements were performed at l D 420 nm along the centeraxis of the channel in the direction of the flow (solidsquares) under diffusion-limited conditions for the oxidationof [Fe(CN)6]4�. The solid curve represents theoretical results(the original paper gives full details)..80/

Table 5 Differential equations and boundary conditions for an EC-typemechanism at a channel-type electrode cell (note that K D kxe/6U)

D@2CR

@y2D Ux

@CR

@xw@2CR

@Y2D .Y � Y2/

@CR

@X

D@2CP

@y2� kCP D Ux

@CP

@xw@2CP

@Y2D .Y � Y2/

@CP

@XCKCP

x D 0 y ½ 0 CR D CoR X D 0 Y ½ 0 CR D 1

CP D 0 CP D 0

0 < x � xe y D 0 CR D CsR 0 < X � 1 Y D 0 CR D Cs

R

CoR

CP D CsP CP D Cs

P

CoR

x > xe y D 0@CR

@yD 0 X > 1 Y D 0

@CR

@YD 0

@CP

@yD 0

@CP

@YD 0

x > 0 y D 2h@CR

@yD 0 X > 0 Y D 1

@CR

@YD 0

@CP

@yD 0

@CP

@YD 0


by theory (solid line in the same figure), lending strongsupport to the validity of the underlying assumptions ofthe model.

Determination of the Rate Constant of an Electrochem-ical–Chemical Mechanism. Consider a simple ECmechanism of the type shown in Scheme 2, where k isthe rate constant of the homogeneous chemical reac-tion. Within the framework of approximations specifiedin section 2.2.2, and assuming DP D DR D D, the steadystate convective diffusion equations for R and P are givenin the right-hand panel of Table 5, where the fluid velocityUx is given by

Ux D 32

U[

1� .h� y/2

h2

].95/

In Equation (95) U is the mean flow velocity, and h is thehalf-height of the channel.

The appropriate boundary conditions, summarizedin the lower section of the same panel, specify thatthe concentration of the two species is constant overthe entire surface of the electrode, which implies thatthe electrochemical process is infinitely fast. The lastentry in that table means that no reactions occur atthe optically transparent surface directly opposite tothe electrode along the entire length of the chan-nel. This problem, cast in terms of the dimension-less variables Y D y/2h,X D x/xe, CR D Cs

R/CoR, and

CP D CsP/C

oR is given on the right-hand panel in the

table.If P is the only absorbing species at the selected

l, plots of absorbance versus � ln w, where w D.Dxe//.24Uh2/, K D .kxe//.6U/, determined by digitalsimulations yielded for different X and w/K D 0.01,showed clearly defined maxima for each of the curves(Figure 55a)..81/ Maxima were also observed for a fixedvalue of X D 1.75 and different values of w/K, as shownin Figure 55(b).

Based on these results, an empirical relationship wasobtained between the flow rate and the position along thex-axis at the absorption maxima, Vm and x, respectively(Equation 96),

log Vm D log(

23

h2xeb)C 1.50 log k1 � 0.50 log D

C log(�4.45C 4.72

xxe

).96/

where, as before, xe is the length of the electrode, andb the channel width. Hence, it becomes possible toextract values for k1 by determining experimentally suchmaxima using the required physical dimensions of thecell and the electrode, as well as the diffusion coefficient.From a practical viewpoint it is more convenient to fix x

Figure 55 (a) Absorbance versus � ln w at w/K D 0.01 fordifferent X: curve a D 1.25, b D 1.75, c D 2.25, d D 2.75.(b) Absorbance versus � ln w at X D 1.75 for different w/K:curve a D 0.025, b D 0.0125, c D 0.008, d D 0.005..81/

and measure the relative absorbance for various valuesof Vm.

Figure 56 shows a plot of f/q, a quantity proportionalto the normalized absorbance ratio at two values ofVm, corrected for contributions due to other absorbingspecies in the media, as a function of Vm, for the oxidationof p-aminophenol (PAP) to yield p-benzoquinoneimine(BQI). This latter species undergoes hydrolysis to formbenzoquinone (BQ)..82/ The solid line in this figurerepresents the best fit to the experimental points. Basedon the maximum in this curve, the pseudo-first-order rateconstant k for the irreversible hydrolysis of BQI can beevaluated using Equation (96), yielding values of about0.33 s�1.

4.6.2 Chronoamperometry under Forced Convection

4.6.2.1 Rotating Disk Electrodes Consider a chrono-amperometric experiment in which the potential of anRDE immersed in a solution containing a nonabsorbing


Figure 56 Plot of f /q versus log V for X D 2.5. Solid squaresare experimental data and the solid line is a fit to obtain themaximum of f /q..82/

electroactive species R is stepped from a value Ei, at whichno reaction occurs, to a potential sufficiently positive (ornegative) Ef for R to undergo oxidation (or reduction)generating an optically absorbing product, P. Accordingto Beer’s law, the instantaneous change in absorbance Aalong y can be written as

A.t/�A.t D 0/ D 2eP

∫ 10

CP.y, t/ dy .97/

In Equation (97), CP.y, t/ is the transient concentra-tion profile of P, which can be determined based on thesolution of the transient convective diffusion equationsubject to the appropriate initial and boundary condi-tions. Solutions to this problem, for a reactant, have beenreported for short times by Krylov and Babak,.83/ interms of parabolic cylinder functions, Dk.z/, and forlong times by Nicancioglu and Newman in terms of(numerically evaluated) eigenvectors and eigenfunctions

Table 6 Transient convective diffusion to a RDE

Governing equation

D@2CR

@y2� vy

@CR

@y� @CR

@tD 0

Boundary conditions for concentration step problemCR.0, t/ D 0

CR.1, t/ D CoCR.y, 0/ D Co

Short-time solution Long-time solution

Dimensionless variables

c D CR

Co, t D .DA2/1/3t, x D

(AD

)1/3

y; A D a(ω3

n

)1/2

;

z D x.2t/�1/2

D Co � CR

Co, q D ω

(Dn

)1/3 (a3

)2/3t; ς D

( an3D

)1/3 (ωn

)1/2y

Convective diffusion equation

@2c@x2C x2 @c

@x� @c

@tD 0

@2

@z2C 3z2 @

@z� @

@qD 0

Boundary conditionsc.0, t/ D 0 .0, q/ D 1c.1, t/ D 1 .1, q/ D 0c.z, 0/ D 1 .z, 0/ D 0

Dimensionless profile

c.z, t/ D1∑

nD0

t3n/2Gn.z/ .z, q/ D ss �t

Gn.z/ D e�z2/43n�1∑

kD�3n�1

ŁŁb.n/k Dk.z/ ss D 1.4/3/

∫ 1z

e�x3dx, t D

1∑nD0

BnZn.z/elnq

Bn D

∫ 10ssez3

Zn.z/ dz∫ 10

ez3Z2

n.z/ dz

Dimensionless flux

j.t/j.1/ D

a1/3

0.62.pt/1/2

[1C

1∑nD1

(�p

3n�1∑kD�3n�1

ŁŁ 2k/2b.n/k

.�k/2/

)t3n/2

]j.q/

j.1/ D �3a1/3

0.62

(@ss

@z

∣∣∣∣zD0

� @t

@z

∣∣∣∣zD0

)


of the associated Sturm-Liouville system..84/ A summaryof the two mathematical formalisms, which include theappropriate dimensionless variables and the dimension-less profiles, are given in Table 6. Explicit expressionsfor the coefficients bk.n/ may be found in the origi-nal literature..83/ Exact concentration profiles based onthese two solutions spanning a wide range of dimension-less times are shown in Figure 57(a). These were usedto calculate the corresponding transient integral pro-files involved in the analysis of the spectroscopic data,assuming DR D DP (Figure 57b).

Figure 58 shows curves of [A.t/�A.t D 0/] versust for measurements performed in 0.01 M K4Fe(CN)6

in 0.5 M K2SO4 aqueous solutions using an Au RDEin the arrangement shown in Figure 45,.85/ with thespectrophotometer set at l D 420 nm (see Table 4), wherethe e value of Fe(CN)6

4� is very small. Reflectionabsorption data were acquired at various rotation ratesfollowing a potential step from 0.0 to 0.4 V versusAg/AgCl, which is positive enough for the oxidation of the

Figure 57 (a) Exact concentration profiles obtained using theshort- and long-time solutions, for (curves from left to right)t D 0.01, 0.03, 0.1, 0.2, 1.0, and the steady state (dashed line).(b) Theoretical integral concentration profiles versus time usingthe data shown in (a); the dashed and the solid lines wereobtained from the short-time and long-time solutions..85/

Figure 58 Experimental (difference) absorbance [A.t/�A.t D 0/] versus t: (a) ω D 400 rpm, (b) ω D 650 rpm, (c) ω D1400 rpm; the dashed lines are the corresponding theoreticalcurves..85/

ferrous species to occur under complete mass transportcontrol. The results obtained for each cycle, consisting of aforward and backward step, were co-added using a signalaverager. Also shown in this figure as dotted lines are thetheoretical results based on values of e for [Fe(CN)6]3� at420 nm D 1.14ð 106 mol�1 cm2, D D 7.3ð 10�6 cm2 s�1,n D 0.01 cm2 s�1, and the specified rotation rateω (radiansper second), using the appropriate conversion betweendimensionless and actual integral profiles (Equation 98):∫

.1� C/ d.zt1/2/ D a1/3(ω

2

)1/2D�1/3n�1/6

∫c dy

.98/where a D 0.51024. As can be seen, the agreementbetween theory and experiment for the three rotationrates examined is very good.

4.6.2.2 Channel Electrodes The transient convectivediffusion equation governing mass transport of a solution


phase species C in a channel is given by Equation (99):

@C@tD D

@2C@y2� vx

@C@x

.99/

where vx D .3Vf/4hd/[1� .h� y/2/h2] and other termshave their usual meanings.

Consider a chronopotentiometric experiment in whicha potential of large enough magnitude is applied to anelectrode in the channel to reduce instantaneously CR

to zero at the surface, assuming, that CP D 0 beforethe potential step is applied. The initial and boundaryconditions for R and P may thus be summarized asEquations (100–103):

for t < 0 : y D 0, 0 < x < .xe C xg C xd/,

CR D CoR,CP D 0 .100/

for t > 0 : 0 < x < xe; CR D 0,


@y

∣∣∣∣yD0D �DP

@CP.y, t/@y

∣∣∣∣yD0

.101/for all t : y D 0, xe < x < .xe C xg C xd/;


@y

∣∣∣∣yD0D DP

@CP.y, t/@y

∣∣∣∣yD0D 0

.102/y D 2h, 0 < x < .xe C xg C xd/ :


@y

∣∣∣∣yD0D DP

@CP.y, t/@y

∣∣∣∣yD0D 0

.103/where xe is the width of the electrode and xg and xd are thedistances from the downstream edge of the electrode tothe area of the solution being monitored optically alongan axis normal to the plane of the electrode, as shown inFigure 52.

The time-dependent concentration profiles for allspecies involved can be obtained by digital simula-tion techniques, and the values of the parameters thenadjusted until a best fit to the experimental data is found.Figure 59(a) shows values of the normalized absorbancefor the one-electron oxidation of ferrocyanide, andFigure 59(b) is the reduction of ferricyanide via chronopo-tentiometric techniques acquired at wavelengths at whichthe absorbance of each of the species is maximum..78/ Thesolid lines in these figures are calculated best-fit curves tothe experimental data. Using the value of DR determinedfrom ilim (Equation 104),

ilim D 0.925nFwCoR

(VfD2

Rx2e

h2 d

)1/3

.104/

for different flow rates and the physical dimensions of thechannel, the ratio of the diffusion coefficients of the two

Figure 59 (a) Transient absorbance at l D 420 nm for theone-electron oxidation of Fe(CN)6

4� and (b) l D 218 nm for theone-electron reduction of Fe(CN)6

3� measured using the chan-nel cell with cell depths of 0.0805 cm and 0.0792 cm, respectively,following a potential step at the working electrode. Solu-tion flow rates: � D 1.44ð 10�3 cm3 s�1; ( ) 7.51ð 10�3 cm3 s�1.Solid lines represent theoretical curves..78/

species was found to be in excellent agreement with datareported in the literature, i.e. Dferro/Dferri D 1.17š 0.05.

Application of this method revealed very small dif-ferences between the diffusing coefficients of electro-generated radical species and the neutral precursors innonaqueous solutions, which suggests that the interac-tions of the two types of species with the solvent areindeed quite similar.

4.7 Modulation Techniques

Application of an external periodic potential to anelectrical system, such as an electrochemical cell, willelicit corresponding periodic variations in the current.Analysis of the amplitudes and phases of the response as


a function of the perturbation frequency constitutes thebasis of a general method for the study of the dynamicbehavior of electronic circuitry known as impedancespectroscopy. The mathematical treatment of modulationtechniques can be simplified considerably by employingperiodic signals of a small enough magnitude so that thebehavior of the system may be represented in terms oflinear equations. This approach allows contributions tothe observed signals derived from other sources, such asnoise, to be minimized or eliminated, by extracting thatcomponent of the response that oscillates at the samefrequency as the exciting perturbation. Also amenable toexperimental determination are periodic changes in theconcentration profiles of species consumed or generatedby faradaic processes brought about by the modulatingpotential, which can be monitored optically by relyingeither on absorption of UV/VIS chromophores, or onbeam-bending effects derived from local changes in theindex of refraction along an axis normal to the beamdirection.

4.7.1 General Considerations

Consider an experimental arrangement in which lightpropagating through the solution, reflects at normalincidence from a flat electrode, placed parallel to andat a distance d from a planar transparent cell window.It will be assumed, for simplicity, that the redox processinvolves consumption of a nonabsorbing species R, andgeneration of a single absorbing product P, where both Rand P are solution phase species, and that only R is presentat the beginning of the experiments. If the attenuation inlight intensity induced by other components in the pathof the beam, including reflection from the electrode, canbe ignored, the intensity I of the light exiting the cell isgiven by (Equation 105),

I D Io exp

[�2ek

∫ d

0c.y, t/ dy

].105/

where Io is the light intensity entering the cell. Attentionis focused hereafter on solutions of one-dimensional masstransport equations of the form

c.y, t/ D Nc.y, t/C Qc.y, t/ .106/

where in Equation (106) Nc.y, t/ is a slowly varyingfunction of time, or steady state, and Qc.y, t/ is theoscillatory contribution. Introducing Equation (106) intoEquation (105), a normalized absorbance may be definedas follows (Equation 107):

I

ID exp

[�2ek

∫ d

0Qc.y, t/ dy

].107/

Provided that the changes in concentration induced bythe periodic perturbation are small, the argument in theexponential can be approximated by the first two termsin the Taylor series expansion, yielding Equation (108)after rearrangement:

I � I

ID Iac

IdcD 2ek

∫ d

0Qc.y, t/ dy .108/

If it is further assumed that the changes in concentrationare confined to a volume of solution very close to theelectrode surface, d may be regarded as arbitrarily large,and therefore the upper limit of integration may beset as infinity, leading to much simpler mathematicalexpressions.

From an experimental viewpoint, the ratio Iac/Idc, canbe measured very accurately, such as by using a lock-inamplifier. A quantitative analysis of the results obtainedusing this modulation technique requires the integral onthe right-hand side of Equation (108) to be evaluated, aproblem that is equivalent to finding solutions for the masstransport equations subject to the appropriate boundaryconditions.

Of particular interest here is derivation of expressionsfor the oscillatory component of the response of the form

Qc.y, t/ D AŁ.y/ exp.jωt/ .109/

where AŁ in Equation (109) is the maximum amplitudeof the sinusoidally varying concentration, and .y/ is afunction of distance.

4.7.2 Quiescent Solutions

Substitution of Equation (109) into Fick’s second lawleads to a differential equation in y in total derivatives,which can be easily solved analytically to yield Equa-tion (110):

.y/ D exp

[�(

jωD

)1/2

y

].110/

Hence, Iac/Idc, also denoted as I.ωt/, may be written asEquation (111):

Iac

IdcD I.ωt/ D 2ek

∫ 10

AŁ exp

[�(

jωD

)1/2

y

]exp.jωt/ dy

D 2ekAŁ(

Djω

)1/2

exp.jωt/

D 2ekAŁ(

Dω

)1/2

exp[j(ωt � p

4

)].111/

that is, the optical response lags the modulated potentialby p/4.


In the case of very fast heterogeneous electron transferreactions, the applied potential prescribes the ratioof concentrations of reactants and products throughthe Nernst equation. For perturbations of very smallamplitude, this equation can be linearized, to yieldEquation (112) that relates the amplitudes of the appliedpotential EŁ and those of the concentrations of R and P,AŁR and AŁP, respectively:

E D EC E D Edc C EŁ exp.jωt/ .112/

where Edc and EŁ are given by Equation (113):

Edc D Eo0 C RTnF

lnNcR.0, t/NcP.0, t/

;

and EŁ D RTnF

(AŁRNcR.0, t/

� AŁPNcP.0, t/

).113/

Because of conservation of mass at the elec-trode surface (see Equation 16) AŁP D �AŁRx, wherex D .DR/DP/1/2; hence, it becomes possible to expresseither one of the AŁi coefficients in terms of EŁ, to yieldEquation (114)

EŁ D 4RTAŁRnFco

Rcosh2

(a2

).114/

where a is given by Equation (115):

a D nFRT

.Edc � E1/2/; and E1/2 D Eo0 C RTnF

ln(

DP

DR

)1/2

.115/The current associated with the faradaic process is

related to the flux of material at the electrode surface viaEquation (116),

i D �nFADR@cR

@y

∣∣∣∣yD0D �nFAAŁP.jωDP/

1/2 exp.jωt/

D �nFAAŁP.ωDP/1/2 exp

[j(ωt C p

4

)].116/

where A is the area of the electrode. Hence, fromEquations (111) and (116), the current and the opticalresponse are 90° out of phase with respect to one another.

4.7.2.1 Alternating Current Solution-phase ReflectanceSpectroscopy Based on Equations (105) and (109),the ratio of the magnitudes of the current and reflectancesignal induced by the modulated applied potential is givenby Equation (117),

ji.ωt/jjI.ωt/j D

nFAω2ek

.117/

and, therefore, for a fixed perturbation frequency,the electrical and optical responses are proportionalto each other. In the case of solution-phase redox

couples involving at least one UV/VIS chromophore,these considerations afford a basis for implementinga spectroscopic analog of a highly sensitive electro-chemical technique known as alternating current (AC)voltammetry. This method relies on the superpositionof an AC signal of small amplitude onto a slow lin-ear potential scan, while monitoring the amplitude ofthe current response. Although restricted to opticallyabsorbing species, this spectroscopic approach offers adefinite advantage over current measurements in that theresponse is not affected by contributions to the electri-cal signal derived from other sources, particularly doublelayer capacity effects.

By way of illustration,.86/ Figure 60 displays a plotof I.ωt/ versus Edc for the oxidation of an unbufferedsolution 10 mM K4Fe(CN)6 in aqueous 1 M KCl obtainedat a frequency of 43.9 Hz at a scan rate of 2 mV s�1, forwhich both for the forward and reverse scans, as indicatedby the arrows, were found to superimpose. The positionof the peak at 0.219 V versus SCE agrees very well withthe reversible half-wave potential for the redox couple.Moreover, the width of the peak at half-height was 94 mV,in harmony with that predicted by theory, i.e. 90 mV. Thisoverall behavior is characteristic of the AC response fora reversible one-electron system.

The direct relationship between the optical and electri-cal response can also be valuable for the determination ofrate constants by examining the dependence of the phaseanglefon the perturbation frequency. In particular, in theabsence of effects due to IR drop in the solution, f may beshown to be related to the rate of a simple heterogeneous

Figure 60 AC reflectance spectra for the oxidation of 10 mMK4Fe(CN)6 in 1 M KCl, at l D 420 nm, ω/2p D 43.9 Hz,n D 2 mV s�1..86/


electron transfer reaction ks (Equation 118):

cotf D 1C .ωD/2/1/2

ks.118/

In fact, a plot of the iR-corrected cotf versus ω1/2

(Figure 61) for the ferro–ferricyanide couple obtainedfrom potential modulated spectroelectrochemical mea-surements was found to be linear, yielding values forks around 0.096š 0.008 cm s�1 in agreement with dataobtained by more conventional means..86/

4.7.2.2 Diffractive Alternating Current ModulationLight striking the edge of a solid object will be scatteredproducing a diffraction pattern on a plane normal tothe beam direction, including regions in the shadow ofthe object, with much of the intensity of the diffractedbeam originating from areas very close to the edge.Furthermore, the diffracted light will be attenuated bya UV/VIS absorber present very near the edge, andthe extent of attenuation will be proportional to theconcentration of the absorber therein, as predicted byBeer’s law. Assuming the concentration of product in thearea sampled by the diffracted beam, i.e. at and near theelectrode edge Cs

P is uniform, the attenuation of the beammay be written as Equation (119):

A D log(

Io

It

)D ewCs

P .119/

Figure 61 Plots of cotf versus ω1/2 for the oxidation of10 mM K4Fe(CN)6 in 1 M KCl. Squares represent cot jS,circles represent calculated cot f; Edc D 0.219 V versus SCE,E D 18 mV..86/

where w is the electrode length along the optical axis.Furthermore, Io and It are the intensities of the diffractedbeam at a specific angle of observation measured beforeP is generated, and after Cs

P reaches a limiting value,respectively. This situation is somewhat equivalent tothat of a conventional spectroelectrochemical cell ofa pathlength equal to the length of the electrodealong the direction of beam propagation, which can beelectrochemically filled or emptied with absorber over avery short period of time.

If A is small, the normalized difference in lightintensities Io � It, denoted as Idiff/Io, may be shownto be given by Equation (120):

Idiff

IoD kebxCo

P .120/

where CoRx D CP, Co

R is the bulk concentration of R,and x D .DR/DP/1/2. On this basis, it becomes possibleto monitor the modulated diffracted light intensity, and,thus, the concentration of electrogenerated product Pin a region of the solution very close to electrodesurface. More specifically, the amplitude of the modulateddiffracted light intensity Idiff

ac for AC voltammetry isrelated to the amplitude of the applied voltage byEquation (121):

Idiffac

IoD kebnxFCo

REŁ

4RT cosh2.a/2/.121/

As before, this latter expression is valid provided theheterogeneous electron transfer reaction is infinitely fast.

Experiments involving TAA in TEAP/acetonitrile andsquare wave modulation of relatively large amplitude, i.e.0.5 V about Eo0, yielded values of Idiff

ac lower than thosepredicted theoretically..29,87/ However, the output of thelock-in amplifier using a modulation frequency of 10 Hzwas found to be proportional to the concentration of TAAin the range from 3ð 10�7 to 1ð 10�4 M. Furthermore,judicious choice of experimental conditions, includinghigher modulation frequencies, lower angles and phaseadjustments, made it possible to increase the detectionsensitivity to less than 2ð 10�8 M. Also in qualitativeagreement with the expected response, were the resultsof spectroelectrochemical AC voltammetry experiments,which yielded superimposable curves for forward andbackward scans for slow scan rates, about 2 mV s�1, andEŁ value in the range 10–50 mV (Figure 62).

4.7.2.3 Transmission Alternating Current VoltammetryApplication of a sinusoidally varying potential to a planarelectrode induces a modulation in the concentration ofan optically absorbing redox product. Changes along anaxis parallel to the electrode surface can be monitoredspectroscopically using a CCD or a photomultiplier in


Figure 62 Lock-in amplifier output versus direct current (DC)potential for small-amplitude square-wave AC potential super-imposed on a slow DC scan (2 mV s�1): modulation frequency10 Hz; phase shift �20°; time constant 0.3 s; Co

TAA D 0.257 mM;curve a,E D 10 mV; b,E D 30 mV; c,E D 50 mV. Reversescans were superimposed on forward scans within the pen width.Peaks occur at C0.52 V versus SCE..87/

conjunction with a narrow slit to illuminate a small volumeof solution. The normalized optically modulated signalmay thus be expressed as Equation (122):

Iac

IdcD ekwQc.y, t/ D ekwAŁ exp

[�(

jωD

)1/2

y

]exp.jωt/

D ekwAŁ exp[�( ω

2D

)1/2y]

ð exp{

j[ωt C

( ω

2D

)1/2y]}

.122/

where w is the length of the electrode along the directionof light propagation, and y is the distance normalto the electrode surface. Although results have beenreported for a CCD, the most interesting data havebeen collected with the slit arrangement..87/ In particular,Figure 63 shows results for the optically monitored ACspectroelectrochemical voltammogram of TAA obtainedfor three different scan rates at a distance of 3 µm fromthe surface, which are similar to those obtained usingdiffraction as described in the previous section. Theexpression above indicates that the phase is a functionnot only of the frequency of the perturbation, but also ofthe specific distance from the electrode surface.

4.7.2.4 Alternating Current Modulated Solution-phaseRefraction According to Fermat’s principle, a beamtravelling along an axis z, in a medium in which the

Figure 63 Optically monitored AC voltammograms for TAAsolutions. Square-wave perturbations of varying height weresuperimposed on a slow DC ramp (2 mV s�1). Frequency D5.0 Hz, phase D �20°. Curve a, E D 10 mV; b, E D 30 mV;c, E D 60 mV. y D 3 µm, Co

TAA D 0.38 mM..87/

index of refraction n varies normal to the direction ofpropagation, say y, will bend toward regions having largern, and that the extent of bending will be proportionalto @c/@y. Assume, more specifically, that z and y areparallel and perpendicular to the electrode surface. Amodulation in the concentration profile of solution phasespecies induced by the applied potential will modify theindex of refraction along y, and consequently the extentof beam bending. Although refraction is insensitive tothe nature of the species that causes the change in theindex of refraction, it is useful from a didactic viewpointto regard these effects as caused by a single species, andthat the changes in n are linear in the concentrationof that species, i.e. @n/@c D N. This situation can berealized experimentally for systems in which a singlespecies is consumed or generated at the electrodesurface. On this basis, and neglecting the effects dueto the much slower nonoscillatory transient contribution,the oscillatory degree of bending will be given byEquation (123),

D wn

N@Qc@y

.123/

where w is the length of the electrode along z. Anexplicit expression for the derivative can be obtainedfrom Equations (109) and (110), yielding

@Qc@yD AŁ

{�(

jωD

)1/2}

exp

[�(

jωD

)1/2

y

]exp.jωt/


D �AŁ( ω

D

)1/2exp

[�( ω

2D

)1/2y]

ð exp[

j{ωt C y

( ω

2D

)1/2C p

4

}].124/

Based on Equations (109) and (124) above, this analysispredicts that Qc and @Qc/@y should be 45° out of phase withrespect to one another. In fact, large differences in themagnitude of the lock-in amplifier output as a functionof phase angle have been reported.87/ for potentialmodulation experiments in solutions containing 0.66 mMTAA and 10 mM BQ, which generate, respectively, anabsorbing, and a nonabsorbing product upon oxidationand reduction (Figure 64). This phenomenon makes itpossible to enhance the response of the absorbing versusthe nonabsorbing product, by simply adjusting the phaseangle. This is illustrated in Figure 64(b–d) in the formof amplitude of the measured light intensity at the imageplane Iimage, as a function of applied DC potential(Edc) for three different phase angles. Figure 64(a) is themagnitude of the AC current as a function of the appliedDC potential, which reflect the much higher concentrationof BQ compared to TAA.

4.7.3 Warburg Impedance

The dynamic properties of electronic circuits arecustomarily defined in terms of a frequency-dependentfunction known as the impedance, Z (Equation 125):

Z D dEdi

.125/

where E is the potential and i the current. It is thenpossible to define a diffusional impedance, also knownas the Warburg impedance, Zw as the ratio of the timederivatives of the voltage and the current.

4.7.3.1 Quiescent Solutions The Warburg impedancefor quiescent solutions can be obtained from Equa-tions (112) and (116), namely Equation (126),

Zw D sp

2.jω/1/2

.126/

where s is defined by Equation (127):

s D RT

n2F2Ap

2

(1

D1/2R NcR.0, t/

C 1

D1/2P NcP.0, t/

).127/

For a reversible reaction, Zw reduces to Equation (128):

Zw D 4RTn2F2A.jωDo/1/2cŁo

cosh2(a

2

).128/

Figure 64 The AC current and AC voltammetric response fora mixture of TAA (0.66 mM) and BQ (0.01 M) for several phaseangles. E D 70 mV, scan rate D 2 mV s�1, y D 3 µm: (a) ACcurrent on a 3.2 mm diameter Pt electrode (phase angle D 0°);(b) optical monitoring at a phase of �20°; (c) at �100°; (d) at�130°..87/

Based on the results presented in the previous section,the Warburg impedance is in phase with the opticalresponse (see Equation 111).

4.7.3.2 Forced Convection Expressions for the War-burg impedance of an RDE can be obtained.88/ by takingthe Laplace transform of the concentration step problem


Figure 65 Plots of Re y and Im y for (a) K D 1.2 and (b) K D 60 as functions of the real axial distance for� D 0 (dashed line) and� D 377 rad s�1 (3600 rpm; solid line)..88/

as specified in section 2.2.2, and regarding the complexparameter s as jω..89/ Plots of the real and imaginary partsof the integral of the concentration profiles as a functionof the dimensionless frequency K are shown in Figure 65.These data can also be represented by plotting the realversus the imaginary part of the function in question andspecifying the values of the frequency directly on thecurve (Figure 66), also known as Cole–Cole or Nyquistdiagrams. It is significant to note that for K > 40, theangle reaches �45°, which implies that at high enoughfrequencies, the response of the electrochemical systemin the presence of forced convection approaches that in aquiescent media.

4.7.4 Determination of Molar Absorptivities ofElectrogenerated Species

Provided that DR D DP, rearrangement of Equation (102)yields Equation (129) for e.k/ in terms of the integral ofthe sinusoidal profile:

e.l/ D Iac

Idc

[2k∫ 1

0Qc.y, t/ dy

]�1

.129/

Setting Iac D IŁ exp[j.KqC f/], where f is the phase,this equation can be rearranged to Equation (130),

Figure 66 Plots of the real and imaginary components of the integral of the dimensionless concentration profile in the Cole–Colerepresentation: ž D exact and D long-time solutions..88/


e.l/ D IŁ

Idc

(2AŁkg

∫ 10 dς

)�1

.130/

where AŁ is the amplitude of the time-varying concentra-tion, and g the factor that converts y into the dimensionlessvariable z. As e.l/ is real, the phase may be expressed asEquation (131):.90/

f D arctan

∫ 1

0Im dς∫ 1

0Re dς

.131/

Plots of∣∣∫1

0 dς∣∣ versus K, and f versus K for an

RDE are shown Figure 67.The most striking verification of the validity of this

theory, is provided by the excellent agreement betweene.l/ obtained for ferricyanide from potential modulationspectroelectrochemical measurements (Figure 68) at anRDE in K4Fe(CN)6/0.5 M K2SO4 aqueous solutions (see

Figure 67 (a) Plot of∣∣∫1

0 dz∣∣ as a function of K, based on

the exact solutions. (b) Plot of the phase f, as a function of thedimensionless frequency K..91/

Figure 68 Comparison between e.l/ versus l data obtainedby conventional transmission spectroscopy (solid line) and thatderived from the magnitude of IŁ/Idc determined from potentialmodulation experiments and the value of

∣∣∫10 dz

∣∣ determinedby numerical means for co D 10 mM (triangles) and co D 3 mM(solid circles). The open squares were obtained in measurementsin which the potential was modulated about 0.0 V..88/

scattered plots), and from conventional transmissionexperiments given by the continuous curve in the samefigure..91/

CONCLUDING REMARKS

The quantitative analysis of UV/VIS spectroelectro-chemical techniques relies on well-known optical andmass transport principles. Although analytic solutions fortransient problems appear to be available only for thesimplest of systems, digital simulations involving an inex-pensive desk computer provide a means of diagnosingmechanisms and extracting kinetic parameters of inter-est from experimental data. Furthermore, the adventof computer-controlled instrumentation including dataacquisition makes it possible to collect large amounts ofinformation so as to achieve reliable statistics. Intrinsictheoretical and practical limitations imposed by the verynature of these measurements, sets limits on the space-,and time-resolution of absorption-based UV/VIS spec-troelectrochemical techniques. Without diminishing itsimportance and future impact in scientific and techno-logical fields, it seems reasonable to conclude that thisspecialized subfield of analytical chemistry has reached asolid level of maturity. On this basis, new developmentsmay not be expected in instrumental principles, but inthe applications area, especially sensor miniaturization.


It may be envisaged that new generations of inexpensive,fully tunable lasers and widespread implementation ofchemometrics, will lead to versatile and expedient meansfor quantitative detection of weak chromophores andthus join the array of existing analytical techniques. Alsoto be expected over the next few years, are applicationsof UV/VIS imaging analysis to the study of current dis-tribution in electrochemical cells, which are expected tohave an impact on the design of electrochemical reactorsfor electrosynthesis. It may be interesting to note thatin contrast to the absorption-based techniques featuredin this article, the analysis of in situ UV/VIS ellipso-metric and electroreflectance measurements, continuesto pose formidable problems in terms of a quantitativetheoretical interpretation. It is hoped that the newlydiscovered links between electrochemistry and surfacescience will prompt scientists in both fields to find novelapproaches for gaining new insights into the fundamen-tal basis of this phenomenon and thus fully exploit itsexquisite surface specificity and sensitivity, which greatlysurpasses our theoretical understanding.

ACKNOWLEDGMENTS

Support for this work was provided by the NationalScience Foundation, and the National Institutes ofHealth. The authors are deeply indebted to Prof. RichardL. McCreery from Ohio State University for his insightfulcomments during the preparation of this manuscript.

ABBREVIATIONS AND ACRONYMS

AC Alternating CurrentAN AcrylonitrileATR Attenuated Total ReflectionBQ BenzoquinoneBQI p-BenzoquinoneimineCCD Charge-coupled DeviceCPZ ChlorpromazineCPZCž Chlorpromazine Cation RadicalDC Direct CurrentDCIP 2,6-DichlorophenolindophenolDOQ Dopamine QuinoneEC Electrochemical–ChemicalEEC Electrochemical–Electrochemical–

ChemicalFeTPPCl Iron Tetraphenylporphyrin ChlorideH2Q HydroquinoneIRE Internal Reflection ElementIRS Internal Reflection SpectroscopyLOPTLC Long Optical Pathlength Thin-layer Cell

LPTLC Long Pathlength Thin Layer CellMB Methylene BlueMPZ MethoxypromazineMVCC Methyl Viologen DicationOD o-DianisidineOTTLE Optically Transparent

Thin-layer ElectrodePAP p-AminophenolPMT Photomultiplier TubePycDcPy 1,2-Bis-(4-pyridine)ethyleneRDE Rotating Disk ElectrodeRRDE Rotating Ring-disk ElectrodeSCE Saturated Calomel ElectrodeTAACž Tri-p-anisylamine Cation RadicalTBAP Tetra-n-butyl Ammonium PerchlorateTEACN Tetraethylammonium CyanideTEAP Tetraethylammonium PerchlorateTPZ Triflupromazine HydrochlorideUV/VIS Ultraviolet/Visible

RELATED ARTICLE

Electroanalytical Methods (Volume 11)Electroanalytical Methods: Introduction

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