Inverse freezing in molecular binary mixtures of alpha-cyclodextrin and 4-methylpyridine

Inverse freezing in molecular binary mixtures of a-cyclodextrin and

4-methylpyridine

Marie Plazanet,*abc Paolo Bartolini,a Claudio Sangregorio,d Andrea Taschin,a

Renato Torreae

and Hand-Peter Trommsdorffbc

Received 13th November 2009, Accepted 17th March 2010

First published as an Advance Article on the web 13th May 2010

DOI: 10.1039/b923682a

Ternary solutions of a-cyclodextrin (aCD) in 4-methylpyridine (4MP)/water mixtures solidify

when heated and melt when cooled, and the crystalline solid phase exhibits a rich phase behavior

as a function of temperature. In this work, we extend these earlier investigations to pure binary

mixtures of aCD in water free 4MP, characterized via temperature and time dependent

measurements of viscosity, X-ray diffraction, and infrared spectroscopy, complemented by

observations of acoustic properties and small angle neutron diffraction. At high concentrations

(4500 g l�1), these solutions enter an amorphous solid phase not only with decreasing but also

with increasing temperature, before crystallizing at higher temperatures. This inverse solidification

is attributed to the growth of hydrogen bonded clusters, leading to a steep increase of the

viscosity with temperature.

1. Introduction

Contrary to everyday experience, reversible solidification

upon heating and melting upon cooling may occur for some

substances. This phenomenon of ‘‘inverse’’ melting or freezing

was already predicted hundred years ago1 and was also

experimentally observed in a number of systems, see for

example ref. 2–4. Liquid–solid transitions with increasing

temperature are usually termed inverse melting when the solid

state is crystalline and inverse freezing for a transition towards

a glassy or gel state. A non exhaustive review of inverse

transitions was recently published by Schupper and Shnerb,5

together with a description of mechanisms leading to these

phenomena. A central issue concerns the source of entropy

upon heating, when at least part of the system enters a more

ordered state. The problem is common to binary mixtures,

undergoing demixing with temperature,6 or to the cold

denaturation of proteins:7 the high temperature state appears

to be more ordered than the low temperature one.

Many organic systems undergoing inverse freezing are

based on polymer mixtures, for example PEO-PPO-PEO3 or

methyl-cellulose.4 In the case of methyl cellulose, the chain

conformation extends upon increasing temperature to form a

network that blocks the polymer mobility and leads to a

dramatic increase of the viscosity. At the same time, this

conformational modification provides a source of the entropy

as more configurations become accessible to the polymer and

also because the water trapped within the chain becomes free

to circulate in the network formed by the aggregated chains.

As a result, a gel is formed.

Other mixtures prone to complex behavior are colloidal

solutions. As a function of concentration and time, these

solutions undergo either a glass transition or crystallization

as well as re-entrant melting8 or enter multiple glassy states.9,10

For example, glass–liquid–glass transitions have been observed

upon increasing the addition of a non adsorbing polymer to a

colloid suspension of nearly hard spheres. In order to induce

the reentrant transition, a difference in size and in short time

mobility of the polymeric components was postulated in

addition to effective depletive attraction at higher polymer

concentrations.11

The terminology employed to describe the dynamical arrest

of a liquid does not always distinguish between a glass transition

and gelation. As addressed by several authors,12–14 a simplified

scenario of the sol–gel transition is characterized by an

aggregation (clusters formation, phase separation. . .), leading

to percolation and eventually the dynamical arrest of the

system. This transition is related to a large increase of the

structure factor, S(Q), at small Q. In contrast, the glass

formation is due to a purely dynamical arrest of a homo-

geneous system at all length scales. However, both transitions

lead to a loss of ergodicity and have numerous other features

in common. In both cases, the entropy lost by the apparent

ordering and/or dynamic arrest of one component is compensated

by an increase of entropy of the other component (solvent).

The phenomenological scenario of inverse freezing described

above requires more work in order to better define common

features of inverse liquid–glass and liquid–gel transitions regarding

both dynamics and thermodynamics. We report here experi-

mental evidence of an inverse freezing transition in a novel binary

mixture composed of relatively simple and non-polymeric

molecules: a-cyclodextrin (aCD) and 4-methylpyridine (4MP).

a European Laboratory for Non-Linear Spectroscopy (LENS),Universita di Firenze, Via N. Carrara 1, I-50019 Sesto Fiorentino,Firenze, Italy. E-mail: [email protected];Fax: +33 (0) 476 63 54 95; Tel: +33 (0) 476 51 43 35

b Institut Laue Langevin, BP 156X, 38042 Grenoble Cx, Francec Laboratoire de Spectrometrie Physique, Universite Joseph Fourier,CNRS (UMR 5588), BP 87, 38402 St Martin d’Heres Cx, France

dDipartimento di Chimica and INSTM, Universita di Firenze,Via Della Lastruccia 3, I-50019 Sesto Fiorentino, Firenze, Italy

eDipartimento di Fisica, Universita di Firenze, Via Sansone 1,I-50019 Sesto Fiorentino, Firenze, Italy

7026 | Phys. Chem. Chem. Phys., 2010, 12, 7026–7031 This journal is �c the Owner Societies 2010

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

For concentrations higher than B500 g l�1 of aCD in 4MP,

the solution becomes an isotropic, transparent solid when

heated to temperatures above B46 1C that returns to the

homogeneous liquid state with unchanged chemical composition

upon cooling. To the best of our knowledge, this is the first

example of such a reversible, inverse liquid–gel transition for

a non-polymeric, molecular system. As explained below in

section 3, the system is metastable with respect to crystal-

lization, which may occur within months at ambient temperature.

Crystallization is also observed to occur within hours above

60 1C.

This binary system has similarities with the solutions of

aCD in 4MP, containing about 2% of water, which have been

studied previously.15–17 For these ternary solutions, the solid

phase, formed upon heating, is inhomogeneous and is a

mixture of crystals of ca. 10 mm size and residual solvent. In

contrast, in the binary solutions studied here, the solid phase is

homogeneous down to at least 100 nm.

In the following, after explaining materials and methods, we

present this system and report in subsequent sections different

characterizations: measurements as a function of temperature

and time of the viscosity, of the structure, and of infrared

spectra. Relevant observations from optical transient grating

and small angle neutron scattering measurements are also

included. Finally, we discuss these results and conclude.

2. Materials and methods

Commercial aCD (Sigma-Aldrich) is a hydrate and contains

six water molecules per aCD. The hydration water was

eliminated by heating the compound under vacuum for about

one hour above 80–90 1C. 4MP (98% Aldrich) was vacuum

distilled and stored over a 3 A molecular sieve to remove

water. Samples are prepared and stored under inert atmosphere

in order to avoid water contamination. Under these conditions,

very high concentration samples, up to 1000 g l�1, could be

prepared. The increase of viscosity with aCD concentration

and the ensuing very long times required to reach homo-

geneous samples become the main limiting factors. Note that

the solubility at ambient temperature of aCD-hydrate in water

free 4MP is limited to about 450 g l�1 and drops to about

350 g l�1 when 2% water is added.16

Except when otherwise specified, all measurements where

made with samples of 600 g l�1 concentration.

The viscosity was measured using a home-built falling ball

viscometer. The measurement tube (1 cm diameter and 10 cm

length) containing a stainless steel ball of 1.58 mm diameter

(weight 16.7 mg) was filled under controlled, water-free

atmosphere with the sample and sealed. The steel ball was

manipulated with magnets and was filmed during its fall. The

speed of the ball is obtained from the movie, and geometric

corrections, taking into account the dimensions of the tube,

are included before extracting the shear viscosity. The

temperature of the tube was regulated to better than �0.2 1C.

The accessible range of viscosities that can be conveniently

measured with this system lies between 10�2 and about

300 Poise and is limited, on one side, by the time it takes

to reach thermal equilibrium and, on the other, by the

requirement that the evolution of the solution should be

negligible during the measurement.

X-ray diffraction measurements were performed using a

perfectly tight cell, built to ensure a homogeneous temperature

of the sample. The sample was placed between thin glass cover

slides (thickness 100 mm) separated by a teflon spacer of 500 mm.

The signal from the empty cell was subtracted. The data were

recorded for a momentum transfer (Q) of 0.13–1.8 A�1, using

the Ka radiation of a rotating copper anode (l = 1.54 A).

Infrared spectra were recorded with a commercial spectro-

meter in the region of the first overtone of the OH stretch

mode using quartz cells of 2 and 10 mm thickness. The

temperature of the cell was controlled to �0.2 1C.

The transient grating measurements of the acoustic properties

as well as the small angle neutron scattering studies on this

system, which have also been made, will be presented in detail

in a separate publication and only some relevant results are

included here.

3. System and phase diagram

aCD, composed of six glucose units, is the smallest member of

the family of cyclodextrins, cyclic glucose oligomers of conical

shape, known to form inclusion compounds with a large

variety of small molecules.18,19 The three OH groups per

glucose unit are capable of forming intra- or inter-molecular

hydrogen bonds. Cyclodextrins easily form supramolecular

assemblies,20,21 for example carbohydrate nanotubular

structures,22 and the formation of isotropic physical gels

has been reported for solutions of rigorously anhydrous

b-cyclodextrine and dry pyridine.23

We recently reported the phase behavior of solutions

composed of aCD, 4MP and water,16 in which the solubility

of aCD decreases with increasing temperature with a sudden

drop around 70 K. The formed solid is a crystalline gel and

undergoes a series of further phase transitions as a function of

temperature. All transitions are endothermic.16,24,25 As all

measurements are strongly dependent on the presence of

water, a rearrangement of hydrogen bonds and the formation

of intermolecular at the expense of intramolecular bonds was

invoked to explain and to model the inverse melting transition.

It therefore seemed important to investigate water-free

solutions of aCD in 4MP. At ambient temperature, these

strictly water free solutions are perfectly transparent and

appear to be homogeneous down to below 5 nm as born out

by small angle neutron scattering.

Below B500 g l�1, the behavior of the dry solution is

reminiscent of solutions containing water: when heated, a

white solid is formed but the fraction of solid phase is much

smaller than in equivalent water-containing solutions.

Solutions with concentrations above ca. 500 g l�1 transform,

when heated, to a perfectly transparent and homogeneous

solid, which returns to the liquid state when cooled to

ambient temperature. This transformation is accompanied

by a significant contraction of the sample and leads to cracks

and voids in the sample. In a 600 g l�1 sample the solidification

takes place around 48 1C in about one hour. Measurements of

the speed of sound during this transformation indicate a

density increase of at least 2%. After several hours, the sample

This journal is �c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 7026–7031 | 7027

becomes slightly translucent. At higher temperatures, the

sample turns turbid in a shorter time (280 min at 60 1C,

45 min at 70 1C). These samples return to the liquid state upon

cooling. At 100 1C, the sample becomes white and X-rays

measurements indicate the formation of crystals. Crystals that

have grown sufficiently by maintaining the sample at 100 1C

do not melt upon cooling.

Cooling of these samples leads to ‘‘normal’’ glass formation

as frequently observed for such molecular systems. At ambient

temperature, solutions can be kept in the liquid state for

several months. However, we observed that some samples

turned solid after long times (months), forming large

(transparent) crystals soaked in a small excess of solvent.

The concentration of aCD in the residual solvent is 120 g l�1.

The crystals show a diffraction pattern that is similar, but not

identical to the one observed for crystals formed at high

temperatures and could not be melted by changing the

temperature by�20 1C. The liquid–solid transitions characterized

in the following take therefore place in a system that is

metastable with respect to crystallization.

4. Viscosity

The measurements were performed at fixed temperatures at

various waiting times, tw: starting at an equilibration temperature

of 40 1C, the final temperature is approached as rapidly as

possible; typically thermalization is reached within 1 min.

Then, the viscosity is measured after variable waiting times,

from a minimum of 1 to a maximum of 120 min. The duration

of viscosity measurements, tm, is always shorter than the

waiting times, tw, for all temperatures/viscosities tm o 0.1 tw.

Between measurements, the sample is cooled to room

temperature for a time laps sufficient to re-establish the

homogeneous liquid state.

The results are shown in Fig. 1. In Fig. 1, left panel, are

shown viscosity data versus temperature taken at three

different waiting times, tw = 1, tw = 8, and tw = 60 min.

For temperatures T o 45 1C, the viscosity shows a typical

Arrhenius dependence as expected for a normal liquid phase,

and does not exhibit any time dependence (even for tens of

hours). In contrast, for T 4 45 1C, the viscosity depends on

the waiting time and a clear departure from Arrhenius behavior

is observed. In the Fig. 1, right panel, the time dependence of

the viscosity is shown for three fixed temperatures. For the

lowest temperature, 45 1C, the viscosity remains nearly stable

at its liquid state value for about 2 h. Afterward a slow

increase is observed. At the other two temperatures, 47 and

50 1C, the viscosity increases strongly after a waiting time,

and both data sets suggest that this increase approaches

asymptotically a power law dependence, the exponent being

the same for both temperatures. In fact, all data can be

represented by the following single master curve:

Z(tw,T) = A(T) F(tw/t) (1)

with F(t) = 1 + tg

This is illustrated in Fig. 2. A(T) is the temperature dependence

of the viscosity at 0 waiting time and the values of A(T)

are obtained by extrapolating the Arrhenius dependence of

the viscosity data in Fig. 1, left panel. The temperature

dependence of the scaling factor, t, is shown as inset of

Fig. 2; t decreases by two orders of magnitude between

45 and 50 1C. At long waiting times, the master function,

F(t), approaches asymptotically a power law, tg, with

g = 3.0 � 0.05. The data show that in this system a physical

process appears on heating that gradually leads to a complete

solidification. In the solid state, the viscosity exceeds 106 poise,

as demonstrated by the arrest of the steel ball to within an

accuracy of 0.1 mm over more than 10 h, but quantitative

measurements with our apparatus are no longer possible for

the reasons explained in section 2.

5. Diffraction

The structure of the solid phase was characterized by X-ray

diffraction. The liquid phase was investigated at fixed

temperatures, and the time dependence of the diffractograms

was also investigated for temperatures of 48, 60 and 100 1C, in

order to determine the kinetics of the solid phase formation.

The measuring time for one spectrum was 60 s, a short time

compared to the characteristic timescale of the kinetics around

48 1C. Diffraction patterns in the top panel of Fig. 3 are shown

for the liquid, the amorphous solid, and the crystal phase that

appears at high temperature.

Fig. 1 Viscosity vs. temperature (left panel) and viscosity vs. time

(right panel) of a 600 g l�1 sample. The straight line fit in the left panel

illustrates the Arrhenius behavior of the viscosity at temperatures

below 47 1C. The straight lines in the right panel are power law fits (t3)

to the data.

Fig. 2 Master plot of the viscosity measured at different times and

temperatures. The continuous line is a fit of eqn (4) to the data. The

inset shows the variation of the scaling factor, t, with temperature.


The bottom graph of Fig. 3 exhibits diffraction patterns for

temperatures r48 1C. The time dependence at 48 1C was

measured over 120 min and no evolution was observed. The

diffractograms are typical of a liquid or amorphous solid state.

The broad peaks at Q higher than ca. 0.6 A�1 are related to the

structure of the two molecules, the one at 1.1 A�1 increases in

intensity with aCD concentration. The peak appearing at the

smallest angles covers the edge of the detector and its position

cannot be measured with precision. Clearly, a significant

increase of the structure factor, S(Q), is observed for

wave-vectors Q o 0.5 A�1. The intensity in this region is

temperature dependent for Q o 0.3 A�1, but time independent.

This feature, at the smallest wave-vector range, suggests the

formation of clusters of about 3 nm size already in the liquid

phase of the binary mixture. This aggregation is temperature

activated, an observation that parallels spectroscopic observations

that will be presented in the next section.

At 48 1C, S(Q) was monitored during 2 h, without

presenting any variation in the spectra. During this time, the

data presented in the previous section showed that the

viscosity increases by two orders of magnitude. During these

measurements, the sample stayed perfectly transparent as

monitored by the transmission of a He–Ne laser beam. Small

angle neutron scattering around these temperatures, exploring

smaller Q-vectors, complete this study and indicate that during

the solidification structures at the scale of 10 nm appear. We

therefore conclude that the reversible formation of the

amorphous solid upon heating is not accompanied by any

significant segregation of the two molecular components and

the formation of larger structural inhomogeneities.

At 60 1C, the scattering at small angles increases drastically,

and visible inspection shows the sample to become opalescent.

This confirms the formation of inhomogeneous structures

extending at this temperature over length scales reaching

B100 nm. On the time scale of our experimental resolution,

this Q-dependence of the structure factor is formed

instantaneously. No further evolution over 20 min, a long

time compared to the timescale of the increase of the viscosity

at 60 1C, was observed. After a sufficient long time (several

hours) the sample becomes white, indicating that it would

eventually crystallize. When increasing the temperature

further, the spectrum changes continuously from the one at

60 1C to the one of the crystalline phase, recorded here at

100 1C. This transition is not instantaneous and the nucleation

process is relatively slow. The scattering at small angles has

dropped, confirming the conversion of the scattering objects

into larger crystals. The sample has turned completely white in

a second transition from the amorphous phase to a crystal

phase on heating. Both transitions are not sharp and show

some metastability phenomena.

We conclude that as a first step toward crystallization,

spatial density fluctuations with increasing length scales

develop due to partial segregation of the two molecular

components. These fluctuations reach sizes that scatter visible

light and the more dense regions finally transform into

crystals.

6. Infra red absorption spectra

In order to get an insight into the physical origin leading to the

dynamical arrest observed on heating, infra-red absorption

spectra of 600 g l�1 solutions of aCD in 4MP were recorded as

a function of temperature and waiting time. In particular, the

4000–8000 cm�1 frequency region was explored, in which the

first overtone of the OH stretch bands is located. The sharp

spectral features around E/2 = 3000 cm�1 correspond to the

first overtone of CH stretch vibrations and are, apart from

small shifts and broadenings, little affected by temperature.

The spectra (Fig. 4) show a transfer of intensity as a function

of temperature, from lower energy (E/2B 2400–2900 cm�1) to

higher energy bands (E/2 B 3300–3600 cm�1). The variations

indicate a rearrangement of hydrogen bonds, in particular the

disruption of stronger, intra-molecular hydrogen bonds of

aCD and the formation of weaker, inter-molecular hydrogen

bonds as well as near free OH groups. Molecular dynamics

simulations on isolated aCD as well as on aCD/4MP solutions

had been performed and indicated that these rearrangements

are accessible in the range of the solidification temperatures.16

In other words, the interaction potential aCD–aCD or

aCD-4MP is modified as a function of temperature, increasing

short-range intermolecular attraction upon heating. No

changes of the absorption peaks as function of the waiting

times at constant temperature of 48 1C are observed, while the

background transmission decreases due to the elastic scattering

of light. During the same time lag, the viscosity increases by

2 orders of magnitude. The spectral changes with temperature

and their independence on time during solidification parallel

the changes observed in diffraction, the relative changes being

the same for both measurements within experimental error.

7. Discussion

The liquid–gel phase transition described in this study is

inverse and reversible, and presents an exceptional case of

such a phenomenon in a molecular non-polymeric material.

The contraction of the sample during solidification with

increasing temperature is quite remarkable and is evocative

Fig. 3 Diffraction patterns of a 600 g l�1 sample. Bottom: temperatures

from 32 to 48 1C. The diffractogram at 48 1C remained unchanged for

120 min. Top: 48, 60 and 100 1C. The diffractogram at 60 1C remained

unchanged for 20 min.


of the unusual phenomenon of expansion of water upon

freezing.

Based on the experimental data, we propose the following

scenario, which is analogous to the one invoked to explain the

crystallization with increasing temperature of the previously

studied 4MP/aCD/H2O system. At low temperatures, the vast

majority of OH protons of aCD are engaged in intramolecular

hydrogen bonds. As temperature increases, these bonds are

broken and intermolecular hydrogen bonds are formed,

generating clusters of aCD molecules. This rearrangement of

hydrogen bonds is clearly illustrated by the changes of the IR

spectra and the parallel formation of clusters is indicated

by the diffraction data. Given that the solution remains

homogeneous in composition down to nm length scales at

the beginning of this transformation, implies that 4MP is not

expelled when these clusters are formed. Assuming homo-

geneous nucleation of clusters with a constant rate, n, as well

as an isotropic three dimensional growth with a constant rate,

g, lead to the following increase with time of the volume

fraction, j, occupied by clusters (Johnson–Mehl–Avrami–

Kolmogorov equation):

j ¼ 1� expð� p3g3nt4Þ ð2Þ

Assuming that in this solution with unchanged chemical

composition the increase of viscosity follows the increase of j:

Z = Z1 + (Z2 � Z1)j (3)

where Z1 and Z2 are the viscosities of the two phases, predicts a

t4 growth of the viscosity in clear contradiction with the

observed t3 behavior.

The crystal structures of the multiple phases of the

4MP/aCD/H2O system show the existence of two dimensional

sheets of aCD separated by variable amounts of solvents, and

suggest a two dimensional growth of clusters which would

indeed predict a t3 increase of viscosity in agreement with the

observed behavior:

Z ¼ Z1 þ ðZ2 � Z1Þ 1� expð� p3dg2nt3Þ

� �ð4Þ

where d is the thickness of the two dimensional structures.

Over the range of the measurements, and since Z2 c Z1, fits byeither eqn (1) or eqn (4) of the data are indistinguishable. A

predominantly two dimensional geometry of the clusters also

accommodates the fact that the 4MP molecules are not

expelled when the clusters are formed so that the solution

remains largely homogeneous. Note that a two dimensional

growth is already suggested by the molecular structure of aCDbut does not imply that the clusters are planar.

The time scaling factor, t, is proportional to (g2n)�1/3. The

growth rate, g, is expected to increase with temperature as the

number of available intermolecular hydrogen bonds increases,

as shown by the IR measurements presented in section 6. The

fit of the data by eqn (4) requires a lower limit of 200 for the

ratio Z2/Z1 so that the assumption underlying eqn (3) needs

only to be valid in the range where the volume fraction

occupied by clusters is small (o10�1). In the temperature

range of 44 to 50 1C, the value of t lies between 6 and

400 min and the crystallographic data suggest for d a value

of about 1.6 nm.16 Together with the lower limit of the ratio

Z2/Z1 given above, these values imply that g2n r 2 � 10�16 to

6 � 10�11 s�3 nm�1 in this temperature range. These are very

small values: for example for a growth rate of only 1 nm s�1

the rate of nucleation in 1 mm3 would be smaller than 2 � 10�7

to 6 � 10�2 s�1. In the sample occur fluctuations of nucleation

and dissolution of small nuclei, so that the rate, n, of

nucleation of stable nuclei (nuclei that will eventually grow)

is very small. It is reasonable to assume that the growth rate

does not vary too much with temperature, but even small

variations of g will lead to large changes of the effective

nucleation rate, n. The rapid change of t reflects therefore

mainly the change of n. This again implies that for low

temperatures, when n is very small (and structural measurements

are possible), the distribution of cluster sizes is very large:

r(V) B 1/V, where V is the volume occupied by a cluster.

Detailed small angle scattering measurements at early stages of

the viscosity increase are required to substantiate this conclusion.

At later times and higher temperatures, the solution

becomes inhomogeneous on the scale of 100 nm with regions

enriched and impoverished in aCD, leading to the observed

increase in opalescence and of light scattering. Finally, crystal-

lization begins in the denser regions. Clearly, however,

more extended and detailed measurements are required to

corroborate the scenario described here. In particular it will

be interesting to monitor the phase behavior of the crystals

and to determine how crystals formed at high and at ambient

temperature are related.

8. Conclusions

The inverse liquid–gel transition in aCD/4MP solutions,

described here, is remarkable in many respects, being the

first example of a reversible transition of this type in a

system composed of relatively simple molecules. In spite

of a high mobility, which must be retained by the 4MP

solvent molecules, the dynamics becomes extremely slow

close to the transition temperature, as shown by the time

evolution of the viscosity at constant temperature. This slow

molecular reorganization contrasts with the equilibration of

Fig. 4 Infra Red spectra as a function of temperature. Top: spectra at

21 and 48 1C. Bottom: difference spectra with respect to the spectrum

at 21 1C for temperatures of 26, 31, 38, 43, and 48 1C.


the hydrogen bonding (intra- vs. inter-molecular), which is

immediate on the timescale of the measurements.

The exploratory measurements made here should be

complemented by more detailed studies to fully understand

more aspects of this unusual phenomenon. Beyond the struc-

tural measurements already mentioned, it will be important to

study the mobility of each of the two molecules by different

complementary methods (NMR, quasi elastic neutron scattering,

optical Kerr effect,. . .). It will also be interesting to vary the

sample composition: aCD concentration, hydrogen/deuterium

replacement, addition of (non-)hydrogen bonding co-solvents.

Given the metastability of the sample with respect to crystal-

lization, all these changes are expected to have profound

influence on the phase behavior of the samples. Additional

and more extended molecular dynamics simulations would

also be of interest, but may be beyond present computational

possibilities, given the complexity of the system and of its

behavior.

Acknowledgements

We are grateful to Efim Kats, Mark Johnson, Roberto Righini

and Paolo Foggi for many interesting discussions and valuable

suggestions. We thank the Interdisciplinary Center for Struc-

tural Crystallography (Crist) of the University of Florence for

the use of the X-ray diffraction facility. This work was

supported by the EC grant N.RII3-CT-2003-506350, by

CRS-INFM-Soft Matter (CNR) and MIUR- COFIN-2005

grant N. 2005023141-003.

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Inverse freezing in molecular binary mixtures of alpha-cyclodextrin and 4-methylpyridine

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