Dynamics of Sorbitol at Elevated Pressure

Viscosity of Ionic Liquids: Theories and Models

Ionic liquids (ILs) offer a wide range of promising applications due to their unique and designable properties compared to conventional solvents. Further development and application of ILs require correlating/predicting their pressure-viscosity-temperature behavior. In this review, we firstly introduce methods for calculation of thermodynamic inputs of viscosity models. Next, we introduce theories, theoretical and semi-empirical models coupling various theories with EoSs or activity coefficient models, and empirical and phenomenological models for viscosity of pure ILs and IL-related mixtures. Our modelling description is followed immediately by model application and performance. Then, we propose simple predictive equations for viscosity of IL-related mixtures and systematically compare performances of the above-mentioned theories and models. In concluding remarks, we recommend robust predictive models for viscosity at atmospheric pressure as well as proper and consistent theories and models for P-η-T behavior. The work that still remains to be done to obtain the desired theories and models for viscosity of ILs and IL-related mixtures is also presented. The present review is structured from pure ILs to IL-related mixtures and aims to summarize and quantitatively discuss the recent advances in theoretical and empirical modelling of viscosity of ILs and IL-related mixtures.

Glassy dynamics in polyalcohols: intermolecular simplicity vs. intramolecular complexity

Using depolarized light scattering, we have recently shown that structural relaxation in a broad range of supercooled liquids follows, to good approximation, a generic line shape with high-frequency power law ω^-1/2. We now continue this study by investigating a systematic series of polyalcohols (PAs), frequently used as model-systems in glass-science, i.a., because the width of their respective dielectric loss spectra varies strongly along the series. Our results reveal that the microscopic origin of the observed relaxation behavior varies significantly between different PAs: while short-chained PAs like glycerol rotate as more or less rigid entities and their light scattering spectra follow the generic shape, long-chained PAs like sorbitol display pronounced intramolecular dynamic contributions on the time scale of structural relaxation, leading to systematic deviations from the generic shape. Based on these findings we discuss an important limitation for observing the generic shape in a supercooled liquid: the dynamics that is probed needs to reflect the intermolecular dynamic heterogeneity, and must not be superimposed by effects of intramolecular dynamic heterogeneity.

Glassy dynamics predicted by mutual role of free and activation volumes

Broadband Dielectric Spectroscopy (BDS) at elevated pressures and Positron Annihilation Lifetime Spectroscopy (PALS) are employed to elucidate the importance of the ratio of activation and free volumes during vitrification. We show that this ratio has a linear correlation with the structural relaxation of glass forming liquids in a wide temperature range hence engendering it as a vital input in the description of the dynamic glass transition.

The effect of hydrogen bonding propensity and enantiomeric composition on the dynamics of supercooled ketoprofen - dielectric, rheological and NMR studies

The aim of this work is to analyze in detail the effect of small hydrogen bonding (HB) structures and enantiomeric composition on the dynamics of glass-forming liquid ketoprofen. For that purpose dielectric relaxation, rheological and NMR studies were performed. Investigated samples are racemic ketoprofen, a single enantiomer of ketoprofen and a racemic ketoprofen methyl ester with no tendency to form HB dimers. The combination of complementary experimental techniques enables us to show that macroscopic viscosity η and α-relaxation time τα have nearly the same temperature dependencies, whereas the relation between the viscosity (or molecular reorientation) and the translational self-diffusion coefficient violates Stokes-Einstein law already at high temperature. Additionally, based on dielectric relaxation studies performed on increased pressure we were able to identify similarities and key differences in the supercooled liquid dynamics of investigated materials affected by their tendency to form intermolecular hydrogen bonds. This includes the effect of pressure on the glass transition temperature Tg, changes in the fragility parameter m and activation volume ΔV, the role of thermal energy and density fluctuations in governing the viscous liquid dynamics (Ev/Ep ratio). Finally, we have also demonstrated that the dynamic behaviour of a single enantiomer and the racemic mixture of the same compound are very much alike. Nevertheless, some slight differences were observed, particularly in the τα(T) dependencies measured in the vicinity of glass transition both at ambient and elevated pressure.

New insight into relaxation dynamics of an epoxy/hydroxy functionalized polybutadiene from dielectric and mechanical spectroscopy studies

Dielectric and mechanical spectroscopy methods have been employed to describe the temperature dependencies of the segmental and macromolecular relaxation rates in epoxy/hydroxy functionalized polybutadiene. Dielectric studies on the dynamics of segments of the polymer as well as the mobility of small ions trapped in the system have been carried out both as a function of temperature and pressure under isobaric and isothermal conditions, respectively.

Temperature and pressure dependence of secondary process in an epoxy system

Dielectric spectroscopy as a function of temperature and pressure was used to study the secondary relaxation in poly [(phenyl glycidyl ether)-co-formaldehyde] at hydrostatic pressure up to 600 MPa and at different temperatures between 315 and 243 K. From the analysis of the isothermal measurements, we observe that the activation volume of the secondary relaxation has nonmonotonic temperature dependence with a maximum at the temperature of the glass transition at ambient pressure. An interpretation in terms of mean hole volume dispersion is proposed based on literature data. Moreover, from isobaric data, we studied the effect of pressure on activation entropy and enthalpy of the secondary relaxation evidencing its local nature but also the presence of a certain complexity of the motion, which supports the idea that this process reflects the motion of a large part of the molecule.

Idealized glass transitions under pressure: dynamics versus thermodynamics

The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic behavior leaves the dynamics unchanged, with important consequences for high-pressure experiments on glassy liquids. Numerical results are obtained within mode-coupling theory (MCT), but the qualitative features are argued to hold more generally. A simple square-well model can be used to explain generic features found in experiment.

Additive property of secondary relaxation processes in di-n-octyl and di-isooctyl phthalates: Signature of non-Johari-Goldstein relaxation

Broadband dielectric spectroscopy was used to study relaxation dynamics of supercooled di-n-octyl phthalate, di-isooctyl phthalate, and their mixtures. Additionally, low temperature measurements were performed to investigate the nature of the secondary relaxation processes in both glass formers. The authors found that the secondary relaxation observed in the mixture is the additive sum of the secondary relaxations of the two components. This experimental evidence indicates that these secondary relaxation processes are intramolecular in origin, and they are non-Johari-Goldstein secondary relaxations.

Changes of relaxation dynamics of a hydrogen-bonded glass former after removal of the hydrogen bonds

Dielectric relaxation spectra of two closely related glass formers, dipropylene glycol [H-(C3H6O)2-OH] and dipropylene glycol dimethyl ether [CH3-O-(C3H6O)2-CH3], were measured at ambient and elevated pressures in the supercooled and the glassy states are presented. Hydrogen bonds formed in dipropylene glycol are removed when its ends are replaced by two methyl groups to become dipropylene glycol dimethyl ether. In the process, the primary relaxation, the excess wing, and the resolved secondary relaxation of dipropylene glycol are all modified when the structure is transformed to become dipropylene glycol dimethyl ether. The modifications include the pressure and temperature dependences of these relaxation processes and their interrelations. Thus, by comparing the dielectric spectra of these two closely related glass formers at ambient and elevated pressures, the differences in the relaxation dynamics and properties in the presence and absence of hydrogen bonding are identified.

Thermodynamic interpretation of the scaling of the dynamics of supercooled liquids

The recently discovered scaling law for the relaxation times, tau(T,upsilon) = I(Tupsilon(gamma)), where T is temperature and upsilon the specific volume, is derived by a revision of the entropy model of the glass transition dynamics originally proposed by Avramov [J. Non-Cryst. Solids 262, 258 (2000)]. In this modification the entropy is calculated by an alternative route. The resulting expression for the variation of the relaxation time with T and upsilon is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover. From this analysis, which is valid for any model in which the relaxation time is a function of the entropy, we find that the scaling exponent gamma can be identified with the Gruneisen constant.

Positronium annihilation lifetimes and dielectric spectroscopy studies on diethyl phthalate: Phenomenological correlations and microscopic analyses in terms of the extended free volume model by Cohen-Grest

A combined positronium annihilation lifetime spectroscopy (PALS) and dielectric spectroscopy (DS) study on a typical van der Waals glass-former diethyl phthalate (DEP) was performed and the results were compared. From phenomenological point of view, the mutual relationships between the characteristic PALS temperatures, the glass temperature TgPALS, and the crossover temperatures Tb1L and Tb2L on the ortho-positronium (o-Ps) lifetime versus the temperature plot, have been discussed with respect to the characteristic DS temperatures, the glass temperature TgDS and the dynamic crossover temperature TBST, concerning the crossover behavior of primary alpha-relaxation times. Next, simultaneous application of the extended free volume (EFV) model by Cohen-Grest on the temperature dependence of both the mean free volume hole size data as extracted from PALS and the dielectric alpha-relaxation time revealed a good agreement between the experimental Tb1L and the characteristic EFV temperatures T0DS and T0PALS at which a free volume percolation should occur. These results indicate the important role of free volume in control of the primary (alpha) dynamics of supercooled DEP.

Why liquids are fragile

The fragilities (T(g)-normalized temperature dependence of alpha-relaxation times) of 33 glass-forming liquids and polymers are compared for isobaric, mP, and isochoric, mV, conditions. We find that the two quantities are linearly correlated: mP = (37+/-3) + (0.84+/-0.05)mV. This result has obvious and important consequences, since the ratio mV/mP is a measure of the relative degree to which temperature and density control the dynamics. Moreover, we show that the fragility itself is a consequence of the relative interplay of temperature and density effects near T(g). Specifically, strong behavior reflects a substantial contribution from density (jammed dynamics), while the relaxation of fragile liquids is more thermally activated. Drawing on the scaling law log(tau) = I(T upsilon(gamma)), a physical interpretation of this result in terms of the intermolecular potential is offered.

Two secondary modes in decahydroisoquinoline: Which one is the true Johari Goldstein process?

Broadband dielectric measurements were carried out at isobaric and isothermal conditions up to 1.75 GPa for reconsidering the relaxation dynamics of decahydroisoquinoline, previously investigated by Richert et al. [R. Richert, K. Duvvuri, and L.-T. Duong, J. Chem. Phys. 118, 1828 (2003)] at atmospheric pressure. The relaxation time of the intense secondary relaxation tau(beta) seems to be insensitive to applied pressure, contrary to the alpha-relaxation times tau(alpha). Moreover, the separation of the alpha- and beta-relaxation times lacks correlation between shapes of the alpha-process and beta-relaxation times, predicted by the coupling model [see for example, K. L. Ngai, J. Phys.: Condens. Matter 15, S1107 (2003)], suggesting that the beta process is not a true Johari-Goldstein (JG) relaxation. From the other side, by performing measurements under favorable conditions, we are able to reveal a new secondary relaxation process, otherwise suppressed by the intense beta process, and to determine the temperature dependence of its relaxation times, which is in agreement with that of the JG relaxation.

Relation between the α-Relaxation and Johari−Goldstein β-Relaxation of a Component in Binary Miscible Mixtures of Glass-Formers

The coupling model was applied to describe the alpha-relaxation dynamics of each component in perfectly miscible mixtures A(1-x)B(x) of two different glass-formers A and B. An important element of the model is the change of the coupling parameter of each component with the composition, x, of the mixture. However, this change cannot be determined directly from the frequency dispersion of the alpha-relaxation of each component because of the broadening caused by concentration fluctuations in the mixture, except in the limits of low concentrations of either component, x --> 0 and x --> 1. Fortunately, the coupling model has another prediction. The coupling parameter of a component, say A, in the mixture determines tau(alpha)/tau(JG), the ratio of the alpha-relaxation time, tau(alpha), to the Johari-Goldstein (JG) secondary relaxation time, tau(JG), of the same component A. This prediction enables us to obtain the coupling parameter, n(A), of component A from the isothermal frequency spectrum of the mixture that shows both the alpha-relaxation and the JG beta-relaxation of component A. We put this extra prediction into practice by calculating n(A) of 2-picoline in binary mixtures with either tri-styrene or o-terphenyl from recently published broadband dielectric relaxation data of the alpha-relaxation and the JG beta-relaxation of 2-picoline. The results of n(A) obtained from the experimental data show its change with composition, x, follows the same pattern as assumed in previous works that address only the alpha-relaxation dynamics of a component in binary mixtures based on the coupling model. There is an alternative view of the thrust of the present work. If the change of n(A) with composition, x, in considering the alpha-relaxation of component A is justified by other means, the theoretical part of the present work gives a prediction of how the ratio tau(alpha)/tau(JG) of component A changes with composition, x. The data of tau(alpha) and tau(JG) of 2-picoline mixed with tri-styrene or o-terphenyl provide experimental support for the prediction.

Primary and secondary relaxations in bis-5-hydroxypentylphthalate

Broadband dielectric spectroscopy was used to study the relaxation dynamics in bis-5-hydroxypentylphthalate (BHPP) under both isobaric and isothermal conditions. The relaxation dynamics exhibit complex behavior, arising from hydrogen bonding in the BHPP. At ambient pressure above the glass transition temperature T(g), the dielectric spectrum shows a broad structural relaxation peak with a prominent excess wing toward higher frequencies. As temperature is decreased below T(g), the excess wing transforms into two distinct peaks, both having Arrhenius behavior with activation energies equal to 58.8 and 32.6 kJmol for slower (beta) and faster (gamma) processes, respectively. Furthermore, the relaxation times for the beta process increase with increasing pressure, whereas the faster gamma relaxation is practically insensitive to pressure changes. Analysis of the properties of these secondary relaxations suggests that the beta peak can be identified as an intermolecular Johari-Goldstein (JG) process. However, its separation in frequency from the alpha relaxation, and both its activation energy and activation volume, differ substantially from values calculated from the breadth of the structural relaxation peak. Thus, the dynamics of BHPP appear to be an exception to the usual correlation between the respective properties of the structural and the JG secondary relaxations.

Sub-Tg relaxations due to dipolar solutes in nonpolar glass-forming solvents

It is well known that rigid dipolar solutes (in smaller quantity) dispersed in a nonpolar glassy matrix exhibit a sub-T(g) (or beta(s)) relaxation due to the solute often designated as Johari-Goldstein (JG) relaxation, which is intermolecular in nature. In this article, we report the results of our study of such a sub-T(g) process in a wide variety of dipolar solutes in different glassy systems using dielectric spectroscopy over a frequency range of 20-10(6) Hz down to a temperature of 77 K. The T(g) of these solutions are determined using differential scanning calorimetry. The solvents used in this study are o-terphenyl (OTP), isopropylbenzene (IPB), and methylcyclohexane. In the case of rigid molecular solutes, like mono-halogen benzenes, the activation energy (DeltaE(beta)) of the beta(s) process is found to increase with decreasing T(g) of the solvent, with a corresponding decrease in the magnitude of the beta(s) process. In the case of more symmetrical molecular solute, for example, tert-butylchloride, the change in DeltaE(beta) is not very appreciable. These results emphasize the importance of the size of the cage of the host matrix in the relaxation of the solute molecules. We have also studied the sub-T(g) relaxation(s) due to some flexible molecular solutes, viz., 1butylbromide, 1hexylbromide, 1butylacetate, and benzylacetate. These solutes in IPB matrix exhibit only one relaxation, whereas in OTP matrix they exhibit an additional sub-T(g) process, which may be identified with a JG type of relaxation. These observations lead us to the conclusion that the beta process observed in the glassy states of these pure solutes is predominantly intramolecular in nature.

Thermodynamical scaling of the glass transition dynamics

Classification of glass-forming liquids based on the dramatic change in their properties upon approach to the glassy state is appealing, since this is the most conspicuous and often-studied aspect of the glass transition. Herein, we show that a generalized scaling, log (tau) proportional, variant T-1 V-gamma, where gamma is a material constant, yields superpositioning for ten glass formers, encompassing van der Waals molecules, associated liquids, and polymers. The exponent gamma reflects the degree to which volume governs the temperature and pressure dependence of the relaxation times.

Effect of large hydrostatic pressure on the dielectric loss spectrum of type- a glass formers

New dielectric spectroscopy results are reported for propylene carbonate (PC), glycerol, and threitol, measured at very high (1.8 GPa) pressure. These glass formers all exhibit an excess wing in their dielectric spectrum above T(g). We show that the shape of the alpha peak and excess wing of PC are invariant to pressure and temperature, when compared at a fixed value of the alpha -relaxation time. However, for the hydrogen-bonded liquids, there is a marked breakdown of this temperature-pressure superpositioning, due to a change in chemical structure (i.e., concentration of hydrogen bonds) with change of temperature or pressure. For all these materials, we can conclude that the excess wing is merely a secondary relaxation, masked under ordinary conditions by the intense, overlapping alpha peak.

Effects of temperature and pressure on the stability and mobility of phases in rigid rod poly (p-phenylenes)

The structure and the associated dynamics have been investigated in melts of hairy-rod macromolecules composed from a poly(p-phenylene) backbone with sulfonate ester and dodecyl side chains. For the structure investigation, polarizing optical microscopy, differential scanning calorimetry, pressure-volume-temperature, and wide-angle x-ray scattering have been employed whereas for the dynamics dielectric spectroscopy as a function of temperature and pressure was used. Based on the combined information from structure and dynamics the relaxation mechanisms were identified and the origin of the glass transition has been discussed in terms of insufficient thermal energy rather than insufficient free volume. The relevant phase diagram has been constructed and the stability and mobility of phases is discussed.

Johari–Goldstein relaxation and crystallization of sorbitol to ordered and disordered phases

The equilibrium permittivity epsilon(s) and the dielectric relaxation spectra of supercooled liquid D-sorbitol were measured during its crystallization to orientationally disordered or ordered phases depending on the sample preparation procedure at several fixed temperatures up to a period of 6 days. The epsilon(s) measurements showed that when the sample was contaminated by a minute amount of crystals, it crystallized to an ordered phase. When the liquid was not contaminated, the sample crystallized to an orientationally disordered phase. When supercooled D-sorbitol was kept close to its T(g), its dielectric spectra did not change over a period of 138.5 h. It was found that the Johari-Goldstein (JG) relaxation rate of the orientationally disordered crystalline phase is higher in comparison with that of the supercooled liquid, the spectrum broader, and the relaxation strength lower. Its glasslike transition temperature is higher than T(g) of the liquid. The results on crystallization showed that the structural changes occurring at a temperature where the alpha relaxation emerges from the JG relaxation affects the crystallization kinetics of the liquid.

Dynamics of supercooled and glassy dipropyleneglycol dibenzoate as functions of temperature and aging: Interpretation within the coupling model framework

Dielectric relaxation measurements of a typical small molecular glassformer, dipropyleneglycol dibenzoate show the presence of two secondary relaxations. Their dynamic properties differ in the equilibrium liquid and glassy states, as well as the changes during structural recovery after rapid quenching the liquid to form a glass. These differences enable us to identify the slower secondary relaxation as the genuine Johari-Goldstein (JG) beta-relaxation, acting as the precursor of the primary alpha-relaxation. Agreement between the JG beta-relaxation time and the independent relaxation time of the coupling model leads to predicted quantitative relations between the JG beta-relaxation and the alpha-relaxation that are supported by the experimental data.

Classification of secondary relaxation in glass-formers based on dynamic properties

Dynamic properties, derived from dielectric relaxation spectra of glass-formers at variable temperature and pressure, are used to characterize and classify any resolved or unresolved secondary relaxation based on their different behaviors. The dynamic properties of the secondary relaxation used include: (1) the pressure and temperature dependences; (2) the separation between its relaxation time taubeta and the primary relaxation time taualpha at any chosen taualpha; (3) whether taubeta is approximately equal to the independent (primitive) relaxation time tau0 of the coupling model; (4) whether both taubeta and tau0 have the same pressure and temperature dependences; (5) whether it is responsible for the "excess wing" of the primary relaxation observed in some glass-formers; (6) how the excess wing changes on aging, blending with another miscible glass-former, or increasing the molecular weight of the glass-former; (7) the change of temperature dependence of its dielectric strength Deltaepsilonbeta and taubeta across the glass transition temperature Tg; (8) the changes of Deltaepsilonbeta and taubeta with aging below Tg; (9) whether it arises in a glass-former composed of totally rigid molecules without any internal degree of freedom; (10) whether only a part of the molecule is involved; and (11) whether it tends to merge with the alpha-relaxation at temperatures above Tg. After the secondary relaxations in many glass-formers have been characterized and classified, we identify the class of secondary relaxations that bears a strong connection or correlation to the primary relaxation in all the dynamic properties. Secondary relaxations found in rigid molecular glass-formers belong to this class. The secondary relaxations in this class play the important role as a precursor or local step of the primary relaxation, and we propose that only they should be called the Johari-Goldstein beta-relaxation.

Does the arrhenius temperature dependence of the Johari-Goldstein relaxation persist above T(g)?

Dielectric spectra of the polyalcohols sorbitol and xylitol were measured under isobaric pressures up to 1.8 GPa. At elevated pressure, the separation between the alpha and beta relaxation peaks is larger than at ambient pressure, enabling the beta relaxation times to be unambiguously determined. Taking advantage of this, we show that the Arrhenius temperature dependence of the beta relaxation time does not persist for temperatures above T(g). This result, consistent with inferences drawn from dielectric relaxation measurements at ambient pressure, is obtained directly, without the usual problematic deconvolution the beta and alpha processes.

Changes in dynamic crossover with temperature and pressure in glass-forming diethyl phthalate

Dielectric relaxation measurements have been used to study the crossover in dynamics with temperature and pressure, onset of breakdown of the Debye-Stokes-Einstein law, and the relation between the alpha and the beta relaxations in diethyl phthalate. The measurements made over 10 decades in frequency and a broad range of temperature and pressure enable the dc conductivity and the alpha- and the beta-relaxations to be studied altogether. The isobaric data show that the alpha-relaxation time tau(alpha) has temperature dependence that crosses over from one Vogel-Fulcher-Tammann-Hesse form to another at T(B) approximately 227 K and tau(alpha) approximately 10(-2) s. The dc conductivity sigma exhibits similar crossover at the same T(B). At temperatures above T(B), tau(alpha) and sigma have the same temperature dependence, but below T(B) they become different and the Debye-Stokes-Einstein law breaks down. The breadth of the alpha relaxation is nearly constant for T<T(B), but decreases with increasing temperature for T>T(B). The time dependence of tau(beta) is Arrhenius, which when extrapolated to higher temperatures intersects tau(alpha) at T(beta) nearly coincident with T(B). Isothermal measurements at various applied pressures when compared with isobaric data show that the shape of the alpha-relaxation depends only on tau(alpha), and not on the T and P combinations. At a constant temperature, while tau(alpha) increases rapidly with pressure, the beta-relaxation time tau(beta) is insensitive to applied pressure. This behavior is exactly the same as found in 1,1(')-bis (p-methoxyphenyl) cyclohexane. The findings are discussed in the framework of the coupling model.

Pressure evolution of the excess wing in a type-B glass former

Glass formers are defined as "type B" when they exhibit a distinct Johari-Goldstein (JG) relaxation, but lack an excess loss ("excess wing," EW) in their structural relaxation peak. By studying the dielectric spectra of a well-known type-B glass former under high pressure, we unequivocally show the existence of an EW, simultaneously with the JG relaxation. Moreover, at very high pressures (0.6 GPa), the EW becomes a distinct relaxation peak, although correlated with the structural relaxation. The implication is that the EW, rather than the higher frequency relaxation ascribed to the JG process, is perhaps a universal feature of glass formers, albeit not always discernible at ambient pressure. Our findings may reconcile all opposing points of view present in the literature, as well as indicate that the type-A or type-B classification of glass formers should be modified or even discontinued.

Influence of molecular structure on the dynamics of supercooled van der Waals liquids

Dielectric spectroscopy was carried out on the van der Waals liquid, 1,1(')-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC) in the supercooled state at pressures up to 218 MPa. The excess wing in this type-A glass former exhibits a response to pressure and temperature changes that is identical to that of the primary structural relaxation peak, indicating that the two processes reflect correlated molecular motions. Under no conditions was a distinct secondary peak observed in BMMPC, unlike the structurally very similar BMPC [1,1(')-bis(p-methoxyphenyl)cyclohexane]. However, the pressure dependences of both the glass temperature and fragility for the two materials are very close. The fragility is a decreasing function of pressure, although there is no concomitant narrowing of the relaxation peak. The pressure dependence of the relaxation times could be described as a simple volume-activated process, with the activation volume at the glass transition having the same magnitude as the molar volume.

Cohen-Grest model for the dynamics of supercooled liquids

Recent experiments have established that, at least for van der Waals glass formers, volume fluctuations contribute significantly to the slowing down of the dynamics near T(g). Accordingly, we use the Cohen-Grest (CG) free-volume model to analyze dielectric relaxation data for six van der Waals liquids. The CG equation accurately describes the structural relaxation times over broader ranges of temperature than the more common Vogel-Fulcher relation. Moreover, the CG equation requires two less adjustable parameters when the data span the Stickel temperature T(B) associated with a change in the dynamics. The characteristic temperature T0 of the CG model can be identified with T(B), suggesting that the crossover reflects onset of percolation of the free volume. The CG parameters used to fit the structural relaxation times allow the free volume per liquidlike molecule to be calculated. These results, however, are at odds with free-volume estimates extracted from pressure-volume-temperature data.