Van Der Waals Liquids Research Articles

The influence of shape on the glassy dynamics of hard nonspherical particle fluids. II. Barriers, relaxation, fragility, kinetic vitrification, and universality

We extend and apply the nonlinear Langevin equation theory of activated barrier hopping dynamics in glassy fluids and colloidal suspensions to study broad families of one-, two-, and three-dimensional hard nonspherical particles. Beyond the ideal kinetic arrest volume fraction, entropic barriers emerge with heights (alpha relaxation times, inverse diffusion constants) that increase nonlinearly (nonexponentially) with volume fraction and in a manner that becomes stronger with particle dimensionality. Partial collapse of the volume fraction dependence of barrier heights and reduced relaxation times of different particle shapes within a fixed dimensionality class are achieved based on a difference volume fraction variable that quantifies the distance from the ideal mode coupling theory dynamic crossover. However, the barrier, alpha relaxation time, and self-diffusion constant results of all shapes are remarkably well collapsed onto a single universal master curve based on a theoretically motivated coupling constant which quantifies the renormalized mean square force on a tagged particle. The latter is determined mainly by the square of the intermolecular site-site contact value of the pair correlation function, thereby providing an explicit microscopic connection between local packing, binary collisions, and slow dynamics. A large variation of the dynamic fragility with particle shape is found with compact cluster particles being the most fragile. A kinetic glass transition map is constructed that is relevant to vitrification of laboratory colloidal suspensions. The possible relevance of the hard particle results for understanding the dynamic fragility of thermal van der Waals liquids is discussed.

Pressure-energy correlations in liquids. II. Analysis and consequences

We present a detailed analysis and discuss consequences of the strong correlations of the configurational parts of pressure and energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the previous paper [N. P. Bailey et al., J. Chem. Phys. 129, 184507 (2008)]. The analysis concentrates specifically on the single-component Lennard-Jones system. We demonstrate that the potential may be replaced, at fixed volume, by an effective power law but not simply because only short-distance encounters dominate the fluctuations. Indeed, contributions to the fluctuations are associated with the whole first peak of the radial distribution function, as we demonstrate by an eigenvector analysis of the spatially resolved covariance matrix. The reason the effective power law works so well depends crucially on going beyond single-pair effects and on the constraint of fixed volume. In particular, a better approximation to the potential includes a linear term, which contributes to the mean values of potential energy and virial, but little to their fluctuations, for density fluctuations which conserve volume. We also study in detail the zero temperature limit of the (classical) crystalline phase, where the correlation coefficient becomes very close, but not equal, to unity, in more than one dimension; in one dimension the limiting value is exactly unity. In the second half of the paper we consider four consequences of strong pressure-energy correlations: (1) analyzing experimental data for supercritical argon we find 96% correlation; (2) we discuss the particular significance acquired by the correlations for viscous van der Waals liquids approaching the glass transition: For strongly correlating viscous liquids knowledge of just one of the eight frequency-dependent thermoviscoelastic response functions basically implies knowledge of them all; (3) we reinterpret aging simulations of ortho-terphenyl carried out by Mossa et al. [Eur. Phys. J. B 30, 351 (2002)], showing their conclusions follow from the strongly correlating property; and (4) we briefly discuss the presence of the correlations (after appropriate time averaging) in model biomembranes, showing that significant correlations may be present even in quite complex systems.

The Protein “Glass” Transition and the Role of the Solvent

Hydrated proteins undergo a change in their dynamical properties in the neighborhood of a temperature. The change of dynamics has been likened to glass transition of glass-forming substances because similar properties were found. However, a complete understanding of the conformation fluctuations of hydrated proteins and their relation to the dynamics of the solvent is still not available, possibly due to the protein molecules being more complex than ordinary glass-formers. For this reason, we turn our attention to the experimental findings of the dynamics of mixtures of water with simpler glass-formers (small molecules and polymers). Two major relaxation processes have been observed in these aqueous mixtures. One is the structural alpha-relaxation of the hydrophilic glass-former hydrogen bonded to the water, which is responsible for glass transition. The other one is the local secondary beta-relaxation of water in the mixture. Remarkably, these two relaxation processes in aqueous mixtures have analogues in hydrated proteins with the same properties. The conformation fluctuations of the protein and the relaxation of the solvent in hydrated proteins behave like the alpha-relaxation of the hydrophilic glass-former hydrogen bonded to the water and the beta-relaxation of water in other aqueous mixtures, respectively. At low temperatures, the Arrhenius activation energy of the relaxation time of the solvent in a hydrated protein is almost the same as that of the beta-relaxation of water in the glassy states of aqueous mixtures. The Arrhenius T-dependence of the solvent relaxation times no longer holds at temperatures that exceed the "glass" transition temperature of the hydrated protein, defined as the temperature at which the conformation relaxation time is very long. This behavior of the solvent in hydrated proteins is similar to that found in the beta-relaxation of water in aqueous mixtures when crossing the glass transition temperature of the mixture (Capaccioli, S.; Ngai, K. L.; Shinyashiki, N. J. Phys. Chem. B 2007, 111, 8197). Furthermore, the same dynamics were found in mixtures of two van der Waals glass-formers, which are even simpler systems than aqueous mixtures because of the absence of hydrogen bonding. The experimental data of these ideal mixtures of van der Waals glass-formers have been given a satisfactory theoretical explanation. Since the properties of hydrated proteins, aqueous mixtures, and the mixtures of van der Waals liquids are similar, we transfer the theoretical understanding gained in the study of the last system sequentially to the two other increasingly more complex systems.

Intermolecular Forces and the Glass Transition

Random first-order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first-order transition theory, is used to treat individual glassy configurations, whereas the liquid phase is treated using common liquid-state approximations. Free energies are calculated using liquid-state perturbation theory. The transition temperature, T*A, the temperature where the onset of activated behavior is predicted by mean field theory; the lower crossover temperature, T*C, where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature); and T*K, the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T*g, the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for DeltaCV and DeltaCp that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the alpha-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.

The Challenging Problem of Glass Transition

The glass transition phenomena are observed in many different classes of materials and have been studied in various disciplines. It is a long-standing problem due to the increasing number of important and general experimental facts that challenge conventional theories to explain. A collection of such experimental facts on the structural relaxation is given here, together with the observation that they are either governed by or correlated with the time/frequency dispersion of the structural relaxation. There is a class of secondary relaxations (named after Johari-Goldstein (JG)) that are well-connected to the structural relaxation in many ways. Thus, a fully successful theory of glass transition must take into consideration the roles played by the dispersion of the structural relaxation and the JG secondary relaxation. The results from our study of mixtures of van der Waals liquids are presented to illustrate these points, and a satisfactory explanation of the data is given. The understanding of the component dynamics gained from the study of these ideal systems is used to elucidate and interpret the experimental data of aqueous mixtures and hydrated proteins, which are more complicated systems. This exercise illustrates the benefit of broadening the study of one class of glass-forming materials to another class normally investigated by workers in another discipline.

Heterogeneous dynamics, ageing, and rejuvenating in van der Waals liquids

It has been shown over the past ten years that the dynamics close to the glass transition is strongly heterogeneous: fast domains coexist with domains three or four decades slower, the size of these regions being about 3 nm at T(g). The authors extend here a model that has been proposed recently for the glass transition in van der Waals liquids. The authors describe in more details the mechanisms of the alpha relaxation in such liquids. It allows then to interpret physical ageing in van der Waals liquids as the evolution of the density fluctuation distribution towards the equilibrium one. The authors derive the expression of macroscopic quantities (volume, compliance, etc.). Numerical results are compared with experimental data (shape, times to reach equilibrium) for simple thermal histories (quenches, annealings). The authors explain the existence of a "Kovacs memory effect" and the temporal asymmetry between down jump and up jump temperatures experiments, even for systems for which there is no energy barriers. Their model allows also for calculating the evolution of small probe diffusion coefficients during ageing.

Correlations between isobaric and isochoric fragilities and thermodynamical scaling exponent for glass-forming liquids

Two correlations concerning the isobaric and isochoric fragilities, m(P) and m(V), as well as the scaling exponent gamma reported by Casalini and Roland [Phys. Rev. E 72, 031503 (2005)] have been examined for several van der Waals and hydrogen-bonded glass formers. It has been pointed out that the correlations lead to some serious inconsistency with the exponent gamma, which is expected to be a constant dependent only on material, but varies also on pressure if experimentally found pressure dependences of m(P) are taken into account. This problem could be solved in the case of van der Waals liquids, but then at least one of the correlations becomes dependent on thermodynamic conditions, and consequently, loses its universality. However, some H-bonded systems, due to properties of hydrogen bonding, have been well argued not to be included to determine the correlations independently of thermodynamic conditions. Furthermore, it has been noticed that another correlation concerning the fragility, between m(P) and the structural relaxation peak breadth, yields discrepancies in comparison with results of experiments under elevated pressure.

Thermodynamic scaling of the viscosity of van der Waals, H-bonded, and ionic liquids

Viscosities eta and their temperature T and volume V dependences are reported for seven molecular liquids and polymers. In combination with literature viscosity data for five other liquids, we show that the superpositioning of relaxation times for various glass-forming materials when expressed as a function of TV(gamma), where the exponent gamma is a material constant, can be extended to the viscosity. The latter is usually measured to higher temperatures than the corresponding relaxation times, demonstrating the validity of the thermodynamic scaling throughout the supercooled and higher T regimes. The value of gamma for a given liquid principally reflects the magnitude of the intermolecular forces (e.g., steepness of the repulsive potential); thus, we find decreasing gamma in going from van der Waals fluids to ionic liquids. For some strongly H-bonded materials, such as low molecular weight polypropylene glycol and water, the superpositioning fails, due to the nontrivial change of chemical structure (degree of H bonding) with thermodynamic conditions.

Dynamics in Supercooled Ionic Organic Liquids and Mode Coupling Theory Analysis

Optically heterodyne-detected optical Kerr effect experiments are applied to study the orientational dynamics of the supercooled ionic organic liquids N-propyl-3-methylpyridinium bis(trifluoromethylsulfonyl)imide (PMPIm) and 1-ethyl-3-methylimidazolium tosylate (EMImTOS). The orientational dynamics are complex with relaxation involving several power law decays followed by a final exponential decay. A mode coupling theory (MCT) schematic model, the Sjögren model, was able to reproduce the PMPIm data very successfully over a wide range of times from 1 ps to hundreds of ns for all temperatures studied. Over the temperature range from room temperature down to the critical temperature Tc of 231 K, the OHD-OKE signal of PMPIm is characterized by the intermediate power law t(-1.00+/-0.04) at short times, a von Schweidler power law t(-0.51+/-0.03) at intermediate times, and a highly temperature-dependent exponential (alpha relaxation) at long times. This form of the decay is identical to the form observed previously for a large number of organic van der Waals liquids. MCT analysis indicates that the theory can explain the experimental data very well for a range of temperatures above Tc, but as might be expected, there are some deviations from the theoretical modeling at temperatures close to Tc. For EMImTOS, the orientational dynamics were studied on the ps time scale in the deeply supercooled region near its glass transition temperature. The orientational relaxation of EMImTOS clearly displays the feature associated with the boson peak at approximately 2 ps, which is the first time domain evidence of the boson peak in ionic organic liquids. Overall, all the dynamical features observed earlier for organic van der Waals liquids using the same experimental technique are also observed for organic ionic liquids.

Buckling of spherical shells adhering onto a rigid substrate

Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., Cs/epsilon and Cb/epsilon where Cs and Cb are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small Cs/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2-3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.

Pressure-induced isothermal glass transition of small organic molecules

We present a complete set of overlapping pressure-volume-temperature and dielectric relaxation data of the glass forming liquids propylene carbonate, meta-fluoroaniline, and glycerol under pressure up to 700 MPa. In all the samples a glass transition is induced by pressure at constant temperature. We compare the spectral shape of the structural relaxation process in the glass forming liquids with increasing pressure using a simple scaling for the maximum of the dielectric loss. Relaxation times measured at various temperatures and pressures can be scaled on a mastercurve by a single control parameter, the product of temperature and specific volume with a material-dependent exponent. This exponent exhibits the numerical value 4 for van der Waals liquids but is smaller for glass formers with hydrogen bonding.

Orientational dynamics of the ionic organic liquid 1-ethyl-3-methylimidazolium nitrate

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments are used to study the orientational dynamics of the ionic organic liquid 1-ethyl-3-methylimidazolium nitrate (EMIM+NO3−) over time scales from ∼1 ps to ∼2 ns, and the temperatures range from 410 to 295 K. The temperatures cover the normal liquid state and the weakly supercooled state. The orientational dynamics exhibit characteristics typical of normal organic glass-forming liquids. The longest time scale portion of the data decays as a single exponential and obeys the Debye–Stokes–Einstein relation. The decay of the OHD-OKE signal begins (∼1 ps) with a temperature independent power law, t−z, z=1.02±0.05, the “intermediate power law.” The power law decay is followed by a crossover region, modeled as a second power law, the von Schweidler power law. The longest time scale decay is the exponential α relaxation. The intermediate power law decay has been observed in van der Waals supercooled liquids previously. These are the first such observations on an ionic organic liquid. The observation of the dynamical signatures observed in other liquids demonstrates that the orientational dynamics of ionic organic liquids are fundamentally the same as van der Waals liquids and supports the universality of the intermediate power law decay in the dynamics of complex liquids. Within the mode-coupling theory (MCT) framework, the MCT critical temperature TC is estimated to be TC≅255 K.

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.

Microscopic theory of network glasses.

A theory of the glass transition of network liquids is developed using self-consistent phonon and liquid state approaches. The dynamical transition and entropy crisis characteristic of random first-order transitions are mapped as a function of the degree of bonding and density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls explaining why highly coordinated liquids are "strong" while van der Waals liquids without coordination are "fragile."

The relative contributions of temperature and volume to structural relaxation of van der Waals molecular liquids

Pressure-volume-temperature measurements were carried out on two van der Waals liquids, 1,1′-bis(p-methoxyphenyl)cyclohexane (BMPC) and 1,1′-di(4-methoxy-5methylphenyl)cyclohexane (BMMPC). In combination with dielectric spectroscopy results, the relative contribution of temperature and density to the structural relaxation times were quantified. We find that the ratio of the isobaric expansion coefficient [−ρ−1 (∂ρ/∂T)P, where ρ is mass density and T is temperature, evaluated at P=0.1 MPa] to the coefficient of isochronal expansivity [−ρ−1 (∂ρ/∂T)τ, evaluated at τ=1 s] equals 0.58 and 0.72 for BMPC and BMMPC, respectively. This indicates that density exerts more influence on the structural relaxation times than does thermal energy. Corroborating this finding, the ratio of the isochoric activation energy to the activation energy at constant pressure is determined to be ca. 0.4 at ambient pressure for both glass formers. The prevalence of density over thermal energy is contrary to prevailing ideas concerning the dynamics of supercooled liquids, and must be taken into account in developing models of the glass transition.

Isochronal temperature–pressure superpositioning of the α-relaxation in type-A glass formers

Dielectric spectra were obtained at ambient and elevated pressures for three ‘type-A’ glass formers, which exhibit excess intensity on the high frequency side of the structural relaxation peak. The response to pressure of the peak maximum and the excess wing suggests categorization of such glass formers into two groups: associated liquids, in which the α-relaxation and the excess wing have a different pressure dependence, and van der Waals liquids, which at fixed value of the α-relaxation time, conform to temperature–pressure superpositioning. This distinction is believed to arise from the change in the number of intermolecular bonds (non-dispersive interactions) with volume.

Heterogeneous dynamics at the glass transition in van der Waals liquids: determination of the characteristic scale.

Recent experiments have demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous. The characteristic size of these heterogeneities has been measured to be a few nanometers at Tg. We extend here a recent model for describing the heterogeneous nature of the dynamics which allows both to derive this length scale and the right orders of magnitude of the heterogeneities of the dynamics close to the glass transition. Our model allows then to interpret quantitatively small probes diffusion experiments.

Molecular dynamics simulations of the liquid–vapor interface of a molten salt. II. Finite size effects and comparison to experiment

An examination of the finite system size effects on the calculated interfacial properties of the molten salt KI is described, as an extension of the work described in the preceding paper [J. Chem. Phys. 115, 8603 (2001)]. It is shown that, for system sizes beyond ∼1000 ions, the finite size effects are accounted for by the predictions of capillary wave (CW) theory, as in van der Waals liquids. Hence, there do not appear to be additional long-range effects arising from the Coulombic interactions. Techniques used to avoid truncation effects in the Coulombic and dispersion interactions appear to have eliminated system size dependent artefacts from these sources. The scaling behavior predicted from CW theory is used to predict the bulk surface tension for the chosen interaction potential, which is then compared with experimental values, and very good agreement found. Examination of the interfacial layers show that the local structure remains strongly charge ordered, but the surface is highly roughened by clustering and, on longer length-scales, by the effect of capillary waves.

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation.