The Kauzmann Paradox Revisited

Two liquid states of distinguishable helium-4: The existence of another non-superfluid frozen by heating

We show that two liquid states can exist in distinguishable helium-4 (4He) obeying Boltzmann statistics by path integral centroid molecular dynamics (CMD) simulations. This is an indication of quantum liquid polyamorphism induced by the nuclear quantum effect. For 0.08-3.3 K and 1-500 bar, we extensively conducted the isothermal-isobaric CMD simulations to explore not only possible states and state diagram but also the state characteristics. The distinguishable 4He below 25 bar does not freeze down to 0.1 K even though it includes no Bosonic exchange effect and, therefore, no Bose condensation. One liquid state, low quantum-dispersion liquid (LQDL), is nearly identical to normal liquid He-I of real 4He. The other is high quantum-dispersion liquid (HQDL) consisting of atoms with longer quantum wavelength. This is another non-superfluid existing below 0.5 K or the temperatures of LQDL. The HQDL is also a low-entropy and fragile liquid to exhibit, unlike conventional liquids, rather gas-like relaxation of velocity autocorrelation function, while there the atoms diffuse without noticeable contribution from quantum tunneling. The LQDL-HQDL transition is not a thermodynamic phase transition but a continuous crossover accompanied by the change in the expansion factor of quantum wavelength. Freezing of HQDL into the low quantum-dispersion amorphous solid occurs by heating from 0.2 to 0.3 K at 40-50 bar, while this P-T condition coincides with the Kim-Chan normal-supersolid phase boundary of real 4He. The obtained state diagram was compared to that of the confined subnano-scale 4He systems, where Bosonic correlation is considerably suppressed.

On the universality of viscosity in supersaturated binary aqueous sugar solutions: Cryopreservation by vitrification

Nowadays, the physical nature of supersaturated binary aqueous sugar solutions in the vicinity of the glass transition represents a very important issue due to their biological applications in cryopreservation of cells and tissues, food science and stabilization and storage of nano genetic drugs. We present the construction of the Supplemented Phase Diagram and the non-equilibrium nature of the undersaturated-supersaturated kinetic transition. The description of its thermodynamic nature is achieved through the study of behavior of their viscosity as temperature is lowered and concentration increased. In this work, we find a universal character for the viscosities of several sugar water solutions.

Ising model for the freezing transition

We introduce a three-state Ising model with entropy-volume coupling suitably incorporating a packing mechanism into a lattice gas with no attractive interactions. On working in a great grand canonical ensemble in which the energy, volume, and number of particles are all allowed to fluctuate simultaneously, the model's mean-field solutions illuminate a strictly first-order transition akin to hard-sphere freezing while describing the thermodynamics of solid and fluid phases. Further implementation of attractive interactions in a natural way allows every aspect of the phase diagram of a simple substance to be reproduced, thereby accomplishing the van der Waals picture of the states of matter from first principles of statistical mechanics. This fairly accurate qualitative description plausibly renders mean-field theory a reasonable approach for freezing in three dimensions. At the same time, our mean-field treatment itself suggests freezing to persist in infinitely many dimensions, as advanced from recent simulations [Charbonneau et al., Eur. Phys. J. E 44, 101 (2021)10.1140/epje/s10189-021-00104-y].

Probing excitations and cooperatively rearranging regions in deeply supercooled liquids

Upon approaching the glass transition, the relaxation of supercooled liquids is controlled by activated processes, which become dominant at temperatures below the so-called dynamical crossover predicted by Mode Coupling theory (MCT). Two of the main frameworks rationalising this behaviour are dynamic facilitation theory (DF) and the thermodynamic scenario which give equally good descriptions of the available data. Only particle-resolved data from liquids supercooled below the MCT crossover can reveal the microscopic mechanism of relaxation. By employing state-of-the-art GPU simulations and nano-particle resolved colloidal experiments, we identify the elementary units of relaxation in deeply supercooled liquids. Focusing on the excitations of DF and cooperatively rearranging regions (CRRs) implied by the thermodynamic scenario, we find that several predictions of both hold well below the MCT crossover: for the elementary excitations, their density follows a Boltzmann law, and their timescales converge at low temperatures. For CRRs, the decrease in bulk configurational entropy is accompanied by the increase of their fractal dimension. While the timescale of excitations remains microscopic, that of CRRs tracks a timescale associated with dynamic heterogeneity, [Formula: see text]. This timescale separation of excitations and CRRs opens the possibility of accumulation of excitations giving rise to cooperative behaviour leading to CRRs.

Reaching the Ideal Glass in Polymer Spheres: Thermodynamics and Vibrational Density of States

The existence of an ideal glass and the resolution to the Kauzmann paradox is a long-standing open question in materials science. To address this problem, we exploit the ability of glasses with large interfacial area to access low energy states. We submit aggregates of spheres of a polymeric glass former to aging well below their glass transition temperature, T_{g}; and characterize their thermodynamic state by calorimetry, and the vibrational density of state (VDOS) by inelastic neutron scattering (INS). We show that, when aged at appropriate temperatures, glassy spheres attain a thermodynamic state corresponding to an ideal glass in time scales of about one day. In this state, the boson peak, underlying the deviation from the Debye level of the VDOS, is essentially suppressed. Our results are discussed in the framework of the link between the macroscopic thermodynamic state of glasses and their vibrational properties.

Dynamical phase transitions and their relation to structural and thermodynamic aspects of glass physics

We review recent developments in structural-dynamical phase transitions in trajectory space based on dynamic facilitation theory. An open question is how the dynamic facilitation perspective on the glass transition may be reconciled with thermodynamic theories that posit collective reorganization accompanied by a growing static length scale and, eventually, a vanishing configurational entropy. In contrast, dynamic facilitation theory invokes a dynamical phase transition between an active phase (close to the normal liquid) and an inactive phase, which is glassy and whose order parameter is either a time-averaged dynamic or structural quantity. In particular, the dynamical phase transition in systems with non-trivial thermodynamics manifests signatures of a lower critical point that lies between the mode-coupling crossover and the putative Kauzmann temperature, at which a thermodynamic phase transition to an ideal glass state would occur. We review these findings and discuss such criticality in the context of the low-temperature decrease in configurational entropy predicted by thermodynamic theories of the glass transition.

Possible instability of one-step replica symmetry breaking in p-spin Ising models outside mean-field theory

The fully connected Ising p-spin model has for p>2 a discontinuous phase transition from the paramagnetic phase to a stable state with one-step replica symmetry breaking (1RSB). However, simulations in three dimension do not look like these mean-field results and have features more like those which would arise with full replica symmetry breaking (FRSB). To help understand how this might come about we have studied in the fully connected p-spin model the state of two-step replica symmetry breaking (2RSB). It has a free energy degenerate with that of 1RSB, but the weight of the additional peak in P(q) vanishes. We expect that the state with full replica symmetry breaking (FRSB) is also degenerate with that of 1RSB. We suggest that finite-size effects will give a nonvanishing weight to the FRSB features, as also will fluctuations about the mean-field solution. Our conclusion is that outside the fully connected model in the thermodynamic limit, FRSB is to be expected rather than 1RSB.

A model-free analysis of configurational properties to reduce the temperature- and pressure-dependent segmental relaxation times of polymers

The segmental relaxation time data for poly(vinyl acetate), poly(vinyl chloride), and linear and star polystyrene are analyzed using a model-free method to determine how the temperature- and pressure-dependent relaxation times, τ, scale with the relative configurational thermodynamic properties. The model-free method assumes no specific mathematical form, such as reciprocal linearity, and the configurational properties are referred to an isochronal state to eliminate the bias associated with the definition of the ideal glassy state. The scaling ability of a given configurational property is strongly material-dependent with the logarithm of τ scaling better with TS_c and H_c for poly(vinyl acetate), with TS_c, H_c, and U_c for poly(vinyl chloride), and with TS_c, H_c, and V_c for linear and star polystyrene. The choice of the isochronal reference state does not qualitatively affect the results.

Pressure densified 1,3,5-tri(1-naphthyl)benzene glass. I. Volume recovery and physical aging

The effects of pressure densification on 1,3,5-tri(1-naphthyl)benzene (TNB) are assessed from volumetric and calorimetric measurements. The pressure densified glass (PDG) has higher density than conventional glass (CG), but unlike ultrastable TNB glass prepared using vapor deposition which also has elevated density, TNB PDG exhibits higher enthalpy and lower thermal stability than when formed at ambient pressure. PDG also exhibits anomalous physical aging. Rather than evolving monotonically toward the equilibrium density, there is an overshoot to a lower density state. Only when the density of the PDG becomes equivalent to the corresponding CG does the density begin a slow approach toward equilibrium.

Vapor-Deposited Ethylbenzene Glasses Approach "Ideal Glass" Density

Spectroscopic ellipsometry was used to characterize vapor-deposited glasses of ethylbenzene (T_g = 115.7 K). For this system, previous calorimetric experiments have established that a transition to the ideal glass state is expected to occur near 101 K (the Kauzmann temperature, T_K) if the low-temperature supercooled liquid has the properties expected based upon extrapolation from above T_g. Ethylbenzene glasses were vapor-deposited at substrate temperatures between 100 (∼0.86 T_g) and 116 K (∼T_g), using deposition rates of 0.02-2.1 nm/s. Down to 103 K, glasses prepared in the limit of low deposition rate have densities consistent with the extrapolated supercooled liquid. The highest density glass is within 0.15% of the density expected for the ideal glass. These results support the hypothesis that the extrapolated properties of supercooled ethylbenzene are correct to within just a few Kelvin of T_K, consistent with the existence of a phase transition to an ideal glass state at T_K.

Configurational entropy of glass-forming liquids

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraught with difficulties, misconceptions, and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.

Topological description of the solidification of undercooled fluids and the temperature dependence of the thermal conductivity of crystalline and glassy solids above approximately 50 K

Topological origins of the thermal transport properties of crystalline and non-crystalline solid states are considered herein, by the adoption of a quaternion orientational order parameter to describe solidification. Global orientational order, achieved by spontaneous symmetry breaking, is prevented at finite temperatures for systems that exist in restricted dimensions (Mermin-Wagner theorem). Just as complex ordered systems exist in restricted dimensions in 2D and 1D, owing to the dimensionality of the order parameter, quaternion ordered systems in 4D and 3D exist in restricted dimensions. Just below the melting temperature, misorientational fluctuations in the form of spontaneously generated topological defects prevent the development of the solid state. Such solidifying systems are well-described using O(4) quantum rotor models, and a defect-driven Berezinskii-Kosterlitz-Thouless transition is anticipated to separate an undercooled fluid from a crystalline solid state. In restricted dimensions, in addition to orientationally-ordered ground states, orientationally-disordered ground states may be realized by tuning a non-thermal parameter in the relevant O(n) quantum rotor model Hamiltonian. Thus, glassy solid states are anticipated to exist as distinct ground states of O(4) quantum rotor models. Within this topological framework for solidification, the finite Kauzmann temperature marks a first-order transition between crystalline and glassy solid states at a 'self-dual' critical point that belongs to O(4) quantum rotor models. This transition is a higher-dimensional analogue to the quantum phase transition that belongs to O(2) Josephson junction arrays (JJAs). The thermal transport properties of crystalline and glassy solid states, above approximately 50 K, are considered alongside the electrical transport properties of JJAs across the superconductor-to-superinsulator transition.

The race to the bottom: approaching the ideal glass?

Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an 'ideal glass', an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations give equally good descriptions of the data available, so it is hard to determine which-if any-is correct. Recently however this situation has begun to change. A consensus has emerged that one powerful means to resolve this longstanding question is to approach the putative thermodynamic transition sufficiently closely, and a number of techniques have emerged to meet this challenge. Here we review the results of some of these new techniques and discuss the implications for the existence-or otherwise-of the thermodynamic transition to an ideal glass.

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.

GLASS TRANSITION IN RUBBERY MATERIALS

When the perturbation frequency imposed on a rubber falls within the glass transition zone of its viscoelastic spectrum, energy absorption is maximized. This phenomenon is the operative mechanism for various applications of elastomers requiring large energy dissipation. Nevertheless, a fundamental understanding of the glass transition is lacking. The diversity of properties that depend both on chemical structure and thermodynamic conditions makes modeling difficult and a first principles theory perhaps unachievable; indeed, the number of models for the glass transition seems to be inversely proportional to their ability to accurately describe the myriad behaviors. The progress made at quantifying the role of the thermodynamic variables temperature, T, and density, ρ, on the dynamics is described. An important aspect of the work was the discovery that relaxation times and viscosities of molecular liquids and polymers superpose when plotted against the scaling variable T/ργ, with the scaling exponent γ a material constant sensibly related to the nature of the intermolecular repulsive potential; thus, dynamic spectroscopy measurements can be used to quantify the forces between molecules. Other properties derive from the scaling behavior, including the Boyer-Spencer rule and the correlation of fluctuations in the potential energy with fluctuations in the virial pressure.

Extracting energy and structure properties of glass-forming liquids from structural relaxation time

A comprehensive examination of the kinetic liquid model (Wang et al 2010 J. Phys.: Condens. Matter 22 455104) is carried out by fitting the structural relaxation time of 26 different glass-forming liquids in a wide temperature range, including most of the well-studied materials. Careful analysis of the compiled reported data reveals that experimental inaccuracies should not be overlooked in any 'benchmark test' of relating theories or models (e.g. in Lunkenheimer et al 2010 Phys. Rev. E 81 051504). The procedure, accuracy, ability, and efficiency of the kinetic liquid model are discussed in detail and in comparison with other available fitting methods. In general, the kinetic liquid model could be verified by 17 of the 26 compiled data sets and can serve as a meaningful approximative method for analyzing these liquids. Nonetheless, further experimental examinations in a wide temperature range are needed and are called for. Through fitting, the microscopic details of these liquids are extracted, namely, the enthalpy, entropy, and cooperativity in structural relaxation, which may facilitate further quantitative analysis to both the liquidus and glassy states of these materials.

Viscosity of glass-forming liquids

The low-temperature dynamics of ultraviscous liquids hold the key to understanding the nature of glass transition and relaxation phenomena, including the potential existence of an ideal thermodynamic glass transition. Unfortunately, existing viscosity models, such as the Vogel-Fulcher-Tammann (VFT) and Avramov-Milchev (AM) equations, exhibit systematic error when extrapolating to low temperatures. We present a model offering an improved description of the viscosity-temperature relationship for both inorganic and organic liquids using the same number of parameters as VFT and AM. The model has a clear physical foundation based on the temperature dependence of configurational entropy, and it offers an accurate prediction of low-temperature isokoms without any singularity at finite temperature. Our results cast doubt on the existence of a Kauzmann entropy catastrophe and associated ideal glass transition.

Constructing explicit magnetic analogies for the dynamics of glass forming liquids

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.

Exploring the potential energy landscape of glass-forming systems: from inherent structures via metabasins to macroscopic transport

In this review a systematic analysis of the potential energy landscape (PEL) of glass-forming systems is presented. Starting from the thermodynamics, the route towards the dynamics is elucidated. A key step in this endeavor is the concept of metabasins. The relevant energy scales of the PEL can be characterized. Based on the simulation results for some glass-forming systems one can formulate a relevant model system (ideal Gaussian glass-former) which can be treated analytically. The macroscopic transport can be related to the microscopic hopping processes, using either the strong relation between energy (thermodynamics) and waiting times (dynamics) or, alternatively, the concepts of the continuous-time random walk. The relation to the geometric properties of the PEL is stressed. The emergence of length scales within the PEL approach as well as the nature of finite-size effects is discussed. Furthermore, the PEL view is compared to other approaches describing the glass transition.

How a vicinal layer of solvent modulates the dynamics of proteins

The dynamics of a folded protein is studied in water and glycerol at a series of temperatures below and above their respective dynamical transition. The system is modeled in two distinct states whereby the protein is decoupled from the bulk solvent at low temperatures, and communicates with it through a vicinal layer at physiological temperatures. A linear viscoelastic model elucidates the less-than-expected increase in the relaxation times observed in the backbone dynamics of the protein. The model further explains the increase in the flexibility of the protein once the transition takes place and the differences in the flexibility under the different solvent environments. Coupling between the vicinal layer and the protein fluctuations is necessary to interpret these observations. The vicinal layer is postulated to form once a threshold for the volumetric fluctuations in the protein to accommodate solvents of different sizes is reached. Compensation of entropic-energetic contributions from the protein-coupled vicinal layer quantifies the scaling of the dynamical transition temperatures in various solvents. The protein adapts different conformational routes for organizing the required coupling to a specific solvent, which is achieved by adjusting the amount of conformational jumps in the surface-group dihedrals.

On the glass temperature under extreme pressures

The application of a modified Simon-Glatzel-type relation [Z. Anorg. Allg. Chem. 178, 309 (1929)] for the pressure evolution of the glass temperature is presented, namely, Tg(P)=Tg0[1+DeltaP/(pi+Pg0)]1/bexp[-(DeltaP/c)], where (Tg0,Pg0) are the reference temperature and pressure, DeltaP=P-Pg0, -pi is the negative pressure asymptote, b is the power exponent, and c is the damping pressure coefficient. The discussion is based on the experimental Tg(P) data for magmatic silicate melt albite, polymeric liquid crystal P8, and glycerol. The latter data are taken from Cook et al. [J. Chem. Phys. 100, 5178 (1994)] and from the authors' dielectric relaxation time (tau(P)) measurements, which employs the novel pressure counterpart of the Vogel-Fulcher-Tammann equation: tau(P)=tau0P exp[DPDeltaP/(P0-P)], where DeltaP=P-PSL (PSL is the stability limit hidden under negative pressure), P0 is the estimation of the ideal glass pressure, and D(P) is the isothermal fragility strength coefficient. Results obtained suggest the hypothetical maximum of the Tg(P) curve, which can be estimated due to the application of the supporting derivative-based analysis. A hypothetical common description of glass formers characterized by dTg/dP>0 and dTg/dP<0 coefficients is suggested. Finally, the hypothetical link between molecular and colloidal glass formers is recalled.

Inverse melting in lattice-gas models

Inverse melting is the phenomenon, observed in both helium isotopes, by which a crystal melts when cooled at constant pressure. I investigate discrete-space analogs of inverse melting by means of two instances of a triangular-lattice-gas system endowed with a soft-core repulsion and a short-ranged attraction. To reconstruct the phase diagram, I use both transfer-matrix and Monte Carlo methods, as well as low-temperature series expansions. In one case, a phase behavior reminiscent of helium emerges, with a loose-packed phase (which is solidlike for low temperatures and liquidlike for high temperatures) extending down to zero temperature for low pressures and the possibility of melting the close-packed solid by isobaric cooling. At variance with previous model studies of inverse melting, the driving mechanism of the present phenomenon is mainly geometrical, related to the larger free-energy cost of a "vacancy" in the loose-packed solid than in the close-packed one.

Dielectric Studies of Molecular Motions in Amorphous Solid and Ultraviscous Acetaminophen

The dielectric permittivity and loss spectra of glassy and ultraviscous states of acetaminophen have been measured over the frequency range 10 Hz-0.4 MHz. The relaxation spectra show an asymmetric distribution of times expressed in terms of the Kohlrausch exponent, beta, which remains constant at 0.79+/-0.02 over the 305-341 K range. The dielectric relaxation time increases on cooling according to the Vogel-Fulcher-Tammann equation. However, the values of the parameters are considerably different from the values deduced from earlier work by other researchers using the heat capacity of ultraviscous acetaminophen and relating it to its molecular mobility. The calorimetric glass softening temperature of 296 K obtained from differential scanning calorimetry is close to the value measured from dielectric relaxation. The equilibrium permittivity of ultraviscous acetaminophen decreases on heating like that of a normal dipolar liquid, as anticipated from the Curie law. But, its value decreases rapidly with time when it begins to crystallize. The equilibrium permittivity of this crystal phase is approximately 3.1 at 300 K and increases with temperature, which indicates a partial, orientational-disordering of its structure. The results show limitations of the procedures used in the modeling of the kinetics of molecular motions, that is, estimating physical stability, using thermodynamic considerations based on thermal analyses of the amorphous solid phase of acetaminophen.

Stable solution of the simplest spin model for inverse freezing

We analyze the Blume-Emery-Griffiths-Capel model with disordered interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram, and the transition lines are computed using the full replica symmetry breaking ansatz. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. 93, 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase.

Spatially Heterogeneous Dynamics and the Adam−Gibbs Relation in the Dzugutov Liquid

We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the Rosenfeld-Tarazona T(3/5) law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S(conf), a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S(conf) and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S(conf), and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S(conf). We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late-beta-relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS(conf), in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S(conf) may be a consequence of the fact that the clusters are composed of strings.

Inherent structures and Kauzmann temperature of confined liquids

Calculations of the thermodynamical properties of a supercooled liquid confined in a matrix are performed with an inherent structure analysis. The liquid entropy is computed by means of a thermodynamical integration procedure. The contributions to the free energy of the liquid can be decoupled also in confinement in the configurational and the vibrational parts. We show that the vibrational entropy can be calculated in the harmonic approximation as in the bulk case. The Kauzmann temperature of the confined system is estimated from the behavior of the configurational entropy.

Theory of dynamic barriers, activated hopping, and the glass transition in polymer melts

A statistical mechanical theory of collective dynamic barriers, slow segmental relaxation, and the glass transition of polymer melts is developed by combining, and in some aspects extending, methods of mode coupling, density functional, and activated hopping transport theories. A coarse-grained description of polymer chains is adopted and the melt is treated as a liquid of segments. The theory is built on the idea that collective density fluctuations on length scales considerably longer than the local cage scale are of primary importance in the deeply supercooled regime. The barrier hopping or segmental relaxation time is predicted to be a function primarily of a single parameter that is chemical structure, temperature, and pressure dependent. This parameter depends on the material-specific dimensionless amplitude of thermal density fluctuations (compressibility) and a reduced segmental density determined by the packing length and backbone characteristic ratio. Analytic results are derived for a crossover temperature T(c), collective barrier, and glass transition temperature T(g). The relation of these quantities to structural and thermodynamic properties of the polymer melt is established. A universal power-law scaling behavior of the relaxation time below T(c) is predicted based on identification of a reduced temperature variable that quantifies the breadth of the supercooled regime. Connections between the ratio T(c)/T(g), two measures of dynamic fragility, and the magnitude of the local relaxation time at T(g) logically follow. Excellent agreement with experiment is found for these generic aspects, and the crucial importance of the experimentally observed near universality of the dynamic crossover time is established. Extensions of the theory to treat the full chain dynamics, heterogeneity, barrier fluctuations, and nonpolymeric thermal glass forming liquids are briefly discussed.

Thermodynamics and the glass transition in model energy landscapes

We determine the liquid-state thermodynamics for a model energy landscape corresponding to soft spheres with a mean-field attraction. We consider two approximations, in which the distribution of potential energy minima is either Gaussian or binomial, and for each we calculate the liquid spinodal, binodal, and "effective" glass transition locus. The resulting models provide a unified description of the liquid state across the complete range from low-temperature glassiness to high-temperature instability with respect to the vapor phase.

Liquid stability in a model for ortho-terphenyl

We report an extensive study of the phase diagram of a simple model for ortho-terphenyl, focusing on the limits of stability of the liquid state. Reported data extend previous studies of the same model to both lower and higher densities and to higher temperatures. We estimate the location of the homogeneous liquid-gas nucleation line and of the spinodal locus. Within the potential energy landscape formalism, we calculate the distributions of depth, number, and shape of the potential energy minima and show that the statistical properties of the landscape are consistent with a Gaussian distribution of minima over a wide range of volumes. We report the volume dependence of the parameters entering in the Gaussian distribution (amplitude, average energy, variance). We finally evaluate the locus where the configurational entropy vanishes, the so-called Kauzmann line, and discuss the relative location of the spinodal and Kauzmann loci.