Experimental test of a predicted dynamics-structure-thermodynamics connection in molecularly complex glass-forming liquids

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

We analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call "complexity reduction". In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature Tg of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2-6 nm at Tg. Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

Theoretical analysis of the structure, thermodynamics, and shear elasticity of deeply metastable hard sphere fluids

The structure, thermodynamics, and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remain a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate microscopic equilibrium liquid state integral equation theory, in conjunction with naïve mode coupling theory of particle localization, to study in a unified manner the structural correlations, thermodynamic properties, and dynamic elastic shear modulus in deeply metastable hard sphere fluids. Distinctive behaviors are predicted including divergent inverse critical power laws for the contact value of the pair correlation function, pressure, and inverse dimensionless compressibility, and a splitting of the second peak and large suppression of interstitial configurations of the pair correlation function. The dynamic elastic modulus is predicted to exhibit two distinct exponential growth regimes with packing fraction that have strongly different slopes. These thermodynamic, structural, and elastic modulus results are consistent with simulations and experiments. Perhaps most unexpectedly, connections between the amplitude of long wavelength density fluctuations, dimensionless compressibility, local structure, and the dynamic elastic shear modulus have been theoretically elucidated. These connections are more broadly relevant to understanding the slow activated relaxation and mechanical response of colloidal suspensions in the ultradense metastable region and deeply supercooled thermal liquids in equilibrium.

Unified Understanding of the Structure, Thermodynamics, and Diffusion of Single-Chain Nanoparticle Fluids

Single-chain nanoparticles (SCNPs) are a fascinating class of soft nano-objects with promising properties and relevance to protein condensates, polymer nanocomposites, nanomedicine, bioimaging, catalysis, and drug delivery. We combine molecular dynamics simulations and equilibrium and time-dependent statistical mechanical theory to construct a unified understanding of how the internal conformational structure of SCNPs, of both a simple fractal globule-like form and more complex objects with multiple internal intermediate length scales, determines nm-scale intermolecular packing correlations, thermodynamic properties, and center-of-mass diffusion over a wide range of concentrations up to dense melts. The intermolecular pair correlations generically exhibit a distinctive deep correlation hole form due to SCNP internal connectivity structure and repulsive interparticle interactions associated with a globular-like conformation on the macromolecular scale, with concentration-dependent deviations at small separations. Unanticipated exponential-like dependences of the equation-of-state, osmotic compressibility, and center-of-mass diffusion constant on SCNP macromolecular packing fraction are theoretically predicted and confirmed via simulations. System-specific behaviors are found associated with SCNP internal structure, but overarching regularities are identified and understood based on a generalized effective globule conformation on macromolecular scales. Diffusivity slows down by 2-3 decades with increasing concentration and is understood as a consequence of a nonactivated excluded volume-driven weak-caging process associated with space-time correlated intermolecular forces experienced by the SCNP. Good agreement between the theory and simulations is established, testable predictions are made, and a quantitative comparison with viscosity measurements on a specific SCNP fluid is carried out. The basic theoretical approach can potentially be extended to treat the chemical and physical consequences of varying the structure of other classes of soft nanoparticles with distinctive internal nanoscale organization relevant in nanotechnology and nanomedicine, and the possible emergence of macromolecular kinetically arrested glasses.

Universal origin of glassy relaxation as recognized by configuration pattern matching

Relaxation processes are crucial for understanding the structural rearrangements of liquids and amorphous materials. However, the overarching principle that governs these processes across vastly different materials remains an open question. Substantial analysis has been carried out based on the motions of individual particles. Here, as an alternative, we propose viewing the global configuration as a single entity. We introduce a global order parameter, namely the inherent structure minimal displacement (IS Dmin), to quantify the variability of configurations by a pattern-matching technique. Through atomic simulations of seven model glass-forming liquids, we unify the influences of temperature, pressure and perturbation time on the relaxation dissipation, via a scaling law between the mechanical damping factor and IS Dmin. Fundamentally, this scaling reflects the curvature of the local potential energy landscape. Our findings uncover a universal origin of glassy relaxation and offer an alternative approach to studying disordered systems.

Solid-that-Flows Picture of Glass-Forming Liquids

This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Development of broad modulus profile upon polymer-polymer interface formation between immiscible glassy-rubbery domains

Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ([Formula: see text]) where previous work has demonstrated a long-range (∼200 nm) profile in local [Formula: see text] is established between immiscible glassy and rubbery polymer domains when the polymer-polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus [Formula: see text] is established when the polymer-polymer interface ([Formula: see text]5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad [Formula: see text] profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus [Formula: see text] spanning [Formula: see text]180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in [Formula: see text] and [Formula: see text] arise from a coupling of the spectrum of vibrational modes across the polymer-polymer interface as a result of acoustic impedance matching of sound waves with [Formula: see text] nm during interface broadening that can then trigger density fluctuations in the neighboring domain.

Penetrant shape effects on activated dynamics and selectivity in polymer melts and networks based on self-consistent cooperative hopping theory

We generalize and apply the microscopic self-consistent cooperative hopping theory for activated penetrant dynamics in polymer melts and crosslinked networks to address the role of highly variable non-spherical molecular shape. The focus is on vastly different shaped penetrants that have identical space filling volume in order to isolate how non-spherical shape explicitly modifies dynamics over a wide range of temperature down to the kinetic glass transition temperature. The theory relates intramolecular and intermolecular structure and kinetic constraints, and reveals how different solvation packing of polymer monomers around variable shaped penetrants impact penetrant hopping. A highly shape-dependent penetrant activated relaxation, including alpha time decoupling and trajectory level cooperativity of the hopping process, is predicted in the deeply supercooled regime for relatively larger penetrants which is sensitive to whether the polymer matrix is a melt or heavily crosslinked network. In contrast, for smaller size penetrants or at high/medium temperatures the effect of isochoric penetrant shape is relatively weak. We propose an aspect ratio variable that organizes how penetrant shape influences the activated relaxation times, leading to a (near) collapse or master curve. The relative absolute values of the penetrant relaxation time (inverse hopping rate) in polymer melts versus in crosslinked networks are found to be opposite when compared at a common absolute temperature versus when they are compared at a fixed value of distance from the glass transition based on the variable Tg/T with Tg the glass transition temperature. Quantitative comparison with recent diffusion experiments on chemically complex molecular penetrants of variable shape but fixed volume in crosslinked networks reveals good agreement, and testable new predictions are made. Extension of the theoretical approach to more complex systems of high experimental interest are discussed, including applications to realize selective transport in membrane separation applications.

Understanding creep suppression mechanisms in polymer nanocomposites through machine learning

While recent efforts have shown how local structure plays an essential role in the dynamic heterogeneity of homogeneous glass-forming materials, systems containing interfaces such as thin films or composite materials remain poorly understood. It is known that interfaces perturb the molecular packing nearby, however, numerous studies show the dynamics are modified over a much larger range. Here, we examine the dynamics in polymer nanocomposites (PNCs) using a combination of simulations and experiments and quantitatively separate the role of polymer packing from other effects on the dynamics, as a function of distance from the nanoparticle surfaces. After showing good qualitative agreement between the simulations and experiments in glassy structure and creep compliance, we use a machine-learned structure indicator, softness, to decompose polymer dynamics in our simulated PNCs into structure-dependent and structure-independent processes. With this decomposition, the free energy barrier for polymer rearrangement can be described as a combination of packing-dependent and packing-independent barriers. We find both barriers are higher near nanoparticles and decrease with applied stress, quantitatively demonstrating that the slow interfacial dynamics is not solely due to polymer packing differences, but also the change of structure-dynamics relationships. Finally, we present how this decomposition can be used to accurately predict strain-time creep curves for PNCs from their static configuration, providing additional insights into the effects of polymer-nanoparticle interfaces on creep suppression in PNCs.

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density-density and hydrostatic pressure-pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. These results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

Soft pinning: Experimental validation of static correlations in supercooled molecular glass-forming liquids

Enormous enhancement in the viscosity of a liquid near its glass transition is a hallmark of glass transition. Within a class of theoretical frameworks, it is connected to growing many-body static correlations near the transition, often called "amorphous ordering." At the same time, some theories do not invoke the existence of such a static length scale in the problem. Thus, proving the existence and possible estimation of the static length scales of amorphous order in different glass-forming liquids is very important to validate or falsify the predictions of these theories and unravel the true physics of glass formation. Experiments on molecular glass-forming liquids become pivotal in this scenario as the viscosity grows several folds (∼ 10 14 ), and simulations or colloidal glass experiments fail to access these required long-time scales. Here we design an experiment to extract the static length scales in molecular liquids using dilute amounts of another large molecule as a pinning site. Results from dielectric relaxation experiments on supercooled Glycerol with different pinning concentrations of Sorbitol and Glucose, as well as the simulations on a few model glass-forming liquids with pinning sites, indicate the versatility of the proposed method, opening possible new avenues to study the physics of glass transition in other molecular liquids.

Cooperative activated hopping dynamics in binary glass-forming liquids: effects of the size ratio, composition, and interparticle interactions

Slow dynamics in supercooled and glassy liquids is an important research topic in soft matter physics. Compared to the traditionally focused one-component systems, glassy dynamics in mixture systems adds in a rich set of new complexities, which are fundamentally interesting and also relevant for many technological applications. In this paper, we apply the recently developed self-consistent cooperative hopping theory (SCCHT) to systematically investigate the effects of the size ratio, composition and interparticle interactions on the cooperative activated hopping dynamics of matrix (in larger size) and penetrant (in smaller size) particles in varied binary sphere mixture model systems, with a specific focus on ultrahigh mixture packing fractions that mimic the deeply supercooled glass transition conditions for molecular/polymeric mixture materials. Analysis shows that in these high activation barrier cases, the long-range elastic distortion associated with a matrix particle hopping over its cage confinement always generates an elastic barrier of a nonnegligible magnitude, although the ratio between the elastic barrier and local barrier contribution is sensitively dependent on all three mixture-specific system factors considered in this work. SCCHT predicts two general scenarios of penetrant-matrix cooperative activated hopping dynamics: matrix/penetrant co-hopping (regime 1) or the penetrant mean barrier hopping time shorter than that of the matrix (regime 2). Increasing the penetrant-to-matrix size ratio or the penetrant-matrix cross-attraction strength is found to universally enlarge the composition window of regime 1. Diverse dynamical properties characterising different aspects of the cooperative activated hopping process, including the penetrant and matrix transient localization lengths, penetrant and matrix hopping jump distances, different types of local and elastic activated barriers, and matrix long-time diffusivity, relaxation time and dynamic fragility are quantitatively studied against a wide range of variations over the three system factors. Of particular interest is the universal "anti-plasticization" phenomenon achievable for sufficiently strong cross-attractive interactions. The prospects this work opens for the exploration of a wide variety of polymer-based mixture materials are briefly discussed at the end.

Dynamics of Associative Polymers with High Density of Reversible Bonds

An associative polymer carries many stickers that can form reversible associations. For more than 30 years, the understanding has been that reversible associations change the shape of linear viscoelastic spectra by adding a rubbery plateau in the intermediate frequency range, at which associations have not yet relaxed and thus effectively act as crosslinks. Here, we design and synthesize new classes of unentangled associative polymers carrying unprecedentedly high fractions of stickers, up to eight per Kuhn segment, that can form strong pairwise hydrogen bonding of ∼20k_{B}T without microphase separation. We experimentally show that reversible bonds significantly slow down the polymer dynamics but nearly do not change the shape of linear viscoelastic spectra. This behavior can be explained by a renormalized Rouse model that highlights an unexpected influence of reversible bonds on the structural relaxation of associative polymers.

Importance of Many Particle Correlations to the Collective Debye-Waller Factor in a Single-Particle Activated Dynamic Theory of the Glass Transition

We theoretically study the importance of many body correlations on the collective Debye-Waller (DW) factor in the context of the Nonlinear Langevin Equation (NLE) single-particle activated dynamics theory of glass transition and its extension to include collective elasticity (ECNLE theory). This microscopic force-based approach envisions structural alpha relaxation as a coupled local-nonlocal process involving correlated local cage and longer range collective barriers. The crucial question addressed here is the importance of the deGennes narrowing contribution versus a literal Vineyard approximation for the collective DW factor that enters the construction of the dynamic free energy in NLE theory. While the Vineyard-deGennes approach-based NLE theory and its ECNLE theory extension yields predictions that agree well with experimental and simulation results, use of a literal Vineyard approximation for the collective DW factor massively overpredicts the activated relaxation time. The current study suggests many particle correlations are crucial for a reliable description of activated dynamics theory of model hard sphere fluids.

Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.

Elucidation of the physical factors that control activated transport of penetrants in chemically complex glass-forming liquids

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S0(T) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S0(T) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S0(T) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (T_g). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with T_g, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τ_α becomes almost a universal function of reduced temperature, (T - T_g)/T_g, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - T_g)/T_g. Evidently, T_g dominates both τ_α and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Role of torsional potential in chain conformation, thermodynamics, and glass formation of simulated polybutadiene melts

For polymer chains, the torsional potential is an important intramolecular energy influencing chain flexibility and segmental dynamics. Through molecular dynamics simulations of an atomistic model for melts of cis-trans-1,4-polybutadiene (PBD), we explore the effect of the torsions on conformational properties (bond vector correlations and mean-square internal distances), fundamental thermodynamic quantities (density, compressibility, internal energy, and specific heat), and glass transition temperature T_g. This is achieved by systematically reducing the strength of the torsional potential, starting from the chemically realistic chain (CRC) model with the full potential toward the freely rotating chain (FRC) model without the torsional potential. For the equilibrium liquid, we find that the effect of the torsions on polymer conformations is very weak. Still weaker is the influence on the monomer density ρ and isothermal compressibility κ_T of the polymer liquid, both of which can be considered as independent of the torsional potential. We show that a van der Waals-like model proposed by Long and Lequeux [Eur. Phys. J. E 4, 371 (2001)] allows us to describe very well the temperature (T) dependence of ρ and κ_T. We also find that our data obey the linear relation between 1/k_BTρκ_T and 1/T (with the Boltzmann constant k_B) that has recently been predicted and verified on the experiment by Mirigian and Schweizer [J. Chem. Phys. 140, 194507 (2014)]. For the equilibrium liquid, simulations result in a specific heat, at constant pressure and at constant volume, which increases on cooling. This T dependence is opposite to the one found experimentally for many polymer liquids, including PBD. We suggest that this difference between simulation and experiment may be attributed to quantum effects due to hydrogen atoms and backbone vibrations, which, by construction, are not included in the classical united-atom model employed here. Finally, we also determine T_g from the density-temperature curve monitored in a finite-rate cooling process. While the influence of the torsional potential on ρ(T) is vanishingly small in the equilibrium liquid, the effect of the torsions on T_g is large. We find that T_g decreases by about 150 K when going from the CRC to the FRC model.

Local-Average Free Volume Correlates with Dynamics in Glass Formers

Glass formers exhibit a pronounced slowdown in dynamics, accompanied by progressive heterogeneity as they approach the glass transition. There is intense debate over whether the dramatic slowdown is caused by dynamical heterogeneity and whether the enhanced dynamical heterogeneity originates from structural causes. However, the connection between dynamical heterogeneity and the spatial distribution of the single-particle free volume (a purely static structural quantity) was found to be rather weak, which raises the question of whether dynamic heterogeneity has a purely structural origin. Here, by introducing the concept of local-average free volume, we present numerical evidence that long-time dynamic heterogeneity shows significantly enhanced correlation with the average local free volume over a length scale of a few neighboring shells. Our results resolve the long-standing controversy about whether free volume plays an important role in particle rearrangements associated with the activated hopping relaxation. The concept of "local average" can be applied to other local structural descriptors to better correlate with dynamic heterogeneity in glass-forming liquids.

Identifying structural signature of dynamical heterogeneity via the local softness parameter

In this work we study the relationship between the softness of a mean-field caging potential and dynamics at the local level. We first describe the local softness, which shows a distribution, thus identifying structural heterogeneity. We show that the lifetime of the softness parameter is connected to the lifetime of the well-known cage structure in supercooled liquids. Finally, our theory predicts that the local softness and the local dynamics is causal below the onset temperature where there is a decoupling between the short and long time dynamics, thus allowing a static description of the cage. With the decrease in temperature, the correlation between structure and dynamics increases. The study shows that at lower temperatures, the structural heterogeneity increases, and since the structure becomes a better predictor of the dynamics, it leads to an increase in the dynamical heterogeneity. We also find that the softness of a hard, immobile region evolves with time and becomes soft and eventually mobile due to the rearrangements in the neighborhood, confirming the well-known facilitation effect.

Long Wavelength Thermal Density Fluctuations in Molecular and Polymer Glass-Forming Liquids: Experimental and Theoretical Analysis under Isobaric Conditions

We establish via an in-depth analysis of experimental data that the dimensionless compressibility (proportional to the dimensionless amplitude of long wavelength thermal density fluctuations) of one-component normal and supercooled liquids of chemically complex nonpolar and weakly polar molecules and polymers follows extremely well a surprisingly simple and general temperature dependence over an exceptionally wide range of pressures and temperatures. A theoretical basis for this behavior is shown to exist in the venerable van der Waals model and its more modern interpretations. Although associated hydrogen-bonding (and to a lesser degree strongly polar) liquids display modestly more complex behavior, rather simple temperature and pressure dependences are also discovered. A new approach to collapse the temperature- and pressure-dependent dimensionless compressibility data onto a master curve is formulated that differs from the empirical thermodynamic scaling approach. As a practical matter, we also find that the dimensionless compressibility scales well as an inverse power law with temperature with an exponent that is system dependent and decreases with pressure. At very high pressures and low temperatures, the thermal liquid behavior appears to approach (but not reach) a repulsion-dominated random close packing limit. All these findings are relevant to our recent theoretical work on the problem of activated relaxation and vitrification of supercooled molecular and polymeric liquids.

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical "slaving onset" stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.