Nonuniversal Coupling of Cage Scale Hopping and Collective Elastic Distortion as the Origin of Dynamic Fragility Diversity in Glass-Forming Polymer Liquids

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.

How Segmental Dynamics and Mesh Confinement Determine the Selective Diffusivity of Molecules in Cross-Linked Dense Polymer Networks

The diffusion of molecules ("penetrants") of variable size, shape, and chemistry through dense cross-linked polymer networks is a fundamental scientific problem broadly relevant in materials, polymer, physical, and biological chemistry. Relevant applications include separation membranes, barrier materials, drug delivery, and nanofiltration. A major open question is the relationship between transport, thermodynamic state, and penetrant and polymer chemical structure. Here we combine experiment, simulation, and theory to unravel these competing effects on penetrant transport in rubbery and supercooled polymer permanent networks over a wide range of cross-link densities, size ratios, and temperatures. The crucial importance of the coupling of local penetrant hopping to polymer structural relaxation and the secondary importance of mesh confinement effects are established. Network cross-links strongly slow down nm-scale polymer relaxation, which greatly retards the activated penetrant diffusion. The demonstrated good agreement between experiment, simulation, and theory provides strong support for the size ratio (penetrant diameter to the polymer Kuhn length) as a key variable and the usefulness of coarse-grained simulation and theoretical models that average over Angstrom scale structure. The developed theory provides an understanding of the physical processes underlying the behaviors observed in experiment and simulation and suggests new strategies for enhancing selective polymer membrane design.

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.

Screening and collective effects in randomly pinned fluids: a new theoretical framework

We propose a theoretical framework for the dynamics of bulk isotropic hard-sphere systems in the presence of randomly pinned particles and apply this theory to supercooled water to validate it. Structural relaxation is mainly governed by local and non-local activated process. As the pinned fraction grows, a local caging constraint becomes stronger and the long range collective aspect of relaxation is screened by immobile obstacles. Different responses of the local and cooperative motions results in subtle predictions for how the alpha relaxation time varies with pinning and density. Our theoretical analysis for the relaxation time of water with pinned molecules quantitatively well describe previous simulations. In addition, the thermal dependence of relaxation for unpinned bulk water is also consistent with prior computational and experimental data.

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 T_g, whether there is an underlying thermodynamic transition at some finite temperature below T_g, 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.

Approaching Polymer Dynamics Combining Artificial Neural Networks and Elastically Collective Nonlinear Langevin Equation

The analysis of structural relaxation dynamics of polymers gives an insight into their mechanical properties, whose characterization is used to qualify a given material for its practical scope. The dynamics are usually expressed in terms of the temperature dependence of the relaxation time, which is only available through time-consuming experimental processes following polymer synthesis. However, it would be advantageous to estimate their dynamics before synthesizing them when designing new materials. In this work, we propose a combined approach of artificial neural networks and the elastically collective nonlinear Langevin equation (ECNLE) to estimate the temperature dependence of the main structural relaxation time of polymers based only on the knowledge of the chemical structure of the corresponding monomer.

Construction of a quantitative relation between structural relaxation and dynamic heterogeneity by vibrational dynamics in glass-forming liquids and polymers

The structural relaxation slows down drastically upon approaching the glass transition, accompanied by the significant growth of dynamic heterogeneity. The fundamental question of elusiveness and interest is whether there exists an underlying quantitative relationship between structural relaxation and dynamic heterogeneity. Here, we reveal that b̃ which is related to the reduced mean square displacements to overcome the energy barriers of activated jumps, instead of the kinetic fragility m, is the genuine key parameter connecting dynamic heterogeneity with structural relaxation for varying types of glass formers. Furthermore, based on the dependence of dynamic heterogeneity on the Debye-Waller factor we obtained a direct quantitative relation between dynamic heterogeneity and structural relaxation is built for different glass-forming liquids. More importantly, a scaling collapse of structural relaxation and dynamic heterogeneity is achieved by the important parameter b̃. These results are of fundamental and critical importance for developing a unified theory of glassy dynamics.

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.

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

Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different "order parameters" including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local-nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply supercooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.

Theory of Pressure-Induced Rejuvenation and Strain Hardening in Metallic Glasses

We theoretically investigate high-pressure effects on the atomic dynamics of metallic glasses. The theory predicts compression-induced rejuvenation and the resulting strain hardening that have been recently observed in metallic glasses. Structural relaxation under pressure is mainly governed by local cage dynamics. The external pressure restricts the dynamical constraints and slows down the atomic mobility. In addition, the compression induces a rejuvenated metastable state (local minimum) at a higher energy in the free-energy landscape. Thus, compressed metallic glasses can rejuvenate and the corresponding relaxation is reversible. This behavior leads to strain hardening in mechanical deformation experiments. Theoretical predictions agree well with experiments.

Determination of Young's Modulus of Active Pharmaceutical Ingredients by Relaxation Dynamics at Elevated Pressures

A new approach is theoretically proposed to study the glass transition of active pharmaceutical ingredients and a glass-forming anisotropic molecular liquid at high pressures. We describe amorphous materials as a fluid of hard spheres. Effects of nearest neighbor interactions and cooperative motions of particles on glassy dynamics are quantified through a local and collective elastic barrier calculated using the elastically collective nonlinear Langevin equation theory. Inserting two barriers into Kramer's theory gives the structural relaxation time. Then, we formulate a new mapping based on the thermal expansion process under pressure to intercorrelate particle density, temperature, and pressure. This analysis allows us to determine the pressure and temperature dependence of α relaxation. From this, we estimate the effective elastic modulus of amorphous materials and capture the effects of conformation on the relaxation process. Remarkably, our theoretical results agree well with experiments.

Microscopic theory of onset of decaging and bond-breaking activated dynamics in ultradense fluids with strong short-range attractions

We theoretically study thermally activated "in cage" elementary dynamical processes that precede full structural relaxation in ultradense particle liquids interacting via strong short-range attractive forces. The analysis is based on a microscopic theory formulated at the particle trajectory level built on the dynamic free energy concept and an explicit treatment of how attractive forces control the formation and lifetime of physical bonds. Mean time scales for bond breaking, the early stage of cage escape, and non-Fickian displacement by a fixed amount are analyzed in the repulsive glass, bonded repulsive (attractive) glass, fluid, and dense gel regimes. The theory predicts a strong length-scale-dependent growth of these time scales with attractive force strength at fixed packing fraction, a much weaker slowing down with density at fixed attraction strength, and a strong decoupling of the shorter bond-breaking time with the other two time scales that are controlled mainly by perturbed steric caging. All results are in good accord with simulations, and additional testable predictions are made. The classic statistical mechanical projection approximation of replacing all bare attractive and repulsive forces with a single effective force determined by pair structure incurs major errors for describing processes associated with thermally activated escape from transiently localized states.

Thermodynamics-Structure-Dynamics Correlations and Nonuniversal Effects in the Elastically Collective Activated Hopping Theory of Glass-Forming Liquids

We employ the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated dynamics in combination with crystal-avoiding simulations to study four inter-related questions for metastable monodisperse hard sphere fluids. The first is how significantly improved integral equation theory structural input (Modified-Verlet (MV) closure) changes the dynamical predictions of ECNLE theory. The main consequence is a modest enhancement of the importance of the collective elastic barrier relative to its local cage contribution, which increases the alpha relaxation time and fragility relative to prior results based on the Percus-Yevick closure. Second, ECNLE-MV theory predictions for the alpha time and self-diffusion constant in the metastable regime are quantitatively compared to our new simulations. The small adjustment of a numerical prefactor that enters the collective elastic barrier leads to quantitative agreement over three decades. Third, using the more accurate MV structural input, ECNLE theory is shown to predict thermodynamics-structure-dynamics "correlations" based on various long and short wavelength scalar properties all related to static two-point collective density fluctuations. The logarithm of the alpha relaxation time scales as a power law with these scalar metrics with an exponent that is significantly lower in the less dense noncooperative activated regime compared to the very dense highly cooperative regime. However, the discovered correlation of activated relaxation with a thermodynamic property (dimensionless compressibility) is not causal in ECNLE theory, but rather reflects a strong connection between the local structural quantities that quantify kinetic constraints in the theory with the amplitude of long wavelength density fluctuations. Fourth, the consequences of chemically specific nonuniversalities associated with the onset condition and relative importance of collective elasticity are studied. The predicted thermodynamics-structure-dynamics correlations are found to be robust, albeit with nontrivial shifts of the onset condition.

Surface diffusion in glasses of rod-like molecules posaconazole and itraconazole: effect of interfacial molecular alignment and bulk penetration

The method of surface grating decay has been used to measure surface diffusion in the glasses of two rod-like molecules posaconazole (POS) and itraconazole (ITZ). Although structurally similar antifungal medicines, ITZ forms liquid-crystalline phases while POS does not. Surface diffusion in these systems is significantly slower than in the glasses of quasi-spherical molecules of similar volume when compared at the glass transition temperature T_g. Between the two systems, ITZ has slower surface diffusion. These results are explained on the basis of the near-vertical orientation of the rod-like molecules at the surface and their deep penetration into the bulk where mobility is low. For molecular glasses without extensive hydrogen bonds, we find that the surface diffusion coefficient at T_g decreases smoothly with the penetration depth of surface molecules and the trend has the double-exponential form for the surface mobility gradient observed in simulations. This supports the view that these molecular glasses have a similar mobility vs. depth profile and their different surface diffusion rates arise simply from the different depths at which molecules are anchored. Our results also provide support for a previously observed correlation between the rate of surface diffusion and the fragility of the bulk liquid.

Theoretical and Experimental Study of Compression Effects on Structural Relaxation of Glass-Forming Liquids

We develop the elastically collective nonlinear Langevin equation theory of bulk relaxation of glass-forming liquids to investigate molecular mobility under compression conditions. The applied pressure restricts more molecular motion and therefore significantly slows down the molecular dynamics when increasing the pressure. We quantitatively determine the temperature and pressure dependence of the structural relaxation time. To validate our model, dielectric spectroscopy experiments for three rigid and nonpolymeric supramolecules are carried out at ambient and elevated pressures. The numerical results quantitatively agree with experimental data.

Theory of Spatial Gradients of Relaxation, Vitrification Temperature and Fragility of Glass-Forming Polymer Liquids Near Solid Substrates

We employ a new force-level statistical mechanical theory to predict spatial gradients of the structural relaxation time and T_g of polymer liquids near microscopically rough and smooth hard surfaces and contrast the results with vapor interface systems. Repulsive rough (smooth) surfaces induce large slowing down (modest speeding up) of the relaxation time compared to the bulk. Nevertheless, a remarkable degree of universality of distinctive dynamical behaviors is predicted for different polymer chemistries and all interfaces, including a double exponential form of the alpha time gradient, power law decoupling of the relaxation time from its bulk value with exponential spatial variation of the exponent, exponential spatial gradient of T_g, weak dependence of normalized T_g gradients on vitrification criterion, and near linear growth with cooling of the slowed down layer thickness near a rough hard interface. The results appear consistent with simulations and experiments, and multiple testable predictions are made.

Theory of Structural and Secondary Relaxation in Amorphous Drugs under Compression

Compression effects on alpha and beta relaxation process of amorphous drugs are theoretically investigated by developing the elastically collective nonlinear Langevin equation theory. We describe the structural relaxation as a coupling between local and nonlocal activated process. Meanwhile, the secondary beta process is mainly governed by the nearest-neighbor interactions of a molecule. This assumption implies the beta relaxation acts as a precursor of the alpha relaxation. When external pressure is applied, a small displacement of a molecule is additionally exerted by a pressure-induced mechanical work in the dynamic free energy, which quantifies interactions between a molecule with its nearest neighbors. The local dynamics has more restriction and it induces stronger effects of collective motions on single-molecule dynamics. Thus, the alpha and beta relaxation times are significantly slowed down with increasing compression. We apply this approach to determine the temperature and pressure dependence of the alpha and beta relaxation time for curcumin, glibenclamide, and indomethacin, and compare numerical results with prior experimental studies. Both qualitative and quantitative agreement between theoretical calculations and experiments validate our assumptions and reveal their limitations. Our approach would pave the way for the development of the drug formulation process.

Coupling between structural relaxation and diffusion in glass-forming liquids under pressure variation

We theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulations.

Progress towards a phenomenological picture and theoretical understanding of glassy dynamics and vitrification near interfaces and under nanoconfinement

The nature of alterations to dynamics and vitrification in the nanoscale vicinity of interfaces-commonly referred to as "nanoconfinement" effects on the glass transition-has been an open question for a quarter century. We first analyze experimental and simulation results over the last decade to construct an overall phenomenological picture. Key features include the following: after a metrology- and chemistry-dependent onset, near-interface relaxation times obey a fractional power law decoupling relation with bulk relaxation; relaxation times vary in a double-exponential manner with distance from the interface, with an intrinsic dynamical length scale appearing to saturate at low temperatures; the activation barrier and vitrification temperature T_g approach bulk behavior in a spatially exponential manner; and all these behaviors depend quantitatively on the nature of the interface. We demonstrate that the thickness dependence of film-averaged T_g for individual systems provides a poor basis for discrimination between different theories, and thus we assess their merits based on the above dynamical gradient properties. Entropy-based theories appear to exhibit significant inconsistencies with the phenomenology. Diverse free-volume-motivated theories vary in their agreement with observations, with approaches invoking cooperative motion exhibiting the most promise. The elastically cooperative nonlinear Langevin equation theory appears to capture the largest portion of the phenomenology, although important aspects remain to be addressed. A full theoretical understanding requires improved confrontation with simulations and experiments that probe spatially heterogeneous dynamics within the accessible 1-ps to 1-year time window, minimal use of adjustable parameters, and recognition of the rich quantitative dependence on chemistry and interface.

Theory of the spatial transfer of interface-nucleated changes of dynamical constraints and its consequences in glass-forming films

We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the dynamic free energy concept of the Nonlinear Langevin Equation (NLE) theory approach. The dynamic free energy at any mean location (cage center) involves contributions from two adjacent layers where confining forces are not the same. At the most fundamental level of the theory, the caging component of the dynamic free energy varies essentially exponentially with distance from the interface, saturating deep enough into the film with a correlation length of modest size and weak sensitivity to the thermodynamic state. This imparts a roughly exponential spatial variation of all the key features of the dynamic free energy required to compute gradients of dynamical quantities including the localization length, jump distance, cage barrier, collective elastic barrier, and alpha relaxation time. The spatial gradients are entirely of dynamical, not structural or thermodynamic, origin. The theory is implemented for the hard sphere fluid and diverse interfaces which can be a vapor, a rough pinned particle solid, a vibrating (softened) pinned particle solid, or a smooth hard wall. Their basic description at the level of the spatially heterogeneous dynamic free energy is identical, with the crucial difference arising from the first layer where dynamical constraints can be weakened, softened, or hardly changed depending on the specific interface. Numerical calculations establish the spatial dependence and fluid volume fraction sensitivity of the key dynamical property gradients for five different model interfaces. A comparison of the theoretical predictions for the dynamic localization length and glassy modulus with simulations and experiments for systems with a vapor interface reveals good agreement. The present advance sets the stage for using the Elastically Collective NLE theory to make quantitative predictions for the alpha relaxation time gradient, decoupling phenomena, T_g gradient, and many film-averaged properties of both model and experimental (colloids, molecules, and polymers) systems with diverse interfaces and chemical makeup.

Effects of cooling rate on structural relaxation in amorphous drugs: elastically collective nonlinear langevin equation theory and machine learning study

Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs. We describe the structural relaxation of a tagged molecule as a coupled process of cage-scale dynamics and collective molecular rearrangement beyond the first coordination shell. The coupling between local and non-local dynamics behaves distinctly in different substances. Theoretical calculations for the structural relaxation time, glass transition temperature, and dynamic fragility are carried out over twenty-two amorphous drugs and polymers. Numerical results have a quantitatively good accordance with experimental data and the extracted physical quantities using the Vogel–Fulcher–Tammann fit function and machine learning. The machine learning method reveals the linear relation between the glass transition temperature and the melting point, which is a key factor for pharmaceutical solubility. Our predictive approaches are reliable tools for developing drug formulations.

Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs.

Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions

We formulate a microscopic, force-level statistical mechanical theory for the activated diffusion of dilute penetrants in dense liquids, colloidal suspensions, and glasses. The approach explicitly and self-consistently accounts for coupling between penetrant hopping and matrix dynamic displacements that actively facilitate the hopping event. The key new ideas involve two mechanistically (at a stochastic trajectory level) coupled dynamic free energy functions for the matrix and spherical penetrant particles. A single dynamic coupling parameter quantifies how much the matrix displaces relative to the penetrant when the latter reaches its transition state which is determined via the enforcement of a temporal causality or coincidence condition. The theory is implemented for dilute penetrants smaller than the matrix particles, with or without penetrant-matrix attractive forces. Model calculations reveal a rich dependence of the penetrant diffusion constant and degree of dynamic coupling on size ratio, volume fraction, and attraction strength. In the absence of attractions, a near exponential decrease of penetrant diffusivity with size ratio over an intermediate range is predicted, in contrast to the much steeper, non-exponential variation if one assumes local matrix dynamical fluctuations are not correlated with penetrant motion. For sticky penetrants, the relative and absolute influence of caging versus physical bond formation is studied. The conditions for a dynamic crossover from the case where a time scale separation between penetrant and matrix activated hopping exists to a "slaved" or "constraint release" fully coupled regime are determined. The particle mixture model is mapped to treat experimental thermal systems and applied to make predictions for the diffusivity of water, toluene, methanol, and oxygen in polyvinylacetate liquids and glasses. The theory agrees well with experiment with values of the penetrant-matrix size ratio close to their chemically intuitive values.