Influence of chemistry, interfacial width, and non-isothermal conditions on spatially heterogeneous activated relaxation and elasticity in glass-forming free standing films.

We employ the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation to study several questions in free standing thin films of glass-forming molecular and polymer liquids. The influence of non-universal chemical aspects on dynamical confinement effects is found to be relatively weak, but with the caveat that for the systems examined, the bulk ECNLE polymer theory does not predict widely varying fragilities. Allowing the film model to have a realistic vapor interfacial width significantly enhances the reduction of the film-averaged glass transition temperature, Tg, in a manner that depends on whether a dynamic or pseudo-thermodynamic averaging of the spatial mobility gradient is adopted. The nature of film thickness effects on the spatial profiles of the alpha relaxation time and elastic modulus is studied under non-isothermal conditions and contrasted with the corresponding isothermal behavior. Modest differences are found if a film-thickness dependent Tg is defined in a dynamical manner. However, adopting a pseudo-thermodynamic measure of Tg leads to a qualitatively new form of the alpha relaxation time gradient where highly mobile layers near the film surface coexist with strongly vitrified regions in the film interior. As a consequence, the film-averaged shear modulus can increase with decreasing film thickness, despite the Tg reduction and presence of a mobile surface layer. Such a behavior stands in qualitative contrast to the predicted mechanical softening under isothermal conditions. Spatial gradients of the elastic modulus are studied as a function of temperature, film thickness, probing frequency, and experimental protocol, and a rich behavior is found.

Theory of activated glassy relaxation, mobility gradients, surface diffusion, and vitrification in free standing thin films.

We have constructed a quantitative, force level, statistical mechanical theory for how confinement in free standing thin films introduces a spatial mobility gradient of the alpha relaxation time as a function of temperature, film thickness, and location in the film. The crucial idea is that relaxation speeds up due to the reduction of both near-surface barriers associated with the loss of neighbors in the local cage and the spatial cutoff and dynamical softening near the vapor interface of the spatially longer range collective elasticity cost for large amplitude hopping. These two effects are fundamentally coupled. Quantitative predictions are made for how an apparent glass temperature depends on the film thickness and experimental probe technique, the emergence of a two-step decay and mobile layers in time domain measurements, signatures of confinement in frequency-domain dielectric loss experiments, the dependence of film-averaged relaxation times and dynamic fragility on temperature and film thickness, surface diffusion, and the relationship between kinetic experiments and pseudo-thermodynamic measurements such as ellipsometry.

Revealing spatially heterogeneous relaxation in a model nanocomposite.

The detailed nature of spatially heterogeneous dynamics of glycerol-silica nanocomposites is unraveled by combining dielectric spectroscopy with atomistic simulation and statistical mechanical theory. Analysis of the spatial mobility gradient shows no "glassy" layer, but the α-relaxation time near the nanoparticle grows with cooling faster than the α-relaxation time in the bulk and is ∼20 times longer at low temperatures. The interfacial layer thickness increases from ∼1.8 nm at higher temperatures to ∼3.5 nm upon cooling to near bulk Tg. A real space microscopic description of the mobility gradient is constructed by synergistically combining high temperature atomistic simulation with theory. Our analysis suggests that the interfacial slowing down arises mainly due to an increase of the local cage scale barrier for activated hopping induced by enhanced packing and densification near the nanoparticle surface. The theory is employed to predict how local surface densification can be manipulated to control layer dynamics and shear rigidity over a wide temperature range.

Communication: Slow relaxation, spatial mobility gradients, and vitrification in confined films.

Two decades of experimental research indicate that spatial confinement of glass-forming molecular and polymeric liquids results in major changes of their slow dynamics beginning at large confinement distances. A fundamental understanding remains elusive given the generic complexity of activated relaxation in supercooled liquids and the major complications of geometric confinement, interfacial effects, and spatial inhomogeneity. We construct a predictive, quantitative, force-level theory of relaxation in free-standing films for the central question of the nature of the spatial mobility gradient. The key new idea is that vapor interfaces speed up barrier hopping in two distinct, but coupled, ways by reducing near surface local caging constraints and spatially long range collective elastic distortion. Effective vitrification temperatures, dynamic length scales, and mobile layer thicknesses naturally follow. Our results provide a unified basis for central observations of dynamic and pseudo-thermodynamic measurements.

Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids.

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.

Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. II. Thermal liquids.

Building on the elastically collective nonlinear Langevin equation theory developed for hard spheres in Paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermal liquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility. The result is a zero adjustable parameter theory that can quantitatively address in a unified manner the alpha relaxation time over 14 or more decades. The theory has no singularities above zero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a roughly Arrhenius form. The two-barrier (local cage and long range collective elastic) description results in a rich dynamic behavior including apparent Arrhenius, narrow crossover, and deeply supercooled regimes, and multiple characteristic or crossover times and temperatures of clear physical meaning. Application of the theory to nonpolar molecules, alcohols, rare gases, and liquids metals is carried out. Overall, the agreement with experiment is quite good for the temperature dependence of the alpha time, plateau shear modulus, and Boson-like peak frequency for van der Waals liquids, though less so for hydrogen-bonding molecules. The theory predicts multiple growing length scales upon cooling, which reflect distinct aspects of the coupled local hopping and cooperative elastic physics. Calculations of the growth with cooling of an activation volume, which is strongly correlated with a measure of dynamic cooperativity, agree quantitatively with experiment. Comparisons with elastic, entropy crisis, dynamic facilitation, and other approaches are performed, and a fundamental basis for empirically extracted crossover temperatures is established. The present work sets the stage for addressing distinctive glassy phenomena in polymer melts, and diverse liquids under strong confinement.

Kinetics of particle wrapping by a vesicle.

We present theoretical results on kinetics for the passive wrapping of a single, rigid particle by a flexible membrane. Using a simple geometric ansatz for the shape of the membrane/particle complex we first compute free energy profiles as a function of the particle size, attraction strength between the particle and vesicle, and material properties of the vesicle--bending stiffness and stretching modulus. The free energy profiles thus computed are taken as input to a stochastic model of the wrapping process, described by a Fokker-Planck equation. We compute average uptake rates of the particle into the vesicle. We find that the rate of particle uptake falls to zero outside of a thermodynamically allowed range of particle sizes. Within the thermodynamically allowed range of particle size, the rate of uptake is variable and we compute the optimal particle size and maximal uptake rate as a function of the attraction strength, the vesicle size, and vesicle material properties.

Translocation of a heterogeneous polymer.

We present results on the sequence dependence of translocation kinetics for a partially charged heteropolymer moving through a very thin pore using theoretical tools and Langevin dynamics simulational techniques. The chain is composed of two types of monomers of differing frictional interaction with the pore and charge. We present exact analytical expressions for passage probability, mean first passage time, and mean successful passage times for both reflecting/absorbing and absorbing/absorbing boundary conditions, showing rich and unexpected dependence of translocation behavior on charge fraction, distribution along the chain, and electric field configuration. We find excellent qualitative and good quantitative agreement between theoretical and simulation results. Surprisingly, there emerges a threshold charge fraction of a diblock copolymer beyond which the success rate of translocation is independent of charge fraction. Also, the mean successful translocation time of a diblock copolymer displays non-monotonic behavior with increasing length of the charged block; there is an optimum length of the charged block where the mean translocation rate is the slowest; and there can be a substantial range of higher charge fractions which make the translocation slower than even a minimally charged chain. Additionally, we find for a fixed total charge on the chain, finer distribution along the backbone significantly decreases mean translocation time.