Elastically Collective Nonlinear Langevin Equation Research Articles

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.

Activated relaxation in supercooled monodisperse atomic and polymeric WCA fluids: Simulation and ECNLE theory

We combine simulation and Elastically Collective Nonlinear Langevin Equation (ECNLE) theory to study the activated relaxation in monodisperse atomic and polymeric Weeks-Chandler-Andersen (WCA) liquids over a wide range of temperatures and densities in the supercooled regime under isochoric conditions. By employing novel crystal-avoiding simulations, metastable equilibrium dynamics is probed in the absence of complications associated with size polydispersity. Based on a highly accurate structural input from integral equation theory, ECNLE theory is found to describe well the simulated density and temperature dependences of the alpha relaxation time of atomic fluids using a single system-specific parameter, ac, that reflects the nonuniversal relative importance of local cage and collective elastic barriers. For polymer fluids, the explicit dynamical effect of local chain connectivity is modeled at the fundamental dynamic free energy trajectory level based on a different parameter, Nc, that quantifies the degree of intramolecular correlation of bonded segment activated barrier hopping. For the flexible chain model studied, a physically intuitive value of Nc ≈ 2 results in good agreement between simulation and theory. A direct comparison between atomic and polymeric systems reveals that chain connectivity can speed up activated segmental relaxation due to weakening of equilibrium packing correlations but can slow down relaxation due to local bonding constraints. The empirical thermodynamic scaling idea for the alpha time is found to work well at high densities or temperatures but fails when both density and temperature are low. The rich and subtle behaviors revealed from simulation for atomic and polymeric WCA fluids are all well captured by ECNLE theory.

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.

A collective elastic fluctuation mechanism for decoupling and stretched relaxation in glassy colloidal and molecular liquids.

We propose a microscopic theory for the decoupling of self-diffusion and structural relaxation in glass-forming liquids within the Elastically Collective Nonlinear Langevin Equation (ECNLE) activated dynamics framework. Our central hypothesis is that the heterogeneity relevant to this problem is static fluctuations of local density on the scale of 3-4 particle diameters and how this changes local packing correlations. These fluctuations modify the degree of dynamical cage expansion that mechanistically couples intracage large amplitude hopping and longer range collective elasticity in ECNLE theory. Decoupling only emerges in the deeply supercooled regime where the strongly temperature dependent elastic barrier becomes non-negligible relative to its noncooperative local analog. The theory makes predictions for various aspects of the decoupling phenomenon, including apparent fractional power law Stokes-Einstein behavior, that appear to be consistent with experiments and simulations on hard sphere fluids and molecular liquids. Of central importance is a microscopic connection between the barrier fluctuation variance and most probable barrier height. Sensible results are also obtained for the nonexponential stretching of a generic relaxation time correlation function and its temperature evolution. Nonuniversality can arise from the relative importance of the local and collective barriers (related to fragility) and the precise magnitude of the length scale that defines the transition from local cage to elastic physics. Comparison is made with a traplike model based on a Gaussian distribution of barriers.

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. An external pressure restricts local motions of a single molecule within its cage and triggers slowing down of cooperative mobility. While the ECNLE theory and simulations generally predict a monotonic increase of the glass transition temperature and dynamic fragility with pressure, the simulations indicate a decrease of fragility as pressures above 1000 bar. The structural relaxation time is found to be linearly coupled with the inverse diffusion constant. Remarkably, this coupling is independent of compression. The theoretical calculations quantitatively agree well with the simulations and are also consistent with prior work.

Microscopic theory of the influence of strong attractive forces on the activated dynamics of dense glass and gel forming fluids.

We theoretically study the nonmonotonic (re-entrant) activated dynamics associated with a finite time scale kinetically defined repulsive glass to fluid to attractive glass transition in high volume fraction particle suspensions interacting via strong short range attractive forces. The classic theoretical "projection" approximation that replaces all microscopic forces by a single effective force determined solely by equilibrium pair correlations is revisited based on the "projectionless dynamic theory" (PDT). A hybrid-PDT approximation is formulated that explicitly quantifies how attractive forces induce dynamical constraints, while singular hard core interactions are treated based on the projection approach. Both the effects of interference between repulsive and attractive forces, and structural changes due to attraction-induced bond formation that competes with caging, are included. Combined with the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation, the resultant approach appears to properly capture both the re-entrant dynamic crossover behavior and the strong nonmonotonic variation of the activated structural relaxation time with attraction strength and range at very high volume fractions as observed experimentally and in simulations. Testable predictions are made. Major differences compared to both ideal mode coupling theory and ECNLE theory based on the full force projection approximation are identified. Calculations are also performed for smaller time and length scale intracage dynamics relevant to the non-Gaussian parameter based on analyzing the dynamic free energy that controls particle trajectories. Implications of the new theory for thermal glass forming liquids with relatively long range attractive forces are briefly analyzed.

Elastically Collective Nonlinear Langevin Equation Theory of Glass-Forming Liquids: Transient Localization, Thermodynamic Mapping, and Cooperativity.

We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the elastically collective nonlinear Langevin equation (ECNLE) theory. By invoking a high-temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron-scattering measurements. In contrast, in the same format, a strongly nonuniversal behavior is found for the activation barrier that controls long-time relaxation. Two measures of cooperativity in the ECNLE theory are analyzed. A particle-level total displacement associated with the alpha relaxation event is found to be only of order 1-2 particle diameters and weakly increases with cooling. In contrast, an alternative cooperativity length is defined as the spatial scale required to essentially recover the full barrier and bulk alpha time. This length scale grows strongly with cooling because of the emergence in the deeply supercooled regime of collective long-range elastic fluctuations required to allow local hopping. It becomes very large as the laboratory Tg is approached, though it is relatively modest at degrees of supercooling accessible with molecular dynamics simulation. The alpha time is found to be exponentially related to this cooperativity length over an enormous number of decades of relaxation time that span the lightly to deeply supercooled regimes. Moreover, the effective barrier height increases almost linearly with the growing cooperativity length scale. An alternative calculation of the collective elastic barrier based on a literal continuum mechanics approach is shown to result in very little change of the theoretical results for bulk properties but leads to a much smaller and less temperature-sensitive cooperativity length scale.

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.