Network dynamics: a computational framework for the simulation of the glassy state

Abstract

An out-of-equilibrium simulation method for tracking the time evolution of glassy systems (or any other systems that can be described by hopping dynamics over a network of discrete states) is presented. Graph theory and complexity concepts are utilised, alongside the method of the dynamical integration of a Markovian web (G. C. Boulougouris and D. N. Theodorou, J. Chem. Phys., 2007, 127, 084903) in order to provide a unified framework for dealing with the long time-scales of non-ergodic systems. Within the developed formalism, the network of states accessible to the system is considered a finite part of the overall universe, communicating with it through well-defined boundary states. The analytical solution of the probability balance equation proceeds without the need for assuming the existence of an equilibrium distribution among the states of the network and the corresponding survival and escape probabilities (as functions of time) are defined. More importantly, the study of the probability flux through the dividing surface separating the system and its environment reveals the relaxation mechanisms of the system. We apply our approach to the network of states obtained by exploring the energy landscape of an atomistically detailed glassy specimen of atactic polystyrene. The rate constants connecting different basins of the landscape are evaluated by multi-dimensional transition-state-theory. We are able to accurately probe the appearance of the δ- and γ-subglass relaxation mechanisms and their relevant time-scales, out of atomistic simulations. The proposed approach can fill a gap in the rational molecular design toolbox, by providing an alternative to molecular dynamics for structural relaxation in glasses and/or other slow molecular processes (e.g., adsorption or desorption) that involve very distant time-scales.