Nikolaos Lempesis¹, Maxime Delhorme^1,2, Georgios G. Vogiatzis¹,
Georgios C. Boulougouris³, Lambert C.A. van Breemen², Markus Hütter²,
and Doros N. Theodorou¹

(1) National Technical University of Athens, School of Chemical Engineering, Greece.
 (2) Eindhoven University of Technology, Mechanical Engineering, Polymer
Technology, Eindhoven, The Netherlands.  (3) Department of Molecular Biology and
Genetics, Democritus University of Thrace, Alexandroupolis, Greece

Many materials systems can be envisioned as evolving through infrequent transitions in a network of discrete states, each state providing a coarse-grained description of a domain in multidimensional configuration space.  This picture seems especially promising for addressing the properties of glasses, whose nonequilibrium nature and extremely broad spectra of relaxation times pose severe challenges for molecular simulation.  Here the role of states is played by “basins” surrounding local minima of the potential energy (“inherent structures”[1]). 

By formulating a thermodynamics for a glassy system arrested in a basin, invoking the  quasiharmonic approximation (QHA), and performing a quenched average over different basins accessed by a given glass formation history, one can estimate the density and elastic constants as functions of temperature in good agreement with molecular dynamics simulations and experiment [2].

Structural relaxation in a glass entails a succession of infrequent jumps from basin to basin.  The rate constants of these jumps can be estimated via Transition State Theory in the QHA.  The Dynamic Integration of a Markovian Web (DIMW) strategy [3] tracks relaxation towards equilibrium from a narrow initial distribution among states by solving the master equation in a network of explored states that is progressively augmented on the fly.  From DIMW one can compute time correlation functions for any observable, assess the contribution of various relaxation modes to the decay of these correlation functions, and elucidate the molecular motions associated with the modes.

DIMW has been combined with external imposition of strain- or stress-controlled mechanical deformation at rates commensurate with those used in experiments.  Results will be presented  for the stress-strain curve of a united-atom model of glassy atactic polystyrene.  

[1] F. H. Stillinger and T.A. Weber, Science 225, 983 (1984).
[2] N. Lempesis, G.G. Vogiatzis, G.C. Boulougouris, L.C.A. van Breemen, M. Hütter, and D.N. Theodorou, Mol. Phys. 111, 3641 (2013).
[3] G.C. Boulougouris and D.N. Theodorou, J. Chem. Phys. 127, 084903 (2007).