Non-Equilibrium Dynamics Of Glass-Forming Liquid Mixtures

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible processes in glass-forming liquids [P. Ram rez-Gonzalez and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010)] is extended here to multi-component systems. The resulting theory describes the statistical properties of the instantaneous local particle concentration profiles n(alpha)(r, t) of species alpha in terms of the coupled time-evolution equations for the mean value (n) over bar (alpha)(r, t) and for the covariance sigma(alpha beta)(r, r'; t) = <(delta n(alpha)(r, t)delta n(beta)(r', t))over bar> of the fluctuations delta n(alpha)(r, t) = n(alpha)(r, t) - (n) over bar (alpha)(r, t). As in the monocomponent case, these two coarse-grained equations involve a local mobility function b(alpha)(r, t) for each species, written in terms of the memory function of the two-time correlation function C-alpha beta(r, r'; t, t') = <(delta n(alpha)(r, t)delta n(beta)(r', t'))over bar>. If the system is constrained to remain spatially uniform and subjected to a non-equilibrium preparation protocol described by a given temperature and composition change program T(t) and (n) over bar (alpha)(t), these equations predict the irreversible structural relaxation of the partial static structure factors S-alpha beta(k; t) and of the (collective and self) intermediate scattering functions F-alpha beta(k, tau; t) and F-alpha beta(S)(k, tau; t). We illustrate the applicability of the resulting theory with two examples involving simple model mixtures subjected to an instantaneous temperature quench: an electroneutral binary mixture of equally sized and oppositely charged hard-spheres, and a binary mixture of soft-spheres of moderate size-asymmetry. (C) 2014 AIP Publishing LLC.