Self-consistent generalized Langevin equation theory of the dynamics of multicomponent atomic liquids

Abstract

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently-discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation (SCGLE) theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid, and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions.

Crossover from equilibration to aging: Nonequilibrium theory versus simulations

“…In essence, following Ref. [40], we use the fact that the NE-SCGLE equations (Eqs. (A1)-(A6)) also describe the non-equilibrium dynamics of the atomic mixture in the long-time diffusive regime, and that a simple manner to interpolate between the correct short-time ballistic and long-time difusive behavior, is provided by the interpolating expressions in Eqs.…”

“…Similarly, to properly compare the NE-SCGLE theoretical predictions (originally derived for Brownian, rather than molecular, liquids) with the present MD simulation data, we applied the long-time dynamic equivalence between Brownian and molecular systems proposed in Ref. [40], to adapt the NE-SCGLE theory to liquids with underlying molecular microscopic dynamics. This allows us to compare on an equal footing the theoretically-predicted results with the simulated dynamics of the atomic liquid.…”

Colloidal Soft Matter Physics

“…One of the most important challenges in Colloidal Soft Matter Physics is to understand the mechanisms that give rise to the non-equilibrium states of matter. Although there have been important contributions in the particular case of colloidal gels and glasses [27][28][29][92][93][94][95][96][97][98], it has not yet been possible to understand and establish the relationship between these states of matter [28,99], or even more, it is important to explore the possibility of introducing a universal definition of gel [29] and, in addition, it is necessary to quantify the effects that the gravitational field has on the formation of non-equilibrium states [100]. As mentioned above, it is also interesting to study the effective potentials between macromolecules near the gelation or vitrification boundary.…”

Noether's Theorem in Statistical Mechanics

“…nonlocal in time) [83]. The study of memory kernels, often carried out in the framework of generalized Langevin equations, is a topic of significant current research activity [84][85][86][87][88][89][90][91].…”