Equilibration and Aging of Liquids of Non-Spherically Interacting Particles

Abstract

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible processes in liquids is extended to describe the positional and orientational thermal fluctuations of the instantaneous local concentration profile n(r, Ω, t) of a suddenly-quenched colloidal liquid of particles interacting through non spherically-symmetric pairwise interactions, whose mean value n(r, Ω, t) is constrained to remain uniform and isotropic, n(r, Ω, t) = n(t). Such self-consistent theory is cast in terms of the time-evolution equation of the covariance σ(t) = δn lm (k; t)δn † lm (k; t) of the fluctuations δn lm (k; t) = n lm (k; t)−n lm (k; t) of the spherical harmonics projections n lm (k; t) of the Fourier transform of n(r, Ω, t). The resulting theory describes the non-equilibrium evolution after a sudden temperature quench of both, the static structure factor projections S lm (k, t) and the two-time correlation function F lm (k, τ ; t) ≡ δn lm (k, t)δn lm (k, t + τ ), where τ is the correlation delay time and t is the evolution or waiting time after the quench. As a concrete and illustrative application we use the resulting self-consistent equations to describe the irreversible processes of equilibration or aging of the orientational degrees of freedom of a system of strongly interacting classical dipoles with quenched positional disorder.

Arrested dynamics of the dipolar hard sphere model

“…Let us also mention that the present work is also an essential and unavoidable first step in a more ambitious program towards a deeper study of the non-equilibrium and nonstationary phenomena, such as the kinetics of the aging associated with these transitions. As it happens, the SCGLE formalism has recently been extended to describe non-stationary non-equilibrium structural relaxation processes, such as aging or the dependence of the dynamical and structural properties on the protocol of fabrication, in liquids constituted by particles interacting through non spherical potentials [63]. The resulting non-equilibrium self-consistent generalized Langevin equation theory, aimed at describing non-equilibrium phenomena in general, leads in particular to a simple and intuitive (but still generic) description of the essential behavior of glass-forming dipolar liquids near and beyond its dynamical arrest transitions.…”

“Inner clocks” of glass-forming liquids

“…that is, in terms of the non-stationary τ-dependent friction functions Δζ * T (τ; t) and Δζ * R (τ; t), for which approximate expressions are provided, 29,64,69 namely,…”

Non-Equilibrium View of the Amorphous Solidification of Liquids with Competing Interactions

“…Extended to multi-component systems [67,72] the NE-SCGLE theory opens the possibility of describing the aging of "double" and "single" glasses in mixtures of neutral [57,73,74] and charged [58,75] particles; the initial steps in this direction are highly encouraging [74]. Similarly, its extension to liquids formed by particles interacting by nonradially symmetric forces [76][77][78], accurately predicts the non-equilibrium coupled translational and rotational dynamic arrest observed in simulations [79].…”