Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids

Abstract

For over 30 years, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the transition from the fluid to glassy state. MCT, however, is limited by its ad hoc construction and lacks a mechanism to institute corrections. We use recent results from a new theoretical framework-developed from first principles via a self-consistent perturbation expansion in terms of an effective two-body potential-to numerically explore the kinetics of systems of classical particles, specifically hard spheres governed by Smoluchowski dynamics. We present here a full solution for such a system to the kinetic equation governing the density-density time correlation function and show that the function exhibits the characteristic two-step decay of supercooled fluids and an ergodic-nonergodic transition to a dynamically-arrested state. Unlike many previous numerical studies,-and in stark contrast to experiment,-we have access to the full time and wavenumber range of the correlation function with great precision, and are able to track the solution unprecedentedly close to the transition, covering nearly 15 decades in scaled time. Using asymptotic approximation techniques analogous to those developed for MCT, we fit the solution to predicted forms and extract critical parameters. Our solution shows a transition at packing fraction η * = 0.60149761(10)-consistent with previous static solutions under this theory and with comparable colloidal suspension experiments-and the behavior in the β-relaxation regime is fit to power-law decays of the typical forms with critical exponents a = 0.375(3) and b = 0.8887(4), and critical exponent parameter λ = 0.5587(18). For the α-relaxation of the ergodic phase, we find a power-law divergence of the time scale τ α as we approach the transition, and in the nonergodic phase we find glass form factors whose amplitudes scale as the square-root of distance from the transition as predicted. Through these results, we establish that this new theory is able to reproduce the salient features of MCT, but has the advantages of being derived from first principles and possessing a clear mechanism for making systematic improvements.

Classical dynamical density functional theory: from fundamentals to applications

“…Smoluchowski dynamics is considered in Refs. [758][759][760] and Newtonian dynamics in Refs. [761,762].…”