Equilibrium and nonequilibrium dynamics of dense liquids

Abstract

Dense liquids do many interesting things: they freeze into crystals, and sometimes get trapped into glassy states along the way. Their behaviour becomes more unusual when they are driven far away from equilibrium, for instance by a shear flow. In this thesis we address some aspects of the physics of each of these phenomena. In one part, we look for a growing correlation length and bond-orientational ordering near the glass transition in binary mixtures of simple liquids. The rest of the thesis deals with colloidal suspensions, which are interesting systems that mimic ordinary liquids in many respects, on larger length scales: they freeze into crystals, and when subjected to shear, display many novel features in their physics; notably, transport properties are modified to yield a variety of interesting phenomena. We study self-diffusion in interacting colloids in two contexts: the suppression of self-diffusion at the equilibrium freezing transition, and its strong dependence on shear rate when the colloid is subjected to a shear flow. We are able to explain several features of these two phenomena observed in recent experiments and simulations. An outline of the thesis is given below. We begin with an Introduction in Chapter 1. Here we give an overview of some aspects of the physics of dense liquids. We also survey the physics of colloidal suspensions. We summarise earlier work pertaining to the problems dealt with in this thesis. Chapter 2 describes a numerical analysis of molecular dynamics data obtained from a simulation of a Lennard-Jones binary mixture, in a search for a growing correlation length, and any bond-orientational ordering, near the glass transition. In particular we look for evidence of icosahedral order. In order to look for a growing correlation length, the system-size dependence of the relaxation times of bond-orientational correlation functions is studied, and compared to a similar analysis of density correlation functions. Our results are the following: (a) there is no particular tendency towards icosahedral ordering near the transition; (b) no effects of finite-size can be seen in the orientational relaxation times near the transition; (c) orientational and density correlation functions decay in a very similar manner, and we can identify the same temperature for the glass transition using either of them. The growth in relaxation times of both density and orientational correlations is of similar magnitude. Our results for orientational correlations match those for density correlations, and allow us to conclude that there indeed is no growing correlation length near the glass transition. This conclusion questions certain earlier theories that claim the existence of an underlying continuous phase transition whenever a liquid forms a glass. In Chapter 3 we study the suppression of self-diffusion in colloidal liquids at freezing. We provide a theoretical explanation for the observed quasi-universality of the ratio D/D? of the long-time to short-time self-diffusion coefficients for different colloidal liquids (interacting with different potentials) on the freezing line. This is the “dynamical freezing criterion” seen in experiments and Brownian dynamics simulations. We also predict that the mean squared displacement at freezing, plotted against a suitably renormalized time, yields a universal curve showing a short-time sub-diffusive regime and a long-time caged diffusion. We obtain C?(k,t), the incoherent part of the intermediate scattering function, for all (k,t), and show that it implies strong non-Gaussian behaviour in the probability distribution of the single-particle displacement at short times. In Chapter 4 we examine some unusual features of the self-diffusion coefficient in an interacting colloidal suspension driven away from equilibrium by a shear flow. In particular, we obtain theoretically the shear-induced enhancement of self-diffusion, which has been observed both in experiments and in simulations. We set up generalized Langevin equations describing coupled single-particle and collective motions in a suspension of interacting colloidal particles undergoing shear. We show that the self-diffusion coefficient should be strongly dependent on shear-rate ?. Three regimes are found: (a) an initial constant + followed by (b) a large regime of behaviour, crossing over asymptotically to the Stokes-Einstein value D? as (c) ? ? ?. We also find that the shear-induced enhancement is isotropic until we reach very large shear rates. This direction-independence of the enhancement is also in agreement with experiments and simulations. Our simple theory explains how shear enhances self-diffusion by a reduction of the effective friction felt by a colloidal particle because of its interactions with other particles. We end the thesis with Chapter 5, which presents briefly a critical review of the material in the previous Chapters. We conclude with a few comments on possible future extensions of our work.