Overdamped van hove function of colloidal suspensions

Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics

We demonstrate that the time evolution of the van Hove dynamical pair correlation function is governed by adiabatic forces that arise from the free energy and by superadiabatic forces that are induced by the flow of the van Hove function. The superadiabatic forces consist of drag, viscous, and structural contributions, as occur in active Brownian particles, in liquids under shear and in lane forming mixtures. For hard sphere liquids, we present a power functional theory that predicts these universal force fields in quantitative agreement with our Brownian dynamics simulation results.

Dynamic equivalences in the hard-sphere dynamic universality class

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

General nonequilibrium theory of colloid dynamics

A nonequilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n(r,t) of a colloidal liquid in terms of the coupled time-evolution equations of its mean value n(r,t) and of the covariance [Formula in text] of its fluctuations δn(r,t)=n(r,t)-n(r,t). These two coarse-grained equations involve a local mobility function b(r,t) which, in its turn, is written in terms of the memory function of the two-time correlation function [Formula in text]. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n(0)(r) and σ(0)(r,r') toward its equilibrium state characterized by the equilibrium local concentration profile n(eq)(r) and equilibrium covariance σ(eq)(r,r'). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities.

Aging of a homogeneously quenched colloidal glass-forming liquid

The nonequilibrium self-consistent generalized Langevin equation theory of colloid dynamics is used to describe the nonstationary aging processes occurring in a suddenly quenched model colloidal liquid with hard-sphere plus short-ranged attractive interactions, whose static structure factor and van Hove function evolve irreversibly from the initial conditions before the quench to a final dynamically arrested state. The comparison of our numerical results with available simulation data are highly encouraging.

Non-equilibrium relaxation and near-arrest dynamics in colloidal suspensions

In this work we propose a theory to describe the irreversible diffusive relaxation of the local concentration of a colloidal dispersion that proceeds toward its stable thermodynamic equilibrium state, but which may in the process be trapped in metastable or dynamically arrested states. The central assumption of this theory is that the irreversible relaxation of the macroscopically observed mean value [Formula: see text] of the local concentration of colloidal particles is described by a diffusion equation involving a local mobility b(*)(r,t) that depends not only on the mean value [Formula: see text] but also on the covariance [Formula: see text] of the fluctuations [Formula: see text]. This diffusion equation must hence be solved simultaneously with the relaxation equation for the covariance σ(r,r';t), and here we also derive the corresponding relaxation equation. The dependence of the local mobility b(*)(r,t) on the mean value and the covariance is determined by a self-consistent set of equations involving now the spatially and temporally non-local time-dependent correlation functions, which in a uniform system in equilibrium reduces to the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics. The resulting general theory considers the possibility that these relaxation processes occur under the influence of external fields, such as gravitational forces acting in the process of sedimentation. In this paper, however, we describe a simpler application, in which the system remains spatially uniform during the irreversible relaxation process, and discuss the general features of the glass transition scenario predicted by this non-equilibrium theory.

Theory of dynamic arrest in colloidal mixtures

We present a first-principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self-consistent generalized Langevin equation theory of colloid dynamics [M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E 72, 031107 (2005); M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E76, 039902 (2007)]. We illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures: namely, hard-sphere and repulsive Yukawa binary mixtures. Our results include observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the ("bifurcation" or fixed-point") equations for the nonergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic-nonergodic phase diagram of the binary hard-sphere mixture.

Simplified self-consistent theory of colloid dynamics

One of the main elements of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E 62, 3382 (2000); 72, 031107 (2005)] is the introduction of exact short-time moment conditions in its formulation. The need to previously calculate these exact short-time properties constitutes a practical barrier for its application. In this Brief Report, we report that a simplified version of this theory, in which this short-time information is eliminated, leads to the same results in the intermediate and long-time regimes. Deviations are only observed at short times, and are not qualitatively or quantitatively important. This is illustrated by comparing the two versions of the theory for representative model systems.

Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics

This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.

Self-consistent generalized Langevin equation for colloidal mixtures

A self-consistent theory of collective and tracer diffusion in colloidal mixtures is presented. This theory is based on exact results for the partial intermediate scattering functions derived within the framework of the generalized Langevin equation formalism, plus a number of conceptually simple and sensible approximations. The first of these consists of a Vineyard-like approximation between collective and tracer diffusion, which writes the collective dynamics in terms of the memory function related to tracer diffusion. The second consists of interpolating this only unknown memory function between its two exact limits at small and large wave vectors; for this, a phenomenologically determined, but not arbitrary, interpolating function is introduced: a Lorentzian with its inflection point located at the first minimum of the partial static structure factor. The small wave-vector exact limit involves a time-dependent friction function, for which we take a general approximate result, previously derived within the generalized Langevin equation formalism. This general result expresses the time-dependent friction function in terms of the partial intermediate scattering functions, thus closing the system of equations into a fully self-consistent scheme. This extends to mixtures a recently proposed self-consistent theory developed for monodisperse suspensions [Yeomans-Reyna and Medina-Noyola, Phys. Rev. E 64, 066114 (2001)]. As an illustration of its quantitative accuracy, its application to a simple model of a binary dispersion in the absence of hydrodynamic interactions is reported.

Self-consistent theory of collective Brownian dynamics: theory versus simulation

A recently developed theory of collective diffusion in colloidal suspensions is tested regarding the quantitative accuracy of its description of the dynamics of monodisperse model colloidal systems without hydrodynamic interactions. The idea is to exhibit the isolated effects of the direct interactions, which constitute the main microscopic relaxation mechanism, in the absence of other effects, such as hydrodynamic interactions. Here we compare the numerical solution of the fully self-consistent theory with the results of Brownian dynamics simulation of the van Hove function G(r,t) and/or the intermediate scattering function F(k,t) of four simple model systems. Two of them are representative of short-ranged soft-core repulsive interactions [(sigma/r)(mu), with mu>>1], in two and in three dimensions. The other two involve long-ranged repulsive forces in two (dipolar, r(-3) potential) and in three (screened Coulomb, or repulsive Yukawa interactions) dimensions. We find that the theory, without any sort of adjustable parameters or rescaling prescriptions, provides an excellent approximate description of the collective dynamics of these model systems, particularly in the short- and intermediate-time regimes. We also compare our results with those of the single exponential approximation and with the competing mode-mode coupling theory.

Self-consistent generalized Langevin equation for colloid dynamics

We present a general self-consistent theory of colloid dynamics which, for a system without hydrodynamic interactions, allows us to calculate F(k,t), and its self-diffusion counterpart F(S)(k,t), given the effective interaction pair potential u(r) between colloidal particles, and the corresponding equilibrium static structural properties. This theory is build upon the exact results for F(k,t) and F(S)(k,t) in terms of a hierarchy of memory functions, derived from the application of the generalized Langevin equation formalism, plus the proposal of Vineyard-like connections between F(k,t) and F(S)(k,t) through their respective memory functions, and a closure relation between these memory functions and the time-dependent friction function Delta zeta(t). As an illustrative application, we present and analyze a selection of numerical results of this theory in the short- and intermediate-time regimes, as applied to a two-dimensional repulsive Yukawa Brownian fluid. For this system, we find that our theory accurately describes the dynamic properties contained in F(k,t) in a wide range of conditions, including strongly correlated systems, at the longest times available from our computer simulations.

Vineyard-like approximations for colloid dynamics

In this paper we propose a hierarchy of higher-order Vineyard-like approximations for colloidal systems. These consist of approximate expressions for the intermediate scattering function F(k,t) in terms of the self-intermediate scattering function F(s)(k,t) (or some memory function associated with it), and of other static structural properties of the suspension. In order to assess the accuracy of the proposed approximations, we perform Brownian dynamics simulations in a simple model system (a two-dimensional Yukawa Brownian fluid), in which we determine F(k,t), F(s)(k,t), and the required static structural properties. We study proposals for "second-order" and "third-order" Vineyard-like approximations. We find that the detailed structure of the relationship between the corresponding collective and self-memory functions turns out to be most important, as quantified by our simulation results.