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

Abstract

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.

Dynamic equivalences in the hard-sphere dynamic universality class

“…This formalism was employed in the construction of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [19][20][21], eventually applied to the description of dynamic arrest phenomena [22][23][24], and more recently, to the construction of a firstprinciples theory of equilibration and aging of colloidal glassforming liquids [25,26]. When applied to model systems with soft repulsive interactions [27], the SCGLE theory of colloid dynamics, together with the condition of static structural equivalence between soft-and hard-sphere systems, predicts the existence of a hard-sphere dynamic universality class, constituted by the soft-sphere systems whose dynamic parameters, such as the α-relaxation time and self-diffusion coefficient, depend on density, temperature, and softness in a universal scaling fashion [28], through an effective hard-sphere diameter determined by the Andersen-Weeks-Chandler [29,30] criterion.…”

Self-diffusion in a system of interacting Langevin particles

“…There are two basic routes to calculate e . The first is based on the direct calculation of the diffusion constant [8][9][10][11][12][13][14][15][16][17][18][19]. The second is based on the calculation of the modification of the response to a small external force on a given particle due to the interaction with the other particles, the so-called relaxation effect; the resulting value of e is then determined from the Einstein or fluctuation dissipation relation [20][21][22][23].…”

“…The second is based on the calculation of the modification of the response to a small external force on a given particle due to the interaction with the other particles, the so-called relaxation effect; the resulting value of e is then determined from the Einstein or fluctuation dissipation relation [20][21][22][23]. One approach to studying the dynamics of a tracer particle is to write an effective one particle Langevin equation with a non-Markovian memory kernel, derived via projection operator techniques [8][9][10][11][12][13]16,17,23,19]. This kernel must then be computed by invoking approximation or closure schemes such as mode coupling-like approximations [15,16], cluster expansions [13], or weak coupling expansions [8,17,18].…”

Aging of a homogeneously quenched colloidal glass-forming liquid

“…In recent related work [21], however, an extension was proposed of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [22][23][24][25][26] and dynamic arrest [27][28][29][30][31][32][33][34], aimed precisely at describing this non-equilibrium evolution of S(k; t) and F (k, τ ; t). This extension was based on Onsager's theory of thermal fluctuations [35][36][37][38][39], adequately extended [40,41] to allow for the description of memory effects.…”