Self-consistent generalized Langevin equation for colloid dynamics

Abstract

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.

From the depletion attraction to the bridging attraction: The effect of solvent molecules on the effective colloidal interactions

“…It will be interesting to calculate the kinetic phase diagrams in future works using existing theories. [69][70][71][72][73] …”

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.…”

Finite Element Analysis of Drug Electrostatic Diffusion: Inhibition Rate Studies in N1 Neuraminidase

“…Computational models of diffusion have been widely studied using both discrete 1,2,3,4,5 and continuum methods 6,7,8,9,10,11 . The discrete methods concentrate on the stochastic processes based on individual particles, which include Monte Carlo 12,13,14,5 , Brownian dynamics (BD) 15,16,17 and Langevin dynamics 18,19 simulations. Continuum modeling describes the diffusional processes via concentration distribution probability in lieu of stochastic dynamics of individual particles.…”