Rescaled mean spherical approximation for colloidal mixtures

Abstract

In this work, the resealed mean spherical approximation (RMSA) for colloidal mixtures interacting via a DLVO-type potential is developed, and its application to suspensions of highly charged macroions is illustrated. For this purpose we introduce a simple scheme to solve the mean spherical approximation (MSA) for Yukawa mixtures with factorized coupling parameters. This scheme consists of the mapping of the Yukawa system onto a corresponding primitive model system. Such a correspondence is used as a device for the calculation of the static structure functions of the original Yukawa mixture. Within this scheme, a straightforward implementation of the resealing procedure is performed, which allows for the calculation of partial structure factors in strongly interacting mixtures. The resealing procedure we use is an extension of that introduced by Hansen and Hayter for monodisperse suspensions. The structure factors obtained with the resealed mean spherical approximation compare well with computer simulation results. The advantages and limitations of the RMSA are also discussed in some detail.

Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

“…48), and for delivering the static input to theoretical schemes predicting equilibrium and nonequilibrium colloidal transport properties and phase boundaries. 6,8,13,16,49,50 Note here that an extension of the rescaled MSA to mixtures of hard-sphere Yukawa particles of differing diameters and Yukawa tails has been discussed by Ruiz-Estrada et al 26 The RMSA constitutes a considerable improvement over the MSA. However, comparisons with computer simulations and results from the highly accurate but numerically more expensive Rogers-Young (RY) integral equation scheme, 51 reveal that the RMSA typically tends to underestimate the local ordering of strongly repulsive particles.…”

“…The electric DLVO potential given by Eqs. (1)- (3) has been derived, as the potential of mean force in the limit φ → 0, on the basis of the linearized Poisson-Boltzmann theory 23 and the linear meanspherical approximation (MSA) for a highly asymmetric ionic mixture, [24][25][26] on assuming point-like (monovalent) counterand coions (microions) and L B Z 2 /σ 1. For more strongly charged macroions, the DLVO potential can be still used, but Z should be interpreted then as an effective macroion charge number smaller than the bare one, since it includes a correction for the fraction of surface-condensed counterions.…”

Reduced colloidal repulsion imparted by adsorbed polymer of particle dimensions

“…In the literature, there have been a few works investigating the structure factors of polydisperse systems for hard spheres [41][42][43], Yukawa spheres [63,64], and adhesive spheres [47,65]. Thus, another log-normal distributionDðRÞ is assumed in calculating the theoretical structure factor using the local monodisperse approximation (LMA) [66], in which the structure factor can be calculated as the weighted sum of the structure factor of the monodisperse subsystems:…”

Solvent and nonlinear effects on the charge renormalization of nanoparticles within a molecular electrolyte model

“…The DLVO model potential has also been derived from the primitive model (PM) level of description by assuming the small ions to be pointlike and using the Ornstein-Zernike (OZ) equation with the mean spherical approximation (MSA) for the description of the correlation functions [14]. Further studies have lifted some of the restrictions involved in this derivation, still within the context of the PM, and allowed the extension of the Yukawa-like screened coulomb interaction to different situations [15][16][17][18]. The molecular structure of the solvent, however, has been completely neglected in this line of work, where the first assumption is the replacement of the solvent by a structureless background with uniform dielectric constant.…”

“…These interactions are described by the effective pair potentials (EPPs) obtained from the two-point correlations of the whole model system [22,24]. Like in the approaches using the PM as the starting point [14][15][16][17], the goal here is to derive the pair potentials that generate the total correlation functions among macroions. The present work continues this line of inquiry by extending the calculations of previous work to larger size asymmetries between macroions and the other components in the solution.…”