Effective Interactions and Volume Energies in Charge-Stabilized Colloidal Suspensions

TL;DR

This paper extends the linear response theory to finite-sized macroions in charge-stabilized colloidal suspensions, deriving explicit effective interactions and volume energies that influence thermodynamics, aligning with DLVO theory.

Contribution

It introduces a generalized response approach for macroions of finite size, deriving explicit effective pair interactions and volume energies, enhancing understanding of colloidal suspension thermodynamics.

Findings

Derives explicit effective pair interactions matching DLVO theory.

Identifies the role of volume energy in suspension thermodynamics.

Incorporates excluded volume effects via inverse screening length modification.

Abstract

Charge-stabilized colloidal suspensions can be conveniently described by formally reducing the macroion-microion mixture to an equivalent one-component system of pseudo-particles. Within this scheme, the utility of a linear response approximation for deriving effective interparticle interactions has been demonstrated [M. J. Grimson and M. Silbert, Mol. Phys. 74, 397 (1991)]. Here the response approach is extended to suspensions of finite-sized macroions and used to derive explicit expressions for (1) an effective electrostatic pair interaction between pseudo-macroions and (2) an associated volume energy that contributes to the total free energy. The derivation recovers precisely the form of the DLVO screened-Coulomb effective pair interaction for spherical macroions and makes manifest the important influence of the volume energy on thermodynamic properties of deionized suspensions. Excluded volume corrections are implicitly incorporated through a natural modification of the inverse screening length. By including nonlinear response of counterions to macroions, the theory may be generalized to systematically investigate effective many-body interactions.