Alexander's prescription for colloidal charge renormalization

TL;DR

This paper revisits and simplifies Alexander's charge renormalization method for charged colloids, providing explicit formulas and clarifying the screening length definition to improve predictive accuracy in electrolyte interactions.

Contribution

The paper offers a simplified, explicit formulation of Alexander's colloidal charge renormalization approach, clarifying the screening length concept and enhancing practical application.

Findings

Explicit formulas for effective charge are provided.

The method improves predictions of colloidal interactions.

Clarification of screening length definition in the literature.

Abstract

The interactions between charged colloidal particles in an electrolyte may be described by usual Debye-H\"uckel theory provided the source of the electric field is suitably renormalized. For spherical colloids, we reconsider and simplify the treatment of the popular proposal put forward by Alexander {\it et al.} [J. Chem. Phys. {\bf 80}, 5776 (1984)], which has proven efficient in predicting renormalized quantities (charge and salt content). We give explicit formulae for the effective charge and describe the most efficient way to apply Alexander's et al. renormalization prescription in practice. Particular attention is paid to the definition of the relevant screening length, an issue that appears confused in the literature.