Many interacting particles in solution. II. Screening-ranged expansion of electrostatic forces

TL;DR

This paper derives exact analytical formulas for electrostatic forces among multiple dielectric spheres in ionic solutions, expanding on screening effects and providing a rigorous foundation for complex particle interactions in various ionic conditions.

Contribution

It introduces exact screening-ranged many-body expansions for electrostatic forces, advancing beyond previous approximate methods within the linearized Poisson--Boltzmann framework.

Findings

Exact analytical relations for interparticle forces derived

Screening-ranged expansions systematically improve previous models

Framework applicable to complex particle systems at finite ionic strength

Abstract

We present a fully analytical integration of the Maxwell stress tensor and derive exact relations for interparticle forces in systems of multiple dielectric spheres immersed in a polarizable ionic solvent, within the framework of the linearized Poisson--Boltzmann theory. Building upon the screening-ranged (in ascending orders of Debye screening) expansions of the potentials developed and rigorously analyzed in the accompanying works arXiv:2512.08407, arXiv:2512.08684, arXiv:2512.09421, we construct exact screening-ranged many-body expansions for electrostatic forces in explicit analytical form. These results establish a rigorous foundation for evaluating screened electrostatic interactions in complex particle systems and provide direct analytical connections to, and systematic improvements upon, various earlier approximate or limited-case formulations available in the literature, both at zero and finite ionic strength.