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

Sergii V. Siryk; Walter Rocchia

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arXiv · 2512.08682

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

Sergii V. Siryk·Walter Rocchia

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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.

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Sergii V. Siryk, Walter Rocchia. 2025-12-11. Many interacting particles in solution. II. Screening-ranged expansion of electrostatic forces. https://arxiv.org/abs/2512.08682

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