PPubMed8 Sep 2022Cited 8×

Manipulating Interactions between Dielectric Particles with Electric Fields: A General Electrostatic Many-Body Framework

Muhammad Hassan, Connor Williamson, Joshua Baptiste, Stefanie Braun, Anthony J. Stace, Elena Besley, Benjamin Stamm

Abstract

between Dielectric Particles with Electric Fields: A General Electrostatic Many-Body Framework Authors: ['Muhammad Hassan' 'Connor Williamson' 'Joshua Baptiste' 'Stefanie Braun' 'Anthony J. Stace' 'Elena Besley' 'Benjamin Stamm'] We derive a rigorous analytical formalism and propose a numerical method for the quantitative evaluation of the electrostatic interactions between dielectric particles in an external electric field. This formalism also allows for inhomogeneous charge distributions, and, in particular, for the presence of pointlike charges on the particle surface. The theory is based on a boundary integral equation framework and yields analytical expressions for the interaction energy and net forces that can be computed in linear scaling cost, with respect to the number of interacting particles. We include numerical results that validate the proposed method and show the limitations of the fixed dipole approximation at small separation between interacting particles. The proposed method is also applied to study the stability and melting of ionic colloidal crystals in an external electric field.

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A linear‑scaling boundary‑integral framework accurately computes electrostatic forces between dielectric particles in external fields, surpassing fixed‑dipole models.

What’s new

i.Derivation of a rigorous analytical formalism for many‑body electrostatic interactions with external fields and surface point charges.
ii.Development of a linear‑scaling boundary integral numerical method to compute interaction energies and forces.
iii.Demonstration that the fixed‑dipole approximation breaks down at short particle separations.
iv.Application of the method to assess stability and melting of ionic colloidal crystals under electric fields.
v.Provision of validation benchmarks against analytical results for neutral and charged dielectric spheres.

How they did it

The approach formulates the problem as a boundary integral equation solved with a Galerkin discretization, yielding analytical expressions for energy and forces that scale linearly with particle number. Numerical implementation uses Lebedev quadrature (up to lmax=30) and linear‑scaling solvers. The method accommodates inhomogeneous surface charge and external electric fields.

What they found

Interaction energy between two neutral 5 µm particles (κ=10) follows a 1/R³ decay and can be up to twice the magnitude predicted by fixed‑dipole models at separations comparable to particle size.
External field strengths of 100 kV/m, 200 kV/m and 300 kV/m produce distinct energy curves, confirming field‑dependent polarization effects.
A 1024‑particle PMMA crystal is stable in vacuum and destabilized by an applied field; the field strength where average force along the field vanishes is identified.
Surface charge density maps for a neutral particle at Eext = 1000 V/m (and 600, 2000 V/m) illustrate dipole alignment and charge redistribution.

Caveats

✕The fixed‑dipole approximation is inaccurate at small separations, limiting its use for closely spaced particles.
✕The current model does not yet incorporate torque calculations on particles.
✕High‑order multipole expansions (lmax=30) and dense integration points are required for convergence, increasing computational cost.

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