Abstract
Theory is developed to address the significant problem of electrostatic interactions between charged polarizable dielectric spheroids. The electrostatic force is defined by particle dimensions and charge, dielectric constants of the interacting particles and medium, and the interparticle separation distance; and it is expressed in the form of an integral over the particle surface. The switching behavior between like charge repulsion and attraction is demonstrated as depending on the ratio of the major and minor axes of spheroids. When the major and minor axes are equal, the theory yields a solution equivalent to that obtained for spherical particles. Limiting cases are presented for nonpolarizable spheroids, which describe the electrostatic behavior of charged rods, discs, and point charges. The developed theory represents an important step toward comprehensive understanding of direct interactions and mechanisms of electrostatically driven self-assembly processes.
Highlights
IntroductionDirect interactions and electrostatic forces often serve as a basis for novel self-assembly mechanisms, where the interacting particles combine to form larger ordered structures, typically when subjected to an external stimulus (solvent polarity, pH factor, irradiation, temperature) and driven by thermodynamic and other constraints
Direct interactions and electrostatic forces often serve as a basis for novel self-assembly mechanisms, where the interacting particles combine to form larger ordered structures, typically when subjected to an external stimulus and driven by thermodynamic and other constraints
We consider the effect of non-sphericity on the nature of electrostatic interactions between two polarisable spheroids of the same shape, size (a1 = a2 ≡ a, c1 = c2 ≡ c) and dielectric constant (k1 = k2 ≡ k), but with different charges Q1/Q2 = 2, whilst keeping the capacitance of spheroids constant
Summary
Direct interactions and electrostatic forces often serve as a basis for novel self-assembly mechanisms, where the interacting particles combine to form larger ordered structures, typically when subjected to an external stimulus (solvent polarity, pH factor, irradiation, temperature) and driven by thermodynamic and other constraints. Breakthroughs in particle synthesis led to the production of particles in the shape of rods,[2] cones[3] and discs, typically containing silica, metals, metal oxides,[4,5,6] and polymers,[7] with high yield and size/shape selectivity; these include some elegant examples of rods and ellipsoids of Au-Pt8, CdSe9, gold[10], gibbsite[6], and polymer latex.[11] These new approaches to particle synthesis have offered a diverse spectrum of particle anisotropy and clustering behaviour, including the formation of low symmetry clusters[12] and spherical self-assembled objects,[13] chain-like structures[13] and bundling.[14]. Some additional chemical and biological application areas reliant on the accurate description of electrostatic interactions between objects with spheroidal, or near spheroidal, shapes are fullerenes of higher order (e.g. C70),[16] complex polyoxometalates (POMs)
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