Chapter 2 - Potential Interactions Among Particles

Abstract

Abstract The basic principles electrostatics are discussed, comprising the Coulomb’s interaction law. Polarization phenomena in dielectric media are described, and basic equations of electrostatics are formulated, among others the Coulomb, Gauss, Maxwell, and Poisson equations. Electric potential and field distributions for simple geometries are analyzed, and expressions describing the electrostatic interactions of particles in dielectric (ion-free) media are given. The Poisson equation is introduced and methods for proper evaluation of electric potential distributions near charged interfaces are discussed. The electric double-layer formed at solid/electrolyte interfaces is described, and methods for calculating the force and energy of interactions among particles bearing electric double-layers are presented. Exact and approximate methods are discussed, including the linear superposition approximation (LSA), the generalized Derjaguin summation method, and the equivalent sphere approach (ESA). The van der Waals interactions comprising the permanent and induced dipole forces are described, the intermolecular potentials are specified, and the Hamaker theory based on the pairwise additivity is discussed. Explicit expression for dispersion interaction energy of various macrobodies, including deformed and rough objects are given, and the macroscopic (continuum) theory of dispersion interactions is presented. Values of Hamaker constants characterizing the magnitude of dispersion interactions in various media are tabulated. The section concluded with the analysis of surface deformations due to dispersion interactions and particle-surface adhesion phenomena. The specific energy profiles originating from the superposition of these potential interactions are discussed. The influence of surface roughness and heterogeneity of charge distributions is analyzed.