Electrostatic interaction between non-identical charged particles at an electrolyte interface

TL;DR

This thesis analytically investigates the electrostatic interactions between non-identical charged colloidal particles at electrolyte interfaces, revealing non-monotonic behaviors and limitations of the superposition approximation.

Contribution

It provides exact and approximate solutions for electrostatic potentials and interaction energies, highlighting the failure of common approximations for non-identical particles.

Findings

Surface and line interactions can vary non-monotonically with separation.

Superposition approximation often fails to predict qualitative behaviors.

Quantitative energy contributions are inaccurate under superposition approximation.

Abstract

In this thesis we study the lateral electrostatic interaction between a pair of non-identical, moderately charged colloidal particles trapped at an electrolyte interface in the limit of short inter-particle separations. Using a simplified model system we solve the problem analytically within the framework of linearised Poisson-Boltzmann theory and classical density functional theory. In the first step, we calculate the electrostatic potential inside the system exactly as well as within the widely used superposition approximation. Then these results are used to calculate the surface and line interaction energy densities between the particles. Contrary to the case of identical particles, depending upon the parameters of the system, we obtain that both the surface and the line interaction can vary non-monotonically with varying separation between the particles and the superposition approximation fails to predict the correct qualitative behaviours in most cases. Additionally, the superposition approximation is unable to predict the energy contributions quantitatively even at large distances. We also provide expression for the constant (independent of the inter-particle separation) interaction parameters, i.e., the surface tension, the line tension and the interfacial tension. Our results are expected to be of use for modelling particle-interaction at fluid interfaces and, in particular, for emulsion stabilization using oppositely charged particles.