Electrostatic Interactions of Bodies Bearing Thin Double‐Layers II. Exact Numerical Solutions

Abstract

AbstractA new numerical algorythm was used to calculate the electrostatic interaction forces between regularly shaped particles bearing thin double‐layers immersed in an arbitrary electrolyte. Our numerical procedure enabled the solution of the nonlinear one‐dimensional Poisson‐Boltzmann (PB) equation in which the excluded volume effect is quantitatively considered for an arbitrary surface charge. These one‐dimensional solutions (parallel‐plate system) were then integrated according to the modified Derjaguin summation method giving the electrostatic force between bodies either convex or concave in the vicinity of their contact area. Calculations were performed for plates and particles bearing similar surface charge (homointeractions) for simple electrolytes and electrolyte mixtures with constant charge and constant potential boundary conditions. From these solutions the range of validity of previously derived analytical approximations (Part I [16]) was estimated. It was shown that the excluded volume effect plays a significant role for β > 10−2 increasing the surface potential of plates (constant charge model) at all separations as well as the absolute value of the interaction force. At the critical separation h̄* the force remains finite in accordance with our previous analytical equations. A significant role of trace amounts of higher valency electrolytes decreasing considerably the interaction force was confirmed.