The interplay between screening properties and colloid anisotropy: towards a reliable pair potential for disc-like charged particles

TL;DR

This study investigates the electrostatic potential of highly charged disc-shaped colloids in electrolytes, revealing that linearized PB theory accurately describes far-field behavior and enabling the construction of an orientation-dependent pair potential.

Contribution

The paper introduces a semi-analytical method for solving the linearized Poisson-Boltzmann equation for charged discs, demonstrating its accuracy and applicability for modeling colloidal interactions.

Findings

Far-field potential matches linearized PB predictions

Potential anisotropy varies significantly with azimuthal angle

Constructed pair potential is strongly orientation dependent

Abstract

The electrostatic potential of a highly charged disc (clay platelet) in an electrolyte is investigated in detail. The corresponding non-linear Poisson-Boltzmann (PB) equation is solved numerically, and we show that the far-field behaviour (relevant for colloidal interactions in dilute suspensions) is exactly that obtained within linearized PB theory, with the surface boundary condition of a uniform potential. The latter linear problem is solved by a new semi-analytical procedure and both the potential amplitude (quantified by an effective charge) and potential anisotropy coincide closely within PB and linearized PB, provided the disc bare charge is high enough. This anisotropy remains at all scales; it is encoded in a function that may vary over several orders of magnitude depending on the azimuthal angle under which the disc is seen. The results allow to construct a pair potential for discs interaction, that is strongly orientation dependent.