Non-Linear Poisson-Boltzmann Theory of a Wigner-Seitz Model for Swollen Clays

TL;DR

This paper develops a non-linear Poisson-Boltzmann model for swollen clay stacks, revealing significant quantitative differences from linear theories and providing more accurate electrostatic force predictions.

Contribution

It introduces a numerical solution to the non-linear PB equation for a Wigner-Seitz model of swollen clays, improving upon previous linearized approaches.

Findings

PB theory predicts smaller inter-platelet forces than LPB theory.

Quantitative differences between PB and LPB are significant at relevant charge levels.

Hybrid models with linear edge effects match potential profiles well.

Abstract

Swollen stacks of finite-size disc-like Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its centre, together with an overall charge-neutral distribution of microscopic co and counterions, within a primitive model description. The non-linear Poisson-Boltzmann (PB) equation for the electrostatic potential profile is solved numerically within a highly efficient Green's function formulation. Previous predictions of linearised Poisson-Boltzmann (LPB) theory are confirmed at a qualitative level, but large quantitative differences between PB and LPB theories are found at physically relevant values of the charge carried by the platelets. A hybrid theory treating edge effect at the linearised level yields good potential profiles. The force between two coaxial platelets, calculated within PB theory, is an order of magnitude smaller than predicted by LPB theory