Nonlinear Poisson-Boltzmann theory of a Wigner-Seitz model for swollen clays

Swollen stacks of finite-size disclike Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its center, together with an overall charge-neutral distribution of microscopic co and counterions, within a primitive model description. The nonlinear Poisson-Boltzmann (PB) equation for the electrostatic potential profile is solved numerically within a highly efficient Green's function formulation. Previous predictions of linearized 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 linearized 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.