Evaluation and improvement of Gay-Berne interaction potential to simulate 3D DLVO interaction of clay particles

Abstract

This paper first presents a set of DLVO-based energy-separation functions for a pair of finite uniformly charged square platelets of infinitesimal thickness in three elementary configurations: face-to-face, edge-to-edge, and edge-to-face. The novel dataset was generated by summing the electrostatic interaction energy computed numerically by solving the non-linear 3D Poisson-Boltzmann equation and the van der Waals interaction energy calculated analytically. The dataset aims to inform qualitatively and quantitatively the energy/force separation functions used in the Discrete Element Method (DEM) and Coarse-Grained Molecular Dynamics (CGMD) modelling of clays. The same dataset was then used to calibrate and evaluate two Gay-Berne (GB)-type potentials: i) a DLVO-adapted Gay-Berne potential, where the Born-van der Waals branches of the underlying Lennard-Jones (LJ) potential are replaced with van der Waals-Columbic branches to represent DLVO interactions; ii) the Mie potential, where the exponents of the two energy terms are ‘unlocked’ instead of being set equal to 12 and 6 as per the original LJ potential. It is shown that the orientation parameter, µ, and the anisotropy parameter, ν, need to be different from µ = 2 and ν = 1 as adopted in CGMD clay modelling to capture the progression of the shape of the pair energy-separation function from face-to-face to edge-to-face and edge-to-edge configuration. It is also shown that the MIE potential (with exponents m = 3 and n = 1.5) better captures the slow decay of the electrostatic repulsive energy component of the DLVO potential energy Coulombic branch of the interaction potential compared to the DLVO-adapted GB potential, which embeds the Lennard-Jones (LJ) exponents m = 12 and n = 6.