Elastic properties of static charge-stabilized colloidal crystal with two-dimensional hexagonal lattice

Abstract

Two-dimensional charge-stabilized colloidal crystal with a hexagonal crystal lattice and constant electric potential on the particles is studied numerically. The properties of the crystal are described by the theory based on the Poisson-Boltzmann non-linear differential equation. The force constants and the equilibrium pressure in the crystals are calculated for a broad range of the lattice parameters. The numerical procedures of the force constant and pressure determination is briefly described. Elastic constants of the first and second order are also calculated on the base of the force constants to obtain information about the many-body effective interactions in the system. It was shown that the Cauchy relation between the elastic constants breaks down in the whole range of the lattice parameter especially at higher densities. This can be interpreted as an effect of the many-body effective interaction between the particles in the crystal.