Force Constants and Many-Body Electrostatic Interactions
in Two-Dimensional Colloidal Crystal

P. E. Dyshlovenko

Ul’yanovsk State Technical University, ul. Severnyii Venets 32, Ul’yanovsk, 432027 Russia

Received November 26, 2007

Abstract—A model of a two-dimensional colloidal crystal with a hexagonal lattice, the electrostatic interac-
tions in which are described by the nonlinear Poisson–Boltzmann equation, is considered. The calculation pro-
cedure for force constants of this crystal is treated in detail. Properties of system symmetry, which make it pos-
sible to significantly decrease the volume of calculations and to classify force constants, are analyzed. Numer-
ical data for force constants of a crystal as functions of lattice parameters at different particle sizes are reported.
A method that allows us to disclose the presence of many-body interactions in a system by the behavior of force
constants at some interval of the values of lattice parameters is proposed. The application of this method to the
system under consideration demonstrated that electrostatic interparticle interactions in the system cannot be
reduced to simply a pair interaction of any kind; the introduction of many-body potentials is required for the
adequate representation of the elastic properties of a crystal.

DOI: 10.1134/S1061933X08060070

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