Evidence of many-particle interactions in two-dimensional charge-stabilized colloidal crystals

Electrostatic interaction in two-dimensional colloidal crystals obeying the nonlinear Poisson-Boltzmann equation is studied numerically. The force constants which are the coefficients of the energy quadratic form of the crystal are obtained. Significant discrepancy between the results of computer experiments and predictions of the harmonic crystal theory based on the idea of pairwise interaction has been detected. Two simple parameters are introduced for uniform quantitative estimation of many-particle effects and validity of the approximation of nearest-neighbor interaction. It is shown that the contribution of many-particle interaction into the total electrostatic interaction in colloidal crystals is significant for a broad range of crystal lattice constants and particles' sizes.