Abstract: The two-particle cluster theory of nematic liquid crystals is generalized to study a two-dimensional model of cholesteric phase. The chiral molecules are placed at the sites of a three-dimensional simple cubic lattice with molecular orientations confined to two dimensions. The theoretical result shows that the helical wave-vector for equilibrium state depends on temperature and the cholesteric-isotropic phase transition exists. The two-particle cluster theory, taking into accout short-range correlations between molecules, yields numerical results which are closer to those of the Monte Carlo simulation than the mean field theory.

Key words: cholesteric liquid crystal, two-particle cluster theory, helical wave-vector