EXISTENCE OF ENANTIOMERIC PHASE-SEPARATION IN A 3-DIMENSIONAL LATTICE-GAS MODEL

A three-dimensional lattice gas model for enantiomeric phase separatio n is introduced. The enantiomeric molecules (d and 1) are the two nons uperimposable mirror images having the molecular structure C(AB)2, whe re C is a tetrahedrally bonded carbon atom with one bond to each end o f two AB groups. The lattice gas model consists of a body-centered cub ic lattice, each site of which can be either vacant or occupied by a m olecule oriented so that the A and B groups point toward neighboring l attice sites. Pairs of molecules interact with short-range, orientatio nally-dependent interactions. For a domain of interaction parameters, the Pirogov-Sinai extension of the Peierls argument is used to prove t hat d-rich and l-rich phases exist in the model at sufficiently low te mperature. For another domain of interaction parameters, at sufficient ly high chemical potential there is an infinite number of ground state s, each containing a racemic mixture of d and l molecules.