  We introduce and numerically solve a mathematical model of the experimentally
established mechanisms responsible for the symmetry breaking transition
observed in the chiral crystallization experiments reported by I. Weissbuch, L.
Addadi, L. Leiserowitz and M. Lahav, J. Am. Chem. Soc. 110 (1988), 561-567. The
mathematical model is based on five basic processes: (1) The formation of
achiral glycine clusters in solution, (2) The nucleation of oriented glycine
crystals at the air/water interface in the presence of hydrophobic amino acids,
(3) A kinetic orienting effect which inhibits crystal growth, (4) The
enantioselective occlusion of the amino acids from solution, and (5) The growth
of oriented host glycine crystals at the interface. We translate these
processes into differential rate equations. We first study the model with the
orienting process (2) without (3) and then combine both allowing us to make
detailed comparisons of both orienting effects which actually act in unison in
the experiment. Numerical results indicate that the model can yield a high
percentage orientation of the mixed crystals at the interface and the
consequent resolution of the initially racemic mixture of amino acids in
solution. The model thus leads to separation of enantiomeric territories, the
generation and amplification of optical activity by enantioselective occlusion
of chiral additives through chiral surfaces of glycine crystals.
