Steady chirality conversion by grinding crystals-Supercritical and subcritical bifurcations

The chirality conversion of crystals by grinding in an open system under circulation is studied. A generalized classical nucleation model and simple reaction-type models both show that steady perfect chirality conversion is possible if circulation is weak. By increasing the circulation rate lambda, the amplification rate of a chirality imbalance becomes small and the imbalance of chiral products in the steady state decreases with lambda. The chiral steady state disappears above a critical strength of circulation. The transition between the racemic and the chiral state is continuous in the system of achiral molecules and discontinuous in the system of chiral molecules. (c) 2010 Elsevier B.V. All rights reserved.