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 λ, the amplification rate of a chirality imbalance becomes small and the imbalance of chiral products in the steady state decreases with λ. 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.