THE FRANK KINETIC MODEL FOR SPONTANEOUS CHIRAL SYMMETRY BREAKING WITH VARIABLE CONCENTRATION OF THE ACHIRAL SUBSTRATE

Abstract

This paper considers the possibility of spontaneous transition of aracemic mixture
(composed of equal amounts of two enantiomeric species, say L and D) into a
monochiral state (in which only one enantiomer, say L, is present). Transitions of this
kind have been recently experimentally observed. A plausible approach to this
phenomenon is a model put forward by Frank, based on simple laws of chemical
kinetics. In order to be able to solve the underlying system of differential equations,
Frank made a drastic assumption, namely that the amount of achiral substrate from
which the enantiomers L and D are formed is time-independent. In this paper, it is
demonstrated that such an assumption is not justified, but that the essential features
of the Frank model are also maintained if the amount of the achiral substrate is allowed
to be time-dependent