Mathematical Models of the Homochiralisation of Crystals by Grinding

We review the existing mathematical models which describe physicochemical mechanisms capable of producing a symmetry-breaking transition to a state in which one chirality dominates the other. A new model is proposed, with the aim of elucidating the fundamental processes at work in the crystal grinding systems of Viedma (Phys Rev Lett 94:065504, 2005) and Noorduin (J Am Chem Soc 130:1158-1159, 2008). We simplify the model as far as possible to uncover the fundamental competitive process which causes the symmetry-breaking, and analyse other simplifications which might be expected to show symmetry-breaking.