Mathematical models of homochiralisation by grinding of crystals

TL;DR

This paper reviews existing mathematical models of homochiralisation in crystal grinding systems, introduces a new simplified model to elucidate the core processes, and analyzes mechanisms leading to symmetry-breaking.

Contribution

A new simplified mathematical model is proposed to better understand the fundamental processes causing symmetry-breaking in crystal homochiralisation.

Findings

The model captures the essential competitive process leading to symmetry-breaking.

Simplifications reveal key mechanisms responsible for chiral dominance.

Analysis suggests specific conditions under which symmetry-breaking occurs.

Abstract

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, (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.