Differences in enantiomeric diffusion can lead to selective chiral amplification

A fundamental question associated with chirality is how mixtures containing equal amounts of interconverting enantiomers can spontaneously convert to systems enriched in only one of them. Enantiomers typically have similar chemical properties, but can exhibit distinct reactivity under specific conditions, and these differences can be used to bias the system's composition in favor of one enantiomer. Transport properties are also expected to differ for enantiomers in chiral solvents, but the role of such differences in chiral symmetry breaking has not been clarified yet. In this work, we develop a theoretical framework to show that asymmetry in diffusion properties can trigger a spontaneous and selective symmetry breaking in mixtures of enantiomers. We derive a generic evolution equation for the enantiomeric excess in a chiral solvent. This equation shows that the relative stability of homochiral domains is dictated by the difference of diffusion coefficients of the two enantiomers. Consequently, deracemization toward a specific enantiomeric excess can be achieved when this difference is large enough. These results hold significant implications for our understanding of chiral symmetry breaking.