In 2005, Viedma found that, with grinding, chirality conversion of crystals occurs in this system[1]. A similar phenomenon has been found recently in organic systems[2,3]. In the latter case, a molecule has chirality, and the chirality of the minority molecules is converted to that of the majority. In order to understand the mechanism, several theoretical models have been proposed. In crystal growth[4,5], recombination of chiral clusters leads to the homochiral state deterministically and, in chemical reaction[6], random fluctuation also realizes a homochiral state eventually.

We studied the chirality conversion in crystal growth with a master equation based on a simple reaction model. With a stochastic crystallization process, although rate equation analysis provides no chiral symmetry breaking, random fluctuations drive the system to a homochiral state. The time necessary for the appearance of the homochiral state is proportional to the total number of molecules in the system[7].

In the present paper, We study a similar system with nucleation and recombination of chiral clusters. Although the system tends to become a racemic state, the chiral symmetry breaking occurs when the nucleation rate is small.

References:
[1] C. Viedma, Phys. Rev. Lett. 94 (2005) 065504.
[2] W. L. Noorduin, et al., Angew. Chem. 47 (2008) 6445.
[3] S. B. Tosogoeva et al., Angew. Chem. Int. Ed. 48 (2009) 590.
[4] M. Uwaha, J. Phys. Soc. Jpn. 73 (2004) 2601.
[5] Y. Saito and H. Hyuga, J. Cryst. Growth 318 (2011) 89.
[6] T. Sugimori et al., J. Phys. Soc. Jpn. 77 (2008) 064606.
[7] H. Katsuno and M. Uwaha, Phys. Rev. E 86 (2012) 051608.

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