Crystal Chirality Selected by Mutual Antagonism

Abstract

To explore the mechanism of chiral symmetry breaking in a process of crystal growth under grinding, we propose a simple irreversible growth model of a lattice-gas with four possible states on a site: occupied by an achiral molecule A, or by a chiral enantiomer R or S, or empty. After two A molecules on neighboring sites form a chiral dimer R 2 or S 2 , clusters grow by incorporating A's at cluster periphery, irreversibly. Only the grinding recycles products R or S back to A. It is then demonstrated in kinetic Monte Carlo (KMC) simulations that chirality selection takes place in the presence of the grinding. The cause for this realization is attributed to mutual antagonistic inhibition: that is, clusters of opposite enantiomeric types are brought into contact through stirring, and they block crystallization sites on cluster peripheries each other. The density evolution obtained by time integration of the rate equations with this antagonistic inhibition fits well with results of KMC simulations.

Grinding-induced homochirality in crystal growth

“…But, due to the complexity of the model, for instance, with dissolution and Ostwald ripening processes, identification of the essential mechanism seems to be elusive. Quite recently, we have further simplified the lattice-gas model such that achiral molecules A crystallize into R or S enantiomeric crystals irreversibly [19]. In the course of fitting simulation results of this ARS model, we have confirmed that the proximity of clusters with opposite enantiomers leads to the mutual antagonism, similar to the process proposed by Frank [9].…”

“…Due to the enhancement factor a ¼ 10, grown crystals are compact in a square-like shape, compared with the ramified clusters at a ¼ 1 shown in Ref. [19].…”

“…The first model we consider is an extension of an ARS lattice gas model introduced previously [19]. On a square lattice of a size L 2 , molecules with a total concentration c are distributed.…”

“…We have previously studied the case with a ¼ 1 [19], where achiral molecules attach everywhere along the periphery of clusters with the same probability. Then, clusters look like Eden clusters with ramified periphery.…”

“…We now include the periodic grinding in KMC simulations, as performed in our previous works [18,19]. The system is randomly shifted and divided into square cells.…”