Three-Dimensional Description of the Spontaneous Onset of Homochirality on the Surface of a Conglomerate Crystal Phase

The spontaneous emergence of homochirality in an initially racemic system can be obtained in far-from-equilibrium states. Traditional models do not take into account the influence of inhomogeneities, while they may be of great importance. What would happen when one configuration emerges at one position, and the opposite one at another position? We present a discrete three-dimensional model of conglomerate crystallization, based on 1,1‘-binaphthyl crystallization experiments, that takes into account the position and environment of every single elementary growth subunit. Stochastic simulations were performed to predict the evolution of the crystallization process. It is shown that the traditional view of the symmetry breaking can then be extended. Fluctuations of the fixed points related to inhomogeneities are observed, and complex behavior, such as local instabilities, transient structures, and chaotic behavior, can emerge. Our modeling indicates that such complex phenomena could cause large fluctuation of the final enantiomeric excess that is observed experimentally in binaphthyl crystallization. The results presented in this article show the importance of inhomogeneities in understanding enantiomeric excess generated in crystallization and the inadequacy of the models based on the assumption of homogeneity.