Chiral patterns arising from electrostatic growth models

Abstract

Recently, unusual and strikingly beautiful seahorse-like growth patterns have been observed under conditions of quasi-two-dimensional growth. These `S'-shaped patterns strongly break two-dimensional inversion symmetry; however such broken symmetry occurs only at the level of overall morphology, as the clusters are formed from achiral molecules with an achiral unit cell. Here we describe a mechanism which gives rise to chiral growth morphologies without invoking microscopic chirality. This mechanism involves trapped electrostatic charge on the growing cluster, and the enhancement of growth in regions of large electric field. We illustrate the mechanism with a tree growth model, with a continuum model for the motion of the one-dimensional boundary, and with microscopic Monte Carlo simulations. Our most dramatic results are found using the continuum model, which strongly exhibits spontaneous chiral symmetry breaking, and in particular finned `S' shapes like those seen in the experiments.