Chiral Symmetry Breaking during Crystallization: An Advection-Mediated Nonlinear Autocatalytic Process

When a chiral chemical compound crystallizes from solution or from its melt, stirring often results in the formation of crystals of just one of the two possible enantiomers, while without fluid advection both enantiomers are formed. We demonstrate with simulations of the dynamics of the system that secondary nucleation is a nonlinear autocatalytic phenomenon that can explain these observations. Furthermore, we present theoretical arguments and experimental results that suggest that at the microscale the mechanism of secondary nucleation is whisker crystal growth and dispersion in the fluid flow.

Figure 1

Simulations of (top) the Metcalfe and Ottino model with primary nucleation and (bottom) our model, demonstrating the importance of secondary nucleation for the production of an enantiomeric excess. Initial conditions are shown on the left; on the right are the final states after seven periods of the flow.

Figure 2

Plot of absolute value of enantiomeric excess $\left|\varepsilon \right|$ for our model against the rate of introduction of primary nuclei (nucleation flux, defined as the fraction of primary crystals produced per rotation cycle, in the range $[0.01,0.5]$) and against advection rate (parametrized by the total angle of rotation $\theta \in [4\pi ,12\pi ]$). The color scale is as a rainbow, with red representing $\left|\varepsilon \right|=1$, and black $\left|\varepsilon \right|=0$.

Figure 3

Whiskers of (left) sodium chlorate crystallized from solution, and (right) 1,1'-binaphthyl crystallized from its melt.