Probability distributions of enantiomeric excess in unstirred and stirred crystallization of 1,1'-binaphthyl melt.

Crystallization of 1, l'-binaphthyl from its melt can generate optical activity spontaneously. Since crystallization is a stochastic process, the enantiomeric excess (ee) generated in each crystallization varies randomly. We investigated the qualitative features of probability distribution of the ee for crystallization at two temperatures, 150 degrees C and 152 degrees C, at which conglomerate crystallization occurs. No clear transparent crystals were produced at either temperature, indicating that the solid states formed in the melt were polycrystalline. The ee randomly fluctuated from run to run, with an average of 26.9% and 2.7% when the crystallization was carried out at 152 degrees C, and 150 degrees C, respectively. The spread of the probability distribution is also substantially different. We also studied the probability distribution of ee in stirred crystallization at different stirring RPM. The results show probability distribution's broadening and evolution to a bimodality with increasing stirring RPM--a typical behavior in symmetry-breaking transitions. These results shed light on the nature of enantioselectivity in secondary nucleation and crystal growth.