Chiral symmetry breaking can be realized in stirred crystallization of Na-C10,. We present experimental and theoretical studies of the random distribution of crystal enantiomeric excess (cee) for various stirring and solvent evaporation rates. For a fixed solvent evaporation rate, as the stirring RPM is increased, the probability distribution of cee initially broadens and subsequently develops a sharp peak close to cee = 1. On further increase of stirring rate, the probability distribution once again broadens. This broad probability distribution becomes narrow, with a sharp peak near cee = 1, if the solvent evaporation rate is decreased. Thus we show some ways in which the probability distribution of cee can be controlled in stirred crystallization. In particular, our study shows that the stirring rate and the solvent evaporation rate can be adjusted to maximize crystal enantiomeric excess. KEY WORDS: chiral symmetry breaking, chiral autocatalysis, asymmetric crystallization, origin of optical activity, secondary nucleation, stirred crystallizationThe origins of chiral asymmetry in nature are of great interest to physics, chemistry, and biology. '-' The generation of chirally asymmetric states by chirally symmetric reactions is the phenomenon of chxal symmetry breaking. Symmetry breaking is a general phenomenon that can occur in equilibrium and nonequilibrium systems, chiral symmetry breaking being one instance. Many second-order phase transitions, for example, are symmetry breaking transitions.Although there are many theoretical chemical models to demonstrate chiral symmetry breaking, unambiguous practical realization of the process in a chemical reaction has been elusive.'.6 Recently, Buhse et reported a system that shows promise and Asakura et reported that a chiral cobalt complex exhibits chiral autocatalysis.In crystallization processes, however, asymmetry is more easily obtained, mainly due to the possibility of large fluctuation~.'-'~ We have recently reported a clear example of chiral symmetry breaking in NaCIO, crystallization. '49 l5 When Na-C103 is crystallized by evaporation of the solvent in an unstirred solution, statistically equal numbers of levo-and dextro-crystals are found.16 In contrast, if the crystallization is done while constantly stimng the solution, nearly 100% of the crystals generated could be either levo or dextro. In a particular stirred crystallization, whether levo-crystals or dextrocrystals will dominate is found to be random. Further, whiie the bection of stimng is found to be uncorrelated with the dominant enantiomer, the amount of asymmetry produced depends on the intensity of stirring and the solvent evaporation rate. We present results of our study on how the asymmetry produced in stirred crystallization depends on the intensity of stirring and the solvent evaporation rate. The 0 1995 Wdey-Liss, Inc. experimental data are compared w i t h theory based on a stochastic kinetic model for the crystallization process.Since crystallization in general, and symmetry breaking ...
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