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Probability of Nucleation in a Metastable Zone: Induction Supersaturation and Implications

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Department of Chemical & Biomolecular Engineering, University of Illinois at Urbana−Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
Cite this: Cryst. Growth Des. 2017, 17, 3, 1132–1145
Publication Date (Web):January 27, 2017
https://doi.org/10.1021/acs.cgd.6b01529
Copyright © 2017 American Chemical Society

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    Abstract

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    The metastable zone in solution crystallization is typically defined as a region of the phase diagram in which no appreciable nucleation occurs. Existing theoretical explanations attribute the appearance of this zone to the low probability of nucleation brought forth by the path-dependency of the nucleation rate. In this work, for the first time we present experimental data for several compounds that contradict this description. We show that the widely adopted theoretical approach which considers a time-dependent nucleation rate does not capture the observed stochastic nature of nucleation in these experiments. Instead, the experimental results are successfully explained through a probability analysis based solely on the energy barrier to nucleation. In this context, for a system that is slowly supersaturated, we develop the idea of an “induction supersaturation” as a lower boundary of metastability that does not depend on the path of the experiment. This work critically examines the limitations of the existing stochastic methods that describe nucleation under variable supersaturation and calls for a fundamental shift in the traditional view of the processes responsible for the manifestation of the metastable zone.

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    The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b01529.

    • Available Supporting Information includes (i) a mass balance model that describes the time dependence of supersaturation S and of rate of change of driving force r, (ii) extended discussion on the stochastic analysis of nucleation, derivation of the Master equation, and the probabilistic relevance of the nucleation rate, (iii) extended discussion on the path dependence of the metastable zone width, and (iv) extended discussion on the effect of solution volume on the metastable zone width (PDF)

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