Solvent fluctuations in the solvation shell determine the activation barrier for crystal growth rates

Anish V. Dighe; Meenesh R. Singh

doi:10.1073/pnas.1910691116

New Research In

Edited by Alexis T. Bell, University of California, Berkeley, CA, and approved October 16, 2019 (received for review June 21, 2019)

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Significance

Solution crystallization is a widely used technique to grow crystalline materials such as pharmaceuticals, agrochemicals, catalysts, semiconductors, and metal–organic frameworks. The highly probabilistic nature and complex molecular processes spanning multiple lengths and time scales have prevented full mechanistic understanding of crystallization processes for over a century. Here we show fluctuations in the solvation shell are key molecular events that explain and unify the empirical observations laid down since the inception of crystallization research. The activation barrier of the growth processes obtained from these molecular fluctuations can be used to estimate growth rates that show reasonable agreement with the experimental observations, hinting at the rise of additional and efficient strategies to control solution crystallization.

Abstract

Solution crystallization is a common technique to grow advanced, functional crystalline materials. Supersaturation, temperature, and solvent composition are known to influence the growth rates and thereby properties of crystalline materials; however, a satisfactory explanation of how these factors affect the activation barrier for growth rates has not been developed. We report here that these effects can be attributed to a previously unrecognized consequence of solvent fluctuations in the solvation shell of solute molecules attaching to the crystal surface. With increasing supersaturation, the average hydration number of the glutamic acid molecule decreases and can reach an asymptotic limit corresponding to the number of adsorption sites on the molecule. The hydration number of the glutamic acid molecule also fluctuates due to the rapid exchange of solvent in the solvation shell and local variation in the supersaturation. These rapid fluctuations allow quasi-equilibrium between fully solvated and partially desolvated states of molecules, which can be used to construct a double-well potential and thereby to identify the transition state and the required activation barrier. The partially desolvated molecules are not stable and can attach spontaneously to the crystal surface. The activation barrier versus hydration number follows the Evans–Polanyi relation. The predicted absolute growth rates of the α-glutamic acid crystal at lower supersaturations are in reasonable agreement with the experimental observations.

Footnotes

↵¹To whom correspondence may be addressed. Email: mrsingh{at}uic.edu.

Author contributions: M.R.S. designed research; A.V.D. performed research; A.V.D. and M.R.S. analyzed data; and A.V.D. and M.R.S. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1910691116/-/DCSupplemental.

Published under the PNAS license.

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