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

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.