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Trends in Physical Chemistry   Volumes    Volume 22 
Kinetic law leading to a hyperbolic growth rate for protein crystals
Douglas A. Barlow, James K. Baird
Pages: 95 - 100
Number of pages: 6
Trends in Physical Chemistry
Volume 22 

Copyright © 2022 Research Trends. All rights reserved

In a recent paper, [Barlow D. A., LaVoie-Ingram E. and Bayat J. 2022, J. Cryst. Growth, 578, 126417], it was demonstrated how reported experimental data giving the time dependence for crystal size in the case of protein crystals growing from a batch supersaturated solution, obey an empirical curve in the shape of the hyperbolic tangent. Using this empirical law, population balance models were used to derive a variety of useful kinetic relationships including the relative supersaturation, the homogeneous nucleation rate and the crystal size distribution function. In this report, we present a model which leads to a governing differential equation that directly yields a solution for the crystal radius as a function of time which is of the form of the hyperbolic tangent function. This model gives the linear growth rate as a sum of incorporation and dissociation terms which are described in detail here. The final result has two undetermined parameters, the maximum size at equilibrium and a rate constant. From other reports in the literature, we note how the maximum equilibrium size can be related to the initial supersaturation. We discuss how the rate constant could be determined assuming that it obeys an Arrhenius law with a negative activation energy.
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