Theory of the intermediate stage of crystal growth with applications to protein crystallization

A closed form solution is found for the Buyevich–Mansurov theory of the intermediate stage of crystal growth. Using a common model for the growth rate, expressions for the time-dependent relative supersaturation and the distribution function for crystal sizes are found. With these results, the rate of homogeneous nucleation is established and need not be given as a boundary condition. The formula for the relative supersaturation is compared with experimental data for the crystallization of lysozyme and canavalin. The theory accurately describes the kinetics of the supersaturation decay during crystallization for both of these proteins.