Theoretical Analysis of the Factors Determining the Crystal Size Distribution (CSD) During Crystallization in Solution: Rates of Crystal Growth - Christo N. Nanev (Crystals)
Crystalline products with a narrow and uniform distribution of crystals by size (CSD), characterized by a desired average size, are necessary in many practices. Therefore, extensive, but mostly experimental, research is devoted to the problem of obtaining such CSDs. Alternatively, this manuscript presents a theoretical approach for calculating CSD resulting from crystallization in unstirred solutions. First, classical equations for the rates of diffusion-controlled and kinetically controlled growth of crystals are used to discuss the size-dependent growth of the nucleated crystals and the initial CSD (which arises from the non-simultaneous nucleation of crystals). Then, applying the law of conservation of matter, it is proved that the CSD continues to expand during the growth stage. Furthermore, it is substantiated that, due to their uneven spatial distribution, crystals of the same size can grow at different rates. This depends on whether the crystals are outside the diffusion fields of other crystals or are clustered together in “nests”. Moreover, by calculating the growth rates of crystals in “nests”, an explanation is given for the observation that closely spaced crystals are smaller in size than the separately growing crystals. Finally, the CSD established during the Ostwald ripening is discussed quantitatively, step-by-step.