Crystal Size Distribution Resulting from the Time Dependence of Crystal Nucleation

Most of the experimental studies show that new-phase nucleation runs over prolonged time periods rather than instantaneously. After crystals nucleate, they start growing immediately. Therefore, the earlier a crystal nucleates, the larger it grows. This instigates a definite crystal size distribution (CSD). The resulting (from the initial crystal growth during the nucleation stage) CSD is calculated from the logistic time dependence of crystal number density. Having the shape of an ogee curve, CSD remains practically unchanged during the following crystal growth stage until the onset of Ostwald ripening. Only earlier born (and hence larger) crystals survive during the Ostwald ripening; the smallest crystals, which are the last born species, are dissolved. As far as the logistic dependence of crystal nuclei number density vs. nucleation time explains small molecule and protein crystallization, the calculated CSD should also describe crystallization of both small and large bio-molecules.