A contemporary look at the accuracy of the ‘double pulse technique’ for measuring rates of crystal nucleation; molecular-kinetic and non-classical mechanisms of initial growth of the just-born crystals

Abstract

Microscopically visible crystals are indispensable for measuring nucleation rates by means of the ‘double pulse technique’ (DPT). Therefore, the accuracy of the DPT depends on the survivability of the just-born crystals during their initial growth and (possible) dissolution. First, because the critical nuclei stay in a labile equilibrium with the mother phase (meaning equal growth and dissolution probabilities), half of the critical nuclei must be dissolved. Second, because of interphase fluctuations and crystal coalescence, the number densities of super-critically sized nuclei can also be decreased. To estimate the survivability of super-critical crystals, the probabilities for attachment/detachment of molecules to/from such crystals are considered in full detail from a molecular-kinetic point of view. It is shown that the probability of decomposition down to subcritical dimension, which is of importance for the accuracy of the DPT, is negligibly small already for crystals by only three molecules larger than the critical size. Besides, except for extremely high supersaturations, also the oriented attachment of nanocrystals is of little consequence for the accuracy of the DPT. The conclusion is that, because the nucleation of crystals is a stochastic process, the nucleation rates measured by means of the DPT are dependable.