Stochasticity in Primary Nucleation: Measuring and Modeling Detection Times

In this work, stochastic nucleation has been investigated analyzing a large set of literature data on the isothermal crystallization of p-aminobenzoic acid in acetonitrile, isopropanol, and ethyl acetate in 1.5/1.8 mL batch reactors. We investigated the basic statistical hypotheses used to model the stochastic process of nucleation and the criteria necessary for their fulfilment: based on a sound mathematical framework, we have developed and implemented a statistical analysis which allows one to assess the statistical representativity of experimental data and their inherent uncertainty. A physical model of the process has been developed including primary nucleation and growth of crystals until detection. On the basis of the statistical analysis developed, the model parameters have been estimated from the measurements, accounting for stochastic nucleation and conditions for detection, according to two alternative methods. In light of such results, this work explores two further aspects in detail: the choice of the appropriate stochastic process to describe nucleation and the sensitivity of the measurements to operating parameters, with a special emphasis on supersaturation and temperature. Finally, we give recommendations on how to measure and interpret stochastic nucleation data.