Crystal Nucleation Rates from Probability Distributions of Induction Times

A novel method for the determination of stationary crystal nucleation rates in solutions has been developed. This method makes use of the stochastic nature of nucleation, which is reflected in the variation of the induction time in many measurements at a constant supersaturation. A probability distribution function was derived which describes, under the condition of constant supersaturation, the probability of detecting crystals as a function of time, stationary nucleation rate, sample volume, and a time needed to grow the formed nuclei to a detectable size. Cumulative probability distributions of the induction time at constant supersaturation were experimentally determined using at least 80 induction times per supersaturation in 1 mL stirred solutions. The nucleation rate was determined by the best fit of the derived equation to the experimentally obtained distribution. This method was successfully applied to measure the nucleation rates at different supersaturations of two model compounds, m-aminobenzoic acid (m-A BA) and L-histidine (L-His). The determined nucleation rates of m-ABA and L-His followed the trend expected from classical nucleation theory (CNT). The behavior indicated that, as expected, heterogeneous nucleation occurred. The relatively low kinetic parameter A for both compounds might indicate that the concentration of the active heterogeneous particles was relatively low. The novel method is a promising technique to determine nucleation rates in stirred solutions.