Interplay between Kinetics and Thermodynamics on the Probability Nucleation Rate of a Urea–Water Crystallization System

In this contribution, by employing the Poisson distribution combined with the regular solution theory in the classical nucleation theory (CNT) framework, we construct a new model to uncover the relationship between induction time (tind) and supercooling (ΔT) and saturation temperature (T0) at different specific probabilities. By choosing the urea aqueous solution as a benchmark system, we show that the value of ln(1/tind) follows a reasonable linear relationship with (T0/ΔT)2/(T0 – ΔT), except the probability value tends to be 0 or 1. Furthermore, we also shed new light on the role of chemical potential difference and nucleation temperature in determining the nucleation rate; namely, although the chemical potential difference is the driving force for the crystallization process, it does not always favor the nucleation process. We demonstrated that when the chemical potential difference increases as the nucleation temperature decreases (ΔT gradually increases), in this case, the kinetic factor overwhelms the thermodynamic factor thus leading to a faster nucleation rate by employing the CNT theory. However, when the chemical potential difference decreases as the nucleation temperature increases, we found that increasing the nucleation temperature favors the nucleation process both in kinetic and thermodynamic aspects.