Theoretical Approach for Modeling Non-Steady-State Nucleation Kinetics in Solutions and Melts

In this work, it is shown that classical nucleation theory (CNT) is readily modified to account for out-of-equilibrium effects that, in many cases, best describe reality. The impact on the nucleation kinetics of two different scenarios are considered: (1) the gradual loss of solution supersaturation during crystallization and (2) the non-instantaneous sample thermalization upon melt quenching. Both cases introduce non-steady-state conditions that must be appropriately captured by the proposed theory to accurately describe the continuously evolving nucleation rate. For solutions that lose supersaturation during crystallization, the critical nucleus size does not remain fixed (as predicted by CNT for steady-state conditions), but rather it grows over the course of the phase transformation. Resultantly, the work of formation of the nucleus increases and the specific nucleation rate correspondingly decreases during the conversion. Contrastingly, for melt-quench crystallizations, the opposite is true in that the critical radius and activation energy both diminish during the conversion such that the specific nucleation rate is faster at the later stages of the conversion compared to the onset of the nucleation event.