Is the Probability of Nucleation in a Metastable Zone Really a Function of the Rate of Nucleation?

Conventionally, in solution crystallization, the probability of nucleation at any supersaturation in a metastable zone width (MZW) experiment is determined using a survival probability analysis based on the functional dependence of the rate of nucleation on time-varying supersaturation.  However, recent experimental results show that this approach leads to incorrect predictions of the probability of nucleation (and hence the mean supersaturation at which nucleation occurs) in an MZW experiment. In this work, we explore the root cause of this discrepancy.  We distinguish the role of time in an MZW experiment from that in an induction time experiment by examining the characteristics of each type of experiment, and discuss the implicit assumptions involved in the traditional theoretical approaches used to model the metastable zone experiment. From this analysis, we show that the assumptions used in the development of the survival probability analysis based on the rate of nucleation are not valid for the case of the MZW experiment, and the concept of nucleation rate is irrelevant in analyzing the results of an MZW experiment. Instead, the experimental results are successfully explained by considering a survival probability analysis based solely on the energy barrier to nucleation.  By developing a characterization of the lower boundary of metastability without reference to rate processes, we arrive at surprising conclusions that the lower limit of a metastable zone cannot be the solubility boundary and the practice of routinely extracting the kinetic parameters of nucleation from a measured metastable zone width needs to be reconsidered.