Experimental induction time distribution (ITD) data are usually analyzed through a survival probability analysis that assumes steady-state kinetics to be influencing the nucleation process. This analysis procedure cannot explain the âapparent dead time in nucleationâ routinely observed in experiments at low supersaturations. Under these conditions, the cumulative probability distributions of induction times exhibit a âsigmoidalâ shape rather than a sharp rise characteristic of an exponential decay of survival probability. To account for this uncharacteristic shape of ITD curves, a âcrystal growth/detection timeâ is often invoked. However, attempts to fit experimental data to this âcorrected process timeâ typically result in dubious and unphysical values for these detection/growth times. Thus, a gap exists in traditional methods used to analyze ITD data.
In this work, by considering transient nucleation phenomena, we show that the sigmoidal shape of the ITD frequently observed at low supersaturations has its origins in the time delay involved in âequilibratingâ the system to the imposed supersaturation. This time lag is significant at low supersaturations, thus resulting in a time-varying process intensity. We revisit experimental ITD data sets published in the literature and show that the proposed approach that considers transient nucleation kinetics (instead of steady-state kinetics) can explain these ITD. Our approach does not require one to assume (often trivial) growth or detection times to explain the âdead timeâ of nucleation observed in ITD at low supersaturations. This analysis method also provides one with information on the transient processes involved in nucleation mechanisms and paves the way for further understanding the metastable behavior of crystallizing solutions.
