The deconvolution of nucleation and growth rates from electrochemical current–time transients

Two new algorithms have been developed for the deconvolution of nucleation and growth rates from electrochemical current–time transients. The first is called Bootstrap, and is based on the method of successive approximations. The second is called Simplefit, and utilizes a curve-fitting procedure based on the simplex method. Both are able to provide numerical estimates of the number of crystals as a function of time, to better than 2% accuracy, in the presence of significant noise. The advantage of the algorithms is that they produce accurate output under conditions where standard methods fail. In particular, the number of crystals versus time can be determined even when crystal growth switches from interfacial control to diffusion control on the timescale of measurements. The efficacy of the algorithms is demonstrated on two real systems, namely the nucleation of zinc on carbon, and the nucleation of lead on carbon. In both cases non-steady states of nucleation are readily observed in the presence of time-varying crystal growth rates. In addition, a new phenomenon is seen for which the name ''nucleation persistence'' is suggested. This is the transient continuation of a high rate of nucleation after a rapid decrease in overpotential. The phenomenon is attributed to the slow readjustment of the size distribution of microscopic nuclei on the electrode surface. Interestingly, the existence of nucleation persistence invalidates the double potential step technique, which has previously been regarded as the standard method for observing electrochemical nucleation and growth. Finally, the mathematical theory of nucleation persistence is briefly sketched.