Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models

Abstract

Using a hierarchy of three sigmoid growth models with increasing complexity, i.e., number of parameters, we reanalyzed kinetic data for heterogeneous nucleation—the number of nuclei N(t) vs. time t—from archetypical experiments on the electrodeposition of mercury on platinum by I. Markov and E. Stoycheva, to obtain two scales: Nmax and τ. The universal character of the studied phenomenon was revealed when replotting the original data as α ≡ N(t)/Nmax vs. t/τ. Yet the simplest model, the recently introduced α21 model which is aimed to describe diffusion-limited growth in 2D, α21 = tanh2(2t/τ21), fits all datasets with an R2 ≥ 0.989. This can be rationalized by attracting the non-classical notion of two-step nucleation—the nuclei form in a metastable phase which, in this case, grows on the electrode surface. Beyond the universality, we find the dependence of the two obtained scales on the overvoltage, which is increased systematically from 83 to 88 mV to generate the six N(t) datasets for each of the two electrode types—planar and hemispherical. Surprisingly, for one of them, the planar electrode, there is a discontinuity in the dependence—an almost horizontal jump from 85 to 86 mV, while for the hemispherical electrode, τ decreases smoothly.

Keywords

• heterogeneous nucleation
• electrodeposition
• <i>N</i>(<i>t</i>)-curves
• <i>α</i>₂₁ model
• Richards model
• model of Johnson–Mehl–Avrami–Kolmogorov (JMAKn)