Review
A review of the analysis of multiple nucleation with diffusion controlled growth

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Abstract

A review is given of the area of electrodeposition of materials via a mechanism of nucleation followed by diffusion controlled growth. A short historical background to the study of nucleation via potentiostatic current transient modelling is provided, followed by an outline of the major methods currently used, with some comments on their relative merits. An overview of the computer simulation of both nucleus distributions and diffusion to growing nuclei is given. Finally, methods, including optical microscopy and SPM, used for studying directly the development of surfaces on which nucleation is occurring are described. A table of some chemical systems to which the theoretical models have recently been applied is included.

Introduction

Electrochemical deposition is an area of considerable interest, both from a fundamental and applied standpoint, with application to areas such as electroplating and solution analysis. As for example, a review in Electrochimica Acta in 2000 indicates [1], much work has been done on investigating the mechanism of such deposition over the last 50 years. However, as the discussion in a recent Journal of Electroanalytical Chemistry [2], [3], [4], [5] reveals, there is still considerable controversy over even the most basic principles involved in modelling such systems.

It has however, become apparent that electrodeposition occurs by a process of nucleation and growth—nuclei appear at active sites on the substrate according to some nucleation rate law, and then grow via the incorporation of further ions from the solution. Given that this is the case, the study of nucleation via electrochemical methods has certain advantages over other methods of investigating heterogeneous nucleation: the driving force of the nucleation can be varied simply by varying the applied potential. Nucleation and growth can be broadly classified into two categories: ‘interfacial (or charge) controlled’, in which the nucleus growth rate is limited by the rapidity with which ions can be incorporated into the new phase, and ‘diffusion controlled’, in which the nucleus growth is limited by the rate at which material is transported through the solution to the electrode surface. The former is favoured by high concentrations and low deposition overpotentials, while the latter is favoured by low concentrations and high overpotentials. Certain systems also tend to one or the other: due to its complex mechanism, PbO2 is usually deposited under charge control [6] while mercury is a classic example of diffusion control [7] (see below).

With this in mind, this review is an attempt to assess the current situation in one restricted area of electrodeposition: deposition with diffusion controlled growth, with a particular emphasis on the extraction of information about the nucleation process from electrochemical data. Three aspects of this are considered—theoretical modelling, computer simulation, and microscopic observation of electrode surfaces.

Section snippets

Early work

Some of the earliest interest in the mechanism of nucleation and growth of electrodeposited materials was shown in the 1950s, by authors such as Fleischmann and Thirsk, and Pangarov [8], [9]. Fleischmann, Thirsk and coworker published several papers relating to the formation of lead dioxide on lead and platinum electrodes [10], [11], [12], pioneering the use of a ‘constant overvoltage’ method, in which a constant potential after a potential step is applied to a cell and the resulting current

Conclusions

During the development of models for the multiple nucleation and diffusion controlled growth of electrodeposited materials, two main schools of thought have emerged. The first consider the use of , to be a well-established principle, and generally apply the Avrami theorem to treat the overlap of diffusion zones. This has led to three relatively widely discussed models; those of Scharifker and Mostany, Sluyters-Rehbach, Wijenberg, Bosco and Sluyters, and Mirkin and Nilov/Heerman and Tarallo. A

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