Stephen Fletcher

The response of some nucleation/growth processes to triangular scans of potential

Abstract The voltammetric response of some nucleation/growth processes is derived, for the early stages of crystal growth where intercrystal collisions are statistically improbable. The theory is formulated for both interfacial and diffusional control of the crystal growth kinetics. It is shown that nucleation on forward scans often triggers current maxima on reverse scans, and numerical data on this phenomenon are obtained from a computer program using realistic values of nucleation and growth rates. Some experimental data are then reported for systems that exhibit maxima. Finally, it is suggested that the existence of maxima can be used to diagnose nucleation/growth kinetics, because other types of rate control, such as charge transfer, adsorption, and semi-infinite linear diffusion, do not generally exhibit this behaviour.

Random assemblies of microelectrodes (RAM™ electrodes) for electrochemical studies

Abstract The application of random assemblies of microdisks (RAM™ electrodes) to electrochemical studies is described. These devices have working surfaces intersected by hundreds or thousands of disk-shaped microelectrodes that are capacitively, resistively, and diffusively independent. They therefore produce current–time responses of the same form as single microelectrodes, but many times larger. This property allows experimental data to be obtained on the benchtop without shielding and without significant mains interference — something that is impossible with single microelectrodes. The design criteria of random assemblies are summarized, and examples of their utility in a wide range of electrochemical experiments are given.

Some new formulae applicable to electrochemical nucleation/growth/collision

Abstract This paper presents some new formulae applicable to electrochemical nucleation/growth/collision, and is divided into six parts. In the first part general formulae for probabilistic effects in space, time and energy are presented. Then in the second part a new paradigm for 2-D nucleation/growth/collision at constant potential is described. Part three summarizes our recent work on the diffusion-controlled growth of hemispherical nuclei, including the effects of non-equilibrium and preceding chemical reaction, while part four consists of a discussion of nucleation as a stochastic process, and includes formulae for spatial and temporal subsampling. Part five discusses the occurrence of inductive loops in sinusoidal and triangular potential scan measurements of nucleating systems, and finally part six lists some formulae in integral geometry applicable to crystal growth problems.

Nucleation on active sites: Part IV. Invention of an electronic method of counting the number of crystals as a function of time; and the discovery of nucleation rate dispersion

Abstract A method is described for counting electronically the number of crystals formed during the course of an electrochemical reaction. It is based on the idea of depositing crystals on an assembly of microelectrodes which are so far apart that the crystals do not interact in any way. This constrains the total, observed, electrical current to be the linear superposition of the electrical currents from each crystal considered independently; a property which then allows N ( t ) data to be deconvoluted numerically from i ( t ) data. The method is shown to produce remarkably precise N ( t ) curves — so precise, in fact, that they can be used to test various published theories of heterogeneous nucleation. These theories are discussed in detail. Finally, we report the discovery of Nucleation Rate Dispersion. In this phenomenon, nucleation occurs at different rates at different active sites on the electrode surface.

Electrochemical and X-ray diffraction study of the redox cycling of nanocrystals of 7,7,8,8-tetracyanoquinodimethane. Observation of a solid–solid phase transformation controlled by nucleation and growth

The redox cycling of nanocrystals of 7,7,8,8-tetracyanoquinodimethane (TCNQ) immobilized on the surface of a variety of electrodes has been carried out in aqueous solutions of 1:1 electrolytes containing Group 1 cations (Na+, K+, Rb+, Cs+). It is found that the overall process follows the general equation [graphic omitted] where M+ is a Group 1 cation. It is also found, by a combination of voltammetric and XRD techniques, that the overall process is rate-controlled by nucleation and growth of the solid phases. Simple intercalation is ruled out by observing that significant structural rearrangement of the solid phases accompanies the redox reactions, and that x and y are integers. In the voltammograms, unusual inert zones are observed between the reduction and re-oxidation peaks, unlike anything that is seen in the conventional redox cycling of solution species. Theoretical analysis reveals that these are caused by the need to expend energy to create the solid/solid interface between the reduced and neutral forms of TCNQ in the critical nuclei of the solid phases.

The relationship between the electrochemistry and the crystallography of microcrystals. The case of TCNQ (7,7,8,8-tetracyanoquinodimethane)†‡

Microcrystals of TCNQ, in the size range 100–2000 nm, may be attached to the surfaces of graphite, glassy carbon, gold, platinum and RAMTM electrodes by a process of dry abrasion. When the resulting surfaces are placed in aqueous solutions of Group I cations, such as Na+, K+, Rb+ and Cs+, and the electrode potential is cycled, reversible phase transformations take place between the TCNQ and its corresponding cation salts. The electrochemical responses of these reversible phase transformations show that, in all cases, nucleation–growth kinetics are rate-determining. Ancillary techniques, such as optical microscopy, scanning electron microscopy and X-ray diffractometry, elucidate the corresponding crystal structure changes. In combination, these techniques provide deep insights into the relationship between the electrochemistry and crystallography of microcrystals.Optical microscopy reveals a colour change from yellow to blue–green upon electrochemical reduction of TCNQ microcrystals, and also reveals that small crystals react faster than large crystals. Unfortunately, analysis of morphological changes in situ in real time is prevented by the limited resolution of optical techniques (500 nm). However, scanning electron microscopy is able to provide ex situ ‘snapshots’ of the microcrystal morphologies before and after the phase transformations with a resolution of 1 nm, and these can be used to reconstitute the reaction pathway. Finally, X-ray diffractometry allows the spatial coordinates of the TCNQ molecules to be determined both before and after the phase transformations with accuracies of ± 0.001 nm. Such data reveal, for the first time, the changes that occur in molecular orientation during electrochemically induced solid–solid phase transformations in pi-stacked organic conductors.

Contribution to the theory of conducting-polymer electrodes in electrolyte solutions

This paper consists of two parts. First, an electrical model circuit is proposed that can reproduce, with high accuracy, the small-amplitude impedance behaviour of conducting-polymer electrodes in electrolyte solutions. Secondly, the electronic structure of the metal/polymer/solution interphase is discussed in terms of a band model. From the outset it is emphasized that a conducting polymer grown in an electrolyte solution is essentially a porous electrode. As a result, the electrical model circuit has the form of a diagonally connected discrete ladder network characterized by three impedances, x, y and z. After showing how these generalized impedances can be replaced by particular arrangements of passive circuit elements corresponding to real processes in the polymer, two limiting behaviours are derived corresponding to readily accessible experimental conditions: these behaviours are the high-frequency impedance response of the reduced polymer, and the low-frequency impedance response of the oxidized polymer. Both responses are identified in experimental data from polypyrrole.Based on the same porous electrode model, it is next proved that, at low frequencies, the total impedance of the polymer is dominated by that of the pore walls. This opens a ‘back door’ to the analysis of conducting-polymer behaviour in the complex plane of impedance, and, in particular, brings to light the importance of charge leakage across the pore walls. This section is followed by a discussion of the electronic structure of the polymer interior, from which an idealized band model is developed showing how the applied potential is dropped across the entire metal/polymer/solution interphase.Finally, critical analysis of the band model reveals the importance of the flatband potential in determining the polymer behaviour. This seems to have been universally neglected in the past. One result of including the flatband potential in the model is that it becomes necessary to postulate the existence of electrostatically stabilized polarons: if real, these would also explain the asymmetry of voltammograms in dilute electrolyte solutions.

An electrical model circuit that reproduces the behaviour of conducting polymer electrodes in electrolyte solutions

An electrical model circuit is proposed that can reproduce, with high accuracy, the small-amplitude impedance behaviour of conducting polymer electrodes in electrolyte solutions. In its most general form, the model consists of a diagonally connected discrete ladder network characterized by three impedances x, y and z. However, some special cases are considered in which x, y and z are replaced by passive circuit elements, such as resistors and capacitors, in arrangements corresponding to particular processes in real polymers. The resulting responses are analysed in the complex plane. One case is explored in detail. In it, a conducting polymer electrode in an electrolyte solution is assumed to be porous, with the pores behaving as simple resistors while the mass of the polymer behaves as a binary composite medium. Concurrently, at the cylindrical walls of the pores, the interfacial electrochemistry is modelled as a Debye-type charging process in which the capacitance depends inversely on frequency. Two semicircles are predicted in the complex plane of impedance, with diameters which have opposite dependences on polymer thickness.

Photoelectrochemistry in the lead-sulphuric acid system

Abstract In this paper we compare photoelectrochemical cyclic voltammograms with ordinary cyclic voltammograms. The two techniques are complementary in the sense that peaks are observed in one type of voltammogram at precisely those electrode potentials at which peaks are absent in the other. Our data allowed us to identify several peaks in the ordinary cyclic voltammograms. In particular, we located peaks corresponding to the reduction of PbO to Pb, and to the oxidation of PbO to α-PbO 2 . In the photoelectrochemical cyclic voltammograms we observed two anodic photocurrent peaks and one cathodic photocurrent peak. We explain the two anodic photocurrent peaks in terms of a Schottky barrier in non-stoichiometric n-type PbO. The cathodic photocurrent peak is more mysterious, but is probably due to the photoreduction of non-stoichiometric p-type PbO, generated in the O 2 -evolution region. The photocatalysis of O 2 -evolution on the surface of β-PbO 2 was also observed.

Invention of cyclic resistometry

Abstract A new technique is described that can measure the time-varying resistance of an electrode during cyclic voltammetry. We call it “cyclic resistometry”. It is based on the principle of measuring the resistance with square galvanostatic pulses, which are so fast that Faradaic reactions and double-layer charging do not respond to them. The pulses are fired very briefly—in less than 200 μs—during which time the potentiostat is switched to a dummy cell and the working electrode is controlled by a potentiostatic/galvanostatic mode switching circuit. A sample-and-hold circuit then provides an analogue output of resistance that is updated every 33 ms. The utility of the technique is demonstrated on three systems of industrial importance; the anodic dissolution of iron and copper from mineral chalcopyrite, the corrosion of lead electrodes in sulphuric acid and the redox cycling of electrochromic films of iridium oxide.