S.K. Rangarajan

Electrochemical phase formation (ECPF) and macrogrowth. Part I. Hemispherical models

The phenomenological theory of hemispherical growth is generalised to time-dependent nucleation and growth-rates. Special cases, which include models with diffusion-controlled rates, are analysed. Expressions are obtained for small and large time behaviour and peak characteristics of potentiostatic transients, and their use in model parameter estimation is discussed. Two earlier equations are corrected. Numerically calculated transients which are presented exhibit some interesting features such as a maximum preceding the steady state, oscillations and shoulder.

Electrochemical phase formation (ECPF): Nucleation growth vis-a-vis adsorption models

The nucleation growth model of electrochemical phase formation is analysed for the linear potential sweep input. Apart from deducing diagnostic criteria and methods of estimating model parameters, the predictions of the nucleation growth model are compared and contrasted with those of a simple adsorption model. A distinction is made possible between adsorption and phase transition, which seems useful for understanding the nature of ECPF phenomena, especially underpotential deposition (UPD).

Effect of surface roughness on diffusion-limited charge transfer

A theory is developed for diffusion-limited charge transfer on a non-fractally rough electrode. The perturbation expressions are obtained for concentration, current density and measured diffusion-limited current for arbitrary one- and two-dimensional surface profiles. The random surface model is employed for a rough electrode\electrolyte interface. In this model the gross geometrical property of an electrochemically active rough surface - the surface structure factor-is related to the average electrode current, current density and concentration. Under short and long time regimes, various morphological features of the rough electrodes, i.e. excess area (related to roughness slope), curvature, correlation length, etc. are related to the (average) current transients. A two-point Pade approximant is used to develop an all time average current expression in terms of partial morphological features of the rough surface. The inverse problem of predicting the surface structure factor from the observed transients is also described. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how the surface roughness enhances the overall diffusion-limited charge transfer current.

A unified approach to linear electrochemical systems: I. The formalism

Summary A unified formalism appropriate to the study of linear electrochemical sys presented. The generalized expressions obtained herein for the admittance or of the half cell—both for the faradaic and the non-faradaic parts in provide insight into the basic mathematical structure present in the apparently disjointed maze of formulae published hitherto. The generalization achieved in this paper encompasses not only both the polarizable and the non-polarizable limits but also the single- and multi-step electron transfer so that it is possible to deduce from simple expressions (as is done in the following papers) simultaneously and effortlessly the results of almost all models of interest to us. A brief discussion on the equivalent circuit and an introduction to the systems approach to electrochemical models are also included.

Two-dimensional phase transitions at electrochemical interfaces

A two-state Ising model has been applied to the two-dimensional condensation of tymine at the mercury-water interface. The model predicts a quadratic dependence of the transition potential on temperature and on the logarithm of the adsorbate concentration. Both predictions have been confirmed experimentally.

Effect of surface roughness on interfacial reaction-diffusion admittance

We develop a theory for the electrical admittance of a rough interface under diffusion-limited and partial diffusion-limited charge transfer conditions. The large and small-frequency expansion brings out the relationships between the various morphological features of the rough electrode i.e. area, curvature and width, and the average admittance. The diffusion-limited reaction admittance is determined on an approximately self-affine corrugated random surface fractal. We obtain exact results for the low roughness and the asymptotic results (in three frequency regions) for the arbitrary and large roughness surfaces. These results show an anomalous frequency dependence for the mean admittance and the mean excess admittance for the large and small roughness surfaces, respectively. The intermediate frequency behavior of the reaction admittance for small roughness interfaces has the following form: 〈Y〉∼(iω)1/2+const.(iω)3/2−H, where H is Hursts exponent, for the large roughness interfaces it has same form as predicted earlier: 〈Y〉∼(iω)1−H/2. This non-universality and dependence of intermediate-frequency behavior on the strength of interfacial fractality has not been previously conceived. We also show the localization of the active zones in the presence of roughness. Finally, these results unravel the connection between the total reaction admittance and the crossover frequency to the roughness characteristics likes the fractal dimension, lower and upper fractal cutoff lengths, and the amplitude of the fluctuations of the fractal.

Diffusion to rough interfaces: finite charge transfer rates

We develop a perturbation formalism for diffusion accompanying the finite charge transfer rates on an arbitrary rough electrode. Second-order perturbation expressions are obtained for the concentration, current density and measured current transients for an arbitrary surface profile electrode. Various results obtained by earlier workers in the area of complex interfacial geometry are generalized. The results reported earlier for diffusion-limited (Nernstian) charge transfer at an arbitrary roughness about plane, sinusoidal, curvature expansion and realistic random surface models are generalized for the case where the effects of finite rates of charge transfer are incorporated. The problems of the screened electrostatic potential of the electric double layer for the one-dimensional arbitrary roughness are generalized for a two-dimensional arbitrary surface. In the random surface model (the gross geometrical property of an electrochemically active rough surface) the surface structure factor is related to the average electrochemical current, the current density and the concentration. Under the short- and long-time regimes, various morphological features of the rough electrode, i.e. roughness factor (related to excess area and slope due to roughness), curvature, correlation length etc. are related to the (average) current transients. The expressions for inner and outer cross-over times are obtained. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how roughness and finite charge transfer rates affect the overall quasi-reversible charge transfer current.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Adsorption isotherms for neutral organic compounds ― a hierarchy in modelling

A simple three-state model permitting two different configurational states for the solvent, together with one for the organic adsorbate, is analysed to derive the adsorption isotherm. The implications of this model regarding pseudo-two-state and pseudo-Frumkin adsorption isotherms are indicated. A critique of the earlier theory of Bockris, Devanathan and Muller is presented in brief.

Adsorption isotherms-microscopic modelling

Abstract A lattice formalism using “spin variables” is employed to analyse multi-state models for the adsorption of neutral dipoles. In particular, a spin-1/2 (two-state) model incorporating permanent and induced dipole moments of the solvent and the organic adsorbate, substrate interactions, and discreteness of charge effects is analysed. The resulting Generalized Ising Hamiltonian is solved under mean field approximation (MFA) in order to derive the adsorption isotherm for organic molecules. A few spin-1 (three-state) models are also analysed under MFA to describe the competitive adsorption of multi-state solvent and organic dipoles, and the appropriate equilibrium relations are derived. The unification and isomorphosm existing at the Hamiltonian level for several diverse realizations, such as adsorption of ions and solvent/organic molecules, is indicated. The possibility of analysing phase transitions using this generalized approach is briefly indicated.