B. M. Grafov

The Shuttleworth equation for a finite surface strain

Abstract It is shown that the Shuttleworth equation g=γ+∂γ/∂e is valid for the interface between a solid isotropic electrode and a liquid electrolyte in the case of an infinitesimal surface deformation only. In the equation above, g is the surface stress, γ is the interfacial tension, and e is the scalar surface strain variable (elastic surface deformation). In the general case of a finite surface strain, the interfacial tension is a function of two scalar strain variables rather than one. Under conditions of an elastic finite surface strain, the modified Shuttleworth equation is deduced for the trace of the tensor of the surface stress. The Shuttleworth equation above takes into account the existence of both scalar elastic surface strain variables.

Fluctuational self-consistency of the theory of the elementary act of electrochemical reactions in the neighbourhood of the equilibrium state

Abstract The analysis of the theory of the elementary act of electrochemical reactions in relation to the fluctuation–dissipation theorem shows that in the neighbourhood of the equilibrium state the fluctuational self-consistency of the theory holds if an integral number of electrons is transferred in the elementary reaction act. The fluctuational self-consistency must also exist for the electrode processes with partial charge transfer. However, this requirement results in a non-zero correlation between fluctuations of the electrochemical reaction rate and the fluctuations of the number of electrons involved in the elementary act.

Median Chebyshev spectroscopy of electrochemical noise

An algorithm for analyzing electrochemical noise based on Chebyshev spectroscopy using the sample median is presented. Chebyshev spectroscopy with the sample median nicely complements Chebyshev spectroscopy with the sample mean. Chebyshev noise spectroscopy with the sample median can be used to distinguish between corrosion processes, which cannot be achieved using Chebyshev spectroscopy with the sample mean. This “median Chebyshev spectroscopy” can be effectively used to diagnose the electrochemical noise of corrosion systems and electrochemical power sources.

Discrete Laplace transformation as a wavelet tool to analyse the electrochemical random time series

In this paper we study the use of discrete Laplace transformation for the analysis of the electrochemical random time series. It is shown that for any stationary discrete time random electrochemical process there is a direct estimator for power spectral density in the Laplace domain. It is of importance that this estimator can be used to analyse random time series of any nature (not only electrochemical).

Theory of the wavelet analysis for electrochemical noise by use of the Laguerre functions

It is shown that the wavelet transform that uses the Laguerre function as a basis function is a useful tool to analyse the stationary electrochemical noise. Knowledge of the variance of the Laguerre wavelet of noise allows the Laplace transform of the correlation function to be found. The Laplace transform of the correlation function may be referred to the spectral density in the Laplace domain as well as to the operational spectral density of noise. It is shown that the operational spectral density of noise can be found not only by averaging over the ensemble of realizations of the noise process but also by averaging over the ensemble of Laguerre wavelets. The results obtained can be useful not only for analysis of electrochemical noise but also for analysis of any stationary random process, in particular for the time series analysis in econometric research.

Use of the Grahame and Grahame—Parsons concepts for modelling the impedance behaviour of a metal electrode in a solution of its salt

Abstract The Grahame and Grahame—Parsons concepts for the double layer structure are used for modelling the impedance behaviour of a metal electrode in contact with a solution of its salt, i.e. in the absence of a base electrolyte. The Lorenz—Salie concept of partial charge transfer is also used. Provided that the faradaic reaction is sufficiently slow, the apparent double-layer capacity, i.e. the capacity describing the impedance behaviour of the electrode at high frequencies, is equal to the thermodynamic capacity even in the case of strong ionic adsorption. A sufficiently fast faradaic reaction changes the structure of the electrode impedance. In this case the apparent double-layer capacity can have a different value and sign from those of the thermodynamic electrode capacity. This is also the case for a completely reversible electrode.

Gibbs fluctuation theory in the context of electrochemical equilibrium noise

The electrochemical noise verification of the Gibbs fluctuation theory shows that the Gibbs ergodic idea works perfectly with respect to the pair correlations of the electrode charge thermal fluctuations. At the same time, the Gibbs formulae for the triple- and higher-order correlations of the electrode charge thermal fluctuations are outside of the ergodic hypothesis. This failure of the Gibbs ergodic idea suggests that the noise version of the electrochemical charge-transfer theory should be developed. In the context of nano-electrochemistry, the second- and higher-order correlations of the electrochemical noise processes may be considered as the quantities suitable for the nano-electrochemical characterization of both the electrode processes and electrochemical devices.

LANGEVIN'S APPROACH TO NON-GAUSSIAN INTERNAL NOISE DESCRIPTION

The dual Langevin stochastic equations for non-Gaussian internal noise that are consistent with Nyquists fluctuation-dissipation theorem are derived. It results in the fact that the equilibrium current-voltage cumulant spectra possess the invariance property. The possibility to use the dual Langevin stochastic equations under the steady-state electrical current condition and in the quantum frequency range is discussed.

Differential and thermodynamic electrode capacity—impedance control of identity

Abstract The partial charge transfer concept is used to construct an impedance theory for an ideally polarizable electrode in mixed electrolyte. The relations between the impedance parameters and electrocapillary data are derived. The latter can be used as the basis for verification of the identity of the measured differential electrode capacity and the thermodynamic electrode capacity.

Fluctuation/dissipation analysis of diffusion and discharge processes

A fluctuation/dissipation analysis of the noise of a microelectrode is performed. It is shown that the mass transfer step and the discharge step are fluctuationally correlated already in the first order in the constant electric current polarizing the electrode. This basic result makes necessary a certain modification of the modern macroscopic theory of electrochemical fluctuations and development of a unified theory of the reaction elementary act and electrochemical fluctuations. # 2002 Elsevier Science B.V. All rights reserved.