Jacobian elliptic functions describe the properties of the diffuse charge region in narrow electrochemical cells

Diffuse double layers merge in narrow electrochemical cells. The distribution of ions, and the accompanying electrical properties, are predicted under static conditions that are mild enough not to engender electrochemical reactions. The predictions rest on assumptions that are not egregiously unreasonable. The potential and concentration profiles are respectively described by Legendre elliptic integrals and Jacobian elliptic functions. The special case of pure water is examined and the relevance of this study to water desalination is briefly addressed.     

The excess current in cyclic voltammetry arising from the presence of an electrode edge

The popular inlaid disc electrode suffers from an edge effect that is usually, and sometimes unwarrantedly, ignored in analyzing transient voltammograms. This study addresses the role played by the edge in linear scan and cyclic voltammetries when the electron transfer is reversible or quasi-reversible. A simulation models the concentrations, current densities and currents in two circumstances—when the edge in important and when it is absent—simultaneously, and thereby the evolving edge current is quantified. Special attention is paid to the effect that the edge has on the heights and positions of the voltammetric peaks. It is demonstrated that disregarding the edge may lead to the bogus classification of a reversible electrode reaction as quasi-reversible.     

How does a reversible electrode respond in a.c. voltammetry? Part 2: solutions for the periodic current amplitudes

Journal of Solid State Electrochemistry - In a.c. voltammetry, a programmed electrical potential—a linear ramp modulated by a sine wave of frequency ω and modest amplitude—is...     

Multi-scan cyclic voltammetry of a solution containing mixed valence states

Journal of Solid State Electrochemistry - When both members of a redox pair are present in a voltammetric cell, the applied signal must start at the null potential if pure cyclic voltammetry is to...     

Pitfalls in the application of statistics to chemical data: the determination of the partition ratio $$K_{\mathrm{ow} }$$ as a case in point

Nowadays those who make replicate measurements of physicochemical properties usually employ spreadsheets or handheld devices to perform averaging and other statistical operations. Using the determination of a partition ratio as an exemplary procedure, and employing statistical simulation, we examine errors that can arise by unthinking reliance on “clicking”. Alternative, more soundly based, procedures are advocated. A serendipitous result is that the logarithm of a partition ratio behaves statistically much better than expected.     

Modelling of solid state voltammetry of immobilized microcrystals assuming an initiation of the electrochemical reaction at a three-phase junction

The electrochemical reduction of a solid compound characterized by mixed ionic/electronic conductivity, immobilized on an electrode surface and in contact with an electrolyte solution, has been studied theoretically. The uptake or expulsion of electrons and electrolyte cation is coupled to maintain electroneutrality and is assumed to obey Fick's law of diffusion. Starting with the fully oxidized species, the simultaneous uptake of cations and electrons will be possible at the three-phase junction only, where electrode, solid and electrolyte solution meet. From this point, electrons and cations diffuse perpendicularly into the crystal lattice. The reaction zone grows owing to the formation of the electronically and ionically conducting reduced product. Two- and three-dimensional models have been utilized to simulate the diffusion and the current flow in response to an applied potential step. The resulting chronoamperometric curves have been analyzed with the help of fitting procedures. Under certain conditions, a transition of the three-phase reaction to a pure two-phase reaction occurs. This transition to a two-phase condition is the reason that a number of equations for the exhaustive conversion are similar to those known for planar diffusion, for example. To illustrate this, and for a better understanding of the phenomena, concentration profiles are presented for different degrees of the reaction and for varied simulation conditions. It is demonstrated how geometrical properties like crystal shape (cuboid with x ≠ y ≠ z) and crystal size as well as physical properties, e.g. the diffusion coefficients, govern the electrochemical behavior of mixed ionic/electronic conductors and form the basis of the current-time functions. The numerical simulation of a two-dimensional semi-infinite model of the reaction at the three-phase junction gives results comparable to an algebraical approach. The finite-difference method turned out to be suitable to solve the problems arising from the three-dimensional and finite diffusion conditions and from different crystal shapes. Received: 24 November 1999 / Accepted: 22 February 2000     

A Green function for the equilateral triangle

Using the image method, a diffusional Green function has been derived analytically for a triangle, when its three sides, all of equal length, have zero intensity. Because many image sites are involved, computational assistance is employed both to construct the Green function and to use it in solving practical problems. An alternative procedure based on eigenfunctions is also summarized.     

A Green function for the equilateral triangle

Using the image method, a diffusional Green function has been derived analytically for a triangle, when its three sides, all of equal length, have zero intensity. Because many image sites are involved, computational assistance is employed both to construct the Green function and to use it in solving practical problems. An alternative procedure based on eigenfunctions is also summarized.Received: November 18, 2003; revised: April 6, 2004