# Keith OldhamTrent University · Department of Chemistry

Keith Oldham

D.Sc (Manchester).,Ph.D.,F.R.I.C.,F.C.I.C.

## About

323

Publications

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Introduction

Keith has skills in electrochemistry and mathematics, having worked at universities in England, the U.S., Canada and Australia. Currently he is an Emeritus Professor at Trent University, Peterborough, Canada.

Additional affiliations

January 1996 - April 2014

September 1970 - present

## Publications

Publications (323)

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 be conducted. Here the current from a limitless number of repetitive cyclic scans is predicted mathematically for any initial reductant to oxidant ratio. The predictions were prompted by, and are...

In a.c. voltammetry, a programmed electrical potential—a linear ramp modulated by a sine wave of frequency ω and modest amplitude—is applied to the working electrode of a voltammetric cell. If the electrolyte solution contains a solute that undergoes a reversible electron exchange at the electrode, then the ensuing faradaic current incorporates two...

2017 is the sesquicentennial of Grünwald’s demonstration that differentiation and integration can be united into a single operation which, moreover, could then be extended to unlimited orders. This text provides an overview of how such “differintegration” may be defined and implemented. The basis of its valuable application in electrochemistry is e...

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 “...

It is often useful to transform a measured signal into a form that is more easily interpreted. Thus, in voltammetry, where the measurement is of a current responding to a perturbation of the electrode potential, the complications arising from diffusional transport may be readily alleviated through the use of semioperators or convolutions. The use o...

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 a...

It is frustrating when a power (or other) series fails to converge, preventing the straightforward calculation of values of a function of interest. Here, the discussion focuses on two algorithms, discovered long ago but not well known, by which the sums of series may be calculated arithmetically, notwithstanding the divergence of the series. A powe...

Beer’s law describes the diminution in intensity as light passes through an absorbing medium. Photometry, the primary application of the law in chemistry, is used to deduce the concentration of a light-absorbing component from the decrease in the intensity of monochromatic radiation during passage through a known length of the medium. This article...

Steady-state voltammetry is easily attained in narrow cells. Here we develop an exact mathematical description of one of the simplest instances, in which a redox pair is present, but without supporting electrolyte. The Nernstian oxidation that depolarizes the anode is partnered at the nearby cathode by the converse reduction. The resulting voltammo...

Linear regression is, perhaps, the statistical technique most widely used by chemists. Regrettably, it is frequently misused. The many nuances in the procedure are commonly overlooked, leading to frequent misapplication of the traditional formulas. Here we discuss a number of alternatives and the circumstances under which each should be employed.

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, curre...

The Beer–Lambert law is inadequate to describe the absorption of radiation by a medium if the absorbing component is being simultaneously destroyed by the radiation. A replacement law is derived and solved in terms of a family of polynomials. The solution is confirmed numerically and by simulation.

A previous article shows that, after an infinite number of cycles, reversible cyclic voltammetry will attain an ultimate state characterized by properties that were identified in that study. Here, reversible multi-scan cyclic voltammetry has been modelled with a view to assessing the circumstances under which the ultimate state is attainable in an...

Multi-scan cyclic voltammetry may lead eventually to a repetitive current-versus-potential graph. Here such “ultimate” cyclic voltammograms are investigated mathematically for reversible electrode reactions. The voltammetric shapes, after an infinite number of cycles, are modelled and their characteristics are documented. It is predicted that the a...

A brief description is given of a novel technique whereby thermodynamic, kinetic, and transport parameters may be extracted from experimental cyclic voltammograms. For simulated data, this “linearization method” yields excellent answers.

Electrochemistry is a discipline of wide scientific and technological interest. Scientifically, it explores the electrical properties of materials and especially the interfaces between different kinds of matter. Technologically, electrochemistry touches our lives in many ways that few fully appreciate; for example, materials as diverse as aluminum,...

Semiconductor ElectrodesPhenomena at Liquid|Liquid InterfacesElectrokinetic PhenomenaSummary

Keith B. Oldham shares his views on some of the emerging trends in electrochemical instrumentation and modeling. Modeling electrochemical events has become the main task of a few mathematically inclined experts, with the majority being content to rely on commercial packages based on obscure algorithms. Advantages of such trends are similar to those...

Measurements of steady-state currents in thin-layer cells provide an opportunity to apply a stringent test of theories of electrochemical transport by simultaneous diffusion and migration. We have applied such a test and find the theory to be vindicated.

The capacitance of a layer of spherical orientable dipoles has been determined. The properties attributed to each dipole are those of two point charges on a diameter of the sphere and equidistant from its centre. A one-dimensional potential distribution is assumed to exist normal to the layer and to be coupled to the charge distribution via Poisson...

Studies of a cell consisting of a sheet of a porous medium soaked with an aqueous electrolyte solution containing the mercurous ion and sandwiched between mercury pools show that steady-state electrolysis may be attained in the absence of convection. Several different porous matrices have been studied and, in some cases, a very simple model of the...

Electrochemistry was one of the first sciences to benefit from the fractional calculus. Electrodes may be thought of as “transducers” of chemical fluxes into electricity. In a typical electrochemical cell, chemical species, such as ions or dissolved molecules, move towards the electrodes by diffusion. Likewise, other species are liberated into solu...

Five methods are described for reducing or eliminating the error oscillations resulting from the application of the Peaceman–Rachford alternating direction implicit algorithm to disk electrode simulation problems involving an initial discontinuity, such as results from a potential jump at an electrode. The methods are: (a) the straight-forward appl...

Analytical mathematics and digital simulation are used to predict the response, to a potential jump, of the junction between
insulating and conducting regions of an electrode. The simulation is carried out differentially and employs other novel features.
Concentrations in the vicinity of edges of positive and negative curvatures, as well as straigh...

Chapter 50 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 37 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 2 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 17 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 34 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 49 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 62 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 35 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 1 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 58 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 3 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 55 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 40 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 44 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 7 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 8 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 56 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 25 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 45 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 31 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 4 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 43 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 32 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 28 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 41 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 36 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 52 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 29 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 30 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.

Chapter 46 of “An Atlas of Functions 2nd Edition”, Springer Verlag, New York, 2008.