Journal of Electroanalytical Chemistry 512 (2001) 1 – 15 Analysis of ramped square-wave voltammetry in the frequency domain D.J. Gavaghan *, D. Elton 1 , K.B. Oldham 2 , A.M. Bond Department of Chemistry, Monash Uniersity, Clayton, Victoria 3800, Australia Received 6 April 2001; received in revised form 6 April 2001; accepted 21 May 2001 Abstract We present a new approach to the analysis of square-wave voltammetry in the frequency domain. By extending our earlier work (J. Electroanal. Chem. 480 (2000) 133) on the numerical simulation of ac sine wave voltammetry, we are able to solve the governing equations when a square waveform of any amplitude is superimposed onto a linearly varying dc potential which is swept at a finite scan rate. By considering the numerical results in the frequency domain by using the fast Fourier transform (FFT) method, we are able to develop a very simple and general form of analysis which will theoretically allow consideration of reaction phenomena over a very wide range of timescales using a single potential sweep. We go on to develop some novel theoretical analyses, which support our numerical results, using an assumption that the applied square-wave signal is superimposed on top of a fixed (or very slowly varying) dc signal. This allows us to give exact and surprisingly simple analytical results relating the amplitude and phase of the output signal at the half-wave potential (at odd multiples of the fundamental frequency), to the amplitude of the applied square-wave signal, for any amplitude of the applied signal. Finally, we give brief experimental results showing qualitative agreement with our simulation results. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Simulation; Ramped square-wave voltametry; Frequency domain www.elsevier.com/locate/jelechem 1. Introduction Pulse voltammetric techniques, which employ sudden changes in the applied potential, are commonly used in mechanistic investigations of electrode processes and in electroanalysis [1]. Square-wave voltammetry, pio- neered by Barker [2,3], is one widely used pulse tech- nique, as is evidenced by the fact that several varieties of this method [4,5] are standard options in almost all modern commercial voltammetric instrumentation. Square-wave voltammetry is usually practised with the square wave being superimposed on a staircase wave- form [4]. In the present study, however, a symmetrical square wave is superimposed on a simple dc ramp as illustrated in Fig. 1 a, c and e. In this regard, the technique resembles ac voltammetry in which the ap- plied signal is synthesised from a dc ramp plus a sine wave, as in Fig. 1a, b and d. Traditionally, square-wave voltammetry has employed large (e.g. 50 mV) ampli- tudes, and the experiment has been analysed in the time domain. In contrast, theoretical analyses of sinusoidal techniques commonly employ the frequency domain and generally use small ( 8/n mV) amplitude modula- tion. Recently, however, the present authors have shown [6–8] that, at least for simple reversible reac- tions, there is no reason to restrict the applied ampli- tude in ac voltammetry. In principle, of course, it is well known that both pulse and sinusoidal techniques can be conducted both instrumentally [9 – 11] and theoretically [11] in the frequency domain. In this paper we will demonstrate that the current response of a simple reversible reaction to the square- wave-plus-linear-ramp waveform 3 illustrated in Fig. 1e * Corresponding author. Permanent address: Oxford University Computing Laboratory, Wolfson Building, Parks Road, and Nuffield Department of Anaesthetics, University of Oxford, Radcliffe Infir- mary, Oxford, UK. Tel.: +44-1865-283574; fax: +44-1865-273839. E-mail address: gavaghan@comlab.ox.ac.uk (D.J. Gavaghan). 1 Permanent address: Department of Electronic Engineering, La- trobe University, Bundoora, Victoria 3083, Australia. 2 Permanent address: Department of Chemistry, Trent University, Peterborough, Canada K9J 7B8. 3 We will term this method ‘ramped square wave voltammetry’ to distinguish it from the more familiar form of square wave voltamme- try. 0022-0728/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII:S0022-0728(01)00575-7