An analytical explicit expression for the current obtained with the well-known multipulse technique square wave voltammetry (SWV), corresponding to the reversible reduction/oxidation of multicenter redox molecules whose centers may or may not interact, has been given in Appendix. This equation is valid for spherical electrodes of any size, including planar electrodes (r 0 f ∞) and ultramicroelectrodes (r 0 f 0) as limit cases, and it also permits us to deduce the behavior of these processes at the limit situations corresponding to small and great square wave amplitudes. For the sake of simplicity, we have analyzed the behavior of bicenter molecules, ranging from noninteracting centers, for which the square wave current obtained is twice that corresponding to a single E mechanism, to strongly interacting centers which present two successive and well-separated signals of one electron each. The results obtained here are easily extendable to molecules with any number of redox centers. The theoretical predictions have been tested with two experimental systems, quinizarine in acetonitrile and pyrazine in aqueous acid media, and an excellent agreement between theory and experiments is found.

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Voltammetric differential-pulse techniques are very useful electrochemical techniques for characterizing electrode processes. [1][2][3] The response obtained in these techniques can be considered as an approximation of the successive derivatives of the I vs. E curve, and it presents one or two peaks which are characteristic of the process analyzed. Thus, for example, differential pulse voltammetry (DPV) is a double-pulse technique whose response emulates the first derivative of the I vs. E curve, 1,4-8 while double differential pulse voltammetry (DDPV) is a recently designed triple-pulse technique whose response emulates the second derivative of the I vs. E curve. 9-11 The signals obtained in these differential and double differential pulse techniques coincide with the first and second derivative of the I vs. E curve, respectively, when the difference between the applied potential pulses, ⌬E, tends to zero.The true derivatives of the I vs. E curve are the responses corresponding to derivative voltammetry (DV), a potentiostatic technique which has received little attention in the literature due to the problems of the differentiation of digitally acquired signals, in particular the low signal-to-noise ratio. 12 However, modern digital filtering techniques can alleviate to a great extent the problems associated with the differentiation of the I vs. E signal, 13 and, therefore, we can use differential and double differential pulse voltammetry together with the derivative voltammetry technique in order to study electrode processes.Another derivative technique which has been much used in recent years for the study of different electrode processes is reciprocal derivative chronopotentiometry, 14-18 due to the fact that this technique, based on the plotting of the reciprocal of the time derivative of the chronopotentiogram vs. the measured potential (dt/dE vs. E), presents a characteristic peak that is quantitatively related to the kinetic and thermodynamic parameters of the electrode process and is scarcely affected by the capacitative effects on account of the fact that it has been obtained from the central zone of the E vs. t curve. This derivative technique is very simple to apply, and it presents high reproducibility in the measure of the peak potentials and peak heights, affording simple diagnosis criteria for the electrode processes analyzed. 17 In a recent paper we gave the conditions under which it is possible to establish a total analogy between the potentiostatic response when a constant potential E is applied and the chronopotentiometric response when a programmed current of the general form I(t) ϭ I 0 t u , u Ն Ϫ1/2 is applied, in the case of a reversible electrode process. 19 This analogy was extended to the potentiostatic technique DPV at the limit in which its response is analogous to that of derivative voltammetry technique (⌬E r 0), and to a new reciprocal derivative chronopotentiometric technique with programmed current proposed in the above mentioned paper which consists of the analysis of the dt uϩ1/...

Reversible surface two-electrons transfer reactions (stepwise processes) are analyzed using square wave voltcoulommetry (SWVC), which is a variety of square wave techniques based on the measurement of the transferred charge. Such reversible surface redox processes are exhibited by many two-redox center and multicenter biomolecules (proteins, enzymes, ...) and inorganic molecules like polyoxometalates (POMs), which have very interesting applications, mainly as electrocatalysts. Because of the stationary character of the response obtained, the key parameters that govern the cooperativity degree of the two reversible electron transfers (ETs) are the difference between their formal potentials, ΔE(0), and the square wave amplitude, |E(SW)|, whose combined effect sets the two peaks → one peak transition in the response. Working curves based on the variation of the peak parameters (peak potentials, half-peak widths, and peak heights) with ΔE(0) and |E(SW)| are given, from which the formal potentials and the total surface excess can be accurately determined. SWVC has been applied to the study of the reduction of polyoxometalate [PMo12O40](3-) adsorbed at a boron doped diamond electrode (BDD), for which three stable and well-defined reversible charge peaks, corresponding to three cooperative EE processes, are obtained in the interval (0.6, -0.2) V by using low square wave frequencies. From the analysis of these peaks, the values of the total surface excess and the formal potentials of the six ETs have been obtained in aqueous media for two electrolytes: HClO4 and LiClO4.

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