Analytical solutions of the multipotential pulse quasi-reversible Q–E–t and I–E–t responses of strongly adsorbed redox molecules Joaquı ´n Gonza ´lez * , Nuria Abenza, A ´ ngela Molina Departamento de Quı ´mica Fı ´sica, Universidad de Murcia, Espinardo, 30100 Murcia, Spain Received 6 June 2006; received in revised form 19 July 2006; accepted 20 July 2006 Available online 1 September 2006 Abstract General analytical and fully explicit equations for the transient charge–potential–time (Q p –E p –t) and current–potential–time (I p –E p –t) responses of quasi-reversible electroactive diffusionless systems valid for any multipotential pulse technique are presented. The expres- sions for the non faradaic contributions to both responses are also deduced and simple and effective methods to quantify and eliminate them are proposed. The use of a discrete potential pulse sequence leads to stepped or continuous sigmoidal Q p –E p –t curves depending on the reversible or non reversible nature of the electrode process, a behaviour which cannot be obtained when a continuous time dependent potential is applied, as in Cyclic Voltammetry. Easy methods for estimating thermodynamic and kinetic parameters of the electroactive film are proposed and experimentally tested. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Monolayer; Slow Charge Transfer Process; Multipotential pulse techniques; Chronoamperometry; Adsorption; Anthraquinone 1. Introduction To date, the method most used to characterise the electrochemical responses of species adsorbed forming organized monolayers has been Cyclic Voltammetry (CV) [1–6]. This technique presents simple criteria for evaluating the rate constants of different electrode processes, although it requires a model, which has to be provided a priori, for the potential dependence of the rate constants. An interesting alternative to CV lies in potential step techniques, for which no a priori models for the potential dependence of the rate constants are needed. The one most used has been single potential chronoamperometry [7–10], and there have been several attempts to obtain the theoret- ical responses corresponding to multistep potential methods such as Square Wave Voltammetry (SWV) or Staircase Voltammetry (SCV). However, to date, the different treat- ments devoted to the study of the application of a given potential pulses sequence to quasi-reversible surface charge transfer reactions taking place in an electroactive mono- layer can only be considered as semi-analytical. Indeed, they lead to both non explicit integral equations [11] and to iterative procedures [12,13]. In order to cover this gap in the study of the behaviour of quasi-reversible electroactive monolayers, in this paper we present simple, analytical and fully explicit equations for the transient charge–potential–time (Q p –E p –t) and cur- rent–potential–time (I p –E p –t) responses of these systems which can be applied in any multipotential step technique such as multipulse potential chronoamperometry, SCV and SWV, and for any value of the kinetic parameters of the charge transfer reaction. The above equations give rise to a better and necessary comprehension of the behaviour of these responses, and they also allow us to deduce particular and much simpler equa- tions corresponding to reversible and totally irreversible pro- cesses. In the former case, the expressions obtained lead to independent of time charge and null current for any discrete pulse technique. We have also analysed on this paper the behaviour of the Q p –t curves corresponding to any potential pulse of an arbitrary sequence, E p , which present a plateau 0022-0728/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2006.07.034 * Corresponding author. Tel.: +34 968 367429; fax: +34 968 364148. E-mail address: josquin@um.es (J. Gonza ´lez). www.elsevier.com/locate/jelechem Journal of Electroanalytical Chemistry 596 (2006) 74–86 Journal of Electroanalytical Chemistry