Contents lists available at ScienceDirect Journal of Electroanalytical Chemistry journal homepage: www.elsevier.com/locate/jelechem Semi-analytical modelling of linear scan voltammetric responses for soluble- insoluble system: The case of metal deposition Imene Atek a,b , Sunny Maye b , Hubert H. Girault b , Abed M. Affoune a, ⁎ , Pekka Peljo b, ⁎ a Laboratoire d'Analyses Industrielles et Génie des Matériaux, Département de Génie des Procédés, Faculté des Sciences et de la Technologie, Université 8 Mai 1945 Guelma, BP 401, Guelma 24000, Algeria b Laboratoire d'Electrochimie Physique et Analytique, École Polytechnique Fédérale de Lausanne, EPFL Valais Wallis, Rue de l'Industrie 17, Case Postale 440, CH-1951 Sion, Switzerland ARTICLE INFO Keywords: Modelling Metal deposition Soluble-insoluble system Linear sweep voltammetry ABSTRACT The absence of general theoretical models describing linear sweep voltammetry (LSV) or cyclic voltammetry (CV) responses for soluble-insoluble systems such as one-step electrodeposition reactions under quasi-reversible condition makes it difficult to extract quantitative kinetic information from experimental voltammograms. In this work, a semi-analytical method for modelling LSV responses for one–step electrodeposition process is de- scribed, for a case where instantaneous nucleation takes place, such as metal deposition on same metal. Voltammetric peaks were analyzed following variation of both dimensionless rate constants and charge transfer coefficients in a broad range. Therefore, kinetic curves for electron transfer processes were established and fitted perfectly by sigmoidal Boltzmann function and linear models. With these models, LSV or CV experimental data can be used to measure electrodeposition reactions kinetics whatever the degree of reversibility. The Cu(I)/Cu(0) couple in acetonitrile was selected as an experimental example. The model developed in this work predicts accurately the current response for Cu electrodeposition reaction and an excellent experiment–theory agreement was found. 1. Introduction Over the years within the field of electrochemistry, many efforts have been devoted to modelling and simulation techniques to help to understand electroanalytical experiments [1–10]. Linear sweep vol- tammetry (LSV) and cyclic voltammetry (CV) are well-known electro- chemical techniques which have played an important role to obtain a clear view about the kinetics, thermodynamics and mechanisms of electrode reactions [3–6]. In LSV, the potential is scanned linearly starting at the initial potential while measuring the current response. CV is an extension of LSV in that the direction of the potential scan is switched at a predetermined value and the potential is scanned again in the reverse direction to the initial value. Thus, a triangular potential- time waveform is used in CV [4]. In this framework and according to Oldham's earlier work, there are three possible pathways for the es- tablishment of a theoretical voltammograms [5]: analytical modelling, semi-analytical modelling and digital simulation. For a single-step reaction and particularly for soluble-soluble sys- tems where both oxidized and reduced species are soluble, a com- plementary theoretical studies by either analytical modelling, semi- analytical modelling or by digital simulation, was presented and extensively discussed for reversible, quasi-reversible and irreversible processes experiments [1–10]. Randles and Ševčík were the pioneers in this field [11,12]. After that many other investigations have been car- ried out, especially the work of Matsuda and Ayabe for quasi-reversible systems [10,13]. A very important theoretical development of cyclic voltammetry was achieved by Nicholson and Shain in their well-known paper published in 1964 [14,15]. For soluble-insoluble system, mod- elling of the voltammograms was first introduced by Berzins and De- lahay [16] who studied the reversible deposition on solid electrodes and derived an analytical expression for current-potential curve for single scan, using the Laplace transform and Dawson's integral. Later on, the theory was extended by Delahay to totally irreversible process [17]. Other researchers have also done similar studies but their main focus was for reversible cyclic voltammetry [18–20]. All these devel- opments concerned the redox reactions of simple ions with a single step. However, in the case involving amalgam formation, some ap- parent anomalies were noted between experiment and theory for cyclic voltammetry. These facts were discussed by Beyerlein, and Nicholson [21] and others [22]. Additionally, more complicated models including ion adsorption have been proposed [23]. On the other hand, to describe the transition between fast and slow https://doi.org/10.1016/j.jelechem.2018.04.021 Received 2 March 2018; Received in revised form 9 April 2018; Accepted 12 April 2018 ⁎ Corresponding authors. E-mail addresses: affoune.abedmohamed@univ-guelma.dz (A.M. Affoune), pekka.peljo@epfl.ch (P. Peljo). Journal of Electroanalytical Chemistry 818 (2018) 35–43 Available online 14 April 2018 1572-6657/ © 2018 Published by Elsevier B.V. T