Transfer function analysis of hydrogen permeation through a metallic membrane in a Devanathan cell. I. Theory C. Gabrielli * , G. Maurin, L. Mirkova 1 , H. Perrot, B. Tribollet UPR15 – CNRS, LISE, Univ. Pierre et Marie Curie, 4 Place Jussieu, case 133, 75252 Paris, France Received 3 May 2005; received in revised form 16 December 2005; accepted 14 January 2006 Available online 24 April 2006 Abstract Various transfer functions were calculated for hydrogen permeation through a metallic membrane in a Devanathan cell. Surface pro- cesses such as hydrogen adsorption and evolution were taken into account in addition to the hydrogen penetration process and its dif- fusion through the bulk metal. The main transfer functions are the input impedance DV 1 /DI 1 and the permeation transfer function DI 2 / DI 1 between the output current and the input current from which the transconductance transfer function DI 2 /DV 1 can be calculated. These quantities were obtained for potentiostatic controls of the input and/or the output sides. The effect of the changes of some char- acteristic kinetic parameters on these transfer functions were analyzed and their simplified expressions were derived for a few limiting cases. This gives a tool to interpret experimental data in a large set of conditions. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Hydrogen; Permeation; Devanathan; Transfer function; Electrochemical impedance; Modeling 1. Introduction Hydrogen evolution reaction (HER) which occurs on iron and iron alloy materials in aqueous environments is accompanied by hydrogen absorption into the metal phase, causing mechanical and structural degradation, particu- larly ‘‘hydrogen embrittlement’’. Hydrogen penetrates the metal from many sources, e.g. corrosion, electroplating, cathodic protection, acid pickling. Recent reviews on this topic have been presented [1–3] and the phenomenon has been widely discussed [4]. Several theories have been pro- posed to explain the mechanism of penetration, e.g.: the pressure theory, the adsorption theory, the decohesion the- ory and the hydride theory [5,6]. Currently, two models of the kinetics of hydrogen entry are generally accepted. According to the indirect entry model (or two-step absorption mechanism) [7–10], hydro- gen entering the metal passes through the same adsorbed state on the metal surface as the intermediate that leads to hydrogen evolution. The rate of hydrogen entry is deter- mined by the surface coverage h H of the adsorbed atomic hydrogen H ads , as intermediate of the HER via the dis- charge-Tafel recombination or the discharge-Heyrovsky desorption. In both cases, the major part of the adsorbed hydrogen reacts to give dihydrogen molecules evolving to atmosphere and a fraction of the adsorbed hydrogen may diffuse into the metallic lattice. The direct hydrogen entry model (or one-step absorp- tion mechanism) is based on the assumption that hydrogen enters the metal in the same elementary act as that in which it is discharged [11,12]. This model may be rather liable to acidic solutions, where the discharge of protons occurs, or to metals that absorb the most part of hydrogen whereas evolution is small [11]. According to [12], this direct mech- anism is valid for palladium at low values of hydrogen per- meation current density, and for HY-130 steel. Various experimental methods have been proposed for studying hydrogen permeation into metals and among 0022-0728/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2006.01.029 * Corresponding author. Tel.: +33 1 44 27 41 36; fax: +33 1 44 27 40 74. E-mail addresses: cg@ccr.jussieu.fr (C. Gabrielli), mirkova@ipchp. ipc.bas.org (L. Mirkova). 1 On leave from Institute of Physical Chemistry, Bulgarian Academy of Sciences, Acad. G. Bonshev Str. Bl 11, Sofia 1113 Bulgaria. Tel.: +359 272 75 50; fax: +359 2971 26 88. www.elsevier.com/locate/jelechem Journal of Electroanalytical Chemistry 590 (2006) 1–14 Journal of Electroanalytical Chemistry