Electrochimica Acta 56 (2011) 7171–7179 Contents lists available at ScienceDirect Electrochimica Acta jou rn al hom epa ge: www.elsevier.com/locate/electacta Model for corrosion of metals covered with thin electrolyte layers: Pseudo-steady state diffusion of oxygen Murali Sankar Venkatraman a,∗ , Ivan S. Cole a , Bosco Emmanuel b a CSIRO Materials Science and Engineering, Clayton, Victoria, Australia b Central Electrochemical Research Institute, Karaikudi, Tamilnadu, India a r t i c l e i n f o Article history: Received 25 January 2011 Received in revised form 4 May 2011 Accepted 4 May 2011 Available online 12 June 2011 Keywords: Thin films Non-integer Order Kinetics Diffusion Model Free-corrosion a b s t r a c t A one-dimensional mathematical model is presented for the free corrosion of a bare metal surface (devoid of any oxide film) under a thin electrolyte layer using mixed potential theory where anodic metal dis- solution is controlled by oxygen diffusion through the electrolyte layer and by the oxygen reduction at the metal surface. A pseudo-steady state is considered wherein the oxygen diffusion is at steady state while the metal and hydroxyl ions keep accumulating in the thin electrolyte layer due to a decoupling arising from the assumed Tafel laws for corrosion kinetics. Under free corrosion the oxygen diffusion is shown to depend on a non-linear boundary condition with a non-integer power on oxygen concentration at the metal surface which makes the model non-trivial. Analytical and numerical results for the oxygen concentration at the metal surface, corrosion potential, and corrosion current density are reported which depend on several kinetic, thermodynamic and transport parameters in the system. The model is applied to iron and zinc systems with input data taken from the literature. The experimental utility of the model for gathering thin-film corrosion parameters from a study of the corrosion current and potential as a function of the thickness of the electrolyte layer is discussed. Precipitation and passivity, though not the main object of study in this work, are briefly discussed. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved. 1. Introduction Characterizing corrosion in a particular environment simulating the service atmosphere has been an object of study over a cen- tury [1,2]. The context of corrosion can range from thin electrolyte layers and droplets covering metals and semiconductors exposed to the daily wet/dry humidity cycles [3–5] to industrial structures in contact with voluminous corrosive environments such as the off-shore structures immersed in the oceans [6]. Though the latter class of the systems have been widely modeled [6] and experimen- tally studied in the electrochemist’s lab, studies of corrosion under thin electrolyte layers [7–10] and droplets [11–14] are of more recent origin which await more extensive investigations. Accord- ing to Stratmann et al. [9] the indoor corrosion of the metals and semi-conductors which are part of circuits and electronic equip- ment, take place under electrolyte layers of varying thickness. In a series of papers [7–9], they developed new techniques using the Kelvin probe to study the corrosion kinetics of metal surfaces cov- ered by very thin electrolyte layers. With a view to understand the experimental results on corrosion under thin electrolyte layers, we ∗ Corresponding author. Tel.: +61 433 412 435; fax: +61 3 9545 2818. E-mail address: murali.s.venkatraman@gmail.com (M.S. Venkatraman). embarked upon a theoretical program of which the present work is the first part. In the case of uniform corrosion, anodic and cathodic sites are distributed randomly over the surface, and are spatially separated over atomic distances. In this situation, the electrode has a “mixed” potential [15] which, like the current density, is macroscopically uniform throughout the metal surface. The metal dissolution reac- tion (MDR) and the oxygen reduction reaction (ORR) are essentially irreversible [16]. MDR is generally faster than ORR and this along with the very low solubility of oxygen in the solution, leads to a very low concentration of dissolved molecular oxygen, albeit non-zero, at the surface of the corroding metal which effectively determines the corrosion rate of the metal. However, the transport of species is usually left out of consideration in the mixed potential theories of corrosion current and corrosion potential. Hence a simple scheme to predict the surface concentration of oxygen would be a helpful tool for predicting the initial corrosion rates more accurately. Modeling transport in electrochemical systems dates back to the classical work on binary electrolytes by Nernst [17] who neglected electric migration by assuming a diffusion layer near an electrode where the variation of the concentration was assumed linear. Since then there have been a number of mathematical mod- els of the evolution of the chemical conditions and transport of ions in various electrochemical systems. Most models for corrosion 0013-4686/$ – see front matter. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2011.05.009