Electrochimica Acta 52 (2006) 1339–1348 Electrochemical impedance spectroscopy response of water uptake in organic coatings by finite element methods O.A. Stafford, B.R. Hinderliter ∗ , S.G. Croll Coatings and Polymeric Materials Department, North Dakota State University, Fargo, ND 58105-5376, USA Received 25 January 2006; received in revised form 27 July 2006; accepted 29 July 2006 Available online 1 September 2006 Abstract The corrosion of metals is a long standing topic of research which is of immense economic importance. One of the principal means of preventing surface corrosion of metals is thin polymer coatings, i.e. paint. These coatings often fail because of the passage of water or other active ionic species into and through the polymer coating. Since both the capacitance and the resistance of a polymer coating change as it absorbs water, electrochemical impedance spectroscopy (EIS) gives a general idea of how much water a polymer has been absorbed. Theories, such as the Brasher–Kingsbury approximation, are effective medium theories based on the assumption that the absorbed water is randomly distributed in spherical inclusions. The water in a coating may be distributed as spherical inclusions, as discrete channels, or as some combination that transports water from the coating surface until the water reaches the metal substrate and corrosion can begin. The resistance and the capacitance of a coating depend on both the amount of water (volume fraction) and the shape of the water inclusions. EIS gives only a general idea of how much water has been absorbed by a coating but does not provide the distribution or shape of the water inclusions. EIS circuit response is often modeled with the equivalent circuit elements describing the material properties for water inclusions that are implicitly assumed to be randomly distributed spherical inclusions. Numerical calculations using the finite element analysis (FEA) are reported here to solve Maxwell’s equations for various shapes and sizes of water inclusions within the polymer. Calculations here have been based on the electrical properties of a polyvinyl fluoride film, as an exemplar, with water inclusions of different shapes and concentrations (water volume fraction). The Brasher–Kingsbury approximation gives the correct outcome only for a random distribution of spherical inclusions, as expected. Other shapes and distributions can vary from the Brasher–Kingsbury prediction of water volume fraction by more than 50% of the actual gravimetric water volume fraction. Results are presented here for spherical and cylindrical randomly distributed water inclusions. Understanding the sensitivity to different distributions and numbers of inclusions is an objective planned for future research. © 2006 Elsevier Ltd. All rights reserved. Keywords: Electrochemical impedance spectroscopy; Finite element; Gravimetric; Brasher–Kingsbury; Polymer coating 1. Introduction A significant amount of work [1–4] has been done to under- stand the penetration of water and other ions through polymer films. Water that enters a coating is likely to be distributed inho- mogeneously with different shapes due to the paths that water takes into the coating, the depth of water advance and the vol- ume fraction of water in the coating. Water is also likely to be mixed with the polymer chains in various concentrations even within inclusions. As a first approximation these regions of high ∗ Corresponding author. Tel.: +1 701 231 8438; fax: +1 701 231 8439. E-mail address: brian.hinderliter@ndsu.edu (B.R. Hinderliter). water concentration will have properties assigned as if the inclu- sions were only water. The water inclusions are assumed to be randomly oriented and all of the same aspect ratio. Actual coat- ing systems would likely have a distribution of water inclusion shapes and sizes. Percolation size distribution, orientation and bulk homogeneity are presently being investigated. Electrochemical impedance spectroscopy (EIS) measures the current going though a coating generated by an alternating elec- tric field applied to the coating (Fig. 1). The magnitude of the cur- rent and the phase of the current relative to the applied alternating voltage can be used to determine the impedance. Both real and imaginary components of the impedance can be used to calculate the change in capacitance of the coating due to water/solution uptake. From the change in the capacitance, the volume fraction 0013-4686/$ – see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2006.07.047