A Gerischer Phase Element in the Impedance Diagram of the Polymer Electrolyte Membrane Fuel Cell Anode ² Anne-Kristine Meland, Dick Bedeaux,* and Signe Kjelstrup Department of Chemistry, Norwegian UniVersity of Science and Technology, 7491 Trondheim, Norway ReceiVed: February 4, 2005; In Final Form: June 21, 2005 We study the isothermal hydrogen adsorption and reaction at the E-TEK electrode of a polymer electrolyte fuel cell with a Nafion 117 membrane by impedance spectroscopy at 30 °C. We find that the impedance diagram must include a Gerischer phase element. Constant phase elements are not sufficient to describe the experimental data. This means that an adsorption reaction takes place in combination with surface diffusion of hydrogen in the carbon layer located before the platinum surface, separate from the charge transfer step at the platinum particle surface. We are not able to distinguish between molecular or atomic hydrogen diffusion on carbon. We predict and find that the relaxation time of the adsorption step is independent of the applied potential. Water may also enter rate-limiting steps in the electrode reaction, but its role needs further clarification. 1. Introduction Electrochemical impedance spectroscopy (EIS) is an experi- mental technique that can separate phenomena with different relaxation times, and is thus useful for determination of rate- limiting steps at electrode surfaces. 1 It has been widely used, also in studies of rather complicated three-phase contacts. 2,3 Such contacts are typical for fuel cell electrodes. Most polymer fuel cell electrodes consist of a porous matrix of carbon black that allow gas diffusion up to the catalyst (Pt) particles. The carbon layer is up to a few hundred micrometers thick. 4 The gas will eventually react at the catalyst, which is also in contact with the proton-conducting membrane electrolyte. This contact is often enhanced by adding a membrane polymer solution to the catalyst layer, as described for instance in the Experimental Section. A complicating factor is the required presence of water in the membrane. 2,5 Impedance studies on fuel cells have mostly concerned rate- limiting processes in the complete cell. 2,6,7 The cathode, or the oxygen electrode, will then dominate the spectrum. We shall study the anode of the fuel cell, the hydrogen electrode in a cell with two identical hydrogen electrodes. Recent impedance studies of this electrode have been motivated by the need to understand the CO tolerance of this electrode. 8,9 As a back- ground for such studies, it is important to have a good understanding of the elementary steps concerning hydrogen alone. Also, with the present discussion on the mode of hydrogen adsorption in carbon nanotubes, 10 it is interesting to see if impedance studies can provide information about the role of carbon in the anode reaction. The aim of this investigation is to give experimental and theoretical support to the first step in the anode reaction. We shall see that this must include a reversible reaction (the adsorption reaction) followed by diffusion of the adsorbed species to the site where the charge transfer takes place. The adsorption reaction takes place in a layer with a thickness estimated to be ∼200 μm, located around the Pt particles. Such an adsorption reaction has earlier been allocated to the Pt particle itself; see, for example, the work of Chen and Kucernak, 11 who studied insulated Pt particles. Various methods have been used to establish a theoretical background for the impedance of a porous electrode. The porous electrode model, e.g., Weber and Newman, 12 consists of a network of normal and charge transfer resistors. Taylor expan- sions around point values of nonlinear equations for reaction kinetics have long been used to find the impedance. 1,6,13 Gomadam et al. 7 derived impedances for composite electrode models, which treat the composite electrode as a superposition of two continuous phases; one phase is a pure ion conductor, and the other phase is a pure electronic conductor. The fractal structure of these materials can also explain the typically depressed semicircles. 14 Pugazhendi et al. 3 divided the heterogeneous region into bulk parts and surfaces, and treated the surface as a two-dimensional system according to the method of Gibbs, 15 with surface properties integrated out to give excess variables. The excess energy dissipation at the electrode (or the excess entropy production) of the surface was used in the derivation of the surface impedance. We shall use this method, which is always in agreement with the second law of thermodynamics. The aim of the study is then, from a chosen model, to first predict an impedance spectrum of the anode. We shall next use the obtained relations to obtain properties of the electrode from experimental results. We shall see that the experiments give support a reaction-diffusion step as the first step in the electrode reaction. We report findings for a common membrane electrode assembly, namely, the E-TEK electrode with 0.5 mg of Pt/cm 2 and a Nafion 117 membrane. It is common to assume that the rate-limiting process in the electrode backing of the anode (as well as the cathode) is diffusion in the gas phase. 2,6,8 The good fit of the data that we obtain to a Gerischer phase element indicates that the reversible adsorption reaction of hydrogen to carbon black along the pore walls and the subsequent diffusion along the surface to the catalyst plays a more important role than has been assumed previously. Gerischer phase elements have been observed for porous electrodes before, but only in ² Part of the special issue “Irwin Oppenheim Festschrift”. * To whom correspondence should be addressed. E-mail: bedeaux@phys.chem.ntnu.no. 10.1021/jp050635q CCC: $30.25 © xxxx American Chemical Society PAGE EST: 8.9 Published on Web 00/00/0000