Potentials Near a Curved Anode Edge in a PEM Fuel Cell: Analytical Solution for Placing a Reference Electrode

Abstract

We consider a PEM fuel cell with concentric circular electrodes: the small anode and the large cathode. A model for in-plane distributions of the cathode overpotential η c and the membrane potential in the anode-free region of the cell is developed. Mathematically, the problem reduces to the axially symmetric Poisson-Boltzmann equation for η c . An approximate analytical solution shows that |η c | exhibits rapid decay to zero with the radius, while | | grows to the value of |η 0 c |, the cathode overpotential in the working domain of the cell. For typical η 0 c , the radial shape of η c far from the anode edge only weakly depends on η 0 c ; this effect is analogous to Debye screening in plasmas. The smaller the anode radius, the faster approaches η 0 c with the distance from the anode. It follows, that a reference electrode for measuring the cathode overpotential in the working area can be placed at a small distance from the curved anode edge. Performance of a polymer electrolyte membrane fuel cell (PEMFC) is determined by overpotentials driving the electrochemical reactions on either side of the cell. One of the most useful techniques for measuring the half-cell overpotentials is a method of reference electrode (RE). A typical schematic of a cell with the RE is depicted in Figure 1a. The hydrogen-fed RE is located at a certain distance L gap from the aligned anode and cathode edges. Neglecting the potential loss for the hydrogen oxidation/evolution reactions, the potential of the RE is equal to the membrane potential at the point of the RE location. If the distance L gap is large enough, the measured corresponds to the membrane potential at some point along the y-axis between the anode and cathode in the working cell area (Figure 1a). Measuring and the electrode potentials allows one to separate the anode and cathode overpotentials in the cell.1,2 Further, RE enables to perform electrochemical impedance spectroscopy between the RE and each of the cell electrodes; this technique has been widely used in SOFC studies. 3-6The problem with the system in Figure 1a is that even a small misalignment of the anode and cathode edges may strongly distort at the RE location. This problem has been intensively studied for different types of fuel cells. [3][4][5]7 Recently, a design free from this drawback has been suggested 8 (Figure 1b). Here, the cathode is continuous and the RE is located at a distance L gap from the straight anode edge. The absence of the cathode edge eliminates the misalignment problem. It has been shown, that for the design in Figure 1b Here, σ m is the membrane proton conductivity, b ox is the Tafel slope of the oxygen reduction reaction (ORR), l m is the membrane thickness, j 0 ox is the superficial exchange current density (A cm −2 ) of the cathode in the working cell area. With typical cell parameters (Table I), L gap appears to be on the order of several centimeters. For a typical laboratory-size cell of about 10 × 10 cm 2 , this value of L gap is quite large. Below, we show that a curved anode edg...

Reference Electrode Positioning in PEM Fuel Cell at a Parabolic Anode Tip

“…It is also evident, that the rate of η decay with this distance is maximal at the symmetry axis x of the problem. It has been shown that the membrane potential Φ increases with the distance from the tip, reaching the value of η 0 as η ( x ) approaches zero (Figure b). Thus, by placing a hydrogen‐fed reference electrode at the point where η ( x ) ≅ 0, one can measure Φ ≅ η 0 (Figure b).…”

“…In the anode‐less area, the cathode overpotential is described by the Poisson–Boltzmann (PB) equation, which in dimensionless form reads , …”

“…This arrangement eliminates the problem of electrodes alignment; however, the distance between the anode edge and RE appears to be rather large (see below). Later, analytical shape of the ORR overpotential at a circular anode edge over the infinite cathode has been calculated [9]. The solution shows that the distance between the anode edge and RE can be significantly lowered if the anode is curved.…”

Water and hydrogen transport modelling through the membrane-electrode assembly of a PEM fuel cell

“…Ubong et al [23] reported in their 3D modeling study for a PEMFC unit cell using Comsol Multiphysics software the following values for the kinetic parameters involved in Butler-Volmer equations: The electrochemical activation potential η act between CL solid matrix and PEM electrolyte at anode and cathode (at boundaries IV and V) was defined as [24]:…”