(241d) Macroscopic Model of Proton Transport Through the Membrane-Ionomer Interface

A membrane-ionomer interface is formed on both sides of the proton exchange membrane in the membrane electrode assembly (MEA) that interlinks the electrodes, catalyst, and membrane, both physically and electrically. The proton conduction through the interface controls the performance of the polymer electrolyte membrane fuel cell. In this study, we have examined the transport of protons (hydronium ions) through the Nafion® membrane-ionomer interface, which has sulfonic acid (–SO₃H) end groups in the side-chain pendants. The ionomer ink has similar properties to the membrane, so that the membrane and interface should behave similarly in the transport of protons and water.

A hydrated Nafion® membrane is a collection of parallel nanochannels and it loses protons to the surrounding water. The interface, formed in the MEA, will also have similar pores. In the present study, a pore in the interface was modeled as a cylindrical tube. The negatively charged pendants (–SO₃^- ends) are uniformly distributed along the length and the circumference of the pore. An external electric field, E_ext, was applied between the anode and the cathode. Seven types of microscopic interaction potentials were considered according to the species-species interaction: hydronium-hydronium, hydronium-water, water-water pendants-hydronium, pendants-water, electric field (external)-hydronium, and electric field-water interaction potentials. Usually, the interface is very thin as compared to the membrane; hence, we considered that water is stagnant, and its density is constant within the tube. We also assumed that the velocity and density of the hydronium ions vary only in the axial direction. The above-mentioned microscopic potential energies were scaled up to the macroscopic potential energies in terms of macroscopic variables for a small test element of the tube, and the Hamiltonian, H, was expressed as a functional of mass density and momentum of the hydronium ions and water molecules. Evolution equations for the variables were derived via nonequilibrium thermodynamic modeling and were solved using a finite difference method (Euler’s method). The results show that the density profile of the hydronium ions is sinusoidal and its value is maximum in between the pendants. The velocity also changes sinusoidally and decreases along the length of the pore. The proton conductivity of a pore of length and radius of 80 and 10 Å, respectively, with 10 and 6 pendants along the length and the circumference, respectively, also changes according to the velocity profile and its average value is 0.1563 S/cm, which is comparable to values appearing in the literature. The effect of pore radius, separation distance between the pendants, and higher number of pendants on the circumference on the proton conductivity have also been studied.