Influence of Proton Activity Gaps between Electrodes on Open-Circuit Potential of H2/H2 and H2/Air Cells
Authors: Yoshida Toshihiko , Hojo TaKemasa , Jozuka Tetsuya , Matsuda Toshihiko , Danilovic Nemanja , Weber Adam Z. , Suzuki Toshiyuki 
Published: December 2020

Polymer -electrolyte-fuel-cell open-circuit voltages (OCVs) are exactly defined by equation (1), where cathode and anode proton activities [(aH+)cathode
and (aH+)anode, respectively] usually are identical, so the third term in the right-hand side of equation (2) is ignored.
OCV=E0+RT/2F*ln(a1/2
O2*(a2
H+)cathode/aH2O)-RT/2F*ln((a2
H+)anode/aH2) (1)
=E0+RT/2F*ln(a1/2
O2*aH2/aH2O)+RT/2F*ln((a2
H+)cathode/(a2
H+)anode) (2)
Water vapor pressure is a colligative property that fundamentally correlates to electrolyte concentrations in aqueous solutions. Proton activity is a function of acid concentration, such as pH, when electrolytes are acids. In polymer-electrolyte membranes, water vapor pressure and acid concentration are understood as relative humidity (RH) and water uptake (λ), respectively, where λ represents number of water molecules per sulfonic acid molecule. Several investigations have reported the relationship between RH and λ, meaning that proton activities and associated water uptakes are intimately related to RH.
In actual fuel cell operation, cathode RH is determined by ambient-atmosphere and/or humidifier RH(s), and anode RH depends on hydrogen-circulator RH. Therefore, RH is not always identical at both electrodes, and the difference between electrode RHs is considerable during dry operation of polymer electrolyte fuel cells. Therefore, the third term in the right-hand side of equation (2) may be significant for dry operation.
We measured OCVs when hydrogen was supplied to both electrodes at 80°C. One electrode (A) was fixed at 30% RH, while RH at the other electrode (B) was varied (0, 5, 10, 20, and 30%). Measured OCVs varied from 0 to 75 mV. For fuel cell tests, electrode A was supplied with hydrogen at 30% RH; electrode B, oxygen at 0, 5, 10, 20, and 30% RH. OCVs deviated from that measured when RH at electrode B was 30%, increasing from 0 to 60 mV with decreasing RH at electrode B. Results are also shown in Figure 1.
Proton activities of both electrodes were thermodynamically calculated. The Gibbs–Duhem relation was applied to obtain molar Gibbs free energies of water and sulfonic acid, and proton activity coefficient was calculated using the Gibbs free energy of sulfonic acid and the relationship between RH and λ1–4, assuming that protons and sulfonic anions show identical ionic-activity coefficients. OCVs were estimated using the third term in the right-hand side of equation (2). Results are shown in Figure 1.
Fuel-cell current–voltage performance was poor when RHs at the anode and cathode were 30 and 20%, respectively. To determine kinetic current, we measured the oxygen-reduction reaction (ORR) using a rotating-disk electrode (RDE) in concentrated-acid aqueous solutions, which modeled catalyst-layer ionomers. Kinetic currents decreased with acid concentrations.
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Figure 1