A Predictive Thermodynamic-Based Model for Proton Conductivity of Proton Exchange Membranes Based on Poly(Benzimidazole)/Poly(Acrylic Acid) Blend

To predict the novel poly(benzimidazole):poly(acrylic acid) (PBI:PAA) blend membranes proton conductivity, an ionic conductivity equation combined with thermodynamic model is proposed where different proton transport mechanisms including Grotthuss, vehicle and surface hopping mechanisms are considered in calculations. Based on the PAA titration behavior, by increasing the number-average molecular weight ( M ¯ n ), apparent acidity of PAA decreases. Hence, to calculate the concentration of protons involved in different mechanisms, a new modification in the predictive model is suggested by considering acidity and its relation with M ¯ n . Effect of temperature, PAA molar ratio and M ¯ n on the membranes proton conductivity is investigated theoretically and compared with experimental data. The conductivity of membranes is increased by increasing the M ¯ n and molar ratio of PAA where the highest proton conductivity is attributed to the membrane with PAA of M ¯ n = 105 g mol−1 and molar ratio of PBI:PAA = 1:4. The experimental proton conductivity and predicted results show a good agreement in comparison to the previous models based on Nernst-Einstein equation, indicating that acidic behavior, which is usually omitted in theoretical models, has an important effect on the total proton conductivity of PBI:Polyacid membranes, especially at higher temperatures.