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A thermodynamic model-combined ionic conductivity equation was used to predict the proton conductivity of Nafion 117 membranes at different water contents and temperatures. Both vehicle and Grotthuss (hopping) mechanisms were considered to be responsible for the proton transport, from which protons and hydronium ions diffusion coefficients and conductivities were then calculated. Moreover, a correction was proposed for calculating the total concentration of ions in the above-mentioned model. It was found that with increasing the temperature and water content, the diffusion coefficients and conductivities enhance and the temperature dependence of the conductivity of Nafion 117 membrane follows a simple Arrhenius behavior. A good agreement between the theoretical and previously reported experimental proton conductivity data was also observed only when the corrected concentration was used in the calculations. The results obtained in the present work showed that the Grotthuss mechanism, which is usually ignored in the theoretical predictions, plays a significant role in the total proton conductivity of Nafion 117 membrane, especially at higher operational temperatures and the membrane water volume fractions.

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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 ¯= 10 5 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.