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

Abstract

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.

Ionic Mobility in Ion-Exchange Membranes

“…Both the pulsed field gradient NMR (PFG-NMR) method and different spin-relaxation techniques can be used for investigation of diffusion coefficients [ 72 , 76 , 79 ]. The relationship between the conductivity ( σ i ) and the diffusion coefficient D i for any given ions i is established by the Nernst–Einstein equation [ 90 , 91 , 92 ]: D i = RT / z i 2 F 2 σ i , where z i is the charge of ion i , F is the Faraday constant, and R is the gas constant. This equation is used to calculate the ionic diffusion coefficients from experimental determinations of conductivity or vice versa.…”

“…Both the pulsed field gradient NMR (PFG-NMR) method and different spin-relaxation techniques can be used for investigation of diffusion coefficients [72,76,79]. The relationship between the conductivity (σ i ) and the diffusion coefficient D i for any given ions i is established by the Nernst-Einstein equation [90][91][92]:…”

Composite membranes consisting of acidic carboxyl-containing polyimide and basic polybenzimidazole for high-temperature proton exchange membrane fuel cells

“…9–12 Nevertheless, higher PA doping amounts should be absorbed on behalf of acquiring higher proton conductivity, which often results in a severe decrease in mechanical strength due to the plasticizing effect of PA. 13–15 Furthermore, this may bring about the loss of PA on account of its low molecular weight during the period of the long-term running of the cell and affect its overall performance. This problem may be conquered by generating interactions with PBI to promote proton conduction by means of substituting amphoteric polyacid for PA. 16–20 Therefore, PA-doped PBI-type PEMs are still facing many challenges in the process of achieving commercialization, such as attaining higher proton conductivity, additional optimal mechanical properties, and PA retention ability with increased stability.…”