Percolative model of proton conductivity of Nafion® membranes

A model is proposed for the simulation of Nafion® proton conductivity, where it is assumed that proton conduction occurs only in the water present in the membrane pores. Water is considered to be present in the pores due to two different phenomena: adsorption and capillary condensation. In the latter case, the pore is flooded and proton conduction occurs throughout the whole pore section. The conditions under which capillary condensation occurs are simulated in the model through the Kelvin–Cohan equation for condensation. The Kelvin–Cohan equation is a function of RH, temperature and the pore radius; the larger the pore, the higher the RH for which capillary condensation takes place. If the conditions for capillary condensation are not satisfied, then water is present in the pore due to adsorption under the form of a water layer which covers the pore walls and provides a path for proton conduction. In this case, the modified Brunauer–Emmet–Teller (BET) equation has been used in the model to simulate the thickness of the water layer. In both cases of capillary condensation and adsorption, the conductance g of a pore has then been calculated through the formula g = κS/l, where κ is the proton conductivity of water, S the cross-section of the pore volume which is occupied by water, and l is the pore length. Pores of different size are present in the membrane (data of pore size distribution have been extracted from the literature); connectivity of the water layers present in the different pores is necessary in order to achieve a continuous path of proton conduction through the membrane, which is a percolation problem. To this end, the structure of the membrane pores has been simulated in the model through the effective medium approximation (EMA). The simulation results of proton conductivity of the membrane show good agreement with literature experimental data, even when varying the RH operating conditions.