A comprehensive pore transport model is proposed to describe proton diffusion within Nafion at various hydration levels by incorporating effects of water uptake and various proton transport mechanisms, namely, proton hopping along surface, Grotthuss diffusion, and ordinary mass diffusion of hydronium ions. The diffusion coefficients are predicted within a general random walk framework. The proton conductivity in contact with water vapor is accurately predicted as a function of relative humidity without any fitted parameters, considering the sorption isotherm proposed in the companion paper ͑Part I͒. A maximum conductivity in contact with liquid water is also predicted by the model for equivalent weight between 900 and 1000, in good agreement with the experimental measurements. The modeling framework could be extended to other proton conducting electrolytes for fuel cell applications.

A thermodynamic model is proposed to describe the sorption of water in Nafion based on the Flory-Huggins activity model and an appropriate osmotic pressure correction term for the chemical potential of water within the swollen membrane. The key variables for sorption are equivalent weight of ionomer, acid strength of the ionic groups, modulus of polymer elasticity, and interaction between water and polymer. The water uptake per unit mass of dry Nafion increases with the increasing acid strength of the functional groups, decreasing Young's modulus, and decreasing equivalent weight of Nafion. The model provides insights into the sorption and swelling behavior of ion-exchange membranes, and thus, may be useful in evaluating and designing alternate proton-exchange membranes for fuel cell applications. In a companion paper ͑Part II͒, a predictive model is presented for the transport of protons in Nafion.

A physicochemical model is proposed to describe sorption in proton-exchange membranes ͑PEMs͒, which can predict the complete isotherm as well as provide a plausible explanation for the long-unresolved phenomenon termed Schroeder's paradox, namely, the difference between the amounts sorbed from a liquid solvent vs. from its saturated vapor. The solvent uptake is governed by the swelling pressure caused within the membrane as a result of stretching of the polymer chains upon solvent uptake, ⌸ M , as well as a surface pressure, ⌸ , due to the curved vapor-liquid interface of pore liquid. Further, the solvent molecules in the membrane are divided into those that are chemically, or strongly, bound to the acid sites, i C , and others that are free to physically equilibrate between the fluid and the membrane phases, i F. The model predicts the isotherm over the whole range of humidities satisfactorily and also provides a rational explanation for the Schroeder's paradox.

No abstract

A phenomenological theory is provided for water sorption and proton transport in polymer electrolyte membranes (PEMs) as well as in polymer-inorganic nanocomposite membranes (NCPEMs) that not only serves to rationalize the sorption and conductivity behavior of conventional PEMs such as Nafion but also provides a framework for rational design of improved PEMs and NCPEMs. The thermodynamic model, which considers the effect of osmotic pressure on the activity of free water within the membrane pores, predicts the entire sorption isotherm and provides a plausible explanation for the so-called Schroeder's paradox. The transport model incorporates the various mechanisms of proton transport, namely, surface hopping, Grotthuss diffusion, and en masse diffusion. As the design of alternate PEMs suitable for effective proton transport under hot and dry conditions is a key current technological goal, the rational design of NCPEMs for this purpose is considered here in detail on the basis of an extension of the transport model to account for the influence of the inclusion of functional additives in NCPEMs. The results also point to the reason that Nafion is an excellent PEM, because the hydrophobic nature of its backbone induces water away from surface into pore bulk where efficient proton diffusion occurs.