Thermodynamics of Water Vapor Uptake in Perfluorosulfonic Acid Membranes

Abstract

A two‐parameter equation describing water vapor uptake in perfluorosulfonic acid membranes is derived based on the Flory‐Huggins model combined with a chemical equilibrium constant for proton transfer. Temperature‐dependent expressions for the proton‐transfer equilibrium constant K(T) = 0.0256 × exp[(22.4 kJ/mol)/RT] and the Flory interaction parameter χ(T) = 1.936 − (2.18 kJ/mol)/RT are discussed. Advantages of the new equation include accurate reduction of activity vs. water vapor uptake data for perfluorosulfonic acid membranes with few parameters and a well‐behaved dependence of activity on composition and temperature. Comparisons of model results with water uptake measurements in the literature are given. An explanation for the difference in water uptake by membranes in contact with liquid water and with saturated vapor is proposed based on an interpretation of the temperature dependence of water uptake. © 1999 The Electrochemical Society. All rights reserved.

Mechanics-based model for non-affine swelling in perfluorosulfonic acid (PFSA) membranes

“…This parameter has to be determined empirically. For PFSA membranes, the value for c has been determined to be 1.0-1.5 in the literature [42,71]. If we use the Flory-Huggins model with our pressure formulation, the resulting sorption isotherms (not shown) turn out to be very similar to those predicted by Eq.…”

“…(7)). The water uptake behavior of PFSA membranes is typically character ized by sorption isotherms which define the relationship between the water content, l, and the vapor activity of water in the surrounding air, a w , (or relative humidity, RH) at a given tempera ture [5,24,40,42,44,45,70,71]. In equilibrium, the confining pressure applied by the polymer matrix is balanced by osmotic swelling pressure, or the tendency of external moisture to diffuse into the membrane and increase the swelling.…”

“…The Flory-Huggins theory for polymer solutions [55] can also be used to describe the swelling equilibrium in PFSA membranes as discussed elsewhere [42,71,73]. This model, however, has an additional parameter, the so-called Flory-Huggins interaction parameter, c, which characterizes the enthalpic energy of mixing between the polymer and solvent.…”

Macroscopic Modeling of Polymer-Electrolyte Membranes

“…In addition, a temperature change in the membrane can cause an appreciable change in water content if the membrane is close to saturation [88,91,122]. Furthermore, the membrane is somewhat resistive and insulating, resulting in possibly significant temperature gradients.…”

“…The most useful set of uptake models are those that strike a balance between robustness and complexity [31,76,88,91,94,95,122,154,155]. They can explain and predict water uptake as a function of operating conditions and membrane properties, but are macroscopic and wieldy enough to be used in various simulations.…”