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The membranes become less stiff with increas- ing temperature and increasing water content. Both the elastic and plastic moduli decrease grad- ually with increasing temperature up to $100 8C; above the Tg of $110 8C, the elastic modulus decreases by over an order of magnitude. The plas- tic modulus also decreases with increasing temper- ature and drops at Tg. Water plasticizes Nafion. From Figure 6, it is evident that at 25 8C, the elas- tic modulus decreases by almost a factor of 6 from a dry membrane to a water-saturated membrane. This decrease in the elastic modulus is comparable to that observed when the temperature of a dry Nafion membrane is increased from 25 to 80 8C. Water sorption has a much smaller effect on the plastic modulus, as shown in Figure 7. The mecha- nism for strain hardening does not show a strong dependence on the water content in the polymer. The plasticizing effect of water and temperature on the elastic modulus of the membranes can explain why water sorption increases with increas- ing temperature. Water sorption by the sulfonic acid moieties is an exothermic process, and as such, it would be expected that water sorption should be greater at lower temperatures. However, it has been documented by many investigations that water sorption by Nafion increases with increasing temperature.48–51 The total energy change due to water sorption (Esorption) is the sum of the chemical energy of water solvating the sul- fonic acid groups and the mechanical energy of swelling the membrane, as expressed in eq 6. The first term in the integral is the heat of solvation, and the second term is the work of polymer swel- ling. Both the solvation energy and the elastic modulus of the polymer decrease with increasing water content. We have approximated these with simple linear functions of k; kmax $ 20 is the maxi- mum solvation of the sulfonic acid groups. For sim- plicity, the enthalpy of water sorption has been set to decrease linearly from DH0 at zero water con- tent to zero at the maximum water uptake, and the elastic modulus, E0, has been scaled to de- crease by a fraction a from its dry state to the fully hydrated state. It has also been assumed that the volume of swelling is linear with the molar volume of water (Vw): Z k EsorptionðkÞ 1⁄4 Ho Figure 15. Swelling, solvation, and sorption energy for water into a Nafion membrane [DH0 1⁄4 20 kJ/mol, E0(25 8C) 1⁄4 350 MPa, kmax 1⁄4 16 water/SO3, a 1⁄4 0.4, E0(80 8C) 1⁄4 100 MPa]. The equilibrium water content (ke) occurs for the minimum in the energy as expressed in eq 7: k e 1⁄4 H o þ E o V" w k m a x ð 7 Þ H o þ a E o V" w Figure 15 shows the total energy of water sorption along with the contributions of the energy of solva- tion and the energy of swelling based on eq 6. The minimum in the total energy corresponds to the ke value predicted by eq 7. As the temperature is increased, the elastic modulus decreases much more than the energy of solvation, and this results in the energy released by solvation being able to further expand the polymer membrane and reduces the total energy of the system. This also shifts the number of water molecules sorbed into the membrane. Figure 15 shows that for typical values of the elastic modulus and solvation en- thalpy, the decrease in the elastic modulus from 350MPaforNafionat258Cto100MPaat808C results in an increase in the number of sorbed water molecules from 12 to 16 water/SO3. The sim- ple model presented here neglects the entropic contributions to the free energy. However, for the large energies associated with water sorption into ionomers, the entropic contribution will be small with respect to the energetic contributions. It is evident from Figures 6 and 7 that the me- chanical properties of Nafion have not been explored in much of the parameter space at ele- vated temperatures and elevated water activity. A synergistic effect between water plasticizing the material and temperature reducing the mechani- cal strength is expected. There are a few data points shown on Figures 6 and 7 taken at elevated temperatures with increased water content. Those ko max þEo1akV"wdkð6Þ Journal of Polymer Science: Part B: Polymer Physics DOI 10.1002/polb kmax k k TITANIA/NAFION COMPOSITE MEMBRANES 2341 kmaxPDF Image | Properties of Nafion and Titania Nafion Composite Membranes
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