Swelling Behavior of Crosslinked Rubber: Does the Peak in Dilational Modulus Exist?

Previous work\footnote{G.B. McKenna and J.M. Crissman.J. Polym. Sci., Part B: Polym. Phys. 35, 817 (1997).} has shown that when handled properly, Frenkel\footnote{J. Frenkel, Acta Phys. USSR, 9, 235 (1938); Rubber Chem. Technol., 13, 264 (1940).}-Flory-Rehner\footnote{P. J. Flory and J. J. Rehner, Jr., J. Chem. Phys.,11, 521 (1943).}(FFR) theory is an excellent model to explain swelling behavior with the exception of failing to describe the peak of the swelling activity parameter S, or dilational modulus. This peak was first observed by Gee et al.\footnote{G. Gee, J. B. M. Herbert, and R. C. Roberts, Polymer, 6, 541 (1965).} and has eluded explanations. In the present work, we explored the importance of fitting procedure to the isopiestic data on the presence of the peak of S. We found the peak in S disappears when using a FFR model based fit instead of the empirical or polynomial fits used previously. We take model material parameters and show that adding less than 1{\%} random error to the theoretical curves can lead to the peak in S. Our findings suggest strongly that the ``peak'' in S is due to experimental errors that are amplified by the fitting method.