Simple Scaling Rules on Swollen and Shrunken Polymer Gels

The equilibrium swelling ratios of temperature sensitive polymer gels have been studied as a function of the initial monomer concentration at preparation in both the swollen and the shrunken states. The linear swelling ratio, d/d 0, was independent of the initial monomer concentration of N-isopropylacrylamide, C 0, where d and d 0 are the diameters of gels at observation and at preparation, respectively. On the other hand, d/d 0 was proportional to C 0 in the shrunken state. The swelling curves of gels with different C 0's were successfully reproduced with a modified Flory−Rehner equation, where the effective cross-link density was modified to be proportional to C 0 by taking account of the contribution of “excess cross-linking” by entanglement. Scaling rules for the polymer fractions were derived for both the swollen and the shrunken states; i.e., φ sw ∼ C 0 and φ sh ∼ C 0 0, where φ sw and φ sh are the equilibrium volume fractions of the network at the swollen and shrunken phases, respectively.