Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels

A full quantitative description of the swelling of smart microgels is still problematic in many cases. The original approach of Flory and Huggins for the monomer–solvent interaction parameter $\chi$ cannot be applied to some microgels. The reason for this obviously is that the cross-linking enhances the cooperativity of the volume phase transitions, since all meshes of the network are mechanically coupled. This was ignored in previous approaches, arguing with distinct transition temperatures for different meshes to describe the continuous character of the transition of microgels. Here, we adjust the swelling curves of a series of smart microgels using the Flory–Rehner description, where the polymer–solvent interaction parameter $\chi$ is modeled by a Hill-like equation for a cooperative thermotropic transition. This leads to a very good description of all measured microgel swelling curves and yields the physically meaningful Hill parameter $\nu$. A linear decrease of $\nu$ is found with increasing concentration of the cross-linker N,N${}^{\prime }$-methylenebisacrylamide in the microgel particles p(NIPAM), p(NNPAM), and p(NIPMAM). The linearity suggests that the Hill parameter $\nu$ corresponds to the number of water molecules per network chain that cooperatively leave the chain at the volume phase transition. Driven by entropy, $\nu$ water molecules of the solvate become cooperatively “free” and leave the polymer network.