Revisiting the Flory–Rehner equation: taking a closer look at the Flory–Huggins interaction parameter and its functionality with temperature and concentration with NIPA as a case example

In this work, the Flory–Rehner equation is revisited to evidence the dependency of the interaction parameter on both polymer volume fraction and temperature. Such an analysis to estimate the true functionality of the interaction parameter is based on experimental data reported in the literature for the swelling behavior of NIPA hydrogels prepared at different temperatures and monomer concentrations. A hydrogel morphology classification is put forward, which coincides with other proposals and identifies two main morphological arrangements, i.e., (i) ideal polymeric networks under Regimes I and II, with positive interaction parameter values following a quadratic trend with polymer volume fraction, and (ii) non-ideal networks under Regimes III and IV, with interaction parameters under negative values depicting a sugarcane dependency at small polymer volume fractions. Ideal polymeric network formation appears in samples prepared at temperatures lower than the poly(N-isopropylacrylamide) [PNIPA] phase separation temperature, or concentrations higher than the minimum monomer concentration for gel formation. With a simple three-parameter sensitivity analysis, focusing on a polymer fraction reference state, the cross-linking density and χ₂, it appeared that the latter showed the strongest effect on the collapsing temperature.