Crossover of the effective charge in ionic thermoresponsive hydrogel particles

We use a generalized nonlinear Poisson-Boltzmann cell model that includes excluded-volume effects to investigate whether the effective charge (Z_{eff}) of charged thermosensitive hydrogel particles increases or decreases upon the hydrogel thermal collapse. We find the existence of a crossover charge, Z^{*}, that separates two regimes. For hydrogel bare charges below Z^{*} the system shows a behavior consistent with theories based on linear approximations, i.e., Z_{eff} increases in the collapsed state. However, for bare charges above Z^{*}, the system enters an anomalous regime, in which Z_{eff} decreases in the collapsed state. We show that diluted hydrogel suspensions at low ionic strength are more likely to follow the anomalous behavior. Our theory provides a full physical justification for the controversial theoretical and experimental results reported in this regard, and describes how the interplay between electrostatic, excluded-volume and entropic effects affects this crossover.