Modelling microgel swelling: Influence of chain finite extensibility

Microgels exhibit the ability to undergo reversible swelling in response to shifts in environmental factors that include variations in temperature, concentration, and pH. While several models have been put forward to elucidate specific aspects of microgel swelling and its impact on bulk behavior, a consistent theoretical description that chains throughout the microscopic degrees of freedom with suspension properties and deepens into the full implications of swelling remains a challenge yet to be met. In this work, we extend the mean-field swelling model of microgels from Denton and Tang (J. Chem. Phys. 145, 164901 (2016)) to include the finite extensibility of the polymer chains. The elastic contribution to swelling in the original work is formulated for Gaussian chains. By using the Langevin chain model, we modify this elastic contribution in order to account for finite extensibility effects, which become prominent for microgels containing highly charged polyelectrolytes and short polymer chains. We assess the performance of both elastic models, namely for Gaussian and Langevin chains, comparing against coarse-grained bead-spring simulations of ionic microgels with explicit electrostatic interactions. We examine the applicability scope of the models under variation of parameters such as ionization degree, microgel concentration and salt concentration. The models are also tested against experimental results. This work broadens the applicability of the microgel swelling model towards a more realistic description, which brings advantages when describing suspensions of nanogels and weak-polyelectrolyte micro/nanogels.