Swelling of Spherical Polyelectrolyte Gels

Polyelectrolyte (PE) gels, distinguished by their unique stimuli-responsive swelling behavior, serve as the basis of broad applications, such as artificial muscles and drug delivery. In this work, we present a theoretical model to analyze the electrostatics and its contribution to the swelling behavior of PE gels in salt solutions. By minimizing the free energy of PE gels, we obtain two distinct scaling regimes for the swelling ratio at equilibrium with respect to the salt concentration. We compare our predictions for the swelling ratio with experimental measurements, which show excellent agreement. In addition, we employ a finite element method to assess the applicability range of our theoretical model and assumptions. We anticipate that our model will also provide valuable insights into drug adsorption and release, deformation of red blood cells, 4D printing and soft robotics, where the underlying mechanism of swelling remains enigmatic.