Osmotic Swelling Behavior of Polyelectrolyte Microcapsules

Polyelectrolyte microcapsules are hydrogel shells composed of cross-linked polymer networks, 10-1000 nm in radius, that are swollen by a solvent. The ability of microcapsules to swell/de-swell in response to external stimuli (e.g., temperature, pH, ionic strength) makes them ideal for a wide range of applications, e.g., drug delivery, sensors, and catalysis. Equilibrium swelling behavior of ionic microcapsules is determined by a balance of electrostatic and elastic forces. The electrostatic contribution to the osmotic pressure – the difference in pressure between outside and inside a capsule – plays an important role in swelling. Within the spherical cell model, we derive an exact expression for the electrostatic contribution to the osmotic pressure, which we compute via molecular dynamics simulation and Poisson-Boltzmann theory. For the elastic contribution to the osmotic pressure, we use the Flory-Rehner theory of swollen polymer networks. By combining the electrostatic and elastic contributions, we predict the equilibrium size of a polyelectrolyte microcapsule as a function of salt concentration. Our results can help guide the design of smart, responsive particles.