Osmotic pressure and swelling behavior of ionic microcapsules

Ionic microcapsules are hollow shells of hydrogel, typically 10-1000 nm in radius, composed of cross-linked polymer networks that become charged and swollen in a good solvent. The ability of microcapsules to swell/deswell in response to changes in external stimuli (e.g., temperature, pH, and ionic strength) suits them to applications, such as drug delivery, biosensing, and catalysis. The equilibrium swelling behavior of ionic microcapsules is determined by a balance of electrostatic and elastic forces. The electrostatic component of the osmotic pressure of a microcapsule-the difference in the pressure between the inside and outside of the particle-plays a vital role in determining the swelling behavior. Within the spherical cell model, we derive exact expressions for the radial pressure profile and for the electrostatic and gel components of the osmotic pressure of a microcapsule, which we compute via Poisson-Boltzmann theory and molecular dynamics simulation. For the gel component, we use the Flory-Rehner theory of polymer networks. By combining the electrostatic and gel components of the osmotic pressure, we compute the equilibrium size of ionic microcapsules as a function of particle concentration, shell thickness, and valence. We predict concentration-driven deswelling at relatively low concentrations at which steric interactions between particles are weak and demonstrate that this response can be attributed to crowding-induced redistribution of counterions. Our approach may help to guide the design and applications of smart stimuli-responsive colloidal particles.