The authors demonstrate how the size and structure of the cavity of hollow charged microgels may be controlled by varying pH and ionic strength. Hollow charged microgels based on N‐isopropylacrylamide with ionizable co‐monomers (itaconic acid) combine advanced structure with enhanced responsiveness to external stimuli. Structural advantages accrue from the increased surface area provided by the extra internal surface. Extreme sensitivity to pH and ionic strength due to ionizable moieties in the polymer network differentiates these soft colloidal particles from their uncharged counterparts, which sustain a hollow structure only at cross‐link densities sufficiently high that stimuli sensitivity is reduced. Using small‐angle neutron and light scattering, increased swelling of the network in the charged state accompanied by an expanded internal cavity is observed. Upon addition of salt, the external fuzziness of the microgel surface diminishes while the internal fuzziness grows. These structural changes are interpreted via Poisson–Boltzmann theory in the cell model.

Ionic microgels are soft colloidal particles, composed of crosslinked polymer networks, that ionize and swell when dispersed in a good solvent. Swelling of these permeable, compressible particles involves a balance of electrostatic, elastic, and mixing contributions to the single-particle osmotic pressure. The electrostatic contribution depends on the distributions of mobile counterions and coions and of fixed charge on the polymers. Within the cell model, we employ two complementary methods to derive the electrostatic osmotic pressure of ionic microgels. In Poisson-Boltzmann (PB) theory, we minimize a free energy functional with respect to the electrostatic potential to obtain the bulk pressure. From the pressure tensor, we extract the electrostatic and gel contributions to the total pressure. In a statistical mechanical approach, we vary the free energy with respect to microgel size to obtain exact relations for the microgel electrostatic osmotic pressure. We present results for planar, cylindrical, and spherical geometries. For models of membranes and microgels with fixed charge uniformly distributed over their surface or volume, we derive analogues of the contact value theorem for charged colloids. We validate these relations by solving the PB equation and computing ion densities and osmotic pressures. When implemented within PB theory, the two methods yield identical electrostatic osmotic pressures for surface-charged microgels. For volumecharged microgels, the exact electrostatic osmotic pressure equals the average of the corresponding PB profile over the gel volume. We demonstrate that swelling of ionic microgels depends on variation of the electrostatic pressure inside the particle and discuss implications for interpreting experiments.

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.