  In recent years, ionic microgels have garnered much attention due to their
unique properties, especially their stimulus-sensitive swelling behavior. The
tunable response of these soft, permeable, compressible, charged colloidal
particles is increasingly attractive for applications in medicine and
biotechnologies, such as controlled drug delivery, tissue engineering, and
biosensing. The ability to model and predict variation of the osmotic pressure
of a single microgel with respect to changes in particle properties and
environmental conditions proves vital to such applications. In this work, we
apply both nonlinear Poisson-Boltzmann theory and molecular dynamics simulation
to ionic microgels (macroions) in the cell model to compute density profiles of
microions (counterions, coions), single-microgel osmotic pressure, and
equilibrium swelling ratios of spherical microgels whose fixed charge is
confined to the macroion surface. The basis of our approach is an exact theorem
that relates the electrostatic component of the osmotic pressure to the
microion density profiles. Close agreement between theory and simulation serves
as a consistency check to validate our approach. We predict that
surface-charged microgels progressively deswell with increasing microgel
concentration, starting well below close packing, and with increasing salt
concentration, in qualitative agreement with experiments. Comparison with
previous results for microgels with fixed charge uniformly distributed over
their volume demonstrates that surface-charged microgels deswell more rapidly
than volume-charged microgels. We conclude that swelling behavior of ionic
microgels in solution is sensitive to the distribution of fixed charge within
the polymer-network gel and strongly depends on bulk concentrations of both
microgels and salt ions.
