  In this work a new density functional theory framework is developed to
predict the salt-concentration dependent swelling state of charged microgels
and the local concentration of monovalent ions inside and outside the microgel.
For this purpose, elastic, solvent-induced and electrostatic contributions to
the microgel free energy are considered together with the free energy of the
ions. In addition to the electrostatic interaction, the model explicitly
considers both the microgel-ion excluded-volume (steric) repulsion and the
ionic correlations, in such a way that the formalism is consistent with the
Hypernetted-Chain Closure approximation (HNC). We explore the role that the
solvent quality, chain elasticity, salt concentration and microgel bare charge
play on the swelling state, the effective charge and on the ionic density
profiles. Our results show that the microgel-ion steric exclusion foments the
increase of the particle size up to 10 %. The role that the steric effect plays
on the counterion distribution becomes more important when the microgel
approaches the shrunken configuration, developing an accumulation peak at the
microgel interface and a reduction in the inner core of the microgel that
induce a significant increase of the microgel effective charge. We further find
that deep inside the particle charge electroneutrality is achieved and a Donnan
potential corrected by the steric exclusion is established.

Soft Condensed Matter