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It is known that a large, charged body immersed in a solution of multivalentcounterions may undergo charge inversion as the counterions adsorb to itssurface. We use the theory of charge inversion to examine the case of adeformable, porous macroion which may adsorb multivalent ions into its bulk toform a three-dimensional strongly-correlated liquid. This adsorption may leadto non-monotonic changes in the size of the macroion as multivalent ions areadded to the solution. The macroion first shrinks as its bare charge isscreened and then reswells as the adsorbed ions invert the sign of the netcharge. We derive a value for the outward pressure experienced by such amacroion as a function of the ion concentration in solution. We find that forsmall deviations in the concentration of multivalent ions away from the neutralpoint (where the net charge of the body is zero), the swollen size growsparabolically with the logarithm of the ratio of multivalent ion concentrationto the concentration at the neutral point.

Non-monotonic swelling of a macroion due to correlation-induced charge inversion