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

TL;DR

This paper investigates how a deformable macroion's size changes non-monotonically due to charge inversion caused by multivalent ion adsorption, revealing a parabolic size growth near the neutral point.

Contribution

It introduces a theoretical model describing non-monotonic swelling behavior of macroions due to correlation-induced charge inversion.

Findings

Macroion size first decreases then increases with ion addition.

Size growth near neutral point is parabolic with respect to ion concentration ratio.

Derived pressure formula relates macroion swelling to ion concentration.

Abstract

It is known that a large, charged body immersed in a solution of multivalent counterions may undergo charge inversion as the counterions adsorb to its surface. We use the theory of charge inversion to examine the case of a deformable, porous macroion which may adsorb multivalent ions into its bulk to form a three-dimensional strongly-correlated liquid. This adsorption may lead to non-monotonic changes in the size of the macroion as multivalent ions are added to the solution. The macroion first shrinks as its bare charge is screened and then reswells as the adsorbed ions invert the sign of the net charge. We derive a value for the outward pressure experienced by such a macroion as a function of the ion concentration in solution. We find that for small deviations in the concentration of multivalent ions away from the neutral point (where the net charge of the body is zero), the swollen size grows parabolically with the logarithm of the ratio of multivalent ion concentration to the concentration at the neutral point.