Gelation of semiflexible polyelectrolytes by multivalent counterions

Filamentous polyelectrolytes in aqueous solution aggregate into bundles by interactions with multivalent counterions. These effects are well documented by experiment and theory. Theories also predict a gel phase in isotropic rodlike polyelectrolyte solutions caused by multivalent counterion concentrations much lower than those required for filament bundling. We report here the gelation of Pf1 virus, a model semiflexible polyelectrolyte, by the counterions Mg ²⁺, Mn ²⁺ and spermine ⁴⁺. Gelation can occur at 0.04% Pf1 volume fraction, which is far below the isotropic-nematic transition of 0.7% for Pf1 in monovalent salt. Unlike strongly crosslinked gels of semiflexible polymers, which stiffen at large strains, Pf1 gels reversibly soften at high strain. The onset strain for softening depends on the strength of interaction between counterions and the polyelectrolyte. Simulations show that the elasticity of counterion crosslinked gels is consistent with a model of semiflexible filaments held by weak crosslinks that reversibly rupture at a critical force.