Complexation of a polyelectrolyte with oppositely charged spherical macroions: Giant inversion of charge

Complexation of a long flexible polyelectrolyte (PE) molecule with oppositely charged spherical particles such as colloids, micelles, or globular proteins in a salty water solution is studied. PE binds spheres winding around them, while spheres repel each other and form almost periodic necklace. If the total charge of PE is larger than the total charge of spheres, repulsive correlations of PE turns on a sphere lead to inversion of the net charge of each sphere. In the opposite case, we predict another correlation effect: under-screened by PE spheres bind to PE in such a great number that they invert charge of PE. The inverted charge by absolute value can be larger than the bare charge of PE even when screening by monovalent salt is weak. At larger concentrations of monovalent salt, the inverted charge can reach giant proportions. Our theory is in qualitative agreement with recent experiments on micelles-PE systems.