Scattering Function in Systems of Charged Polymers: From Polyelectrolyte Solutions to Polyelectrolyte Complexes

The peak in the scattering function, appearing at intermediate length scales, is a unique feature of solutions of charged polymers. To elucidate the effect of counterion valence (degree of polymerization of neutralizing chains) on the peak position and the form of the scattering function, we use a combination of coarse-grained molecular dynamics simulations and analytical calculations in the framework of the Random Phase Approximation (RPA). Both simulations and RPA calculations show that the peak location q* in the structure factor S(q) moves towards smaller q values with decreasing solution concentration. In particular, we find that q* scales with concentration as ρ^-0.25. Furthermore, we demonstrate that the plateau in S(q) at small q is controlled by the system compressibility and increases with increasing degree of polymerization of polymeric counterions. The observed changes in the shape of the structure factor S(q) obtained from simulations can be fit by a scattering function derived in the framework of RPA by considering a solution of neutral chains as a reference system.