Polymeric Salts: Static and Dynamic Debye−Hückel Theory

Abstract

We study polymeric salts formed by connecting ionic end groups by a soluble polymeric backbone: this can be done either by linking similarly charged ions (anions and cations) and then mixing positively charged and negatively charged chains or by linking oppositely charged ions. This last case where the chains are globally neutral is of special interest: due to the connectivity constraint, the polymeric solution behaves as a dielectric at large length scales (in the absence of any small free ions) but it locally screens the electrostatic interactions such as a salt. In a suited range of end charge and chain length the strength of the macroscopic long-range interaction between test charges can be monitored by tuning the polymeric salt concentration. The relaxation of thermal fluctuations in the solution has three eigenmodes: a fast plasmon mode corresponding to the relaxation of charge fluctuations, and two modes independent of the strength of the electrostatic interaction, one being the cooperative mode found in usual semidilute solutions. The plasmon mode resembles that in free salt solutions except that the chain connectivity restricts the size of the charge fluctuations to the coil size.