A bead–spring chain as a one-dimensional polyelectrolyte gel

Abstract

The physical principles underlying expansion of a single-chain polyelectrolyte coil caused by Coulomb repulsions among its ionized groups, and the expansion of a cross-linked polyelectrolyte gel, are probably the same. In this paper, we analyze a “one-dimensional” version of a gel, namely, a linear chain of charged beads connected by Hooke's law springs. In the Debye–Hückel range of relatively weak Coulomb strength, where counterion condensation does not occur, the springs are realistically stretched on a nanolength scale by the repulsive interactions among the beads, if we use a spring constant normalized by the inverse square of the solvent Bjerrum length. The persistence length and radius of gyration counter-intuitively decrease when Coulomb strength is increased, if analyzed in the framework of an OSF-type theory; however, a buckling theory generates the increase that is consistent with bead–spring simulations.