Polyelectrolyte Persistence Length: Attractive Effect of Counterion Correlations and Fluctuations

– The persistence length of a single, strongly charged, stiff polyelectrolyte chain is investigated theoretically. Path integral formulation is used to obtain the effective electrostatic interaction between the monomers. We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. An induced attraction between monomers is due to thermal fluctuations and correlations between bound counterions. The electrostatic persistence length is found to be smaller than the OSF value and indicates a possible mechanical instability (collapse) for highly charged polyelectrolytes with multivalent counterions. In addition, we calculate the amount of condensed counterions on a slightly bent polyelectrolyte. More counterions are found to be adsorbed as compared to the Manning condensation on a cylinder. Polyelectrolytes (PEs) are polymers that have ionizable groups. When dissolved in solution, they dissociate into charged polymer chains and a cloud of free, mobile counterions carrying opposite charges [1, 2]. Such macromolecules appear in numerous industrial applications as well as in biological systems, introducing a new kind of biologically inspired electrostatics [3]. The spatial conformation of a single PE chain has been at the focus of attention of experiments [4, 5], simulations [6, 7] and theoretical models [8, 9, 10, 11, 12, 13], showing a wide range of behavior. The delicate balance between counterion entropy and long range electrostatic repulsion can have opposite effects on different PEs. Broadly speaking, in systems containing weakly charged PEs and monovalent counterions, the electrostatic repulsion dominates and makes the chains stiffer [11, 14]. On the other hand, highly charged PEs with multivalent counterions experience an effective attraction [15] which is not well understood. This attraction leads to enhanced flexibility and, in some cases, induces collapse into a globular conformation [15]. For DNA macromolecules, this is known as DNA condensation [5]. On a mean-field level, the Poisson-Boltzmann (PB) theory predicts only intra-chain repulsion [11]. Another important prediction is the Manning condensation [2, 16], where some of the counterions are loosely bound to the PE chain. Models going beyond mean-field theory take into account correlations and thermal fluctuations [12, 13]. Correlations between bound counterions become more significant at lower temperatures, where the ions are considered to