Electrostatic correlations and the polyelectrolyte self energy

We address the effects of chain connectivity on electrostatic fluctuations in polyelectrolyte solutions using a field-theoretic, renormalized Gaussian fluctuation (RGF) theory. As in simple electrolyte solutions [Z.-G. Wang, Phys. Rev. E 81, 021501 (2010)], theRGFprovides a unified theory for electrostatic fluctuations, accounting for both dielectric and charge correlation effects in terms of the self-energy. Unlike simple ions, the polyelectrolyte self energy depends intimately on the chain conformation, and our theory naturally provides a self-consistent determination of the response of intramolecular chain structure to polyelectrolyte and salt concentrations. The effects of the chain-conformation on the self-energy and thermodynamics are especially pronounced for flexible polyelectrolytes at low polymer and salt concentrations, where application of the wrong chain structure can lead to a drastic misestimation of the electrostatic correlations. By capturing the expected scaling behavior of chain size from dilute to semi-dilute regimes, our theory provides improved estimates of the self energy at lowpolymer concentrations and correctly predicts the eventual N-independence of the critical temperature and concentration of salt-free solutions of flexible polyelectrolytes. We show that the self energy can be interpreted in terms of an infinite-dilution energy mu(el)(m,0) and a finite concentration correlation correction mu(corr) which tends to cancel out the former with increasing concentration. Published by AIP Publishing.