Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts

Recasting a many-particle problem in a field-theoretic formalism is nowadays a well-established theoretical tool used by scientists across a wide spectrum of research areas, ranging from polymer physics to molecular electronic structure theory. It has shown to provide useful results in many complex situations, where the physics of the system involves many degrees of freedom and a multitude of different length scales, generally rendering its numerical treatment on a detailed level computationally intractable. To reduce the computational burden, field-theoretic methodologies usually take advantage of the mean-field approximation. This approximation technique is known to give reliable information about the system in the high concentration regime, where the interactions are highly screened. However, it is well established that the ranges of physical interest in most biological and technological applications lie in the intermediate to low concentration regimes, where fluctuations beyond the mean-field level of approximation become important and dominate the overall physical behavior. In this work we introduce a new self-consistent field theory for flexible polyelectrolyte chains, in which the monomers interact via a pair potential of screened Coulomb type, and derive suitable thermodynamic expressions for all concentration regimes. Our approach combines the renormalization concepts of tadpole renormalization, which has recently been successfully employed in calculations of prototypical neutral polymer and polyelectrolyte solutions, with the Hartree renormalization procedure. By comparing our approach to experimental measurements as well as alternative theoretical approaches, we demonstrate that it provides useful osmotic pressure results for polyelectrolyte systems composed of sodium poly(styrene-sulfonate) without and with added salt over the whole range of monomer concentrations.