Welcoming Remarks

Electrostatic correlations are responsible for a variety of important phenomena in polyelectrolyte (PE) systems, such complex coacervation and salting-in/salting-out of proteins. A key theoretical challenge is the proper account of the dependence of the chain conformation on the concentration and/or salt condition, and its impact on solution thermodynamics. In this talk, I present a new theory for electrostatic correlations in polyelectrolyte solutions that self-consistently accounts for the adaption of the chain conformation to changes in polyelectrolyte and salt concentrations. For small Bjerrum length and low backbone charge densities, charge fluctuations primarily manifest in the form of an ionic atmosphere and result in a length-scale and chain-length dependent screening of the effective charge-charge interactions. However, even at weak interaction strengths, we find that charge fluctuations can significantly modify the chain structure, which in turn affects the ionic atmosphere and the predicted thermodynamic quantities. Our theory captures the expected scaling behavior in both structural and thermodynamic properties from the dilute to beyond semi-dilute regimes. We use this theory to predict a number of interesting phase behaviors in both single-component PE solutions and mixtures of oppositely charged PEs, such as a closed-loop salt-PE concentration phase diagram. At large Bjerrum length and high backbone charge densities, a significant fraction of the counterions condense onto the polymer backbone, reducing its effective charge density. We extend our theory to examine how screening, chain structure, and degree of condensation couple together and modulate the counterion condensation driving force, conveniently summarized in terms of an effective binding constant, and explore the consequence of this charge regulation on the polyelectrolyte structural and thermodynamic properties.