Conformations and Charge Fluctuations in Polyelectrolyte Solutions

From DNA and RNA encoding life to flocculation agents used in water remediation, charged polymers (polyelectrolytes) are prevalent in nearly all facets of our lives. The charged nature of polyelectrolytes has rendered them useful in many applications, from the stabilization of colloids to the formation of nanoparticles for drug or gene delivery. There are open questions regarding the factors that dictate polyelectrolyte stability, and electrostatic fluctuations, first elucidated by Debye and Hückel for simple electrolytes, are key to the thermodynamic description of such charged systems. Electrostatic fluctuations lead to ionic clouds around charges, leading to favorable energy decreases. While charge-fluctuations are well-described for simple electrolytes, the impact of polyelectrolyte (PE) charge connectivity on charge fluctuations is much less well understood: a huge number of degrees of freedom must be considered in order to describe the multicomponent nature of polyelectrolyte solutions and the large number of conformations the polyelectrolytes themselves can assume. Past theories have both under- and over-estimated the connectivity effects on electrostatic fluctuations, and do not give a clear picture of the transition from weak to strong electrostatic fluctuations. My work has focused on coming up with a theory that self-consistently accounts for the coupling of chain connectivity and electrostatic fluctuations, thus spanning electrostatic fluctuations from weak to intermediate fluctuation strengths. In particular, I present a novel renormalized Gaussian fluctuation (RGF) theory that identifies the renormalization of chain structure as a key physical consequence of intermediate-strength electrostatic fluctuations. The theory self-consistently couples chain structure with the thermodynamics, and mediates the transition from weak, linearized fluctuations to the onset of stronger fluctuation effects like ion pairing. While the onset of these different fluctuation effects has a clear sequence, they are all coupled and must be determined self-consistently. A key concept introduced by the theory is the notion of the polyelectrolyte self energy, which describes the electrostatic work required to charge the molecule in solution, and provides a useful perspective from which to understand and rationalize the effects of chain conformation on thermodynamic behavior. We use the theory to study the phase behavior of polyelectrolyte solutions and connect theory to experimental results.