Range-Optimized Theory of Polyelectrolyte Solutions: Basic Theory and Application to Rod Polymers

Abstract

We present a theory for the equilibrium structure of polyelectrolyte solutions. The main element is a simple and general optimization scheme that allows theories such as the random phase approximation to handle the strong repulsive forces present in such systems. Charged hydrophilic rods in salt-free solution at semidilute densities are examined. The effect of including condensed counterions is analyzed. Comparison with other theories is made. Results of experiments of hydrophilic polyelectrolytes with monovalent counterions in salt-free solution have shown that the structure factor peak position and height can become invariant at high charge fraction. We show that this invariance may be the result of polymer−polymer correlations rather than the conventional explanation involving counterion condensation. On the other hand, as determined by the osmotic pressure, it is found that the solution can become mechanically unstable to macrophase separation at high charge fraction. In this case, adding explicit condensed counterions acts to stabilize the liquid, that is, intrachain correlations between condensed counterions, not contained in the idealized Manning−Oosawa theory, must be included.