Double screening in polyelectrolyte solutions: Limiting laws and crossover formulas

We have derived general expressions for the Helmholtz free energy of a polyelectrolyte solution and the average size of a labeled chain as functions of polyelectrolyte concentration, salt concentration, and the strengths of excluded volume and electrostatic interaction all varying from very low to very high. We have shown that the bare excluded volume interaction and the electrostatically screened Coulomb interaction between any two segments are both screened by the presence of polyelectrolyte chains at nonzero concentrations. The screening length associated with this excluded volume screening is a function of Debye length and the entropy of the connected polymer and consequently depends on the polyelectrolyte concentration differently at different salt concentrations. By treating the correlation of the monomer density fluctuations, we have derived integral equations coupling the effective interaction between any two segments and the effective step length of a labeled chain. In the limit of the excluded volume screening length and the effective step length being independent of wave vectors, they are related by algebraic equations. These equations reduce to scaling laws with numerical prefactors for semidilute and concentrated polyelectrolyte solutions. Our development provides limiting laws and analytical interpolation formulas for the excluded volume screening length, effective step length, free energy of the polyelectrolyte solution, and the average size of a chain for various polyelectrolyte concentrations in an isotropic solution and for arbitrary strengths of excluded volume and electrostatic interactions. The excluded volume screening leads to an attractive component in the effective potential interaction at intermediate distances between two segmental charges of the same sign. The strength and range of the attractive potential are determined by the concentrations of the polyelectrolyte and the various ions. (C) 1996 American Institute of Physics.