SIMPLIFIED MEAN-FIELD THEORY FOR POLYELECTROLYTE PHASE-BEHAVIOR

Simplified mean field theory for the phase behaviour of polyelectrolyt es in solution is described in detail. It can be viewed as the polyele ctrolyte analogue of Flory-Huggins theory. A basic model is analyzed, then extended to look at the effects of multivalent:ions (specifically divalent colons), of distinguishable counterions, and of an ionizatio n equilibrium between counterions and polyelectrolyte. Analytic transf ormation of the free energy to reduce the number of extensive variable s facilitates the calculation of binodal curves, tielines, spinodal cu rves, and the spinodal instability directions. Typical salting out beh aviour and salt partitioning are seen. Unexpectedly, a small region of three phase coexistence is found: it is examined in detail for the ba sic model. In addition, the mean field spinodal is found to be identic al to that occurring in common applications of the random phase approx imation, and to have an interpretation in terms of electrostatic exclu ded volume, including for the ionizable polyelectrolyte case where flu ctuations in the ionization equilibrium give an additional contributio n to the Debye-Huckel screening length. The reasons for this are eluci dated in an Appendix.