Electrostatic free energy of weakly charged macromolecules in solution and intermacromolecular complexes consisting of oppositely charged polymers

When oppositely charged polyelectrolytes are mixed in water, attraction between oppositely charged groups may lead to the formation of polyelectrolyte complexes (associative phase separation, complex coacervation, interpolymer complexes). Theory is presented to describe the electrostatic free energy change when ionizable (annealed) (macro-)molecules form a macroscopic polyelectrolyte complex. The electrostatic free energy includes an electric term as well as a chemical term that is related to the dissociation of the ionic groups in the polymer. An example calculation for complexation of polyacid with polybase uses a cylindrical diffuse double layer model for free polymer in solution and electroneutrality within the complex and calculates the free energy of the system when the polymer is in solution or in a polyelectrolyte complex. Combined with a term for the nonelectrostatic free energy change upon complexation, a theoretical stability diagram is constructed that relates pH, salt concentration, and mixing ratio, which is in qualitative agreement with an experimental diagram obtained by Bungenberg de Jong (1949) for complex coacervation of arabic gum and gelatin. The theory furthermore explains the increased tendency toward phase separation when the polymer becomes more strongly charged and suggests that complexation of polyacid or polybase with zwitterionic polymer (e.g., protein) of the same charge sign (at the "wrong side" of the iso-electric point) may be due (in part) to an induced charge reversal of the protein.