Macromolecules zyxwvut 1990,23, 3625-3632 3625 (7) (a) Takenaka, K.; Hirao, A.; Hattori, T.; Nakahama, S. Macromolecules 1987,20,2034. zyxwvutsr (b) Takenaka, K.; Hirao, zyxwvuts A,; Hattori, T.; Nakahama, zyxwvutsr S. Macromolecules 1989,22, 1563. (8) Fieser, L. F.; Fieser, M. Reagents for Organic Synthesis; John Wiley and Sons: New York, 1967; Vol. 1, p 778. (9) Rachapudy, H.; Smith, G. C.; Raju, V. R.; Graessley, W. W. J. Polym. Sci. Polym. Phys. Ed. 1979, 17, 1211. (IO) Rosedale, J. H.; Bates, F. S. J. Am. Chem. zyxwvutsr SOC. 1988,110,3542. (11) Mays, J.; Hadjichristidis, N.; Fetters, L. J. Macromolecules 1984, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 17, 2723. (12) Zotteri, L.; Giuliani, G. P. Polymer 1978,19, 476. (13) Bellamy, L. J. The Infra-red Spectra of Complex Molecules; John Wiley and Sons: New York, 1975; Vol. 1, p 374. (14) Osbom, A. J.; Jardine, F. H.; Young, J. F.; Wilkinson, G. J. Chem. SOC. A 1966, 1711. (15) Doi, Y.; Yano, A.; Soga, K.; Bunfield,D. R. Macromolecules 1986, 19, 2409. (16) Gilliom, L. R. Macromolecules 1989,22,662. (17) Freifelder, M. Catalytic Hydrogenation in Organic Synthesis; John Wiley and Sons: New York, 1978; p 22. (18) Mohammadi, N. A.; Rempel, G. L. Macromolecules 1987,20, 2362. (19) Anatasiadis, S. H.; zyxwv Gancan, I.; Koberatein, J. T. Macromolecules 1989,22,1449. (20) Commercially available as Kraton G from Shell Chemical Co. Registry No. 1 (homopolymer), 104955-52-4; (l)(isoprene) (block copolymer), 117861-50-4; 2 (homopolymer), 104955-47- 7; 3 (homopolymer), 126726-58-7; 4 (homopolymer), 113177-19-8 5 (homopolymer), 116767-56-7. A Statistical Theory of Globular Polyelectrolyte Complexes V. Yu. Borue Council of Cybernetics of the Academy of Sciences, USSR, Laboratory of Nonlinear Problems in Computational Physics, Vavilova 40, 11 7333, Moscow, USSR 1. Ya. Erukhimovich' Institute of Mineralogy, Geochemistry and Crystallochemistry of the Rare Elements of the Academy of Sciences, USSR, Sadounicheskay Nabereznaya 71, 113035, Moscow, USSR Received June 28,1989; Revised Manuscript Received January 19, 1990 ABSTRACT A microscopic statistical theory of a symmetrical polyelectrolyte complex (PEC) is developed. PEC is shown to form a polymer globule. The equilibrium density of PEC, the width of a PEC surface layer, and the surface tension of PEC are calculated as a function of salt concentration. Description of PEC as a polymer globule enables us to simplify theoretical treatment of the phenomenon of phase separation in poly- electrolyte solutions (complex coacervation). Numerous experimental facts concerning complex coacerva- tion are easily explained within this approach. Complex coacervation is considered as precipitation of polymer globules owing to minimization of surface energy. The theory is based on the Lifshitz-Grosberg theory of polymer globules and our previous work concerning the equation of state of polyelectrolyte solutions. It is limited to the case of polyions with the low linear density of charge, which is most clear from the theoretical point of view and is also of practical and, in particular, of biological interest. I. Introduction I t is well-known that oppositely charged macromolecules in a solution form polyelectrolyte complexes (PEC). Their theoretical investigation is important for the development of a theory of phase separation in a polyelectrolyte (PE) system containing polyions of opposite charges. This phenomenon studied for the first time by Bungenberg de Jong' was called complex coacervation (see also refs 2-4). Parts of the condensed phase (coacervate)are usually called coacervate drops and are often considered as model systems for precellular structure^.^ The numerous phenomena that occur in the PE solutions are complicated, and generally their theoretical interpretation is qualitative and controversial. Therefore, it is reasonable to start the consistent consideration of these systems with the most simple solvable model, where main qualitative features are already seen. As the first step in the study of PEC properties we shall consider in this paper a symmetric PEC, formed by two flexible oppositely charged polyions with the same degree of polymerization N and each having one charge per m monomers (each polyion has charges of one sign). Charges should be distributed more or less uniformly along the chain (for example, randomly). Only for simplicity we consider polyions as flexible filaments on which interacting monomers are strung (the model "beads on a filamentns) with Gaussian correlations between adjacent monomers and the mean-square distance, u2, between them. All the monomers interact by means of non-Coulombic forces of the van der Waals type. These assumptions are typical for the theoretical consideration of this kind2-" and can be easily generalized. The influence of ionic bonds between oppositely charged monomers is supposed to be small (for example, the energy of an ionic bond is small in comparison with temperature T, given in energy units). Thus PEC is formed, owing to fluctuation electrostatic energy. This energy was calculated in ref 7 for polyelectrolyte solution (PES) containing weakly charged macromolecules. (Polyions are called weakly charged when the parameter u/m1/2 is small, where u = zy l/a, 1 = e2/tT is the Bjerrum length (see also ref 8), and t is the dielectric constant of the solvent. It wm ais0 shown' that Coulombic and nonelectrostatic contributions to the free energy may be of the same order of magnitude, which can ,lead to PEC formation. Weakly charged PE are of 0 1990 American Chemical Society