Thermo dynamic theory of counterion association in rigid polyelectrolytes

Journal de Physique I

Volumn 7, Issue 1, 1997, Pages 37-55

  Levin, Yan ^a   Barbosa, Marcia C ^a  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF STATE; FUNCTIONS; IONS; MATHEMATICAL MODELS; MOLECULES; SOLUTIONS; THERMODYNAMICS;

COUNTERION ASSOCIATION; DEBYE-HUCKEL LIMITING LAW; POLYIONS; RIGID POLYELECTROLYTES; THERMODYNAMIC FUNCTIONS;

POLYELECTROLYTES;

EID: 0030784159     PISSN: 11554304     EISSN: None     Source Type: Journal    
DOI: 10.1051/jp2:1997113     Document Type: Article

References (56)

1. (a) Debye P.W. and Huckel E., Phys. Z. 24 (1923) 185;
2. (b) For a good exposition see McQuarrie D.A., Statistical Mechanics (Harper and Row, New York 1976) Chap. 15.
3. Manning G.S., J. Chem. Phys. 51 (1969) 924.
4. (a) Bjerrum N., Kgl Dan. Vidensk. Selsk. Mat. -Fys. Medd. 7 (1926) 1;
5. (b) Falkenhagen H. and Ebeling \V., in Ionic Interactions, S. Petrucci, Ed. (Academic, New York, 1971).
6. (a) Fisher M.E. and Levin Y., Phys. Rev. Lett. 71 (1993) 3826;
7. (b) Fisher M.E., J. Stat. Phys. 75 (1994) 1;
8. for application of DHBj theory to polyampholytes see Levin Y. and Barbosa M.C., Europhys. Lett. 31 (1995) 513.
9. (a) Singh R.R. and Pitzer K.S., J. Chem. Phys. 92 (1990) 6775;
10. (b) Japas M.L. and Levelt Sengers J.M.H., J. Phys. Chem. 94 (1990) 5361;
11. Narayanan T. and Pitzer K.S., Phys. Rev. Lett. 73 (1994) 3002.
12. Valleau J.P., J. Chem. Phys. 95 (1991) 584;
13. Panagiotopoulos A.Z., Fluid Phase Equil. 76 (1992) 97;
14. Caillol J.-M., J. Chem. Phys. 100 (1994) 2161;
15. Orkoulas G. and Panagiotopou los A.Z., J. Chem. Phys. 101 (1994) 1452.
16. Kosterlitz J.M. and Thouless D.J., J. Phys. CG (1973) 1181.
17. (a) Levin Y., Li X.-J. and Fisher M.E., Phys. Rev. Lett. 73 (1994) 2716;
18. (b) Fisher M.E., Li X.-J. and Levin Y., J. Stat. Phys. 79 (1995) 1.
19. (a) Caillol J.M. and Levesque D., Phys. Rev. B 33 (1986) 499;
20. (b) Lee J.-R. and Teitel S., Phys. Rev. Lett. 64 (1990) 1483;
21. Orkoulas G. and Panagiotopoulos A.Z., J. Chem. Phys. 104 (1996) 7205.
22. (a) Genz U., Klein R. and Benmouna M., J. Phys. France 50 (1989) 449;
23. (b) Martin C., Weyerich B., Biegel J., Deike R., Johner C., Klein R. and Weber R., J. Phys. II France 5 (1995) 697.
24. Fuoss R.M., Katchalsky A. and Lifson S., Proc. Natl. Acad. Sei. U.S. 37 (1951) 579.
25. Imai N. and Onishi T., J. Chem. Phys. 30 (1959) 1115;
26. (b) Onishi T., Imai N. and Oosawa F., J. Phys. Soc. Jpn 15 (1960) 896;
27. Oosawa F., Polyelectrolytes (Dekker, New York, 1991);
28. see also MacGillivray A.D. and Winkleman Jr. J.J., J. Chem. Phys. 45 (1960) 2184.
29. Onsager L., Chem. Rev. 13 (1933) 73.
30. Levin Y. and Fisher M.E., Physica A 225 (1996) 164.
31. (a) Stevens M.J. and Kremer K., Phys. Rev. Lett. 71 (1993) 2228;
32. for electrostatic contribution to persistance length see (b) Fixman M., J. Vhem. Phys. 76 (1982) 6346;
33. Odijk T. and Mandel M., Physica 93 (1978) 298.
34. Fenley M.O., Manning G.S. and Oison W.K., Biopolymers 30 (1990) 1191.
35. (a) Manning G.S., J. Chem. Phys. 51 (1969) 3249;
36. (b) Le Bret M.C., J. Chem. Phys. 76 (1982) 6243;
37. Ramanathan G.V. and Woodbury Jr. C.P., J. Chem. Phys. 77 (1982) 4133;
38. Le Bret M. and Zimm R.H., Biopolymers 287 (1984);
39. (e) for lattice theory see Hao M.-H. and Harvey S.C., Macromolecules 25 (1992) 2200.
40. Hauge E.H. and Hemmer P.C., Phys. Norvegica 5 (1971) 209.
41. Li X.-J., University of Maryland Ph. D thesis (1995).
42. the main results of the theory were presented in Levin Y., Europhys. Lett. 34 (1996) 405.
43. Manning G.S., Q. Rev. Biophys. 11 (1978) 179.
44. This assumption is highly non trivial. Thus, for example, if the condensed counterions would not interact with each other the internal partition function for the n-cluster would be £n = C,i jn\. Within our theory the counterions, however, interact with each other through the renormalization of the effective charge of the polyion. Even though, it remains unclear to what extent the form presented in text will remain valid for real polyelectrolytes such as ;
45. DNA. Clearly in such a complicated molecule the nature of the binding mechanism will be dictated by the details of the intermolecular interactions. In practice, however, since the simple Manning approach seems to work quite well for real polyelectrolytes, we suppose that the proposed form of the internal partition function, and therefore of the equilibrium constant which is related to it through equation (20), can not be too far from reality. We do indeed find that our results are quite insensitive to the exact form of the equilibrium constant. See the discussion following equation (37).
46. More careful calculations in (a) Onsager L., Ann. N. Y. Acad. Sei. 51 (1949) 627;
47. (b) Stigter D., Bioplymers 16 (1977) 1435;
48. Fixman M. and Skolnick J., Macromolecules 11 (1978) 863;
49. Odijk T., J. Chem. Phys. 93 (1990) 5172, sugest that the polyionpolyion contribution to free energy density scales as /?/pp (Pp)3/2 ln(Pp).
50. Fixman M., J. Chem. Phys. 70 (1979) 4995.
51. Gonzalez-Mozuelos P. and de la Cruz M.O., J. Chem. Phys. 103 (1995) 3145.
52. Kholodenko A.L. and Beyerlein A.L., Phys. Rev. Lett. 74 (1995) 4679;
53. see also a Comment by Levin Y., Phys. Rev. Lett., submitted.
54. Chu P. and Marinsky J.A., J. Phys. Chem. 71 (1967) 4352.
55. Alexandrowicz Z., J. Polymer Sei. 43 (1960) 337.
56. A Monte Carlo simulation of one rodlike polyion and counterions was done by Bratko D. and Vlachy V., Chem. Phys. Lett. 90 (1982) 434. However to explore the properties of a polyelectrolyte solution addressed in this paper, it is essential to have simulations of the full PMP, with more than one polyion.