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Theory of Dilute Macromolecular Solutions

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Book cover Fortschritte der Hochpolymeren-Forschung

Part of the book series: Advances in Polymer Science ((POLYMER,volume 5/2))

Abstract

The object of this paper is to lay the foundations of the Theory of Dilute Macromolecular Solutions in a unified, simplified, and yet rigorous manner. It also aims to acquaint chemists and physicists with a field of rapidly increasing significance, in view of possible applications to biophysics (and biochemistry). The Introduction gives a brief outline of the historical development of macromolecular solution theory. Roughly, one can distinguish between (a) lattice- and (b) gas-type theories, just as in the theory of liquids. The former, because of their apparent simplicity, have enjoyed great popularity for a long time among polymer chemists. However, lately, again just as for liquids, the gas-type approach has been proven to be more fundamental.

Our general approach is a proper adaptation and generalization of the gas-type theories of McMillan and Mayer and of Kirkwood and Buff. These were originally developed for simple (monomer) solutions. We use the cluster development of McMillan and Mayer, which itself is an adaptation of the original (Ursell)-Mayer cluster development. We then combine this procedure with the distribution function approach of Kirkwood and Buff.

Section 2 brings the cluster development for the osmotic pressure. Section 3 generalizes the approach of Section 2 to distribution functions, including a new and simple derivation of the cluster expansion of the pair distribution function. Section 4 presents a new expression for the chemical potential of solvents in dilute solutions. Section 5 contains an application of our general solution theory to compact macromolecular molecules. Section 6 contains the second osmotic virial coefficient of flexible macromolecules, followed in Section 7 by concluding remarks.

This work was partly supported by the National Science Foundation.

Operated by Union Carbide Corporation for the U.S. Atomic Energy Commission.

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References

  1. Meyer, K. H.: Z. physik. Chem. (Leipzig) B 44, 383 (1939).

    Google Scholar 

  2. Fowler, R. H., and G. S. Rushbrooke: Trans. Faraday Soc. 33, 1272 (1937).

    Article  CAS  Google Scholar 

  3. Chang, T. S.: Proc. Cambridge Phil. Soc. 35, 265 (1939).

    Article  Google Scholar 

  4. Miller, A. R.: Proc. Cambridge Phil. Soc. 38, 109 (1942).

    CAS  Google Scholar 

  5. —The theory of solutions of high polymers. Oxford: Clarendon Press 1948.

    Google Scholar 

  6. Huggins, M. L.: J. Chem. Phys. 9, 440 (1941).

    Article  CAS  Google Scholar 

  7. Flory, P. J.: J. Chem. Phys. 9, 660 (1941).

    Article  CAS  Google Scholar 

  8. Guggenheim, E. A.: Proc. Roy. Soc. A 183, 203 (1944).

    Google Scholar 

  9. —Mixtures. Oxford: Clarendon Press 1952.

    Google Scholar 

  10. Hildebrand, J. H.: J. Chem. Phys. 15, 225 (1947).

    Article  CAS  Google Scholar 

  11. —, and R. L. Scott: Regular Solutions. Englewood Cliffs, New Jersey: Prentice-Hall 1962.

    Google Scholar 

  12. Salsburg, Z. W., and J. G. Kirkwood: J. Chem. Phys. 21, 2169 (1953).

    Article  CAS  Google Scholar 

  13. McMillan, W. G., and J. E. Mayer: J. Chem. Phys. 13, 276 (1945).

    Article  CAS  Google Scholar 

  14. Kirkwood, J. G., and F. P. Buff: J. Chem. Phys. 19, 774 (1951).

    Article  CAS  Google Scholar 

  15. Buff, F. P., and R. Brout: J. Chem. Phys. 23, 455 (1955).

    Google Scholar 

  16. Hill, T.: J. Chem. Phys. 30, 93 (1959).

    Article  CAS  Google Scholar 

  17. The application of McMillan-Mayer theory to high polymer solutions was first made by B. H. Zimm. J. Chem. Phys. 14, 104 (1946).

    Article  Google Scholar 

  18. Various developments followed this paper: Isihara, A.: J. Chem. Phys. 18, 1446 (1950), and 19, 1162 (1951).

    Article  Google Scholar 

  19. —J. Phys. Soc. Japan 6, 40, 66 (1951).

    Article  Google Scholar 

  20. Zimm, B. H., W. H. Stockmayer, and M. Fixman: J. Chem. Phys. 21, 1716 (1953).

    Article  CAS  Google Scholar 

  21. —J. Chem. Phys. 21, 934 (1953).

    Article  CAS  Google Scholar 

  22. More recent developments will be referred to later.

    Google Scholar 

  23. Fisher, M. E.: Phys. Rev. 124, 1664 (1961).

    Article  Google Scholar 

  24. Kasteleyn, P. W.: Physica 27, 1209 (1961).

    Article  Google Scholar 

  25. Isihara, A.: J. Chem. Phys. 19, 397 (1951).

    Article  Google Scholar 

  26. Domb, C.: Advances in Physics 9, 149, 245 (1960).

    Article  CAS  Google Scholar 

  27. Wall, F. T., S. Windwer, and P. J. Gans: J. Chem. Phys. 38, 2220 (1963).

    Article  CAS  Google Scholar 

  28. Methods in computational physics I. Editors B. Alder, S. Fernbach, and M. Rotenberg, p. 217. New York: Academic Press 1963.

    Google Scholar 

  29. Domb, C., J. Gillis, and G. Wilmers: Proc. Phys. Soc. 85, 625 (1965).

    Article  CAS  Google Scholar 

  30. Schatzki, T. F.: J. Polymer Sci. 57, 337 (1962).

    Article  CAS  Google Scholar 

  31. Fisher, M. E., and B. J. Hiley: J. Chem. Phys. 34, 1253 (1961).

    Article  CAS  Google Scholar 

  32. Mazur, J., and L. Joseph: J. Chem. Phys. 38, 1292 (1963).

    Article  CAS  Google Scholar 

  33. Edwards, S. F.: Proc. Phys. Soc. 85, 613 (1965).

    Article  CAS  Google Scholar 

  34. Alder, B. J.: J. Chem. Phys. 23, 263 (1955).

    Article  CAS  Google Scholar 

  35. Hildebrand, J. H., and R. L. Scott: Solubility of nonelectrolytes. New York: Reinhold 1950.

    Google Scholar 

  36. Guggenheim, E. A.: Mixtures. Oxford: Clarendon Press 1952.

    Google Scholar 

  37. Gee, G., and L. R. G. Treloar: Trans. Faraday Soc. 38, 147 (1942).

    Article  CAS  Google Scholar 

  38. —, and W. J. C. Orr: Trans. Faraday Soc. 42, 507 (1946).

    Article  CAS  Google Scholar 

  39. Münster, A.: A. Naturforsch. 2, 272 (1947).

    Google Scholar 

  40. Stuart, H. A.: Die Physik der Hochpolymeren. Berlin, Göttingen, Heidelberg: Springer 1952.

    Google Scholar 

  41. Kurata, M., M. Tamura, and T. Watari: J. Chem. Phys. 23, 991 (1955).

    Article  CAS  Google Scholar 

  42. Stockmayer, W. H.: Makromol. Chem. 35, 54 (1960) gives an interesting and short discussion of the theory of dilute polymer solutions in general. He also compares the lattice and distribution function theories somewhat similarly to our discussion.

    Article  CAS  Google Scholar 

  43. Kirkwood, J. G., and F. P. Buff: Loc. cit., used the q-concentration which is ϕ/N.

    Google Scholar 

  44. Isihara, A.: J. Chem. Phys. 18, 1446 (1950).

    Article  Google Scholar 

  45. —, and T. Hayashida: J. Phys. Soc. Japan 6, 40, 46 (1951).

    Article  Google Scholar 

  46. Adair, G. S.: Proc. Roy. Soc. London 120 A, 573 (1923).

    Google Scholar 

  47. Burk, N. F.: J. Biol. Chem. 98, 353 (1932).

    CAS  Google Scholar 

  48. Tanford, C.: Physical Chemistry of Macromolecules, p. 234. New York: John Wiley & Sons 1961.

    Google Scholar 

  49. Simha, R.: J. Appl. Phys. 13, 147 (1942).

    Article  CAS  Google Scholar 

  50. Oparin, A. I.: The Origin of Life on Earth. Edinburgh: Oliver and Boyd 1957.

    Google Scholar 

  51. Onsager, L.: Phys. Rev. 82, 558 (1942).

    Google Scholar 

  52. —Ann. N. Y. Acad. Sci. 51, 627 (1949).

    CAS  Google Scholar 

  53. An improved treatment is given by A. Isihara: J. Chem. Phys. 19, 1142 (1951).

    Article  Google Scholar 

  54. Robinson, C.: Trans. Faraday Soc. 52, 57 (1956).

    Google Scholar 

  55. Ward, J. C., and R. B. Beevers: Discussion. Trans. Faraday Soc. 25, 29 (1958).

    Google Scholar 

  56. Verwey, E. J. W., and J. Th. G. Overbeek: Theory of the stability of lypophobic colloids. Amsterdam: Elsevier Publ. Co. 1948.

    Google Scholar 

  57. Mayer, J. E.: J. Chem. Phys. 18, 1426 (1950).

    Article  CAS  Google Scholar 

  58. Hill, T.: Discussion. Trans. Faraday Soc. 21, 31 (1956).

    Article  Google Scholar 

  59. Isihara, A.: J. Phys. Soc. Japan 5, 201 (1950).

    Article  Google Scholar 

  60. See also Debye, P., and F. Bueche: J. Chem. Phys. 20, 1337 (1952).

    Article  CAS  Google Scholar 

  61. Flory, P. J., and W. R. Krigbaum: J. Chem. Phys. 18, 1085 (1950).

    Google Scholar 

  62. Krigbaum, W. R., and P. J. Flory: J. Am. Chem. Soc. 75, 5256 (1953).

    Google Scholar 

  63. Orofino, T. A., and P. J. Flory: J. Chem. Phys. 26, 1067 (1957).

    Article  Google Scholar 

  64. Fixman, M.: J. Chem. Phys. 23, 1656 (1955).

    Article  CAS  Google Scholar 

  65. Albrecht, A. C.: J. Chem. Phys. 27, 1002 (1957).

    Article  CAS  Google Scholar 

  66. Kurata, M., and H. Yamakawa: J. Chem. Phys. 29, 311 (1958).

    Article  CAS  Google Scholar 

  67. Casassa, E. F.: J. Chem. Phys. 31, 800 (1959).

    Article  CAS  Google Scholar 

  68. Kurata, M., and W. H. Stockmayer: Advances in Polymer Sci. 3, 196 (1963).

    Article  CAS  Google Scholar 

  69. Kirste, R., and G. V. Schultz: Z. phys. Chem. (Frankfurt) 27, 301 (1961).

    Google Scholar 

  70. Casassa, E. F., and W. H. Stockmayer: Polymer (London) 3, 53 (1962).

    CAS  Google Scholar 

  71. Rouse Jr., R. E.: J. Chem. Phys. 21, 1272 (1953).

    Article  CAS  Google Scholar 

  72. Bueche, F.: J. Chem. Phys. 22, 603 (1954).

    Article  CAS  Google Scholar 

  73. Nakada, O.: J. Phys. Soc. Japan 10, 804 (1955).

    Article  CAS  Google Scholar 

  74. Zimm, B. H.: J. Chem. Phys. 24, 269 (1956).

    Article  CAS  Google Scholar 

  75. Kramers, H. A.: J. Chem. Phys. 14, 415 (1946).

    Article  CAS  Google Scholar 

  76. Kirkwood, J. G.: Rec. Trav. Chim. 68, 649 (1949).

    CAS  Google Scholar 

  77. Cf. also J. Riseman, and J. G. Kirkwood, Ch. 13, in Rheology, Vol. I. F. R. Eirich, ed. New York: Academic Press 1956.

    Google Scholar 

  78. Zimm, B. H., and J. L. Lundberg: J. Phys. Chem. 60, 425 (1956).

    Article  CAS  Google Scholar 

  79. Kurata, M.: Ann. N. Y. Acad. Sci. 89, 635 (1960).

    Google Scholar 

  80. Yamakawa, H.: J. Chem. Phys. 43, 1334 (1965).

    Article  CAS  Google Scholar 

  81. Longuet-Higgins, H. C.: Discussion. Trans. Faraday Soc. 15, 73 (1953).

    Article  Google Scholar 

  82. Tompa, H.: Polymer solutions. New York: Academic Press 1956.

    Google Scholar 

  83. Prigogine, I., et al.: The molecular theory of solutions. New York: North Holland Publ. Co. 1957.

    Google Scholar 

  84. Rowlinson, J. S.: Liquids and Liquid Mixtures. New York: Academic Press 1959.

    Google Scholar 

  85. Morawetz, H.: Macromolecules in solution. New York: Interscience Publ. 1965.

    Google Scholar 

  86. Weissberg, S. G., R. Simha, and R. Rothmans: J. Res. Natl. Bur. Std. 47, 298 (1951).

    Google Scholar 

  87. Fixman, M.: J. Polymer Sci. 47, 91 (1960).

    Article  CAS  Google Scholar 

  88. Grimley, T. B.: Trans. Faraday Soc. 57, 1074 (1961).

    Article  Google Scholar 

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Author notes

  1. A. Isihara

    Present address: Department of Physics and Astronomy, State University of New York at Buffalo, USA

Authors and Affiliations

  1. Oak Ridge National Laboratory, Oak Ridge, Tennessee

    A. Isihara & E. Guth

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  1. A. Isihara
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  2. E. Guth
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© 1967 Springer-Verlag

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Isihara, A., Guth, E. (1967). Theory of Dilute Macromolecular Solutions. In: Fortschritte der Hochpolymeren-Forschung. Advances in Polymer Science, vol 5/2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0051283

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  • DOI: https://doi.org/10.1007/BFb0051283

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  • Print ISBN: 978-3-540-03707-1

  • Online ISBN: 978-3-540-34921-1

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