Skip to main content

Abstract

This chapter presents the statistical-mechanical treatments of equilibrium conformational or static properties, such as the mean-square radius of gyration, scattering function, mean-square optical anisotropy, and mean-square electric dipole moment, of the unperturbed HW chain, including the KP wormlike chain as a special case, by an application of its chain statistics developed in Chap. 4. A comparison of theory with experiment is made with experimental data obtained for several flexible polymers in the Θ state over a wide range of molecular weight, including the oligomer region, and also for typical semiflexible polymers (without excluded volume) in some cases. It must be noted that well-characterized samples have recently been used for measurements of dilute-solution properties of the former; they are sufficiently narrow in molecular weight distribution, and have a fixed stereochemical composition independent of the molecular weight in the case of asymmetric polymers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Konishi, T. Yoshizaki, T. Saito, Y. Einaga, and H. Yamakawa: Macromolecules 23, 290 (1990).

    Article  CAS  Google Scholar 

  2. T. Konishi, T. Yoshizaki, and H. Yamakawa: Macromolecules 24, 5614 (1991).

    Article  CAS  Google Scholar 

  3. Y. Tamai, T. Konishi, Y. Einaga, M. Fujii, and H. Yamakawa: Macromolecules 23, 4067 (1990).

    Article  CAS  Google Scholar 

  4. M. Kamijo, N. Sawatari, T. Konishi, T. Yoshizaki, and H. Yamakawa: Macromolecules 27, 5697 (1994).

    Article  CAS  Google Scholar 

  5. M. R. Ambler, D. Mclntyre, and L. J. Fetters: Macromolecules 11, 300 (1978).

    Article  CAS  Google Scholar 

  6. J. E. Godfrey and H. Eisenberg: Biophys. Chem. 5, 301 (1976).

    Article  CAS  Google Scholar 

  7. Y. Kashiwagi, T. Norisuye, and H. Fujita: Macromolecules 14, 1220 (1981).

    Article  CAS  Google Scholar 

  8. T. Norisuye: Prog. Polym. Sci. 18, 543 (1993).

    Article  CAS  Google Scholar 

  9. T. C. TYoxell and H. A. Scheraga: Macromolecules 4, 528 (1971).

    Article  Google Scholar 

  10. U. Schmueli, W. Traub, and K. Rosenheck: J. Polym. Sci. Part A-2 7, 515 (1969).

    Article  Google Scholar 

  11. T. Yoshizaki and H. Yamakawa: Macromolecules 13, 1518 (1980).

    Article  CAS  Google Scholar 

  12. P. Debye: J. Phys. Coll. Chem. 51, 18 (1947).

    Article  CAS  Google Scholar 

  13. T. Neugebauer: Ann. Phys. 42, 509 (1943).

    Article  CAS  Google Scholar 

  14. J. des Cloizeaux: Macromolecules 6, 403 (1973).

    Article  Google Scholar 

  15. M. Fujii and H. Yamakawa: J. Chem. Phys. 66, 2578 (1977).

    Article  CAS  Google Scholar 

  16. A. Peterlin: J. Polym. Sci. 47, 403 (1960).

    Article  CAS  Google Scholar 

  17. S. Heine, O. Kratky, G. Porod, and P. J. Schmitz: Makromol. Chem. 44, 682 (1961).

    Article  Google Scholar 

  18. R. Koyama: J. Phys. Soc. Japan 34, 1029 (1973).

    Article  CAS  Google Scholar 

  19. P. Sharp and V. A. Bloomfield: Biopolymers 6, 1201 (1968).

    Article  CAS  Google Scholar 

  20. H. Yamakawa and M. Fujii: Macromolecules 7, 649 (1974).

    Article  CAS  Google Scholar 

  21. T. Norisuye, H. Murakami, and H. Fujita: Macromolecules 11, 966 (1978).

    Article  CAS  Google Scholar 

  22. R. G. Kirste and W. Wunderlich: Makromol. Chem. 73, 240 (1964).

    Article  CAS  Google Scholar 

  23. W. Wunderlich and R. G. Kirste: Ber. Bunsen-Ges. Phys. Chem. 68, 646 (1964).

    CAS  Google Scholar 

  24. R. G. Kirste and R. C. Oberthür: In Small Angle X-ray Scattering, O. Glatter and O. Kratky, ed. ( Academic Press, New York, 1982 ), p. 387.

    Google Scholar 

  25. D. Y. Yoon and P. J. Flory: Macromolecules 9, 299 (1976).

    Article  CAS  Google Scholar 

  26. P. R. Sundararajan: Macromolecules 19, 415 (1986).

    Article  CAS  Google Scholar 

  27. K. Nagasaka, T. Yoshizaki, J. Shimada, and H. Yamakawa: Macromolecules 24, 924 (1991).

    Article  CAS  Google Scholar 

  28. A. Baram and W. M. Gelbart: J. Chem. Phys. 66, 617 (1977).

    Article  CAS  Google Scholar 

  29. G. Porod: In Small Angle X-ray Scattering, O. Glatter and O. Kratky, ed. ( Academic Press, New York, 1982 ), p. 17.

    Google Scholar 

  30. W. Burchard and K. Kajiwara: Proc. Roy. Soc. London A316, 185 (1970).

    Google Scholar 

  31. H. Koyama, T. Yoshizaki, Y. Einaga, H. Hayashi, and H. Yamakawa: Macromolecules 24, 932 (1991).

    Article  CAS  Google Scholar 

  32. T. Yoshizaki, H. Hayashi, and H. Yamakawa: Macromolecules 26, 4037 (1993).

    Article  CAS  Google Scholar 

  33. K. Horita, T. Yoshizaki, H. Hayashi, and H. Yamakawa: Macromolecules 27, 6492 (1994).

    Article  Google Scholar 

  34. T. Yoshizaki, H. Hayashi, and H. Yamakawa: Macromolecules 27, 4259 (1994).

    Article  CAS  Google Scholar 

  35. K. Huber, W. Burchard, and S. Bantle: Polymer 28, 863 (1987).

    Article  CAS  Google Scholar 

  36. A. Dettenmaier, A. Maconnachie, J. S. Higgins, H. H. Kausch, and T. Q. Nguyen: Macromolecules 19, 773 (1986).

    Article  CAS  Google Scholar 

  37. J. M. O’Reilly, D. M. Teegarden, and G. D. Wignall: Macromolecules 18, 2747 (1985).

    Article  Google Scholar 

  38. M. Vacatello, D. Y. Yoon, and P. J. Flory: Macromolecules 23, 1993 (1990).

    Article  CAS  Google Scholar 

  39. H. Yamakawa, M. Fujii, and J. Shimada: J. Chem. Phys. 71, 1611 (1979).

    Article  CAS  Google Scholar 

  40. B.J. Berne and R. Pecora: Dynamic Light Scattering( Interscience, New York, 1976 ).

    Google Scholar 

  41. K. Nagai: Polym. J. 3, 563 (1972).

    Article  CAS  Google Scholar 

  42. P. Horn: Ann. Phys. (Paris) 10, 386 (1955).

    CAS  Google Scholar 

  43. H. Utiyama and M. Kurata: Bull. Inst. Chem. Res. Kyoto Univ. 42, 128 (1964); H. Utiyama: J. Phys. Chem. 69, 4138 (1965).

    Google Scholar 

  44. Y. Tagami: J. Chem. Phys. 54, 4990 (1971).

    Article  CAS  Google Scholar 

  45. P. Horn, H. Benoit, and G. Oster: J. Chim. Phys. 48, 530 (1951).

    CAS  Google Scholar 

  46. K. Nagai: Polym. J. 3, 67 (1972).

    Article  CAS  Google Scholar 

  47. M. Arpin, C. Strazielle, G. Weill, and H. Benoit: Polymer 18, 262 (1977).

    Article  CAS  Google Scholar 

  48. P. J. Flory, P. R. Sundararajan, and L. C. DeBold: J. Am. Chem. Soc. 96, 5015 (1974).

    Article  CAS  Google Scholar 

  49. G. D. Patterson and P. J. Flory: J. Chem. Soc. Faraday Trans. 2 68, 1098 (1972).

    CAS  Google Scholar 

  50. G. D. Patterson and P. J. Flory: J. Chem. Soc. Faraday Trans. 2 68, 1111 (1972).

    CAS  Google Scholar 

  51. U. W. Suter and P. J. Flory: J. Chem. Soc. Faraday Trans. 2 73, 1521 (1977).

    CAS  Google Scholar 

  52. P. J. Flory, E. Saiz, B. Erman, P. A. Irvine, and J. P. Hummel: J. Phys. Chem. 85, 3215 (1981).

    Article  CAS  Google Scholar 

  53. C. W. Carlson and P. J. Flory: J. Chem. Soc. Faraday Trans. 2 73, 1505 (1977).

    CAS  Google Scholar 

  54. D. Y. Yoon and P. J. Flory: Polymer 16, 645 (1975).

    Article  CAS  Google Scholar 

  55. T. Konishi, T. Yoshizaki, J. Shimada, and H. Yamakawa: Macromolecules 22, 1921 (1989).

    Article  CAS  Google Scholar 

  56. Y. Takaeda, T. Yoshizaki, and H. Yamakawa: Macromolecules 26, 3742 (1993).

    Article  CAS  Google Scholar 

  57. Y. Takaeda, T. Yoshizaki, and H. Yamakawa: Macromolecules 28, 4167 (1995).

    Article  CAS  Google Scholar 

  58. M. Fujii and H. Yamakawa: J. Chem. Phys. 72, 6005 (1980).

    Article  CAS  Google Scholar 

  59. H. Yamakawa, J. Shimada, and K. Nagasaka: J. Chem. Phys. 71, 3573 (1979).

    Article  CAS  Google Scholar 

  60. A. R. Edmonds: Angular Momentum in Quantum Mechanics(Princeton Univ., Princeton, 1974 ).

    Google Scholar 

  61. W. H. Stockmayer: Pure Appi. Chem. 15, 539 (1967).

    Article  Google Scholar 

  62. T. Yamada, T. Yoshizaki, and H. Yamakawa: Macromolecules 25, 1487 (1992).

    Article  CAS  Google Scholar 

  63. A. J. Bur and D. E. Roberts: J. Chem. Phys. 51, 406 (1969).

    Article  CAS  Google Scholar 

  64. S. Takada, T. Itou, H. Chikiri, Y. Einaga, and A. Teramoto: Macromolecules 22, 973 (1989).

    Article  CAS  Google Scholar 

  65. K. Nagai and T. Ishikawa: J. Chem. Phys. 43, 4508 (1965).

    Article  CAS  Google Scholar 

  66. P. J. Flory: Statistical Mechanics of Chain Molecules( Interscience, New York, 1969 ).

    Google Scholar 

  67. H. Benoit: Ann. Phys. (Paris) 6, 561 (1951).

    CAS  Google Scholar 

  68. A. Peterlin and H. A. Stuart: J. Polym. Sci. 5, 551 (1950).

    Article  Google Scholar 

  69. W. H. Stockmayer and M. E. Baur: J. Am. Chem. Soc. 86, 3485 (1964).

    Article  CAS  Google Scholar 

  70. J. A. Schellman: Chem. Rev. 75, 323 (1975).

    Article  CAS  Google Scholar 

  71. H. Yamakawa: Modem Theory of Polymer Solutions( Harper & Row, New York, 1971 ).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yamakawa, E.H. (1997). Equilibrium Properties. In: Helical Wormlike Chains in Polymer Solutions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60817-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-60817-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64569-3

  • Online ISBN: 978-3-642-60817-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics