- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Some problems of the statistical physics of polymer chains with volume interaction

I. M. Lifshitz, A. Yu. Grosberg, and A. R. Khokhlov

I. M. Lifshitz

  • Institute for Physical Problems, USSR Academy of Sciences, Moscow 117334, USSR

A. Yu. Grosberg

  • Institute of Chemical Physics, USSR Academy of Sciences, Moscow 117334, USSR

A. R. Khokhlov

  • Physics Department, Moscow State University, Moscow 17234, USSR

PDF

Rev. Mod. Phys. 50, 683 – Published 1 July, 1978

DOI: https://doi.org/10.1103/RevModPhys.50.683

Abstract

The present state of the theory of volume effects in a polymer chain is reviewed. The theory of coils (i.e., chains with predominately repulsive volume interaction of monomers) and the analogy between the excluded volume problem and the theory of second-order phase transitions are briefly described. The theory of globules, formed by attractive interaction of monomers or by external attractive fields, is considered in greater detail. The coil-globule transition under various conditions is analyzed. A theory is constructed for the simplest model of the polymer chain—the model of "interacting beads on a flexible string." The connection of this model with more realistic ones is discussed. This review is based on the approach proposed by I. M. Lifshitz in 1968. While attention is focused on the physical aspects of the problems, some questions concerning biological applications are discussed in the conclusion.

View figure in article

References (90)

  1. Berry, G. S., and E. F. Casassa, 1970, J. Polym. Sci. D 1, 1
  2. Birshtein, T. M., and O. B. Ptitsyn, 1964, Conformation of Macromolecules, Moscow [Interscience, New York, (1966)]
  3. Birshtein, T. M., A. M. Elyashevich, and L. A. Morgenstern, 1974, Biophys. Chem. 1, 242
  4. Birshtein, T. M., A. M. Skvortsov, and A. A. Sariban, 1975, Vysokomol. Soedin. B 17, 607 [Polym. Sci. USSR 17, No. 8]
  5. Blumenfeld, L. A., 1973, Problems of Biological Physics (Nauka, Moscow)
  6. Bowers, R. G., and A. McKerrell, 1973, J. Phys. C 6, 2721
  7. Brézin E., J. C. Le Guillou, J. Zinn-Justin, and B. G. Nickel, 1973, Phys. Lett. A 44, 227
  8. Cron, A. K., O. B. Ptitsyn, A. M. Skvortsov, and A. M. Fedorov, 1967, Mol. Biol. (Mosc.) 1, 576 [Mol. Biol. USSR 1, No. 4]
  9. Cuniberti, C., and U. Bianchi, 1974, Polymer 15, 346
  10. Daoud, M., J. P. Cotton, B. Farnoux, G. Jannink, G. Sarma, H. Benoit, R. Duplessix, C. Picot, and P. G. de Gennes, 1975, Macromolecules 8, 804
  11. Daoud, M., and G. Jannink, 1976, J. Phys. (Paris) 37, 973
  12. de Gennes, P. G., 1969, Rep. Prog. Phys. 32, 187
  13. de Gennes, P. G., 1972, Phys. Lett. A 38, 339
  14. de Gennes, P. G., 1975, J. Phys. (Paris) Lett. 36, 55
  15. de Gennes, P. G., 1976, J. Phys. (Paris) 37, 1445
  16. des Cloizeaux, J., 1970, J. Phys. (Paris) 31, 715
  17. des Cloizeaus, J., 1975, J. Phys. (Paris) 36, 281
  18. des Cloizeaux, J., 1976, J. Phys. (Paris) 37, 431
  19. Domb, C., 1974, Polymer 15, 259
  20. Domb, C., and A. J. Barrett, 1976, Polymer 17, 179
  21. Edwards, S. F., 1965, Proc. Phys. Soc. Lond. 85, 613
  22. Edwards, S. F., 1975, J. Phys. A 8, 1171
  23. Eisner, Yu. E., 1969, Vysokomol. Soedin. A 11, 364 [Polym. Sci. USSR 11, 409, (1969)]
  24. Elyashevich, A. M., and A. M. Skvortzov, 1971, Mol. Biol. (Mosc.) 5, 204 [Mol. Biol. USSR 5, No. 2]
  25. Emery, V. J., 1975, Phys. Rev. B 11, 239
  26. Eskin, V. E., and A. E. Nesterov, 1965, Dokl. Akad. Nauk SSSR 165, 623
  27. Eskin, V. E., and I. I. Serduk, 1969, Vysokomol. Soedin. A 11, 372 [Polym. Sci. USSR 11, 418 (1969)]
  28. Finsy, R., M. Janssens, and A. Bellemans, 1975, J. Phys. A 8, L106
  29. Fisher, M. E., 1974, Rev. Mod. Phys. 46, 597
  30. Fixman, M., 1955, J. Chem. Phys. 23, 1656
  31. Flory, P. J., 1949, J. Chem. Phys. 17, 303
  32. Flory, P. J., 1953, Principles of Polymer Chemistry (Cornell University, Ithaca)
  33. Flory, P. J., 1969 Statistical Mechanics of Chain Molecules (Interscience, New York)
  34. Freed, K. F., 1972, Adv. Chem. Phys. 22, 1
  35. Grosberg, A. Yu., 1972, Vestn. Mosk. Univ. Ser. Fiz. No. 1, 14
  36. Grosberg, A. Yu., 1976a, Biofizika 21, 820 [Biophys. USSR 21, No. 5]
  37. Grosberg, A. Yu., 1976b, Biofizika 21, 603 [Biophys. USSR 21, No. 4]
  38. Grosberg, A. Yu., 1977, Biofizika 22, No. 3 [Biophys. USSR 22, No. 3]
  39. Grosberg, A. Yu., and B. D. Liberol, 1976, Biofizika 21, 610 [Biophys. USSR 21, No. 4]
  40. Helfand, E., 1975a, Acc. Chem. Res. 8, 295
  41. Helfand, E., 1975b, J. Chem. Phys. 62, 999
  42. Helfand, E., 1975c, J. Chem. Phys. 63, 2192
  43. Helfand, E., 1975d, Macromolecules 8, 559
  44. Helfand, E., 1976, Macromolecules 9, 307
  45. Helfand, E., and Y. Tagami, 1972, J. Chem. Phys. 56, 3592
  46. Helfand, E., and A. M. Sapse, 1975, J. Chem. Phys. 62, 1327
  47. Helfand, E., and A. M. Sapse, 1976, J. Polym. Sci. C No. 54
  48. Helfand, E., and Z. Wasserman, 1976, Macromolecules 9, No. 6
  49. Hoeve, C. A., E. A. Di Marzio, and P. Peyser, 1965, J. Chem. Phys. 42, 2558
  50. Joly, M., 1965, A Physico-Chemical Approach to the Denaturation of Proteins (Academic, New York)
  51. Khokhlov, A. R., 1977, J. Phys. (Paris) 38, No. 7
  52. Lax, M., 1974, J. Chem. Phys. 61, 4133
  53. Lax, M., 1975, Chem. Phys. 10, 285
  54. Lifshitz, I. M., 1968, Zh. Eksp. Teor. Fiz. 55, 2408 [Sov. Phys.—JETP 28, 1280 (1969)]
  55. Lifshitz, I. M., 1973, Zh. Eksp. Teor. Fiz. 65, 1100 [Sov. Phys.-JETP 38, 545 (1974)]
  56. Lifshitz, I. M., and A. Yu. Grosberg, 1973, Zh. Eksp. Teor. Fiz. 65, 2399 [Sov. Phys.-JETP 38, 1198 (1974)]
  57. Lifshitz, I. M., and A. Yu. Grosberg, 1975, Dokl. Akad. Nauk. SSSR 220, 468
  58. Lifshitz, I. M., A. Yu. Grosberg, and A. R. Khokhlov, 1976a, Biofizika 21, 780 [Biophys. USSR 21, No. 5]
  59. Lifshitz, I. M., A. Yu. Grosberg, and A. R. Khokhlov, 1976b, Zh. Eksp. Teor. Fiz. 71, 1634 [Sov. Phys.-JETP 44, No. 4 (1976)]
  60. Mashimo, S., Y. Iwasa, A. Chiba, and K. Shinohara, 1975, J. Phys. Soc. Jpn. 39, 1529
  61. Massih, A. R., and M. A. Moore, 1975, J. Phys. A 8, 237
  62. Mazur, J., and D. McIntyre, 1975, Macromolecules 8, 464
  63. McCrackin, F. L., J. Mazur, and C. M. Guttman, 1973, Macromolecules 6, 859
  64. McKenzie, D. S., 1976, Phys. Rep. 27, 35
  65. Moore, M. A., 1977, J. Phys. A 10, 305
  66. Murakami, J., 1976, J. Phys. Soc. Jpn. 41, 633
  67. Nagle, J. F., 1974, Proc. R. Soc. Lond. A 337, 569
  68. Onsager, L., 1949, Ann. N. Y. Acad. Sci. 51, 627
  69. Oono, Y., 1975, J. Phys. Soc. Jpn. 39, 25
  70. Oono, Y., 1976, J. Phys. Soc. Jpn. 41, 787
  71. Ptitsyn, O. B., and Yu. E. Eisner, 1965, Biofizika 10, 3 [Biophys. USSR 10, No. 1]
  72. Saito, N., and M. Inoue, 1974, Rep. Prog. Polym. Phys. Jpn. 17, 17
  73. Skvortsov, A. M., T. M. Birshtein, and E. B. Julina, 1976, Vysokomol. Soedin. A 18, 1993 [Polym. Sci. USSR 18, No. 9]
  74. Skvortsov, A. M., and T. M. Birshtein, 1976, Vysokomol. Soedin. A 18, 2479 [Polym. Sci. USSR 18, No. 11]
  75. Skvortsov, A. M., T. M. Birshtein, E. B. Julina, and A. A. Gorbunov, 1976, Vysokomol. Soedin. A 18, 2097 [Polym. Sci. USSR 18, No. 9]
  76. Slagowski, E., B. Tsai, and D. McIntyre, 1976, Macromolecules 9, 687
  77. Stephen, M. J., 1975, Phys. Lett. A 53, 363
  78. Teramoto, E., 1951 a,b,c, Busseiron Kenkyu 39, 1 ibid.40, 18 ibid.41, 14
  79. Vedenov, A. A., A. M. Dykhne, and M. D. Frank-Kamenetskii, 1971, Usp. Fiz. Nauk 105, 479 [Sov. Phys.-Usp. 14, 715 (1972)]
  80. Volkenstein, M. V., 1959, Configurational Statistics of Polymeric Chains, Moscow [Interscience, New York, (1963)]
  81. Volkenshtein, M. V., 1975, Molecular Biophysics (Nauka, Moscow)
  82. Vologodskii, A. V., A. V. Lukashin, M. D. Frank-Kamenetskii, and V. V. Anshelevich, 1974, Zh. Eksp. Teor. Fiz. 66, 2153 [Sov. Phys.-JETP 39, 1059 (1974)]
  83. Vologodskii, A. V., A. V. Lukashin, and M. D. Frank-Kamenetskii, 1974, Zh. Eksp. Teor. Fiz. 67, 1875 [Sov. Phys.-JETP 40, 932 (1975)]
  84. Watson, J. D., 1965, Molecular Biology of the Gene (Benjamin, New York)
  85. Weber, T. A., and E. Helfand, 1976, Macromolecules 9, 311
  86. Wiegel, F. W., 1977, J. Phys. A 10, 299
  87. Wilson, K. G., and J. Cogut, 1974, Phys. Rep. 12, 75
  88. Yamakawa, H., 1971, Modern Theory of Polymer Solutions (Harper and Row, New York)
  89. Yeh, R., and A. Isihara, 1969, J. Chem. Phys. 51, 1215
  90. Zimm, B. H., 1946, J. Chem. Phys. 14, 164

Outline

Information

Rev. Mod. Phys. 50, 683– Published 1 July, 1978

    © 1978 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation