Skip to main content
SpringerLink
Log in

Polymer Configuration

  • Chapter
Monte Carlo Applications in Polymer Science

Part of the book series: Lecture Notes in Chemistry ((LNC,volume 27))

  • 145 Accesses

Abstract

A basic prototype for polymer chains can be represented as where R is the monomer unit. The configuration shown above is only one of the enormous number which can be assumed by the chain, since the molecule can perform internal rotations around each of the R - R bonds. Because of its flexibility a polymer chain fluctuates constantly, acquiring various configurations within very short time invervals. Therefore, at any given moment different chains belonging to the same ensemble can be found in states having different configurations. Consequently, a polymer described by an ideal chemical formula is, generally speaking, a mixture of a multiplicity of different configurations. Thus the problem of the geometry of polymer chains acquires a statistical character. The chain can be described therefore only by its averaged parameters. The size and shape of a polymer chain are of great interest to the polymer scientist, since physical properties such as light scattering, diffusion, and viscosity can only be understood if they are discussed in the light of configurational properties.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

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. H. Yamakawa, Modern Theory of Polymer Solutions, Chap. 1 (Harper & Row, New York, 1971).

    Google Scholar 

  2. K. Šolc, J. Chem. Phys. 55, 335 (1971)

    Google Scholar 

  3. W. Bruns, Colloid & Polymer Sci. 254, 325 (1976)

    CAS  Google Scholar 

  4. W. Bruns, Makromol. Chem. 158, 177 (1972)

    CAS  Google Scholar 

  5. P.J. Flory, Statistical Mechanics of Chain Molecules, Chap. 8 (Interscience Publ., New York 1969)

    Google Scholar 

  6. M. Fixman, J. Chem. Phys. 36, 306 (1962)

    CAS  Google Scholar 

  7. W. Bruns, Makromol. Chem. 170, 191 (1973)

    CAS  Google Scholar 

  8. W.W. Wood, Monte Carlo Calculation of the Equation of State of Systems of 12 and 48 Hard Circles. Los Alamos Scientific Laboratory Report LA-2827 (Los Alamos, New Mexico, Juli 1, 1963)

    Google Scholar 

  9. S. Windwer in “Markov chains and Monte Carlo Calculations in Polymer Science, ed. by G.G. Lowry, Marcel Dekker, New York 1970.

    Google Scholar 

  10. R. Grishman, J. Chem. Phys. 58, 220 (1973)

    CAS  Google Scholar 

  11. W. Bruns, J. Phys. A: Math. Nucl. Gen. 10, 1963 (1977).

    CAS  Google Scholar 

  12. W. Bruns, Makromol. Chem. 124, 91 (1969)

    CAS  Google Scholar 

  13. W. Bruns, Makromol. Chem. 134, 193 (1970).

    CAS  Google Scholar 

  14. W. Bruns, Makromol. Chem. 176, 813 (1975)

    CAS  Google Scholar 

  15. W. Bruns and J. Naghizadeh, J. Chem. Phys. 65, 747 (1976)

    CAS  Google Scholar 

  16. P.J. Gans, J. Chem. Phys. 42, 4159 (1965)

    CAS  Google Scholar 

  17. R.J. Fleming, Proc. Roy. Soc. 90, 1003 (1967)

    CAS  Google Scholar 

  18. Z. Alexandrowicz and Y. Accad, J. Chem. Phys. 54, 5338 (1971)

    CAS  Google Scholar 

  19. P.C. Jurs and J.E. Reissner, J. Chem. Phys. 55, 4948 (1971)

    CAS  Google Scholar 

  20. J.M. Hammersley and K.W. Morton, J. Roy. Statistical Soc. B 16, 23 (1954)

    Google Scholar 

  21. M.N. Rosenbluth and A.R. Rosenbluth, J. Chem. Phys. 23, 256 (1955)

    Google Scholar 

  22. N.C. Smith and R.J. Fleming, J. Phys. A: Math. Gen. 8, 929 (1975)

    Google Scholar 

  23. F.T. Wall and J.J. Erpenbeck, J. Chem. Phys. 30, 634 (1959)

    CAS  Google Scholar 

  24. W. Bruns and L. Vogel, unpublished results.

    Google Scholar 

  25. Z. Alexandrowicz, J. Chem. Phys. 51, 561 (1969)

    CAS  Google Scholar 

  26. P.H. Verdier and W.H. Stockmeyer, J. Chem. Phys. 36, 227 (1962)

    CAS  Google Scholar 

  27. A. Baumgärtner and K. Binder, J. Chem. Phys. 71, 2541 (1979)

    Google Scholar 

  28. S.D. Stellman and P.J. Gans, Makromolecules 5, 516 (1972)

    CAS  Google Scholar 

  29. A.K. Kron, Vysokomol. soyed. 7, 1228 (1965)

    CAS  Google Scholar 

  30. F.T. Wall and F. Mandel, J. Chem. Phys. 63, 4592 (1975)

    CAS  Google Scholar 

  31. J.G. Curro, J. Chem. Phys. 61, 1203 (1974)

    CAS  Google Scholar 

  32. W.W. Wood and F.R. Parker, J. Chem. Phys. 27, 720 (1957)

    CAS  Google Scholar 

  33. S.G. Brush, H.L. Sahlin, and G. Teller, J. Chem. Phys. 45, 2102 (1966)

    CAS  Google Scholar 

  34. F.T. Wall, L.A. Hiller, Jr., and D.J. Wheeler, J. Chem. Phys. 22, 1036 (1953)

    Google Scholar 

  35. J.J. Hermans, Rec. Trav. chim. 69, 220 (1950)

    CAS  Google Scholar 

  36. J.J. Hermans, M.S. Klamkin, and R. Ullman, J. Chem. Phys. 20, 1360 (1952)

    CAS  Google Scholar 

  37. R. Ullman and J.J. Hermans, J. Polymer Sci. 10, 559 (1953)

    CAS  Google Scholar 

  38. F.T. Wall, J. Chem. Phys. 21, 1914 (1953)

    CAS  Google Scholar 

  39. P.J. Flory, J. Chem. Phys. 17, 303 (1949)

    CAS  Google Scholar 

  40. H.M. James, J. Chem. Phys. 21, 1628 (1953)

    CAS  Google Scholar 

  41. F.T. Wall, L.A. Hiller, Jr., and W.F. Atchinson J. Chem. Phys. 23, 913 (1955).

    CAS  Google Scholar 

  42. F.T. Wall, L.A. Hiller, Jr., and W.F. Atchinson J. Chem. Phys. 23, 2314 (1955)

    CAS  Google Scholar 

  43. F.T. Wall, L.A. Hiller, Jr., and W.F. Atchinson J. Chem. Phys. 26, 1742 (1957)

    CAS  Google Scholar 

  44. C. Domb, J. Chem. Phys. 38, 2957 (1963)

    CAS  Google Scholar 

  45. S.F. Edwards, Proc. Phys. Soc. (London) 85, 613 (1965)

    CAS  Google Scholar 

  46. H. Reiss, J. Chem. Phys. 47, 186 (1967)

    CAS  Google Scholar 

  47. F.T. Wall and J. Mazur, see ref. 70.

    Google Scholar 

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

    CAS  Google Scholar 

  49. P. Mark, S. Windwer, J. Chem. Phys. 47, 708 (1967)

    CAS  Google Scholar 

  50. L.V. Gallacher and S. Windwer, J. Chem. Phys. 44, 1139 (1966)

    CAS  Google Scholar 

  51. A. Rice and S. Windwer, J. Chem. Phys. 43, 3773 (1965)

    Google Scholar 

  52. S. Windwer, J. Chem. Phys. 43, 115 (1965)

    CAS  Google Scholar 

  53. E. Loftus and P.J. Gans, J. Chem. Phys. 49, 3828 (1968)

    CAS  Google Scholar 

  54. N.C. Smith and R.J. Fleming, J. Phys. A: Math. Gen. 8, 729 (1975)

    Google Scholar 

  55. R.J. Fleming, J. Phys. A: Math. Gen. 12, 2157 (1979)

    CAS  Google Scholar 

  56. K.G. Wilson and J.B. Kogur, Phys. Rep. (c) 12, 75 (1974)

    Google Scholar 

  57. P. de Gennes, Phys. Lett. (A) 38, 339 (1972)

    Google Scholar 

  58. P.J. Flory and S. Fisk, J. Chem. Phys. 44, 2243 (1966)

    CAS  Google Scholar 

  59. A. Baumgärtner, J. Phys. A: Math. Gen. 13, L39 (1980)

    Google Scholar 

  60. K. Kremer, A. Baumgärtner, and K. Binder (in press).

    Google Scholar 

  61. A.K. Kron and O.B. Ptitsyn, Vysokomol. soyed. 6, 862 (1964)

    CAS  Google Scholar 

  62. M. Lax and J. Gillis, Macromolecules 10, 334 (1977)

    CAS  Google Scholar 

  63. W. Bruns, J. Chem. Phys. 73, 1970 (1980)

    CAS  Google Scholar 

  64. K. Šolc and W.H. Stockmayer, J. Chem. Phys. 54, 2756 (1971)

    Google Scholar 

  65. D.E. Kranbuehl, P.H. Verdier, and J.M. Spencer, J. Chem. Phys. 59, 3861 (1973)

    CAS  Google Scholar 

  66. J. Mazur, C.M. Guttman, and F.L. McCrackin, Macromolecules 6, 872 (1973)

    Google Scholar 

  67. R.J. Rubin and J. Mazur, Macromolecues 10, 139 (1977)

    CAS  Google Scholar 

  68. C. Domb, J. Gillis, and G. Willmers Proc. Phys. Soc. London 85, 625 (1965)

    CAS  Google Scholar 

  69. F.T. Wall and F.T. Hioe, J. Phys. Chem. 74, 4410 (1970)

    CAS  Google Scholar 

  70. S.D. Stellman and P.J. Gans, Macromolecues 5, 720 (1972)

    CAS  Google Scholar 

  71. R. Grishman, J. Chem. Phys. 58, 5309 (1973)

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  73. F.T. Wall and R.A. White, Macromolecules 7, 849 (1974)

    CAS  Google Scholar 

  74. F.T. Wall and W.A. Seitz, J. Chem. Phys. 67, 258 (1977)

    CAS  Google Scholar 

  75. F.T. Wall and J. Mazur, Ann. N.Y. Acad. Sci. 89, 608 (1961)

    CAS  Google Scholar 

  76. F.T. Wall, S. Windwer, and P.J. Gans, J. Chem. Phys. 38, 2228 (1963)

    CAS  Google Scholar 

  77. J. Mazur and F.L. McCrackin, J. Chem. Soc. 49, 648 (1968)

    CAS  Google Scholar 

  78. R.G. Kirste, Disc. Faraday Soc. 49, 51 (1970)

    Google Scholar 

  79. F.L. McCrackin, J. Mazur, and C.M. Guttman, Macromolecules 6, 859 (1973)

    CAS  Google Scholar 

  80. A.T. Clark and M. Ial, Brit. Polym. J. 9, 92 (1977)

    CAS  Google Scholar 

  81. A. Baumgärtner, J. Chem. Phys. 72, 871 (1980)

    Google Scholar 

  82. M. Janssens and A. Bellemans, Macromolecules 9, 303 (1976)

    CAS  Google Scholar 

  83. K. Suzuki and Y. Nakata Bull. Chem. Soc. Japan 43, 1006 (1970)

    CAS  Google Scholar 

  84. K.K. Knaell and R.A. Scott III, J. Chem. Phys. 54, 566, 3556 (1971)

    CAS  Google Scholar 

  85. H.E. Warvari, K.K. Knaell, and R.A. Scott III, J. Chem. Phys. 55, 2020 (1971).

    CAS  Google Scholar 

  86. H.E. Warvari, K.K. Knaell, and R.A. Scott III, J. Chem. Phys. 56, 2903 (1972).

    CAS  Google Scholar 

  87. H.E. Warvari, K.K. Knaell, and R.A. Scott III, J. Chem. Phys. 57, 1161 (1972)

    CAS  Google Scholar 

  88. H.E. Warvari and R.A. Scott III, J. Chem. Phys. 57, 1146, 1154 (1972)

    CAS  Google Scholar 

  89. S. Tanaka and A. Nakajima, Macromolecules 5, 708, 714 (1972)

    CAS  Google Scholar 

  90. S. Preliminat and J. Hermans, Jr., J. Chem. Phys. 59, 2602 (1973)

    Google Scholar 

  91. Y. Nakata and K. Suzuki, Polymer J. 6, 242 (1974)

    CAS  Google Scholar 

  92. D.E. Neves and R.A. Scott III, Macromolecules 8, 267 (1975).

    CAS  Google Scholar 

  93. D.E. Neves and R.A. Scott III, Macromolecules 9, 554 (1976).

    CAS  Google Scholar 

  94. D.E. Neves and R.A. Scott III, Macromolecules 10, 339 (1977)

    CAS  Google Scholar 

  95. M. Sisido, Y. Imanishi/ and T. Higashimura, Macromolecules 9, 320, 389 (1976)

    CAS  Google Scholar 

  96. N. Go and H.A. Scheraga, Macromolecules 11, 552 (1978)

    CAS  Google Scholar 

  97. S. Bluestone and M.J. Vold, J. Polymer Sci. A2, 289 (1964).

    Google Scholar 

  98. S. Bluestone and M.J. Vold, J. Chem. Phys. 42, 4175 (1965)

    CAS  Google Scholar 

  99. J.G. Curro, J. Chem. Phys. 61, 1203 (1974).

    CAS  Google Scholar 

  100. J.G. Curro, J. Chem. Phys. 64, 2496 (1976).

    CAS  Google Scholar 

  101. J.G. Curro, Macromolecules 12, 467 (1979)

    Google Scholar 

  102. E. de Vos and A. Bellemans, Macromolecules 7, 812 (1974).

    Google Scholar 

  103. E. de Vos and A. Bellemans, Macromolecules 8, 651 (1975)

    Google Scholar 

  104. T.M. Birshtein, A.M. Skvortsov, and A.A. Sariban, Vysokomol. soyed. A 19, 63 (1977)

    Google Scholar 

  105. F.T. Wall, J.C. Chin, and F. Mandel, J. Chem. Phys. 66, 3143 (1977)

    CAS  Google Scholar 

  106. F.T. Wall and W.A. Seitz, J. Chem. Phys. 67, 3722 (1977)

    CAS  Google Scholar 

  107. H. Okamoto, J. Chem. Phys. 70, 1690 (1979)

    CAS  Google Scholar 

  108. H. Okamoto, J. Chem. Phys. 64, 2686 (1976)

    CAS  Google Scholar 

  109. A.M. Skvortov, A.A. Sariban, and T.M. Birshtein, Vysokomol. soyed. A 19, 1014 (1977)

    Google Scholar 

  110. R. de Santis and H.G. Zachmann, Colloid a. Polymer Sci. 255, 729 (1977).

    Google Scholar 

  111. F.T. Wall, F. Mandel, and J.C. Chin, J. Chem. Phys. 65, 2231 (1976)

    CAS  Google Scholar 

  112. F.T. Wall, J.C. Chin and F. Mandel, J. Chem. Phys. 66, 3066 (1977)

    CAS  Google Scholar 

  113. J.B. Smitham and D.H. Napper, J. Polymer Sci., Symposium No. 55, 51 (1976)

    CAS  Google Scholar 

  114. L. Ma, K.M Midellemiss, G.M. Torrie, and S.G. Whittington, J. Chem. Soc, Faraday Trans. II, 74, 721 (1978)

    CAS  Google Scholar 

  115. G.M. Torrie, J. Barrett, and S.G. Whittington, J. Chem. Soc., Faraday Trans.II, 75, 369 (1979)

    CAS  Google Scholar 

  116. P.H. Verdier and W.H. Stockmayer, J. Chem. Phys. 36, 227 (1962)

    CAS  Google Scholar 

  117. P.H. Verdier, J. Chem. Phys. 45, 2118 (1966).

    Google Scholar 

  118. P.H. Verdier, J. Chem. Phys. 59, 6119 (1973)

    CAS  Google Scholar 

  119. L. Monnerie and F. Gény, J. Chim. Phys. 66, 1691 (1969)

    CAS  Google Scholar 

  120. L. Monnerie, F. Gény, and J. Fouquet, J. Chim. Phys. 66, 1698 (1969)

    CAS  Google Scholar 

  121. F. Gény and L. Monnerie, J. Chim. Phys. 66, 1708, 1872 (1969)

    Google Scholar 

  122. E. Dubois-Violette, F. Gény, L. Monnerie, and O. Parodi J. Chim. Phys. 66, 1865 (1969)

    CAS  Google Scholar 

  123. G. Ågren, J. Chim. Phys. 69, 329 (1972)

    Google Scholar 

  124. M. Doi, Polymer J. 5, 288 (1973)

    Google Scholar 

  125. R. Kimmich and W. Doster, J. Polymer Sci. 14, 1671 (1976)

    CAS  Google Scholar 

  126. T.M. Birshtein, V.N. Gridnev, Yu.Ya. Gotlib, and A.M. Skvortsov, Vysokomol. soyed. A 19, 1398 (1977)

    CAS  Google Scholar 

  127. A. Baumgärtner and K. Binder (in press).

    Google Scholar 

Download references

Authors
  1. W. Bruns
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bruns, W. (1981). Polymer Configuration. In: Monte Carlo Applications in Polymer Science. Lecture Notes in Chemistry, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93195-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-93195-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11165-8

  • Online ISBN: 978-3-642-93195-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation