Skip to main content

Polymers

  • Chapter
Book cover Fractals in Science
  • 270 Accesses

Abstract

Even people living in a remote part of the jungle have probably heard about nylon, polystyrene, or plexiglas. If they have not, they may be forgiven; they are good (and wise) savages. Macromolecules or polymers are essential products in everyday life and tend to become more and more so, because they are essentially synthetic materials that substitute for natural materials that are becoming scarce and expensive. Plastics is the best-known name to designate them, but they are much more than that: rubbers, paints, adhesives, fibers, and glasses are made of polymers, and probably very soon batteries, will be too. They have in common the fact that they are huge macromolecules, made of millions of atoms. They are usually the repetition of a unit called a monomer. But they may also be made of two different monomers A and B in either regular or random succession. They are then called copolymers. They may be neutral or electrically charged. In the latter case they are named polyelectrolytes. All biological molecules are copolymers of this type. They may be linear or branched. In the latter case, they may eventually form a solid, a gel. Finally, they may be either amorphous or crystalline. In the former case, their structure is random, whereas in the latter, they form a regular structure which is never completely ordered: an amorphous fraction is most usually present between organized regions.

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

Access this chapter

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. B.B. Mandelbrot: The Fractal Geometry of Nature (Freeman, San Francisco 1977)

    Google Scholar 

  2. P.G. de Gennes: Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca 1979)

    Google Scholar 

  3. J. des Cloizeaux, G. Jannink: Polymers in Solution (Clarendon Press, Oxford 1987)

    Google Scholar 

  4. P.J. Flory: Principles of Polymer Chemistry (Cornell University Press, Ithaca 1953)

    Google Scholar 

  5. M. Gordon, S.B. Ross-Murphy: Pure Appl. Chem. 43, 1 (1975)

    Google Scholar 

  6. D. Stauffer: Phys. Rep. 54, 1 (1979)

    ADS  Google Scholar 

  7. D. Stauffer Introduction to Percolation Theory (Taylor and Francis, London 1985)

    MATH  Google Scholar 

  8. A. Bunde, S. Havlin, eds.: Fractals and Disordered Systems (Springer, Berlin 1991 )

    MATH  Google Scholar 

  9. J. Teixeira, in: On Growth and Form , ed. by H.E. Stanley, N. Ostrowski (Martinus, Nijhoff 1985)

    Google Scholar 

  10. P. Cotton, D. Decker, H. Benoit, B. Farnoux, J. Higgins, G. Jannink, R. Ober, C. Picot, J. des Cloizeaux: Macromolecules 7, 863 (1974)

    ADS  Google Scholar 

  11. S.F. Edwards: Proc. Phys. Soc. 65, 613 (1965)

    ADS  Google Scholar 

  12. P.G. de Gennes: Phys. Lett. 38A, 339 (1972)

    ADS  Google Scholar 

  13. M.J. Stephen: Phys Lett. 53A, 363 (1975)

    ADS  Google Scholar 

  14. M. Daoud, G. Jannink: J. Physique Lett. 37, 973 (1976)

    Google Scholar 

  15. M. Moore: J. Phys. A 10, 305 (1977)

    ADS  Google Scholar 

  16. I.M. Lifshitz, A. Grosberg, A. Khakholov: Rev. Mod. Phys. 50, 685 (1978)

    ADS  Google Scholar 

  17. M. Nierlich, J.P. Cotton, B. Farnoux: J. Chem. Phys. 69, 1379 (1978)

    ADS  Google Scholar 

  18. C. Williams, F. Brochard, H.L. Frisch: Ann. Rev. Phys. Chem. 32, 433 (1981)

    ADS  Google Scholar 

  19. B. Duplantier: Phys. Rev. Lett, 59, 539 (1987)

    ADS  Google Scholar 

  20. B. Derrida: J. Phys. A 14, L5 (1981)

    ADS  MathSciNet  Google Scholar 

  21. H.J. Hilhorst: Phys. Rev. B 16, 1253 (1977)

    ADS  MathSciNet  Google Scholar 

  22. S.F. Edwards: Proc. Phys. Soc. 88, 265 (1966)

    ADS  Google Scholar 

  23. M. Daoud, J.P. Cotton, B. Farnoux, G. Jannink, G. Sarma, H. Benoit, R. Duplessix, C. Picot, P.G. de Gennes: Macromolecules, 8, 804 (1975)

    ADS  Google Scholar 

  24. J. des Cloizeaux: J. Physique, 36, 281 (1975)

    Google Scholar 

  25. I. Noda, N. Kato, T. Kitano, M. Nagasawa: Macromolecules 14, 668 (1981)

    ADS  Google Scholar 

  26. M. Doi, S.F. Edwards: The Theory of Polymer Dynamics (Oxford Science, London 1986)

    Google Scholar 

  27. J.F. Joanny, S.J. Candau, in: Comprehensive Polymer Science ,ed by G. Allen (Pergamon, New York 1989)

    Google Scholar 

  28. T.P. Lodge, N.A. Rotstein, S. Prager: Adv. Chem. Phys. 79, 1 (1990)

    Google Scholar 

  29. W.W. Graessley: Adv. Pol. Sci. 47, 68 (1982)

    Google Scholar 

  30. G.H. Weiss, J.T. Bendler, M.F. Slesinger: Macromolecules 21, 317 (1988)

    Google Scholar 

  31. J.T. Bender, M. Dishon, H. Kesten, G.H. Weiss: J. Stat. Phys. 50, 1069 (1988)

    ADS  Google Scholar 

  32. L. Leger, H. Hervet, F. Rondelez: Macromolecules 14, 1732 (1982)

    ADS  Google Scholar 

  33. A. Baumgartner, K. Binder: J. Chem. Phys. 75, 2994 (1981)

    ADS  Google Scholar 

  34. K. Kremer, G.S. Grest: J. Chem. Phys. 92, 5057 (1990)

    ADS  Google Scholar 

  35. A. Kolinski, J. Skolnick, R. Yaris: J. Chem. Phys. 86, 7174 (1987)

    ADS  Google Scholar 

  36. D. Richter, K. Binder, B. Ewen, B. Stuhn: J. Phys. Chem. 88, 6618 (1984)

    Google Scholar 

  37. J.S. Higgins, J.E. Roots: J. Chem. Soc. Faraday Trans. II 81, 755 (1985)

    Google Scholar 

  38. R.H. Ottewill,. C.H. Rochester, A.L. Smith, eds.: Adsorption from Solutions (Academic, New York 1983)

    Google Scholar 

  39. T.C. Lubensky, M.H. Rubin: Phys. Rev. B 11, 543 (1975)

    Google Scholar 

  40. T.C. Lubensky, M.H. Rubin: Phys. Rev. B 12, 3885 (1975)

    ADS  Google Scholar 

  41. K. Binder, in: Phase Transitions and Critical Phenomena , vol. 8, ed. by C. Domb, J. Lebowitz (Academic, New York 1983)

    Google Scholar 

  42. A.J. Bray, M.A. Moore: J. Phys. A 11, 1927 (1977)

    ADS  MathSciNet  Google Scholar 

  43. E. Eisenriegler, K. Binder, K. Kremer: J. Chem. Phys. 77, 6296 (1982)

    ADS  Google Scholar 

  44. P.G. de Gennes: J. Physique 37, 1445 (1976)

    Google Scholar 

  45. E. Bouchaud, M. Daoud: J. Physique 48, 1991 (1987)

    Google Scholar 

  46. P.G. de Gennes: Macromolecules 13, 1069 (1980)

    ADS  Google Scholar 

  47. P.G. de Gennes, P. Pincus: J. Physique Lett. 44, 241 (1983)

    Google Scholar 

  48. P.G. de Gennes: Comptes Rendus Ac. Sci. (Paris) II, 294, 1317 (1982)

    Google Scholar 

  49. E. Bouchaud, M. Daoud: J. Phys. A 20, 1463 (1987)

    ADS  Google Scholar 

  50. M.F. Shlesinger: Ann. Rev. Phys. Chem. 39, 269 (1988)

    ADS  Google Scholar 

  51. M.F. Klafter, in: On Growth and Form: Fractal and Non-Fractal Patterns in Physics ,ed. by H.E. Stanley and N. Ostrowsky (Nijhoff, Dordrecht 1985)

    Google Scholar 

  52. F. Shlesinger, G.M. Zaslavshy, J. Klafter: Nature 363, 31 (1993)

    ADS  Google Scholar 

  53. M. Kawaguchi, M. Mikura, A. Takahashi: Macromolecules 17, 2063 (1984)

    ADS  Google Scholar 

  54. R. Varoqui, P. Dejardin: J. Chem. Phys. 66, 4395 (1977)

    ADS  Google Scholar 

  55. E. Pefferkorn, A. Carroy, R. Varoqui: J. Pol. Sci. Pol. Phys. Ed. 23, 1997 (1985)

    Google Scholar 

  56. L. Auvray, J.P. Cotton: Macromolecules, 20, 202 (1986)

    ADS  Google Scholar 

  57. X. Sun, B. Farnoux, E. Bouchaud, A. Lapp, M. Daoud, G. Jannink: Europhys. Lett. 6, 207 (1988)

    ADS  Google Scholar 

  58. T. Cosgrove, T.G. Heath, K. Ryan, T.L. Crowley: Macromolecules 20, 2879 (1987)

    ADS  Google Scholar 

  59. D. Hone, H. Ji, P. Pincus: Macromolecules 20, 2543 (1987)

    ADS  Google Scholar 

  60. F. Brochard: J. Physique 46, 2117 (1985)

    Google Scholar 

  61. D. Stauffer: J. Chem. Soc. Faraday Trans. II 72, 1354 (1976)

    Google Scholar 

  62. H. Nakanishi, H.E. Stanley: Phys. Rev. B 22, 2466 (1980)

    ADS  MathSciNet  Google Scholar 

  63. P.J. Reynolds, W. Klein, H.E. Stanley: J. Phys. C 10, L167 (1977)

    ADS  Google Scholar 

  64. P.J. Reynolds, H.E. Stanley, W. Klein: Phys. Rev. B 21, 1223 (1980)

    ADS  Google Scholar 

  65. T.C. Lubensky, J. Isaacson: Phys. Rev. Lett. 41, 829 (1978)

    ADS  Google Scholar 

  66. T.C. Lubensky, J. Isaacson: Phys. Rev. A 20, 2130 (1979)

    ADS  Google Scholar 

  67. B. Derrida, J. Vannimenus: J. Physique Lett. 41, 473 (1980)

    MathSciNet  Google Scholar 

  68. G. Parisi, N. Sourlas: Phys. Rev. Lett. 46, 891 (1981)

    ADS  MathSciNet  Google Scholar 

  69. B. Derrida, L. de Seze: J. de Phys. 43, 475 (1982)

    Google Scholar 

  70. F. Family: J. Phys. A 16, L97 (1983)

    ADS  MathSciNet  Google Scholar 

  71. B. Derrida, D. Stauffer, H.J. Herrmann, J. Vannimenus: J. de Phys. Lett. 44, 701 (1983)

    Google Scholar 

  72. H.J. Herrmann, B. Derrida, J. Vannimenus: Phys. Rev. B 30, 4080 (1984)

    ADS  Google Scholar 

  73. J. Isaacson, T.C. Lubensky: J. Phys. 42, 175 (1981)

    MathSciNet  Google Scholar 

  74. M.E. Cates: J. de Phys. Lett. 38, 2957 (1985)

    MathSciNet  Google Scholar 

  75. M. Daoud, J.E. Martin, in: The Fractal Approach to Heterogeneous Chemistry ed. by D. Avnir (Wiley, New York 1990)

    Google Scholar 

  76. P.G. de Gennes: J. Pol. Sci. Pol., Symp. 61, 313 (1977)

    Google Scholar 

  77. B.H. Zimm, W.H. Stockmayer: J. Chem. Phys. 17, 1301 (1949)

    ADS  Google Scholar 

  78. E.V. Patton, J.A. Wesson, M. Rubinstein, J.C. Wilson, L.E. Oppenheimer: Macromolecules 22, 1946 (1989)

    ADS  Google Scholar 

  79. M. Daoud, J.F. Joanny: J. de Phys. 42, 1359 (1981)

    Google Scholar 

  80. M. Daoud, F. Family, G. Jannink: J. de Phys. Lett. 45, 119 (1984)

    Google Scholar 

  81. S.J. Candau, M. Ankrim, J.P. Munch, P. Rempp, G. Hild, R. Osaka, in: Physical Optics of Dynamical Phenomena in Macromolecular Systems (W. De Gruyter, Berlin 1985), p. 145

    Google Scholar 

  82. F. Schosseler, L. Leibler: J. Phys. Lett. 45, 501 (1984)

    Google Scholar 

  83. F. Schosseler, L. Leibler: Macromolecules 18, 398 (1985)

    ADS  Google Scholar 

  84. J.E. Martin, B.J. Ackerson, Phys. Rev. A 31, 1180 (1985)

    ADS  Google Scholar 

  85. E. Bouchaud, M. Delsanti, M. Adam, M. Daoud, D. Durand: J. Physique Lett. 47, 1273 (1986)

    Google Scholar 

  86. M. Daoud, L. Leibler: Macromolecules, 41, 1497 (1988)

    ADS  Google Scholar 

  87. P.G. de Gennes: J. de Phys. Lett. 38, 355 (1977)

    ADS  Google Scholar 

  88. M. Daoud: J. de Phys. Lett. 40, 201 (1979)

    Google Scholar 

  89. C. Allain, L. Salome: Macromolecules, 20, 2957 (1987)

    ADS  Google Scholar 

  90. L. Salome: Ph.D. Thesis, Universite Paris 11 (1987)

    Google Scholar 

  91. M. Daoud, A. Johner: J. Physique 50, 2147 (1989)

    Google Scholar 

  92. S.J. Candau, J. Bastide, M. Delsanti: Adv. Pol. Sci. 44, 27 (1982)

    Google Scholar 

  93. R.W. Richards, N.S. Davidson: Macromolecules, 19, 1381 (1986)

    ADS  Google Scholar 

  94. J.P. Cohen Addad, C. Scmit: J. Pol. Sci., Pol. Lett. 25, 487 (1987)

    Google Scholar 

  95. S. Mallam, F. Horkay, A.M. Hecht, E. Geissler: Macromolecules, 22, 3356 (1989)

    ADS  Google Scholar 

  96. J.P. Munch, M. Delsanti, D. Durand: Europhys. Lett. 18, 557 (1992)

    ADS  Google Scholar 

  97. J. des Cloizeaux, G. Jannink: Physica, 102 A, 120 (1980)

    ADS  Google Scholar 

  98. P.G. de Gennes: J. Physique Lett. 37, 1 (1976)

    Google Scholar 

  99. P.G. de Gennes: J. Physique Lett. 40, 197 (1979)

    ADS  Google Scholar 

  100. M.J. Stephen: Phys. Rev. B 17, 4444 (1978)

    ADS  Google Scholar 

  101. A. Coniglio, H.E. Stanley: Phys. Rev. Lett. 52, 1068 (1984)

    ADS  Google Scholar 

  102. J. Kertesz: J. Phys. A 16, L471 (1983)

    ADS  Google Scholar 

  103. A.L. Efros, B.I. Shklovskii: Physica Status Solidi, B 76 475 (1976)

    ADS  Google Scholar 

  104. D.C. Hong, H.E. Stanley, A. Coniglio, A. Bunde: Phys. Rev. B 33, 4564 (1984)

    ADS  Google Scholar 

  105. J.M. Laugier, J.P. Clerc, G. Giraud, J.M. Luck: J. Phys. A 19, 3153 (1986)

    ADS  Google Scholar 

  106. M. Daoud, D.C. Hong, F. Family: J. Phys, A 21, L917 (1988)

    ADS  Google Scholar 

  107. D. Durand, M. Delsanti, M. Adam, J.M. Luck: Europhys. Lett. 3, 297 (1987)

    ADS  Google Scholar 

  108. M. Rubinstein, R.H. Colby, J.R. Gillmor: Pol. Preprint, 30, 1 (1989)

    Google Scholar 

  109. J.E. Martin, D. Adolf, J.P. Wilcoxon: Phys. Rev. Lett. 61, 2620 (1988)

    ADS  Google Scholar 

  110. M. Axelos, M. Kolb: Phys. Rev. Lett. 64, 1457 (1990)

    ADS  Google Scholar 

  111. F. Devreux, J.P. Boilot, F. Chaput, L. Malier, M.A.V. Axelos, to be published.

    Google Scholar 

  112. J.D. Ferry: Viscoelastic Properties of Polymers (Wiley, New York 1980)

    Google Scholar 

  113. M. Daoud: J. Phys. A 21, L973 (1988)

    ADS  Google Scholar 

  114. J.E. Martin, J. Wilcoxon, D. Adolf: Phys. Rev. A 36, 3415 (1987)

    ADS  Google Scholar 

  115. M. Daoud, A. Coniglio: J. Phys. A 14, L301 (1981)

    ADS  Google Scholar 

  116. W.H. Stockmayer, in: Molecular Fluids ,ed. by R. Balian and G. Weill (Gordon and Breach, New York 1977)

    Google Scholar 

  117. J. Kertesz: J. Phys. A 16, L471 (1983)

    ADS  Google Scholar 

  118. A. Coniglio, H.E. Stanley: Phys. Rev. Lett. 52, 1068 (1984)

    ADS  Google Scholar 

  119. A. Coniglio, F. Family: J. Physique Lett. 46, 9 (1985)

    ADS  Google Scholar 

  120. S. Roux: C.R. Ac. Sci. (Paris) 301, 367 (1985)

    MathSciNet  Google Scholar 

  121. J.E. Martin, J. Wilcoxon, J. Odine: Phys Rev. A 43, 858 (1991)

    ADS  Google Scholar 

  122. see also J. E. Martin, in: Time Dependent Effects in Disordered Systems ,ed. by R. Pynn and T. Riste (Plenum, New York 1987), p. 425

    Google Scholar 

  123. M. Rubinstein, R. Colby, J.R. Gillmor: Space-Time Organization in Complex Fluids ,ed. by F. Tanaka, M. Doi, T. Ohta, (Springer Series in Chemical Physics 51, 1989)

    Google Scholar 

  124. W.F. Shi, W.B. Wang, CM. Sorensen: unpublished

    Google Scholar 

  125. M. Adam, M. Delsanti: Contemporary Physics 3, 203 (1989)

    ADS  Google Scholar 

  126. S. Alexander, in: The Physics of Finely Divided Matter ,ed. by M. Daoud and N. Boccara (Springer Verlag, Berlin 1985)

    Google Scholar 

  127. D.J. Bergman, Y. Kantor: Phys. Rev. Lett. 53, 511 (1984)

    ADS  MathSciNet  Google Scholar 

  128. Y. Kantor, I. Webman: Phys. Rev. Lett. 52, 1891 (1984)

    ADS  Google Scholar 

  129. S. Feng, P. Sen: Phys. Rev. Lett. 52, 216 (1984)

    ADS  Google Scholar 

  130. S. Alexander: J. Physique 45, 1939 (1984)

    Google Scholar 

  131. S. Arbabi, M. Sahimi: Phys. Rev. Lett. 65, 725 (1990)

    ADS  Google Scholar 

  132. S. Alexander, R. Orbach: J. de Phys. Lett. 43, 625 (1982)

    Google Scholar 

  133. R. Rammal, G. Toulouse: J. de Phys. Lett. 44, 13 (1983)

    Google Scholar 

  134. E. Courtens, J. Pelous, J. Phalippou, R. Vacher, T. Woignier: Phys. Rev. Lett. 58, 128 (1987)

    ADS  Google Scholar 

  135. S. Havlin, D. Ben Avraham: Adv. in Phys. 36, 695 (1987)

    ADS  Google Scholar 

  136. H.E. Roman, M. Schwartz, A. Bunde, S. Havlin: Europhys. Lett. 7, 389 (1988)

    ADS  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Daoud, M. (1994). Polymers. In: Bunde, A., Havlin, S. (eds) Fractals in Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77953-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-77953-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77955-8

  • Online ISBN: 978-3-642-77953-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics