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Polymer Science Series C

, Volume 55, Issue 1, pp 4–22 | Cite as

Computer simulation of stiff-chain polymers

  • V. A. Ivanov
  • J. A. Martemyanova
  • A. S. Rodionova
  • M. R. Stukan
Article

Abstract

A review of studies on the computer simulation of the phase behavior of various stiff-chain polymer systems is presented. Methods for calculating phase diagrams of a polymer solution in a computer experiment are discussed, including the methods of extended ensembles, entropic simulation, and the Wang-Landau algorithm to obtain the density-of-states function. The authors’ original results on studying the intramolecular orientational and spatial ordering of monomer units in a single stiff-chain macromolecule in the bulk and near a planar adsorbing surface by means of the Wang-Landau algorithm and using the bond-fluctuation lattice model are presented. Corresponding state diagrams are presented for these two cases. For systems of multiple chains, the phenomenon of nematic liquid-crystalline ordering in semi-dilute solutions in the bulk and in a planar layer is considered, and the phase diagrams for these cases are presented. A survey of the published data on some other promising directions of investigation of stiff-chain polymer systems is presented.

Keywords

Monte Carlo Polymer Science Series Monomer Unit Order Phase Transition Nematic Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1992).Google Scholar
  2. 2.
    S. Chandrasekhar, Liquid Crystals (Cambridge Univ. Press, Cambridge, 1992).CrossRefGoogle Scholar
  3. 3.
    S. P. Papkov and V. G. Kulichikhin, Liquid Crystalline State of Polymers (Khimiya, Moscow, 1977) [in Russian].Google Scholar
  4. 4.
    Liquid Crystallinity in Polymers: Principles and Fundamental Properties, Ed. by A. Ciferri (VCH, New York, 1991).Google Scholar
  5. 5.
    V. P. Shibaev and L. Lam, Liquid Crystalline and Mesomorphic Polymers (Springer, New York, 1994).CrossRefGoogle Scholar
  6. 6.
    A. Donald, A. Windle, and S. Hanna, Liquid Crystalline Polymers (Cambridge Univ. Press, Cambridge, 2006).CrossRefGoogle Scholar
  7. 7.
    X.-J. Wang and Q. Zhou, Liquid Crystalline Polymers (World Scientific, Singapore, 2004).Google Scholar
  8. 8.
    M. Warner and E. Terentjev, Liquid Crystal Elastomers (Oxford Univ. Press, Oxford, 2007).Google Scholar
  9. 9.
    A. Abe, H. Furuya, Zh. Zhou, T. Hiejima, and Y. Kobayashi, Adv. Polym. Sci. 181, 121 (2005).CrossRefGoogle Scholar
  10. 10.
    G.-Z. Yang, X.-L. Chen, L.-M. Wang, J.-G. Shi, C.-Z. Li, and T. Liu, Polym. Adv. Technol. 20, 104 (2009).CrossRefGoogle Scholar
  11. 11.
    J. Guo, H. Cao, J. Wei, D. Zhang, F. Liu, G. Pan, D. Zhao, W. He, and H. Yang, Appl. Phys. Lett. 93, 201901 (2008).CrossRefGoogle Scholar
  12. 12.
    M. Mucha, Prog. Polym. Sci. 28, 837 (2003).CrossRefGoogle Scholar
  13. 13.
    M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).Google Scholar
  14. 14.
    D. Frenkel and B. Smit, Understanding Molecular Simulation. From Algorithms to Applications (Academic, San Diego, 2002).Google Scholar
  15. 15.
    Simulation Methods for Polymers, Ed. by M. Kotelyanskii and D. N. Theodorou, (Marcel Dekker, New York, 2004).Google Scholar
  16. 16.
    Computer Simulations in Condensed Matter: From Materials to Chemical Biology, Ed. by M. Ferrario, G. Ciccotti, and K. Binder (Springer, Heidelberg, 2006).Google Scholar
  17. 17.
    Methods of Computer Simulation for Polymers and Biopolymers, Ed. by V. A. Ivanov, A. L. Rabinovich, and A. R. Khokhlov (Knizhnyi Dom “Librokom”, Moscow, 2009) [in Russian].Google Scholar
  18. 18.
    J. Baschnagel, K. Binder, P. Doruker, A. A. Gusev, O. Hahn, K. Kremer, W. L. Mattice, F. Mueller-Plathe, M. Murat, W. Paul, S. Santos, U. W. Suter, and V. Tries, Adv. Polym. Sci. 152, 41 (2000).CrossRefGoogle Scholar
  19. 19.
    S. C. Glotzer and W. Paul, Annu. Rev. Mater. Res. 32, 401 (2002).CrossRefGoogle Scholar
  20. 20.
    Q. H. Zeng, A. B. Yu, and G. Q. Lu, Prog. Polym. Sci. 33, 191 (2008).CrossRefGoogle Scholar
  21. 21.
    I. Carmesin and K. Kremer, Macromolecules 21, 2819 (1988); J. Phys. 51, 915 (1990).CrossRefGoogle Scholar
  22. 22.
    H. P. Deutsch and K. Binder, J. Chem. Phys. 94, 2294 (1991).CrossRefGoogle Scholar
  23. 23.
    W. Paul, K. Binder, D. W. Heermann, and K. Kremer, J. Chem. Phys. 95, 7726 (1991).CrossRefGoogle Scholar
  24. 24.
    H.-P. Hsu, W. Paul, and K. Binder, Macromolecules 43, 3094 (2010).CrossRefGoogle Scholar
  25. 25.
    H.-P. Hsu, W. Paul, and K. Binder, Europhys. Lett. 95, 68004 (2011).CrossRefGoogle Scholar
  26. 26.
    F. T. Wall and F. Mandel, J. Chem. Phys. 63, 4592 (1975).CrossRefGoogle Scholar
  27. 27.
    N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).CrossRefGoogle Scholar
  28. 28.
    A. Yu. Grosberg and A. R. Khokhlov, Statistical Physics of Macromolecules (Nauka, Moscow, 1989; AIP, Ithaca, 1994).Google Scholar
  29. 29.
    Y. Iba, Int. J. Mod. Phys. C 12, 623 (2001).CrossRefGoogle Scholar
  30. 30.
    A. P. Lyubartsev, A. A. Martsinovskii, S. V. Shevkunov, and P. N. Vorontsov-Velyaminov, J. Chem. Phys. 96, 1776 (1992).CrossRefGoogle Scholar
  31. 31.
    E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).CrossRefGoogle Scholar
  32. 32.
    B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).CrossRefGoogle Scholar
  33. 33.
    V. A. Ivanov, W. Paul, and K. Binder, J. Chem. Phys. 109, 5659 (1998).CrossRefGoogle Scholar
  34. 34.
    W. Paul and M. Müller, J. Chem. Phys. 115, 630 (2001).CrossRefGoogle Scholar
  35. 35.
    J. A. Martemyanova, M. R. Stukan, V. A. Ivanov, M. Müller, W. Paul, and K. Binder, J. Chem. Phys. 122, 174907 (2005).CrossRefGoogle Scholar
  36. 36.
    F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001); F. Wang and D. P. Landau, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 64, 056101 (2001).CrossRefGoogle Scholar
  37. 37.
    T. Wüst and D. P. Landau, Phys. Rev. Lett. 102, 178101 (2009); D. T. Seaton, T. Wüst, and D. P. Landau, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 81, 011802 (2010).CrossRefGoogle Scholar
  38. 38.
    C. Junghans, M. Bachmann, and W. Janke, Phys. Rev. Lett. 97, 218103 (2006).CrossRefGoogle Scholar
  39. 39.
    S. Schnabel, D. T. Seaton, D. P. Landau, and M. Bachmann, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 84, 011127 (2011).CrossRefGoogle Scholar
  40. 40.
    M. P. Taylor, W. Paul, and K. Binder, J. Chem. Phys. 131, 114907 (2009); M. P. Taylor, W. Paul, and K. Binder, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 79, 050801 (2009).CrossRefGoogle Scholar
  41. 41.
    J. Luettmer-Strathmann, F. Rampf, W. Paul, and K. Binder, J. Chem. Phys. 128, 064903 (2008).CrossRefGoogle Scholar
  42. 42.
    J. I. Siepmann and D. Frenkel, Mol. Phys. 75, 59 (1992).CrossRefGoogle Scholar
  43. 43.
    D. Frenkel, G. C. A. M. Mooij, and B. Smit, J. Phys.: Condens. Matter 4, 3053 (1992).CrossRefGoogle Scholar
  44. 44.
    J. J. De Pablo, M. Laso, and U. W. Suter, J. Chem. Phys. 96, 2395 (1992).CrossRefGoogle Scholar
  45. 45.
    L. R. Dodd, T. D. Boone, and D. N. Theodorou, Mol. Phys. 78, 961 (1993).CrossRefGoogle Scholar
  46. 46.
    E. Leontidis, J. J. De Pablo, M. Laso, and U. W. Suter, Adv. Polym. Sci. 116, 283 (1994).CrossRefGoogle Scholar
  47. 47.
    B. Smit, Mol. Phys. 85, 153 (1995).CrossRefGoogle Scholar
  48. 48.
    N. Wilding, M. Müller, and K. Binder, J. Chem. Phys. 105, 802 (1996).CrossRefGoogle Scholar
  49. 49.
    M. N. Rosenbluth and A. W. Rosenbluth, J. Chem. Phys. 23, 356 (1955).CrossRefGoogle Scholar
  50. 50.
    V. A. Ivanov and J. A. Martemyanova, Macromol. Symp. 252, 12 (2007).CrossRefGoogle Scholar
  51. 51.
    V. A. Ivanov, J. A. Martemyanova, M. Muller, W. Paul, and K. Binder, J. Phys. Chem. B 113, 3653 (2009).CrossRefGoogle Scholar
  52. 52.
    I. M. Lifshits, A. Yu. Grosberg, and A. R. Khokhlov, Usp. Fiz. Nauk 7, 353 (1979).CrossRefGoogle Scholar
  53. 53.
    A. Yu. Grosberg and D. V. Kuznetsov, Macromolecules 25, 1996–2003 (1996).CrossRefGoogle Scholar
  54. 54.
    A. Yu. Grosberg and A. R. Khokhlov, Adv. Polym. Sci. 41, 53 (1981).CrossRefGoogle Scholar
  55. 55.
    A. Yu. Grosberg and A. V. Zhestkov, J. Biomol. Struct. Dyn. 3, 859 (1986).CrossRefGoogle Scholar
  56. 56.
    K. Yoshikawa, M. Takahashi, V. V. Vasilevskaya, and A. R. Khokhlov, Phys. Rev. Lett. 76, 3029 (1996).CrossRefGoogle Scholar
  57. 57.
    V. V. Vasilevskaya, A. R. Khokhlov, S. Kidoaki, and K. Yoshikawa, Biopolymers 41, 51 (1997).CrossRefGoogle Scholar
  58. 58.
    J. Ubbink and T. Odijk, Biophys. J. 68, 54 (1995).CrossRefGoogle Scholar
  59. 59.
    Yu. A. Kuznetsov, E. G. Timoshenko, and K. A. Dawson, J. Chem. Phys. 105, 7116 (1996).CrossRefGoogle Scholar
  60. 60.
    A. M. El’yashevich and A. M. Skvortsov, Mol. Biol. 5, 204 (1971).Google Scholar
  61. 61.
    T. M. Birshtein, A. M. Skvortsov, and A. A. Sariban, Vysokomol. Soedin., Ser. A 17, 1962 (1975); 18, 1978 (1976); A. M. Skvortsov, T. M. Birshtein, and A. A. Sariban, Vysokomol. Soedin., Ser. A 18, 2734 (1976).Google Scholar
  62. 62.
    T. M. Birshtein, A. M. Skvortsov, and A. A. Sariban, Macromolecules 10, 202 (1977).CrossRefGoogle Scholar
  63. 63.
    P. G. Khalatur, Vysokomol. Soedin., Ser. A 22, 2226 (1980).Google Scholar
  64. 64.
    H. Noguchi and K. Yoshikawa, J. Chem. Phys. 109, 5070 (1998).CrossRefGoogle Scholar
  65. 65.
    I. R. Cooke and D. R. M. Williams, Phys. A 339, 45 (2004).CrossRefGoogle Scholar
  66. 66.
    T. Sakaue and K. Yoshikawa, J. Chem. Phys. 117, 6323 (2002).CrossRefGoogle Scholar
  67. 67.
    Y. Zhou, M. Karplus, J. M. Wichert, and C. K. Hall, J. Chem. Phys. 107, 10691 (1997).CrossRefGoogle Scholar
  68. 68.
    F. Rampf, W. Paul, and K. Binder, Eur. Lett. 70, 628 (2005); F. Rampf, K. Binder, and W. Paul, J. Polym. Sci., Part B: Polym. Phys. 44, 2542 (2006).CrossRefGoogle Scholar
  69. 69.
    W. Paul, F. Rampf, T. Strauch, and K. Binder, Macromol. Symp. 252, 1 (2007); W. Paul, T. Strauch, F. Rampf, and K. Binder, Phys. Rev. E: 75, 060801(R) (2007).CrossRefGoogle Scholar
  70. 70.
    A. Siretskiy, C. Elvingson, P. Vorontsov-Velyaminov, and M. O. Khan, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 84, 016702 (2011).CrossRefGoogle Scholar
  71. 71.
    A. Bloomfield, Biopolymers 44, 269 (1998).CrossRefGoogle Scholar
  72. 72.
    C. Wu and X. Wang, Phys. Rev. Lett. 80, 4092 (1998).CrossRefGoogle Scholar
  73. 73.
    G. Maurstad and B. T. Stokke, Biopolymers 74, 199 (2004).CrossRefGoogle Scholar
  74. 74.
    S. Danielsen, K. M. Varum, and B. T. Stokke, Biomacromolecules 5, 928 (2004).CrossRefGoogle Scholar
  75. 75.
    V. A. Ivanov, M. R. Stukan, V. V. Vasilevskaya, W. Paul, and K. Binder, Macromol. Theory Simul. 9, 488 (2000).CrossRefGoogle Scholar
  76. 76.
    M. R. Stukan, V. A. Ivanov, A. Yu. Grosberg, W. Paul, and K. Binder, J. Chem. Phys. 118, 3392 (2003).CrossRefGoogle Scholar
  77. 77.
    W. Paul, M. Müller, K. Binder, M. R. Stukan, and V. A. Ivanov, in Computer Simulations of Liquid Crystals and Polymers, Ed. by P. Pasini, C. Zannoni, and S. Zumer (Kluwer Academic, Dordrecht, 2005), Vol. 177, p. 171.Google Scholar
  78. 78.
    M. R. Stukan, E. A. An, V. A. Ivanov, and O. I. Vinogradova, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 73, 051804–1 (2006).CrossRefGoogle Scholar
  79. 79.
    H. Zhou, J. Zhou, Z. C. Ou-Yang, and S. Kumar, Phys. Rev. Lett. 97, 158302 (2006).CrossRefGoogle Scholar
  80. 80.
    T. M. Birshtein, E. B. Zhulina, and A. M. Skvortsov, Biopolymers 19, 805 (1980).CrossRefGoogle Scholar
  81. 81.
    A. Yethiraj, J. Chem. Phys. 100, 4691 (1994).CrossRefGoogle Scholar
  82. 82.
    E. Yu. Kramarenko, R. G. Winkler, P. Reineker, and A. R. Khokhlov, J. Chem. Phys. 104, 4806 (1996).CrossRefGoogle Scholar
  83. 83.
    S. Stepanow, J. Chem. Phys. 115, 1565 (2001).CrossRefGoogle Scholar
  84. 84.
    A. N. Semenov, Eur. Phys. J. E 9, 353 (2002).CrossRefGoogle Scholar
  85. 85.
    W. Hu and D. Frenkel, Adv. Polym. Sci. 191, 1 (2005).CrossRefGoogle Scholar
  86. 86.
    A. Chatterji and R. Rahul Pandit, J. Stat. Phys. 110, 1219 (2003).CrossRefGoogle Scholar
  87. 87.
    V. Barsegov and D. Thirumalai, J. Phys. Chem. B 109, 21979 (2005).CrossRefGoogle Scholar
  88. 88.
    A. R. Khokhlov and A. N. Semenov, J. Stat. Phys. 38, 161 (1985).CrossRefGoogle Scholar
  89. 89.
    A. N. Semenov and A. R. Khokhlov, Usp. Fiz. Nauk 156, 427 (1988).CrossRefGoogle Scholar
  90. 90.
    Z. Y. Chen, Macromolecules 26, 3419 (1993).CrossRefGoogle Scholar
  91. 91.
    K. M. Jaffer, S. B. Opps, D. E. Sullivan, B. G. Nickel, and L. Mederos, J. Chem. Phys. 114, 3314 (2001).CrossRefGoogle Scholar
  92. 92.
    K. Kubo, Mol. Cryst. Liq. Cryst. 74, 1671 (1981).CrossRefGoogle Scholar
  93. 93.
    T. M. Birshtein, A. A. Sariban, and A. M. Skvortsov, Polymer 23, 1481 (1982).CrossRefGoogle Scholar
  94. 94.
    P. G. Khalatur, Y. G. Papulov, and S. G. Pletneva, Mol. Cryst. Liq. Cryst. 130, 195 (1985).CrossRefGoogle Scholar
  95. 95.
    A. S. Pavlov, Y. G. Papulov, and P. G. Khalatur, Zh. Fiz. Khim. 70, 288 (1996).Google Scholar
  96. 96.
    A. Baumgartner, J. Chem. Phys. 84, 1905 (1986).CrossRefGoogle Scholar
  97. 97.
    A. Kolinski, J. Skolnick, and R. Yaris, Macromolecules 19, 2560 (1986).CrossRefGoogle Scholar
  98. 98.
    H. Weber, W. Paul, and K. Binder, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 59, 2168 (1999).CrossRefGoogle Scholar
  99. 99.
    M. R. Wilson and M. P. Allen, Mol. Phys. 80, 277 (1993).CrossRefGoogle Scholar
  100. 100.
    D. Levesque, M. Mazars, and J.-J. Weis, J. Chem. Phys. 103, 3820 (1995).CrossRefGoogle Scholar
  101. 101.
    F. A. Escobedo and J. J. De Pablo, J. Chem. Phys. 106, 9858 (1997).CrossRefGoogle Scholar
  102. 102.
    Y.-J. Sheng, A. Z. Panagiotopoulos, and S. K. Kumar, Macromolecules 29, 4444 (1996).CrossRefGoogle Scholar
  103. 103.
    M. Hamm, G. Goldbeck-Wood, A. V. Zvelindovsky, G. J. A. Sevink, and J. G. E. M. Fraaije, J. Chem. Phys. 116, 3152 (2002).CrossRefGoogle Scholar
  104. 104.
    J. P. K. Doye and D. Frenkel, Phys. Rev. Lett. 81, 2160 (1998).CrossRefGoogle Scholar
  105. 105.
    A. Yethiraj, J. Chem. Phys. 101, 2489 (1994).CrossRefGoogle Scholar
  106. 106.
    P. J. Camp, C. P. Mason, M. P. Allen, A. A. Khare, and D. Kofke, J. Chem. Phys. 105, 2837 (1996).CrossRefGoogle Scholar
  107. 107.
    P. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 666 (1997).CrossRefGoogle Scholar
  108. 108.
    M. Dijkstra and D. Frenkel, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 51, 5891 (1995).CrossRefGoogle Scholar
  109. 109.
    H. Fynewever and A. Yethiraj, J. Chem. Phys. 108, 1636 (1998).CrossRefGoogle Scholar
  110. 110.
    A. Yethiraj and H. Fynewever, Mol. Phys. 93, 693 (1998).Google Scholar
  111. 111.
    A. A. Darinskii, Yu. Ya. Gotlib, A. V. Lyulin, and I. M. Neelov, Vysokomol. Soedin., Ser. A 33, 1211 (1991); A. A. Darinskii, A. V. Lyulin, and I. Neelov, Vysokomol. Soedin., Ser. A 34, 73 (1992).Google Scholar
  112. 112.
    C. McBride and C. Vega, J. Chem. Phys. 117, 10370 (2002); C. Vega, C. McBride, and L. G. MacDowell, Phys. Chem. Chem. Phys. 4, 853 (2002).CrossRefGoogle Scholar
  113. 113.
    V. Padmanabhan, S. K. Kumar, and A. Yethiraj, J. Chem. Phys. 128, 124908 (2008).CrossRefGoogle Scholar
  114. 114.
    C. Junghans, M. Bachmann, and W. Janke, Europhys. Lett. 87, 40002 (2009).CrossRefGoogle Scholar
  115. 115.
    V. A. Ivanov, M. R. Stukan, M. Muller, W. Paul, and K. Binder, J. Chem. Phys. 118, 10333 (2003).CrossRefGoogle Scholar
  116. 116.
    M. R. Stukan, V. A. Ivanov, M. Muller, W. Paul, and K. Binder, Zh. Fiz. Khim. 78, 2204 (2004).Google Scholar
  117. 117.
    M. R. Stukan, V. A. Ivanov, M. Muller, W. Paul, and K. Binder, e-Polymers, No. 062 (2003).Google Scholar
  118. 118.
    M. R. Stukan, V. A. Ivanov, M. Muller, W. Paul, and K. Binder, J. Chem. Phys. 117, 9934 (2002).CrossRefGoogle Scholar
  119. 119.
    R. Dickman and C. K. Hall, J. Chem. Phys. 85, 3023 (1986).CrossRefGoogle Scholar
  120. 120.
    R. Dickman, J. Chem. Phys. 87, 2246 (1987).CrossRefGoogle Scholar
  121. 121.
    V. A. Ivanov, E. A. An, L. A. Spirin, M. R. Stukan, M. Muller, W. Paul, and K. Binder, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 76, 026702 (2007).CrossRefGoogle Scholar
  122. 122.
    C. I. Addison, J.-P. Hansen, and A. A. Louis, Chem. Phys. Chem. 6, 1760 (2005).CrossRefGoogle Scholar
  123. 123.
    R. Van Roij, M. Dijkstra, and R. Evans, Europhys. Lett. 49, 350 (2000).CrossRefGoogle Scholar
  124. 124.
    L. Harnau and S. Dietrich, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 66, 051702 (2002).CrossRefGoogle Scholar
  125. 125.
    R. Evans, J. Phys.: Condens. Matter 2, 8989 (1990).CrossRefGoogle Scholar
  126. 126.
    L. D. Gelb, K. E. Gubbins, R. Radhakrishnan, and M. Sliwinska-Bartkowiak, Rep. Prog. Phys. 62, 1573 (1999).CrossRefGoogle Scholar
  127. 127.
    K. Binder, D. P. Landau, and M. Muller, J. Stat. Phys. 110, 1411 (2003).CrossRefGoogle Scholar
  128. 128.
    R. Lipowsky, Phys. Rev. Lett. 49, 1575 (1982); R. Lipowsky, Z. Phys. B 51, 165 (1983); R. Lipowsky, J. Appl. Phys. 55, 2485 (1984).CrossRefGoogle Scholar
  129. 129.
    W. Schweika, K. Binder, and D. P. Landau, Phys. Rev. Lett. 65, 3321 (1990); W. Schweika, K. Binder, and D. P. Landau, Phys. Rev. B: Condens. Matter 53, 8937 (1996).CrossRefGoogle Scholar
  130. 130.
    J.-S. Wang and K. Binder, J. Chem. Phys. 94, 8537 (1991).CrossRefGoogle Scholar
  131. 131.
    A. Werner, F. Schmid, M. Mueller, and K. Binder, J. Chem. Phys. 107, 8175 (1997); A. Werner, M. Mueller, F. Schmid, and K. Binder, J. Chem. Phys. 110, 1221 (1999); A. Werner, F. Schmid, M. Mueller, and K. Binder, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 59, 728 (1999).CrossRefGoogle Scholar
  132. 132.
    A. Yethiraj, Adv. Chem. Phys. 121, 89 (2002).CrossRefGoogle Scholar
  133. 133.
    F. Schmid, G. Germano, S. Wolfsheimer, and T. Schilling, Macromol. Symp. 252, 110 (2007).CrossRefGoogle Scholar
  134. 134.
    A. J. McDonald, M. P. Allen, and F. Schmid, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 63, 010701 (2001).CrossRefGoogle Scholar
  135. 135.
    N. Akino, F. Schmid, and M. P. Allen, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 63, 041706 (2001).CrossRefGoogle Scholar
  136. 136.
    R. L. C. Vink, S. Wolfsheimer, and T. Schilling, J. Chem. Phys. 123, 074901 (2005); R. L. C. Vink and T. Schilling, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 71, 051716 (2005).CrossRefGoogle Scholar
  137. 137.
    S. Wolfsheimer, C. Tanase, K. Shundyak, R. Van Roij, and T. Schilling, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 73, 061703 (2006).CrossRefGoogle Scholar
  138. 138.
    M. P. Allen, J. Chem. Phys. 112, 5447 (2000).CrossRefGoogle Scholar
  139. 139.
    M. S. Al-Barwani and M. P. Allen, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 62, 6706 (2000).CrossRefGoogle Scholar
  140. 140.
    Yu. Trukhina and T. Schilling, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 77, 011701 (2008).CrossRefGoogle Scholar
  141. 141.
    R. Vink, Phys. Rev. Lett. 98, 217801 (2007).CrossRefGoogle Scholar
  142. 142.
    G. Morrison and D. Thirumalai, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 79, 011924 (2009).CrossRefGoogle Scholar
  143. 143.
    D. Micheletti, L. Muccioli, R. Berardi, M. Ricci, and C. Zannoni, J. Chem. Phys. 123, 224705 (2005).CrossRefGoogle Scholar
  144. 144.
    J. M. Kosterlitz and D. J. Thouless, J. Phys. C: Solid State Phys. 6, 1181 (1973).CrossRefGoogle Scholar
  145. 145.
    D. Frenkel and R. Eppenga, Phys. Rev. A 31, 1776 (1985).CrossRefGoogle Scholar
  146. 146.
    P. J. Flory, Proc. Natl. Acad. Sci. U. S. A. 79, 4510 (1982).CrossRefGoogle Scholar
  147. 147.
    A. Baumgartner and D. Y. Yoon, J. Chem. Phys. 79, 521 (1984); A. Baumgartner, J. Phys. A: Math. Gen. 17, L971 (1984).CrossRefGoogle Scholar
  148. 148.
    A. L. Rodriguez, H.-P. Wittmann, and K. Binder, Macromolecules 23, 4327 (1990).CrossRefGoogle Scholar
  149. 149.
    Z. Y. Chen, Phys. Rev. Lett. 71, 93 (1993).CrossRefGoogle Scholar
  150. 150.
    A. M. Gupta and S. F. Edwards, J. Chem. Phys. 98, 1588 (1993).CrossRefGoogle Scholar
  151. 151.
    M. Dijkstra and D. Frenkel, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 50, 349 (1994).CrossRefGoogle Scholar
  152. 152.
    T. Fischer and R. L. C. Vink, Eur. Phys. Lett. 85, 56003 (2009).CrossRefGoogle Scholar
  153. 153.
    R. L. C. Vink, Eur. Phys. J. B 72, 225 (2009).CrossRefGoogle Scholar
  154. 154.
    H. H. Wensink and R. L. C. Vink, J. Phys.: Condens. Matter 19, 466109 (2007).CrossRefGoogle Scholar
  155. 155.
    M. A. Bates and D. Frenkel, J. Chem. Phys. 112, 10034 (2000).CrossRefGoogle Scholar
  156. 156.
    V. A. Ivanov, A. S. Rodionova, E. A. An, J. A. Martemyanova, M. R. Stukan, M. Müller, W. Paul, and K. Binder, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 84, 041801 (2011).CrossRefGoogle Scholar
  157. 157.
    G. A. Petsko and D. Ringe, Protein Structure and Function (Oxford Univ. Press, Oxford, 2009).Google Scholar
  158. 158.
    P. D. Topham, A. J. Parnell, and R. C. Hiorns, J. Polym. Sci. Part B: Polym. Phys. 49, 1131 (2011).CrossRefGoogle Scholar
  159. 159.
    P. W. K. Rothemund, Nature 440, 297 (2006).CrossRefGoogle Scholar
  160. 160.
    T. Torring, N. V. Voigt, J. Nangreave, H. Yan, and K. V. Gothelf, Chem. Soc. Rev. 40, 5636 (2011).CrossRefGoogle Scholar
  161. 161.
    I. R. Cooke and D. R. M. Williams, Macromolecules 37, 5778 (2004); E. Hernandez-Zapata, I. R. Cooke, and D. R. M. Williams, Phys. A 339, 40 (2004).CrossRefGoogle Scholar
  162. 162.
    I. V. Neratova, P. V. Komarov, A. S. Pavlov, and V. A. Ivanov, Russ. Chem. Bull., Int. Ed. 60P, 229 (2011).CrossRefGoogle Scholar
  163. 163.
    E. Lieberman-Aiden, N. L. Van Berkum, L. Williams, M. Imakaev, T. Ragoczy, A. Telling, I. Amit, B. R. Lajoie, P. J. Sabo, M. O. Dorschner, R. Sandstrom, B. Bernstein, M. A. Bender, M. Groudine, A. Gnirke, J. Stamatoyannopoulos, L. A. Mirny, E. S. Lander, and J. Dekker, Science 326, 289 (2009).CrossRefGoogle Scholar
  164. 164.
    L. A. Mirny, Chromosome Res. 19, 37 (2011).CrossRefGoogle Scholar
  165. 165.
    A. Y. Grosberg, S. K. Nechaev, and E. I. Shakhnovich, J. Phys. 49, 2095 (1985).Google Scholar
  166. 166.
    C. Micheletti, D. Marenduzzo, and E. Orlandini, Phys. Rev. 504, 1 (2011).Google Scholar
  167. 167.
    D. Reith, P. Cifra, A. Stasiak, and P. Virnau, Nucleic Acids Res. 40, 5129 (2012).CrossRefGoogle Scholar
  168. 168.
    A. Kudlay, M. S. Cheung, and D. Thirumalai, PRL 102, 118101 (2009).CrossRefGoogle Scholar
  169. 169.
    H.-P. Hsu and K. Binder, J. Chem. Phys. 136, 024901 (2012).CrossRefGoogle Scholar
  170. 170.
    V. A. Ivanov, L. I. Klushin, and A. M. Skvortsov, Polymer Sci., Ser. A 54, 1222 (2012).Google Scholar
  171. 171.
    V. A. Ivanov and A. N. Semenov, Vysokomol. Soedin., Ser. A 32, 399 (1990).Google Scholar
  172. 172.
    V. A. Ivanov and A. N. Semenov, Vysokomol. Soedin., Ser. A 32, 2217 (1990).Google Scholar
  173. 173.
    D. A. Head, A. J. Levine, and F. C. MacKintosh, Phys. Rev. Lett. 91, 108102 (2003); D. A. Head, A. J. Levine, and F. C. MacKintosh, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 68, 061907 (2003).CrossRefGoogle Scholar
  174. 174.
    P. R. Onck, T. Koeman, T. Van Dillen, and E. Van der Giessen, Phys. Rev. Lett. 95, 178102 (2005); T. Van Dillen, P. R. Onck, and E. Van der Giessen, J. Mech. Phys. Solids 56, 2240 (2008).CrossRefGoogle Scholar
  175. 175.
    B. Didonna and T. Lubensky, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 72, 066619 (2005).CrossRefGoogle Scholar
  176. 176.
    Q. Wen, A. Basu, J. P. Winer, A. Yodh, and P. A. Janmey, New J. Phys. 9, 428 (2007).CrossRefGoogle Scholar
  177. 177.
    G. A. Buxton and N. Clarke, Phys. Rev. Lett. 98, 238103 (2007).CrossRefGoogle Scholar
  178. 178.
    G. H. Koenderink, M. Atakhorrami, F. C. MacKintosh, and C. F. Schmidt, Phys. Rev. Lett. 96, 138307 (2006).CrossRefGoogle Scholar
  179. 179.
    Y.-C. Lin, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, Macromolecules 40, 7714 (2007).CrossRefGoogle Scholar
  180. 180.
    Y.-C. Lin, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, Soft Matter 7, 902 (2011).CrossRefGoogle Scholar
  181. 181.
    J. Kierfeld, K. Baczynski, P. Gutjahr, T. Kuhne, and R. Lipowsky, Soft Matter 6, 5764 (2010).CrossRefGoogle Scholar
  182. 182.
    A. V. Dobrynin and J.-M. Y. Carrillo, Macromolecules 44, 140 (2011).CrossRefGoogle Scholar
  183. 183.
    L. T. Nguyen and L. S. Hirst, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 83, 031910 (2011).CrossRefGoogle Scholar
  184. 184.
    F. J. M. Hoeben, P. Jonkheijm, E. W. Meijer, and A. P. H. J. Schenning, Chem. Rev. 105, 1491 (2005).CrossRefGoogle Scholar
  185. 185.
    C. K. Lee, C. C. Hua, and S. A. Chen, J. Phys. Chem. B 113, 15937 (2009).CrossRefGoogle Scholar
  186. 186.
    J. Kirkpatrick, V. Marcon, J. Nelson, K. Kremer, and D. Andrienko, Phys. Rev. Lett. 98, 227402 (2007); J. Kirkpatrick, V. Marcon, K. Kremer, J. Nelson, and D. Andrienko, J. Chem. Phys. 129, 094506 (2008); X. Feng, V. Marcon, W. Pisula, M. Hansen, J. Kirkpatrick, F. Grozema, D. Andrienko, K. Kremer, and K. Muellen, Nat. Mater. 8, 421 (2009); A. Lukyanov, A. Malafeev, V. Ivanov, H.-L. Chen, K. Kremer, and D. Andrienko, J. Mater. Chem. 20, 10475 (2010).CrossRefGoogle Scholar
  187. 187.
    D. Bonn and D. Ross, Rep. Prog. Phys. 64, 1085 (2001).CrossRefGoogle Scholar
  188. 188.
    K. Binder, Z. Phys. B 43, 119 (1981).CrossRefGoogle Scholar
  189. 189.
    P. Cifra, Z. Benkova, and T. Bleha, J. Phys. Chem. B 112, 1367 (2008); P. Cifra, Z. Benkova, and T. Bleha, Faraday Discuss. 139, 377 (2008); P. Cifra, J. Chem. Phys. 131, 224903 (2009).CrossRefGoogle Scholar
  190. 190.
    P. Cifra and T. Bleha, Macromol. Symp. 256, 105 (2007); P. Cifra and T. Bleha, Polymer 48, 2444 (2007).CrossRefGoogle Scholar
  191. 191.
    H. E. Amuasi and C. Storm, Phys. Rev. Lett. 105, 248105 (2010); E. M. Huisman, C. Heussinger, C. Storm, and G. T. Barkema, Phys. Rev. Lett. 105, 118101 (2010).CrossRefGoogle Scholar
  192. 192.
    M. P. Allen, M. A. Warren, M. R. Wilson, A. Sauron, and W. Smith, J. Chem. Phys. 105, 2850 (1996); A.V. Lyulin, M. P. Allen, M. R. Wilson, and N. K. Allsopp, Macromolecules 31, 4626 (1998).CrossRefGoogle Scholar
  193. 193.
    J. Cottaar, L. J. A. Koster, R. Coehoorn, and P. A. Bobbert, Phys. Rev. Lett. 107, 136601 (2011); J. Cottaar, R. Coehoorn, and P. A. Bobbert, Phys. Rev. B: Condens. Matter 85, 125203 (2012).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • V. A. Ivanov
    • 1
  • J. A. Martemyanova
    • 1
  • A. S. Rodionova
    • 1
  • M. R. Stukan
    • 2
  1. 1.Faculty of PhysicsMoscow State UniversityMoscowRussia
  2. 2.Schlumberger Dhahran Carbonate Research CenterAl KhobarSaudi Arabia

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