Nematic ordering problem as the polymer problem of the excluded volume

A. Yakunin 1
  • 1 Karpov Institute of Physical Chemistry, 103064, Moscow, Russia


Based on a solution of the polymer excluded volume problem, a technique is proposed to estimate some parameters at the isotropic-nematic liquid crystal phase transition (the product of the volume fraction of hard sticks and the ratio of the stick length, L, to its diameter, D; the maximum value of this ratio at which one cannot regard the stick as hard). The critical exponents are estimated. The transition of a swelling polymer coil to ideal is revealed as the polymerization degree of a macromolecule increases. The entanglement concentration obtained agrees with experimental data for polymers with flexible chains. The number of monomers between neighbor entanglements is assumed to be the ratio L/D. A comparison of the theory with other ones and recent experimental data is made.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] M.E. Fisher: “Shape of a Self-Avoiding Walk or Polymer Chain”, J. Chem. Phys., Vol. 44, (1966), pp. 616–622.

  • [2] P.-G. de Gennes: “Exponents for the Excluded Volume Problem as Derived by the Wilson Method”, Phys. Lett., Vol. 38A, (1972), pp. 339.

  • [3] K.G. Wilson and J. Kogut: “The renormalization group and the ε-expansion”, Phys. Rep., Vol. 12C, (1974), pp. 75–199.

  • [4] L.D. Landau and E.M. Lifshitz: Statistical Physics, 3rd ed., Pergamon, Oxford, 1980.

  • [5] A.Yu. Grosberg and A.R. Khokhlov: Statistical Physics of Macromolecules. American Institute of Physics Press, New York, 1994.

  • [6] P.-G. de Gennes: Scaling Concepts in Polymer, Physics, Cornell University Press, New York, Ithaca and London, 1979.

  • [7] A.N. Yakunin: “A Globule in a Stretching Field. The Role of Partial Melting During Drawing of Crystalline Polymers”, Intern. J. Polymeric Mater., Vol. 22, (1993), pp. 57–64.

  • [8] S. Caracciolo, M.S. Causo, A. Pelissetto: “High-precision determination of the critical exponent γ for self-avoiding walks”, Phys. Rev. E, Vol. 57, (1998), pp. R1215-R1218.

  • [9] G. Besold, H. Guo, M.J. Zuckermann: “Off-Lattice Monte Carlo Simulation of the Discrete Edwards Model”, J. Polym. Sci.: Part B: Polym. Phys., Vol. 38, (2000), pp. 1053–1068.<1053::AID-POLB6>3.0.CO;2-J

  • [10] J. Zinn-Justin: “Precise determination of critical exponents and equation of state by field theory methods”, Phys. Rep., Vol. 344, (2001), pp. 159–178.

  • [11] R.P. Wool: “Polymer Entanglements”, Macromolecules, Vol. 26, (1993), pp. 1564–1569.

  • [12] P.-G. de Gennes: The physics of liquid crystals, Clarendon Press, Oxford, 1974.

  • [13] A. Brûlet, V. Fourmaux-Demange, J.P. Cotton: “Temperature Dependence of the Conformation of a Comblike Liquid Crystalline Polymer in a NI Nematic Phase”, Macromolecules, Vol. 34, (2001), pp. 3077–3080.


Journal + Issues