Theoretical and Experimental Chemistry

, Volume 23, Issue 3, pp 298–303 | Cite as

The renormalization group for centrosymmetric gauge transformations of the dynamic motion for a Markov-ordered polymer chain

  • I. D. Mikhailov
  • L. V. Zhuravskii


A method is proposed for calculating the vibrational-state density averaged over all configurations for a polymer chain with Markov disorder. The method is based on using a group of centrally symmetric gauge transformations that reduce the dynamic matrix for a long polymer chain to renormalized dynamic matrices for short fragments. The short-range order is incorporated exactly in the averaging procedure, while the long-range order is incorporated in the self-consistent field approximation. Results are given for a simple skeletal model for a polymer containing tacticity deviations of Markov type.


Polymer Polymer Chain Renormalization Group Gauge Transformation Average Procedure 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    R. Zbinden, Infrared Spectroscopy of High-Polymer, Academic Press (1964).Google Scholar
  2. 2.
    L. A. Gribov, The Theory of Polymer Infrared Spectra [in Russian], Nauka, Moscow (1977).Google Scholar
  3. 3.
    I. Dechant, R. Dents, W. Kimmer, and R. Schmolke, Polymer Infrared Spectroscopy [Russian translation], Khimiya, Moscow (1976).Google Scholar
  4. 4.
    R. Elliot, J. Krumhansle, and P. Lees, Theory and Properties of Disordered Materials [Russian translation], Mir, Moscow (1977).Google Scholar
  5. 5.
    Shi-Yu-Wu, S. P. Bowen, and K. S. Dy, “Lattice vibrations of one-dimensional disordered systems,” Crit. Rev. Solid State Mater. Sci., 10, No. 1, 43–98 (1980).Google Scholar
  6. 6.
    V. N. Kozyrenko, I. V. Kumpanenko, and I. D. Mikhailov, “Green's function analysis of the vibrational spectra of polymer chains. 1. Several approaches to the problem,” J. Polym. Sci, Polym. Phys. Ed., 15, No. 10, 1721–1738 (1977).Google Scholar
  7. 7.
    P. Deane, Computational Methods in Solid-State Theory [Russian translation], Mir, Moscow (1975).Google Scholar
  8. 8.
    G. Zerbi, L. Piseri, and F. Cabassi, “Vibrational spectrum of chain molecules with conformational disorder: polyethylene,” Mol. Phys., 22, sNo.2, 241–255 (1971).Google Scholar
  9. 9.
    L. V. Zhuravskii, “Numerical analysis of clustering effects in the vibrational spectrum of deuterated polyethylene,” Vysokomol. Soedin., B, 23, No. 6, 461–465 (1981).Google Scholar
  10. 10.
    Ma Shang-Keng, Modern Theory of Critical Phenomena, Benjamin-Cummings (1976).Google Scholar
  11. 11.
    J. Hubbard, “Electronic structure of one-dimensional alloys,” Phys. Rev. B, 19, No. 4, 1828–1839 (1979).Google Scholar
  12. 12.
    C. Bamford, W. Barb, A. Jenkins, and P. O'Nion, Kinetics of Vinyl Polymerization by Radical Mechanisms, Butterworths (1958).Google Scholar
  13. 13.
    M. O. Robbins and B. Koiller, “Renormalization-group method for the spectra of disordered chains,” Phys. Rev. B, 27, No. 12, 7703–7715 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • I. D. Mikhailov
    • 1
  • L. V. Zhuravskii
    • 1
  1. 1.Patrice Lumumba Peoples' Friendship UniversityMoscow

Personalised recommendations