View PDF Version
 
DOI: 10.1039/A703567E (Paper) Reference Section for: Chem. Commun., 1997, 1801-1802

Cycles frustrating fractal formation in an AB2 step growth polymerization

(Note: The full text of this document is currently only available in the PDF Version )

Colin Cameron, Allan H. Fawcett, Cecil R. Hetherington, Richard A. W. Mee and Frederick V. McBride

Abstract

The step growth of a flexible AB2 monomer, normally considered to produce dendrimers or fractal molecules, as they are themselves self-similar to their branches, is frustrated by the formation of one cycle within each molecule, according to a Monte Carlo lattice study of the evolution of the topological trees that are embedded in three-dimensional space; the number of cycles of m residues is well fitted by the relationship Rm = K0 pam m-e, pa being the extent of reaction of the A groups; at the end of a polymerization of N0 monomers the total number of cycles, and of molecules, is given by the product of K0 and the Euler–Riemann function ξ(e) so there is a simple relationship between these quantities and the mean number average degree of polymerization at infinite time: N0 = K0 <x>n,∞ ξ(e).

References

  1. P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, New York, 1953, ch. 9 Search PubMed.
  2. P. J. Flory, J. Phys. Chem., 1942, 42, 132 CrossRef.
  3. R. J. Wilson, Introduction to Graph Theory, Longman, Harlow, 4th edn., 1996 Search PubMed.
  4. B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, Oxford, 1982 Search PubMed.
  5. E. Malmstrom and A. Hult, Macromolecules, 1996, 29, 1222 CrossRef.
  6. R. H. Jin and Y. Andou, Macromolecules, 1996, 29, 8010 CrossRef CAS.
  7. P. J. Flory, Statistical Mechanics of Chain Molecules, Interscience, New York, 1969 Search PubMed.
  8. Collected Papers of Wallace H. Carothers on Polymerization, ed. H. Mark and C. S. Whitby, Interscience, New York, 1940 Search PubMed.
  9. K. Dusek, Recl. Trav. Chim. Pays-Bas, 1991, 110, 507 CAS.
  10. A. H. Fawcett, R. A. W. Mee and F. V. McBride, Macromolecules, 1995, 28, 481 CrossRef.
  11. Monte Carlo Methods in Statistical Physics, ed. K. Binder, Springer Verlag, Berlin, 1979 Search PubMed.
  12. A. H. Fawcett, in Macromolecular Chemistry, Specialist Periodical Reports, ed. A. D. Jenkins and J. F. Kennedy, Royal Society of Chemistry, 1984, vol. 3 Search PubMed.
  13. I. Carmesin and K. Kremer, Macromolecules, 1988, 21, 2819 CrossRef CAS.
  14. L. J. Mathias, T. W. Carothers and R. Bozen, ACS Polym. Prep., 1991, 32, 82 Search PubMed.
  15. A. H. Fawcett, R. A. W. Mee and F. V. McBride, J. Chem. Phys., 1996, 104, 1743 CrossRef CAS.
  16. A. H. Fawcett, F. V. McBride, D. McKay and R. A. W. Mee, work in progress.
  17. P. Romiszowski and W. H. Stockmayer, J. Chem. Phys., 1984, 80, 485 CrossRef CAS.
  18. M. Gordon and S. B. Ross-Murphy, Pure Appl. Chem., 1975, 43, 1 CAS.
  19. C. R. Hetherington, PhD Thesis, Queen's University of Belfast.
  20. J. J. Volberg, Prediction Analysis, Van Nostrand, London, 1967 Search PubMed.
  21. Encyclopedia of Mathematics, ed. I. M. Kinogradov, Reidel, Lancaster, 1988, vol. 1A–B Search PubMed.
  22. C. Cameron, A. H. Fawcett, C. R. Hetherington, R. A. W. Mee and F. V. McBride, submitted.
  23. C. B. Boyer and U. C. Merzbach, A History of Mathematics, Wiley, Chichester, 2nd edn., 1989 Search PubMed.
Click here to see how this site uses Cookies. View our privacy policy here.