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Journal of Materials Science

, Volume 15, Issue 7, pp 1680–1683 | Cite as

A theory of the molecular-mass dependence of glass transition temperatures for polydisperse homopolymers

  • P. R. Couchman
Papers

Abstract

Arbitrary distributions of finite molecular-mass homopolymers are treated as one-phase solutions of chain ends and high polymers in order to derive an entropie relation for the dependence of their glass transition temperatures on the number-average degree of polymerization. Absolute predictions of this equation from high molecular-mass and dimer properties are found to be in good agreement with dilatometric transition temperatures for polystyrene. The theoretical equation is generalized to allow for the characterization of chain ends by properties other than those of dimers. An initial approximation to the entropic expression is obtained by neglect of the difference between chain-end and high-polymer transition increments of heat capacity. Two subsequent approximations arise from a series expansion of logarithmic functions. In order of decreasing accuracy these three approximations are: a new form of the Ueberreiter-Kanig equation, a logarithmic expression, and a new form of the Fox-Flory relation.

Keywords

Heat Capacity Polystyrene Glass Transition Temperature Logarithmic Function High Polymer 
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.
    T. G. Fox and P. J. Flory, J. Appl. Phys. 21 (1950) 581; J. Polymer Sci. 14 (1954) 315.Google Scholar
  2. 2.
    K. Ueberreiter and G. Kanig, J. Colloid Sci. 7 (1952) 569.Google Scholar
  3. 3.
    G. Kanig, Kolloid-Z.u.Z. Polymere 190 (1963) 1.Google Scholar
  4. 4.
    T. G. Fox and S. Loshaek, J. Polymer Sci. 15 (1955) 371.Google Scholar
  5. 5.
    P. Meares, Trans. Faraday Soc. 53 (1957) 31.Google Scholar
  6. 6.
    F. N. Kelley and F. Bueche, J. Polymer Sci. 50 (1961) 549.Google Scholar
  7. 7.
    J. H. Gibbs and E. A. Dimarzio, J. Chem. Phys. 28 (1958) 373.Google Scholar
  8. 8.
    T. Somcynsky and D. Patterson, J. Polymer Sci. 62 (1962) S151.Google Scholar
  9. 9.
    D. C. W. Morley, J. Mater. Sci. 9 (1974) 619.Google Scholar
  10. 10.
    K. Onder, R. H. Peters and L. C. Spark, Polymer 13 (1972) 133.Google Scholar
  11. 11.
    M. Gordon, P. Kapadis and A. Malakis, J. Phys. A 9 (1976) 751.Google Scholar
  12. 12.
    K. Ueberreiter and E. Otto-Laupenmühlen, Z. Naturforsch. A 8 (1953) 664.Google Scholar
  13. 13.
    P. R. Couchman, Macromol. 11 (1978) 1156; Phys. Letters 70A (1979) 155, and references therein.Google Scholar

Copyright information

© Chapman and Hall Ltd. 1980

Authors and Affiliations

  • P. R. Couchman
    • 1
  1. 1.Department of Mechanics and Materials ScienceRutgers UniversityNew BrunswickUSA

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