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Computation of the generalized Debye functionsδ(x, y) andD(x, y)

  • Polymer Science
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Abstract

Automatic computer programs (BASIC-PLUS) are developed to calculate Debye functions also for non integer exponents. Functions of this type occur in the heat capacity analysis of polymer crystals, if simple continuum approximations are used. The heat capacity of completely crystalline polyethylene is calculated and compared with experimental data.

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References

  1. Debye, P., Ann. d. Phys.39, 789 (1912).

    Google Scholar 

  2. Kittel, Ch., Einführung in die Festkörperphysik, p. 257, R. Oldenbourg Verlag München-Wien, John Wiley & Sons GmbH Frankfurt (1973).

    Google Scholar 

  3. Tarasov, V. V., Zhur. Fiz. Khim.24, 111 (1950).

    Google Scholar 

  4. Tarasov, V. V., Zhur. Fiz. Khim.27, 1430 (1953).

    Google Scholar 

  5. Tarasov, V. V., G. A. Yunitskii, Zhur. Fiz. Khim.39, 2077 (1965).

    Google Scholar 

  6. Landau, L. D., E. M. Lifschitz, Lehrbuch der theoretischen Physik, vol. V, p. 197, Akademie-Verlag Berlin (1966).

    Google Scholar 

  7. Baur, H., Kolloid-Z. u. Z. Polymere241, 1057 (1970);244, 293 (1971).

    Google Scholar 

  8. Desorbo, W., W. W. Tyler, Phys. Review83, 878 (1951).

    Google Scholar 

  9. Dworkin, A. S., D. J. Sasmor, E. R. van Artsdalen, J. Chem. Phys.22, 837 (1954).

    Google Scholar 

  10. Westrum, F., J. J. Bride, Bull. Am. Phys. Soc.8, 22 (1954).

    Google Scholar 

  11. Brekow, G., M. Meißner, M. Scheiba, A. Tausend, D. Wobig, J. Phys. C: Solid State Phys.6, 462 (1973).

    Google Scholar 

  12. Engeln, I., M. Meißner, J. Pol. Sci. Phys. Ed.18, 2227 (1980).

    Google Scholar 

  13. Wunderlich, B., H. Baur, Adv. Polymer Sci.7, 151 (1970).

    Google Scholar 

  14. Perepechko, I. I., “Low Temperature Properties of Polymers”, Pergamon Press, Oxford (1980).

    Google Scholar 

  15. Beatty, J. A., J. Math. Phys. (MIT)6, 1 (1926).

    Google Scholar 

  16. Wunderlich, B., J. Chem. Phys.37, 1207 (1962).

    Google Scholar 

  17. Cheban, Yu. V., S.-F. Lau, B. Wunderlich, Colloid & Polymer Sci.260, 9 (1982).

    Google Scholar 

  18. Abramowitz, M., I. A. Stegun, “Debye functions”, Handbook of Mathematical Functions, p. 998, Dover Publications, Inc., New York (1964).

    Google Scholar 

  19. Geiger, H., K. Scheel, Handbuch der Physik, Band X, p. 17ff., Julius Springer Verlag, Berlin (1926).

    Google Scholar 

  20. Caratheodory, C., „Funktionstheorie“, vol. 1, p. 267, Birkhäuserverlag Basel und Stuttgart (1960).

    Google Scholar 

  21. Abramowitz, M., I. A. Stegun, “Bernoulli and Euler Polynominals-Riemann Zeta Function”, s. Zitat 18, p. 803.

    Google Scholar 

  22. Jahnke-Emde, „Die Riemannsche Zetafunktion“, Tafeln Höherer Funktionen, p. 265, B. G. Teubner Verlagsgesellschaft Leipzig (1952).

    Google Scholar 

  23. Schaefer, C., Einführung in die Theoretische Physik, p. 581, Walter de Gruyter & Co. Berlin (1944).

    Google Scholar 

  24. Abramowitz, M., I. A. Stegun, “Gamma Function and Related Functions”, s. Zitat 18, p. 255.

    Google Scholar 

  25. Luke, Y. L., “Polynominal and Rational Approximations for the Incomplete Gamma Function”, Volume 53-II, p. 186, Mathematics in Science and Engineering, Academic Press, New York/London (1969).

    Google Scholar 

  26. Engeln, I., M. Meißner, H. E. Pape, B. Tempelhof, to be published.

  27. Tasumi, M., T. Shimanoushi, T. Miyazawa, J. Mol. Spectr.9, 261 (1962).

    Google Scholar 

  28. Tasumi, M., S. Krimm, J. Chem. Phys.46, 755 (1967).

    Google Scholar 

  29. Engeln, I., M. Meißner, Colloid & Polymer Sci.259, 827 (1981).

    Google Scholar 

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Engeln, I., Wobig, D. Computation of the generalized Debye functionsδ(x, y) andD(x, y) . Colloid & Polymer Sci 261, 736–743 (1983). https://doi.org/10.1007/BF01410947

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  • DOI: https://doi.org/10.1007/BF01410947

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