Abstract
Automatic computer programs are developed to calculate one- two-, and three-dimensional Debye functions. Prior tables of these functions are critically reviewed. Also, strategies are derived to calculate Debye temperatures from heat capacities. Both, simple three-dimensional Debye analyses and Tarasov analyses were carried out on 35 linear macromolecules. The experimental heat capacities for these analyses were collected in the ATHAS data bank. It is shown that the skeletal heat capacity of linear macromolecules is often best represented by only two vibrations per chain atom. For most of the all-carbon chain macromolecules the intramolecular skeletal heat capacity can be given by Cvs=D1[520 (28/MW)1/2] whereMW is the molecular mass andD 1 represents the one-dimensional Debye function. Polyoxides show a higher intramolecular theta temperature, but a lower intermolecular theta temperature. Double bonds and phenylene groups in the chain increase the intramolecular theta temperature.
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Müller, F. H., H. Martin, Kolloid Z.172, 97 (1960).
O'Neill, M. J., Anal. Chem.36, 1238 (1964);38, 1331 (1966).
Gaur, U., A. Mehta, B. Wunderlich, J. Thermal Anal.13, 71 (1978).
Wunderlich, B., H. Baur, Adv. Polymer Sci.7, 151 (1970).
Gaur, U., B. Wunderlich and several coworkers, J. Phys. Chem. Ref. Data, 1981–1982 a series of 9 publications.
Einstein, A., Ann. Physik22, 180, 800 (1907).
See for example Blackman, M. in: “Handbuch der Physik”7, 325 (1955) Springer Berlin-Göttingen-Heidelberg (S. Flügge ed.).
Debye, P., Ann. Physik39, 789 (1912).
Tarasov, V. V., Zh. Fiz, Khim.24, 111 (1950), see also Zh. Fiz. Khim.39, 2077 (1965).
Perepechko, I. I., “Low-Temperature Properties of Polymers”, Pergamon Press, Oxford (1980).
Hilsenrath, J., G. G. Ziegler, “Tables of Einstein Functions”. Natl. Bur. Std. Monograph49 (1962).
Beatty, J. A., J. Math. Phys. (MIT)6, 1 (1926).
Gaur, U., G. Pultz, H. Wiedemeier, B. Wunderlich, J. Thermal Anal, to be published.
Wunderlich, B., J. Chem. Phys.37, 1207 (1962).
Lau, S.-F., Thesis, Rensselaer Polytechnic Institute, Department of Chemistry, Troy, N. Y. expected completion date 1982, available through microfilm University Microfilms, Ann Arbor, Mich., approximately 1983.
McCracken, D. D., W. S. Dorn, “Numerical Methods and Fortran Programming”, J. Wiley and Sons, New York, London (1964).
Patterson, T. N. L., Math. Comp.22, 847, 877 (1968).
Clenshaw, C. W., A. R. Curtis, Num. Math.2, 197 (1960); Oliver, J., Comp. J.15, 141 (1972).
Numerical Algorithms Group Ltd. NAG Central Office, 7 Banbury Road, Oxford OX2 6NN, United Kingdom; NAG (USA) Inc. 1250 Grace Court, Downer's Grove, Illinois 60515 USA.
Choy, C. L., M. Huq, D. Moody, Phys. Lett.54A, 375 (1975).
Gaur, U., B. Wunderlich, Macromolecules13, 439 (1980).
Wunderlich, B., “Macromolecular Physics, Vol. 3, Crystal Melting.” Academic Press, New York (1980).
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Dedicated to Prof. Dr. F. H. Müller.
On leave from the Lumumba Peoples' Friendship University, Moscow, USSR.
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Cheban, Y.V., Lau, S.F. & Wunderlich, B. Analysis of the contribution of skeletal vibrations to the heat capacity of linear macromolecules in the solid state. Colloid & Polymer Sci 260, 9–19 (1982). https://doi.org/10.1007/BF01447670
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DOI: https://doi.org/10.1007/BF01447670