Saturday, April 19, 2008

Calculation of the Glass Transition Temperatures of Polymers. Part I.

Calculation of the Glass Transition Temperatures of Polymers. Part I. Homopolymers and Copolymers with Alkyl Side Chains

W. A. LEE, Materials Department, Royal Aircraft Establishment, Farnborough, Hampshire, U.K.

From: Journal of Polymer Science Part A-2 Polymer Physics, Volume 8, Issue 4 (p 555-570)


Four equations, relating the glass transition temperatures Tg, of homopolymers and copolymers to invariant additive temperature parameters (ATP) associated with their constituent groups, but weighted in different ways, have been applied to the calculation of the Tg, of seven series of polymers having alkyl side chains. It is shown that the Tg, of the 32 polymers considered may be calculated, within 7K of the observed values, without the use of interaction coefficients from 15 independent variables, representing summations of the ATP's. The present calculations are confined to those structures which may be formed by a recombination of the structures corresponding to these independent variables. It is an essential feature of the approach that a distinction is made between groups with different nearest neighbors. Alternative methods of calculation are considered. The temperature parameter for a sequence of three or more methylene groups is estimated as 141K, in conformity with the transition in polyethylene at 148K. Nearest-neighbor interactions, stereoregularity, and crystallinity effects are discussed.


The glass-to-rubber transition temperature Tg, is of special interest in the development of new amorphous polymers because many properties of technological importance show a significant change in magnitude, or in temperature dependence, at this temperature. A method for calculating the Tg, of polymers from a knowledge of the chemical structure alone is therefore of great value in designing new polymers with desired properties and is of considerable theoretical interest. Many previous attempts have been reported, but the relations proposed [1-10] have been limited in application, though usefully descriptive of specific polymer systems.


1. M. Gordon and J. S. Taylor, J. Appl. Chem., 2, 493 (1952); Rubber Chem. Technol. 26, 323 (1953)

2. L. Mandelkern, G. M. Martin, and F. A. Quinn, J . Res. Nat. Bur. Stand., 58, 137 (1957)

3. T. G. Fox, Bull. Am. Phys. Soc., 1, 123 (1956)

4. L. A. Wood, J. Polym. Sci., 28, 319 (1968)

5. E. A. DiMarzio and J. H. Gibbs, J. Polym. Sci., 40, 121 (11959)

6. A. J. Marei, I. V. Rokityanskii, and V. V. Samoletova, Soviet. Rubber Technol. (Engl. Trams.), 19, 1 (1960)

7. R. A. Hayes, J. Appl. Polym. Sci., 5, 318 (1961)

8. G. Kanig, Kolbid-Z., 190, 1 (1963); RAE Library Transl. 1135

9. W. F. Bartoe, SPE Trans., 4, 98 (1964)

10. W. E. Wolstenholrne, Polym. Eng. Sci., 8, 142 (1968)

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