In a polymer there exist a large number of degrees of freedom; however, only the translational modes have appreciable volume dependence. This fact leads to low values of the Gruuml;neisen parameter defined byggr;lpar;Trpar;equals;Vlpar;part; Psol;part; Erpar;V, since much of the internal energy is stored in the volume independent degrees of freedom. Assuming only the translational modes are volume dependent, the formulaggr;lpar;Trpar;equals;thinsp;ggr;0CTRsol;CVis derived, where ggr;0andCTRsol;CVare the Gruuml;neisen parameter and heat capacity fraction for translation. The translational Gruuml;neisen parameter ggr;0is calculated from a cell model and the translational heat capacity fraction is estimated for polystyrene and polymethyl methacrylate. The Gruuml;neisen parameters of these polymers are then calculated from the above formula. These results agree with Gruuml;neisen parameters obtained from available data on thermal expansion, heat capacity, and compressibility at high temperatures. At low temperatures the cell model predicts thatggr;0rarr; 3.16asTrarr; 0. Further low temperature data is needed to assess the accuracy of the theory in this region.
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