Calculation of Grüneisen parameters of polymers

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 Grüneisen parameter defined by ${}_{\gamma }{\mathrm{(T)=V(\partial \; P/\partial \; E)}}_V$ , since much of the internal energy is stored in the volume independent degrees of freedom. Assuming only the translational modes are volume dependent, the formula ${}_{\gamma }{\mathrm{(T)=\hspace{0.17em}}}_{{\gamma }_0}{C}_{\mathrm{TR}}{\mathrm{/C}}_V$ is derived, where γ₀ and C_TR/C_V are the Grüneisen parameter and heat capacity fraction for translation. The translational Grüneisen parameter γ₀ is calculated from a cell model and the translational heat capacity fraction is estimated for polystyrene and polymethyl methacrylate. The Grüneisen parameters of these polymers are then calculated from the above formula. These results agree with Grüneisen parameters obtained from available data on thermal expansion, heat capacity, and compressibility at high temperatures. At low temperatures the cell model predicts that ${}_{{\gamma }_0}\text{→ 3.16}$ as $\text{T→ 0}$ . Further low temperature data is needed to assess the accuracy of the theory in this region.