Equation of State and Entropy Theory Approach to Thermodynamic Scaling in Polymeric Glass-Forming Liquids

Abstract

We show that thermodynamic scaling can be derived by combining the Murnaghan equation of state (EOS) with the generalized entropy theory (GET) of glass formation. In our theory, thermodynamic scaling arises in the non-Arrhenius relaxation regime as a scaling property of the fluid configurational entropy density $s_c$, normalized by its value $s_c^*$ at the onset temperature $T_A$ of glass formation, $s_c / s_c^*$, so that a constant value of $TV^{\gamma}$ corresponds to a \textit{reduced isoentropic} fluid condition. Molecular dynamics simulations on a coarse-grained polymer melt are utilized to confirm that the predicted thermodynamic scaling of $\tau_{\alpha}$ by the GET holds both above and below $T_A$ and to test whether the extent $L$ of stringlike collective motion, normalized its value $L_A$ at $T_A$, also obeys thermodynamic scaling, as required for consistency with thermodynamic scaling. While the predicted thermodynamic scaling of both $\tau_{\alpha}$ and $L/ L_A$ is confirmed by simulation, we find that the isothermal compressibility $\kappa_T$ and the long wavelength limit $S(0)$ of the static structure factor do not exhibit thermodynamic scaling, an observation that would appear to eliminate some proposed models of glass formation emphasizing fluid `structure' over configurational entropy. It is found, however, that by defining a low temperature hyperuniform reference state, we may define a compressibility relative to this condition, $\delta \kappa_T$, a transformed dimensionless variable that exhibits thermodynamic scaling and which can be directly related to $s_c / s_c^*$. Further, the Murnaghan EOS allows us to interpret $\gamma$ as a measure of intrinsic anharmonicity of intermolecular interactions that may be directly determined from the pressure derivative of the material bulk modulus.