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

Numerous experimental and computational studies have established that most liquids seem to exhibit a remarkable, yet poorly understood, property termed “thermodynamic scaling”, in which the structural relaxation time τα, and many other dynamic properties, can be expressed in terms of a “universal” reduced variable, TV γ, where T is the temperature, V is the material volume, and γ is a scaling exponent describing how T and V are linked to each other when either quantity is varied. Here, we show that this scaling relation 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 γ corresponds to a reduced isoentropic fluid condition. Molecular dynamics simulations on a coarse-grained polymer melt are utilized to confirm that the predicted thermodynamic scaling of τα 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 τα and L/L A is confirmed by simulation, we find that the isothermal compressibility κT 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 compressibility relative to this condition, δκT, 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 γ as a measure of intrinsic anharmonicity of intermolecular interactions that may be directly determined from the pressure derivative of the material bulk modulus. Finally, we show that many phenomenological relationships related to the glass formation and melting of materials can be understood based on the Murnaghan EOS and thermodynamic scaling.