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

Abstract

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 τ α , 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 τ α 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 τ α and L/L A is confirmed by simulation, we find that the isothermal compressibility κ 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 compressibility relative to this condition, δκ 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 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.

Influence of Ionic Interaction Strength on Glass Formation of an Ion-Containing Polymer Melt

“…These temperatures include the onset at T A , the middle or crossover at T c , and the termination at T 0 of glass formation as well as the common glass-transition temperature T g , where T 0 is often termed the “ideal glass-transition temperature” . We determine these characteristic temperatures in our simulations using the established method in our previous works, − , which is briefly described below.…”

“…The wave number is chosen to be q = 7.0σ –1 in the present work, which is close to the first peak position of S ( q ). The self-intermediate scattering function then permits estimation of the structural relaxation time τ α for a given T , which we define by the time where F s ( q , t ) decays to 0.2, as in our previous works. − , …”

“…The selfintermediate scattering function then permits estimation of the structural relaxation time τ α for a given T, which we define by the time where F s (q,t) decays to 0.2, as in our previous works. [60][61][62][63]69 As an example, Figure 5a exhibits the t dependence of F s (q,t) for a range of T for the polymer melt with l B /σ = 5.6. It is a typical result of GF liquids that the structural relaxation slows down drastically upon cooling.…”

“…We follow the protocol in our previous works [60][61][62][63]69 to study polymer glass formation. Specifically, an equilibrated ioncontaining polymer melt is first prepared by running simulations at a relatively high temperature and a pressure of P = 0.0ε/σ 3 in the NPT ensemble, where the temperature and pressure are maintained using a Nose−Hoover thermostat and barostat, respectively, as implemented in LAMMPS.…”

Experimental Tests of a Theoretically Predicted Noncausal Correlation between Dynamics and Thermodynamics in Glass-forming Polymer Melts

“…However, the underlying physics is a mystery, although a recent interesting theoretical and simulation work has been done on this problem by Douglas and Xu. 80 Since S 0 follows from a volumetric second derivative of the free energy, the analysis of Dyre 78 implies that it is not an "isomorph invariant" property and hence cannot lead to the traditional thermodynamic scaling. However, this does not imply that the dynamical ideas of ECNLE theory "fail", as incorrectly stated in ref 80.…”