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

The connection between slow activated relaxation in glass-forming liquids and various equilibrium thermodynamic properties remains intensely debated. The microscopic elastically collective nonlinear Langevin equation theory, a force-level approach that causally relates the structure and dynamics, describes the activated relaxation as a mixed local-nonlocal process involving local caging constraints coupled with longer-range collective elasticity. Rather surprisingly, we recently showed that this theory predicts a noncausal connection between dynamics and thermodynamics (via the dimensionless compressibility, S-0, an equation-of-state property) for the hard-sphere fluid as a consequence of fundamental relations between local and long-wavelength density fluctuations in equilibrium statistical mechanics. The effective activation barrier is predicted to grow in a power law manner with the inverse S o with an exponent of one in the high-temperature regime and three in the deeply supercooled regime. These predictions have been experimentally verified to hold well in both molecular and inorganic glass-forming liquids. Here, we show that this same basic S-0-space behavior also describes segmental relaxation in the more chemically complex case of polymer melts under isobaric atmospheric- and high-pressure conditions. Linear master curves in S o - space are constructed based on a fragility-dependent crossover from local caging to collective elasticity as the primary origin of slow dynamics. Predicted implications in temperature space include a fragile-to-strong crossover as a function of polymer chemistry signaling the unimportance of collective elasticity effects, a power law scaling of the activation barrier with inverse temperature in the deeply supercooled regime (with a polymer-specific exponent determined entirely from thermodynamics), an alternative approach to collapse the temperature- and pressure-dependent dynamic relaxation data onto a master curve, and a new practical method to more accurately determine fragility.

Automated summary

The connection between slow activated relaxation in glass-forming liquids and various equilibrium thermodynamic properties is debated. The microscopic elastically collective nonlinear Langevin equation theory predicts a noncausal connection between dynamics and thermodynamics, experimentally verified in both molecular and inorganic glass-forming liquids. Predictions include a power law scaling of the activation barrier with inverse temperature and a fragile-to-strong crossover in temperature space.