Medium-Range Structural Order as the Driver of Activated\nDynamics and Complexity Reduction in Glass-Forming Liquids

We analyze in depth the Elastically\nCollective Nonlinear Langevin\nEquation theory of activated dynamics in metastable liquids to establish\nthat the predicted inter-relationships between the alpha relaxation\ntime, local cage and collective elastic barriers, dynamic localization\nlength, and shear modulus are causally related within the theory to\nthe medium range order (MRO) static correlation length. The latter\ngrows exponentially with density for metastable hard sphere fluids\nand as a nonuniversal inverse power law with temperature for supercooled\nliquids under isobaric conditions. The physical origin of predicted\nconnections between the alpha time and other metrics of cage order\nand the thermodynamic inverse dimensionless compressibility is fully\nestablished. It is discovered that although kinetic constraints from\nthe real space first coordination shell are important for the alpha\ntime, they are of secondary importance compared to the consequences\nof the more universal MRO correlations in both the modestly and deeply\nmetastable regimes. This understanding sheds new light on the theoretical\nbasis for, and prior successes of, the predictive mapping of chemically\ncomplex thermal liquids to effective hard sphere fluids based on matching\ntheir dimensionless compressibilities, a scheme we call “complexity\nreduction”. In essence, the latter is equivalent to the physical\nrequirement that the thermal liquid MRO correlation equals that of\nits effective hard sphere analog. The mapping alone is shown to provide\na remarkable level of quantitative predictive power for the glass\ntransition temperature <i>T</i><sub>g</sub> of 21 molecular\nand polymer liquids. Predictions for the chemically specific absolute\nmagnitude and growth with cooling of the MRO correlation length are\nobtained and lie in the window of 2–6 nm at <i>T</i><sub>g</sub>. Dynamic heterogeneity, elastic facilitation, and beyond\npair structure issues are briefly discussed. Future opportunities\nto theoretically analyze the equilibrated deep glass regime are outlined.