Elastically Collective Nonlinear Langevin Equation Theory of Glass-Forming Liquids: Transient Localization, Thermodynamic Mapping, and Cooperativity

Abstract

We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the elastically collective nonlinear Langevin equation (ECNLE) theory. By invoking a high-temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron-scattering measurements. In contrast, in the same format, a strongly nonuniversal behavior is found for the activation barrier that controls long-time relaxation. Two measures of cooperativity in the ECNLE theory are analyzed. A particle-level total displacement associated with the alpha relaxation event is found to be only of order 1-2 particle diameters and weakly increases with cooling. In contrast, an alternative cooperativity length is defined as the spatial scale required to essentially recover the full barrier and bulk alpha time. This length scale grows strongly with cooling because of the emergence in the deeply supercooled regime of collective long-range elastic fluctuations required to allow local hopping. It becomes very large as the laboratory T is approached, though it is relatively modest at degrees of supercooling accessible with molecular dynamics simulation. The alpha time is found to be exponentially related to this cooperativity length over an enormous number of decades of relaxation time that span the lightly to deeply supercooled regimes. Moreover, the effective barrier height increases almost linearly with the growing cooperativity length scale. An alternative calculation of the collective elastic barrier based on a literal continuum mechanics approach is shown to result in very little change of the theoretical results for bulk properties but leads to a much smaller and less temperature-sensitive cooperativity length scale.

Influence of Longer Range Transfer of Vapor Interface Modified Caging Constraints on the Spatially Heterogeneous Dynamics of Glass-Forming Liquids

“…Equation 29 is an almost universal relation except for the ratio, Θ, of the onset to glass transition temperatures. It can depend on chemistry (increases as fragility decreases), pressure, and the vitrification time scale criterion [24,43]. But we recall that ECNLE theory predicts T g,bulk varies roughly logarithmically with time scale criterion [43], so Θ is expected to be weakly dependent on vitrification criterion (consistent with normalized T g gradients being weakly dependent on vitrification criterion).…”

“…of the collective elastic versus local cage barrier. For low fragility PIB, the elastic barrier is far less important than the local cage barrier F B [24,43]. The major trends in Figure 5 are the larger absolute enhancement, and more temperature sensitivity, of the alpha time at the vapor surface at fixed T /T g for a higher fragility system.…”

“…Its roughly linear temperature variation appears to be understandable as follows. From our previous work [43], the mapping from thermal liquids to hard spheres corresponds to the connection . The curves through the discrete theoretical data points are a guide-tothe-eye.…”

Effects of cooling rate on structural relaxation in amorphous drugs: elastically collective nonlinear langevin equation theory and machine learning study

“…, and j n (x) indicates the spherical Bessel function of order n. Based on many previous studies of thermal liquids, polymers and amorphous drugs [6][7][8]11], one can assume τ E = 10 −13 s. To convert our hard-sphere calculations into the temperature dependence of the structural relaxation time, we proposed [11] a thermal mapping, which is based on the thermal expansion process during temperature variation, to convert from a volume fraction of hard-sphere fluid to temperature of experimental material. The mapping is…”

Theoretical Model for the Structural Relaxation Time in Coamorphous Drugs

“…Recall that the thermal noise force obeys the force-force correlation function δf (0)δf (t) = 2k B T ζ s δ(t), where k B is the Boltzmann constant and T is temperature. From this, one can derive an analytical expression for the dynamic free energy [9,[15][16][17] F dyn (r)…”