For a deeply supercooled liquid near its glass transition temperature, we suggest a possible way to connect the temperature dependence of its molar excess entropy to that of its viscosity by constructing a macroscopic model, where the deeply supercooled liquid is assumed to be a mixture of solid-like and liquid-like micro regions. In this model, we assume that the mole fraction x of the liquid-like micro regions tends to zero as the temperature T of the liquid is decreased and extrapolated to a temperature Tg*, which we assume to be below but close to the lowest glass transition temperature Tg attainable with the slowest possible cooling rate for the liquid. Without referring to any specific microscopic nature of the solid-like and liquid-like micro regions, we also assume that near Tg, the molar enthalpy of the solid-like micro regions is lower than that of the liquid-like micro regions. We then show that the temperature dependence of x is directly related to that of the molar excess entropy. Close to Tg, we assume that an activated motion of the solid-like micro regions controls the viscosity and that this activated motion is a collective motion involving practically all of the solid-like micro-regions so that the molar activation free energy for the activated motion is proportional to the mole fraction, 1-x, of the solid-like micro regions. The temperature dependence of the viscosity is thus connected to that of the molar excess entropy through the temperature dependence of the mole fraction x. As an example, we apply our model to a class of glass formers for which the molar excess entropy at temperatures near Tg is proportional to 1-T/TK with TK < Tg \sim Tg* and find their viscosities to be well approximated by the Vogel-Fulcher-Tamman equation for temperatures very close to Tg. We estimate the values of three parameters in our model for three glass formers in this class.
A theoretical treatment of deeply supercooled liquids is difficult because their properties emerge from spatial inhomogeneities that are self-induced, transient, and nanoscopic. I use computer simulations to analyse self-induced static and dynamic heterogeneity in equilibrium systems approaching the experimental glass transition. I characterise the broad sample-to-sample fluctuations of salient dynamic and thermodynamic properties in elementary mesoscopic systems. Findings regarding local lifetimes and distributions of dynamic heterogeneity are in excellent agreement with recent single molecul…
One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecula…
We combine the swap Monte Carlo algorithm to long multi-CPU molecular dynamics simulations to analyse the equilibrium relaxation dynamics of model supercooled liquids over a time window covering ten orders of magnitude for temperatures down to the experimental glass transition temperature $T_g$. The analysis of \rev{several} time correlation functions coupled to spatio-temporal resolution of particle motion allow us to elucidate the nature of the equilibrium dynamics in deeply supercooled liquids. We find that structural relaxation starts at early times in rare localised regions characterised …
Importance of nuclear quantum effects on the structure of supercooled water around its liquid--liquid critical point
Center for Advanced Systems Understanding (CASUS)（先进系统理解中心）；Helmholtz Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；Paderborn University（帕德博恩大学）；Technische Universität Dresden（德累斯顿工业大学）
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 strongly non-universal behavior is found for the activation barrier that controls lo…
A simplified nonlinear memory function is proposed in the ideal time-convolutionless mode-coupling theory equation to study the dynamics of glass-forming liquids. The numerical solutions are then compared with the simulation results performed on fragile liquids and strong liquids. They are shown to recover the simulation results in a supercooled state well within error, except at a $β$-relaxation stage because of the ideal equation. A temperature dependence of the nonlinearity $μ$ in the memory function then suggests that the supercooled state must be clearly separated into two substates, a we…
In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by these findings, we construct a minimal empirical model to describe this physics and introduce dynamic facilitation in the trap model, which was initially developed to capture the thermally-activated dynamics of glassy systems. We fully characterise the relaxation dynamics of this facilitated trap model varying the functional form of energy distributions and the…
We propose and numerically implement a local probe of the static self-induced heterogeneity characterizing glass-forming liquids. The method relies on the equilibrium statistics of the overlap between pairs of configurations measured in mesoscopic cavities with unconstrained boundaries. By systematically changing the location of the probed cavity, we directly detect spatial variations of the overlap fluctuations. We provide a detailed analysis of the statistics of a local estimate of the configurational entropy and we infer an estimate of the surface tension between amorphous states, ingredien…
By employing a simplified nonlinear memory function proposed recently by the present author, a universal equation for a collective-intermediate scattering function derived based on the time-convolutionless mode-coupling theory is numerically solved to study the dynamics of glass-forming liquids. The numerical calculation is based on the simulation results performed on two types of liquids, fragile liquids and strong liquids. The numerical solutions are then shown to be uniquely determined by the long-time collective diffusion coefficient $D(q_m)$, where $q_m$ is a first peak position of a stat…
