Glass formation is encountered in diverse materials. Experiments have revealed that dynamic relaxation spectra of supercooled liquids generically become asymmetric near the glass transition temperature, $T_g$, where an extended power law emerges at high frequencies. The microscopic origin of this "wing" remains unknown, and was so far inaccessible to simulations. Here, we develop a novel computational approach and study the equilibrium dynamics of model supercooled liquids near $T_g$. We demonstrate the emergence of a power law wing in numerical spectra, which originates from relaxation at rare, localised regions over broadly-distributed timescales. We rationalise the asymmetric shape of relaxation spectra by constructing an empirical model associating heterogeneous activated dynamics with dynamic facilitation, which are the two minimal physical ingredients revealed by our simulations. Our work offers a glimpse of the molecular motion responsible for glass formation at relevant experimental conditions.
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…
Using a novel thermodynamic integration scheme, we compute the excess free energy, $γ$, of a glass-forming, binary Lennard-Jones liquid in contact with a frozen amorphous wall, formed by particles frozen into a similar structure as the liquid. We find that $γ$ is non-zero, becoming negative at low temperature. This indicates that the thermodynamics of the system is perturbed by the effect of the amorphous wall.
Dielectric loss spectra of glass-forming propylene carbonate and glycerol at temperatures above and below T_g are presented. By performing aging experiments lasting up to five weeks, equilibrium spectra below T_g have been obtained. During aging, the excess wing, showing up as a second power law at high frequencies, develops into a shoulder. The results strongly suggest that the excess wing, observed in a variety of glass formers, is the high-frequency flank of a beta-relaxation.
A detailed dielectric investigation of liquid, supercooled liquid, and glassy ethanol reveals a third relaxation process, in addition to the two processes already known. The relaxation time of the newly detected process exhibits strong deviations from thermally activated behavior. Most important, this process is the cause of the apparent excess wing, which was claimed to be present in the dielectric loss spectra of glass-forming ethanol. In addition, marked deviations of the spectra of ethanol from the scaling proposed by Dixon and Nagel have been detected.
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…
We present nonlinear dielectric measurements of glass-forming glycerol and propylene carbonate applying electrical fields up to 671 kV/cm. The measurements extend to sufficiently high frequencies to allow for the investigation of the nonlinear behavior in the regime of the so-far mysterious excess wing, showing up in the loss spectra of many glass formers as a second power law at high frequencies. Surprisingly, we find a complete lack of nonlinear behavior in the excess wing, in marked contrast to the alpha-relaxation where, in agreement with previous reports, a strong increase of dielectric c…
The relaxational dynamics in glass-forming glycerol and glycerol mixed with LiCl is in-vestigated using different neutron scattering techniques. The performed neutron spin-echo experiments, which extend up to relatively long relaxation-time scales of the order of 10 ns, should allow for the detection of contributions from the so-called excess wing. This phenomenon, whose microscopic origin is controversially discussed, arises in a variety of glass formers and, until now, was almost exclusively investigated by dielectric spectros-copy and light scattering. Here we show that the relaxational pro…
In order to describe the slow response of a glass former we discuss some distribution of correlation times, e.g., the generalized gamma distribution (GG) and an extension thereof (GGE), the latter allowing to reproduce a simple peak susceptibility such as of Cole-Davidson type as well as a susceptibility exhibiting an additional high frequency power law contribution (excess wing). Applying the GGE distribution to the dielectric spectra of glass formers exhibiting no beta-process peak (glycerol, propylene carbonate and picoline) we are able to reproduce the salient features of the slow response…
For a deeply supercooled liquid just above its glass transition temperature, we present a simple thermodynamic model, where the deeply supercooled liquid is assumed to be a mixture of solid-like and liquid-like micro regions. The mole fraction of the liquid-like regions controls the thermodynamic properties of the supercooled liquid while that of the solid-like regions controls its relaxation time or viscosity. From the universal temperature dependence of the molar excess entropy for the deeply supercooled liquids, we derive the temperature dependence of the mole fraction of the liquid-like re…
An advance was made by Guiselin et al. [arXiv:2103.01569 (2021)] in molecular dynamics simulations of the equilibrium dynamics of supercooled liquids near the experimental glass transition by utilizing the giant equilibration speedup provided by the swap Monte Carlo algorithm. The found emergence of a power law in relaxation spectra at lower temperatures on the high frequency flank of the alpha-loss peak in analogy to the excess wings observed experimentally in molecular glass-formers. Their remarkable finding leads to the question of where the excess wing is located relative to the alpha-loss…
We present the relaxation dynamics of glass-forming glycerol mixed with 1.1 nm sized polyhedral oligomeric silsesquioxane (POSS) molecules using dielectric spectroscopy (DS) and two different neutron scattering (NS) techniques. Both, the reorientational dynamics as measured by DS and the density fluctuations detected by NS reveal a broadening of the alpha relaxation when POSS molecules are added. Moreover, we find a significant slowing down of the alpha-relaxation time. These effects are in accord with the heterogeneity scenario considered for the dynamics of glasses and supercooled liquids. T…
The properties of nanoconfined fluids can be strikingly different from those of bulk liquids. A basic unanswered question is whether the equilibrium and dynamic consequences of confinement are related to each other in a simple way. We study this question by simulation of a liquid comprising asymmetric dumbbell-shaped molecules, which can be deeply supercooled without crystallizing. We find that the dimensionless structural relaxation times - spanning six decades as a function of temperature, density, and degree of confinement - collapse when plotted versus excess entropy. The data also collaps…
Analysis of excess wings in broadband dielectric spectroscopy data of glass forming materials is found to provide evidence for anomalous time evolutions and fractional semigroups. Solutions of fractional evolution equations in frequency space are used to fit dielectric spectroscopy data of glass forming materials with a range between 4 and 10 decades in frequency. We show that with only three parameters (two relaxation times plus one exponent) excellent fits can be obtained for 5-methyl-2-hexanol and for methyl-m-toluate over up to 7 decades. The traditional Havriliak-Negami fit with three par…
The temperature evolution of the broadband $10^{-6}$-$10^{10}$ Hz dielectric susceptibility of the paradigmatic glass formers glycerol, propylene carbonate, and fluoro-aniline is analyzed assuming a three-step relaxation due to the $α$-process, its excess wing, and a $β$-process. We find that the $α$-peak and the wing can be described by susceptibility functions with temperature-independent high-frequency exponents, while the relative weight of these contributions does depend on the temperature. The excess wing and the $β$-process are distinct phenomena; in particular, the relaxation strength …
We compute partial structure factors, Kirkwood-Buff integrals (KBIs) and chemical potentials of model supercooled liquids with and without attractive interactions. We aim at investigating whether relatively small differences in the tail of the radial distribution functions result in contrasting thermodynamic properties. Our results suggest that the attractive potential favours the nucleation of long-range structures. Indeed, upon decreasing temperature, Bathia-Thornton structure factors display anomalous behaviour in the $k\to 0$ limit. KBIs extrapolated to the thermodynamic limit confirm this…
The classical nucleation equation, applied to two liquids, is completed by an additional enthalpy for solid supercluster formation governing the liquid and glass transformations. This model, successfully applied to d-mannitol, triphenyl phosphite and n-butanol, defines a formation rule of strong glacial phase, explaining the origin of the first-order transition of water from fragile-to-strong liquid at TLL = 228.5 K, only knowing Tg = 137.1 K, the melting heat and the melting temperature Tm. All thermodynamic properties and transitions, even under pressure P, are now predicted in agreement wit…
Dielectric spectroscopy covering more than 18 decades of frequency has been performed on propylene carbonate in its liquid and supercooled-liquid state. Using quasi-optic submillimeter and far-infrared spectroscopy the dielectric response was investigated up to frequencies well into the microscopic regime. We discuss the alpha-process whose characteristic timescale is observed over 14 decades of frequency and the excess wing showing up at frequencies some three decades above the peak frequency. Special attention is given to the high-frequency response of the dielectric loss in the crossover re…
We have performed a detailed dielectric investigation of the relaxational dynamics of glass-forming benzophenone. Our measurements cover a broad frequency range of 0.1 Hz to 120 GHz and temperatures from far below the glass temperature well up into the region of the small-viscosity liquid. With respect to the alpha relaxation this material can be characterized as a typical molecular glass former with rather high fragility. A good agreement of the alpha relaxation behavior with the predictions of the mode coupling theory of the glass transition is stated. In addition, at temperatures below and …
The glass transition in hydrogen-bonded glass formers differs from the glass transition in other glass formers. The Eshelby rearrangements of the highly viscous flow are superimposed by strongly asymmetric hydrogen bond rupture processes, responsible for the excess wing. Their influence on the shear relaxation spectrum is strong in glycerol and close to zero in PPE, reflecting the strength of the hydrogen bond contribution to the high frequency shear modulus. A recent theory of the highly viscous flow enables a quantitative common description of the relaxation spectra in shear, linear and non-…
We numerically study the equilibrium relaxation dynamics of a two-dimensional Mari-Kurchan glass model. The tree-like structure of particle interactions forbids both non-trivial structural motifs and the emergence of a complex free-energy landscape leading to a thermodynamic glass transition, while the finite-dimensional nature of the model prevents the existence of a mode-coupling singularity. Nevertheless, the equilibrium relaxation dynamics is shown to be in excellent agreement with simulations performed in conventional glass-formers. Averaged time-correlation functions display a phenomenol…
The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. Varying the external thermodynamic par…
The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how h…
We address the relaxation dynamics in hydrogen-bonded super-cooled liquids near the glass transition, measured via Broad-Band Dielectric Spectroscopy (BDS). We propose a theory based on decomposing the relaxation of the macroscopic dipole moment into contributions from hydrogen bonded clusters of $s$ molecules, with $s_{min}\le s \le s_{max}$. The existence of $s_{max}$ is due to dynamical arrest and its value may depend on the cooling protocol and on the aging time. The existence of $s_{max}$ is translated into a sum-rule on the concentrations of clusters of size $s$. We construct the statist…
Frequency dependent specific heat, introduced by Grest and Nagel, offers valuable insight into the vitrification of supercooled liquid. We calculate this quantity and other thermodynamic properties of supercooled liquid water by varying temperature and density across the "no man's land" all the way to the formation of amorphous ice. The calculations are aided by very long computer simulations, often more than 50 $μs$ long. Density fluctuations that arise from the proximity to a putative liquid-liquid (LL) transition at 228 K, cast a long shadow on the properties of water, both above and below …
We investigate the static and dynamic properties of a weakly polydisperse hard sphere system in the deeply supercooled state, i.e. at densities higher than that corresponding to the mode-coupling transition. The structural analysis reveals the emergence of icosahedral locally favoured structures, previously only found in trace quantities. We present a new approach to probe the shape of dynamically heterogeneous regions, which is insensitive to particle packing effects that can hamper such analysis. Our results indicate that the shape of the dynamically heterogeneous regions changes only weakly…
A number of general trends are known to occur in systems displaying secondary processes in glasses and glass formers. Universal features can be identified as components of large and small cooperativeness whose competition leads to excess wings or apart peaks in the susceptibility spectrum. To the aim of understanding such rich and complex phenomenology we analyze the behavior of a model combining two apart glassy components with a tunable different cooperativeness. The model salient feature is, indeed, based on the competition of the energetic contribution of groups of dynamically relevant var…
We provide broadband dielectric loss spectra of glass-forming glycerol with varying additions of LiCl. The measurements covering frequencies up to 10 THz extend well into the region of the fast beta process, commonly ascribed to caged molecule dynamics. Aside of the known variation of the structural alpha relaxation time and a modification of the excess wing with ion content, we also find a clear influence on the shallow loss minimum arising from the fast beta relaxation. Within the framework of mode-coupling theory, the detected significant broadening of this minimum is in reasonable accord w…
Nearly all glass-forming liquids feature, along with the structural alpha-relaxation process, a faster secondary process (beta-relaxation), whose nature belongs to the great mysteries of glass physics. However, for some of these liquids, no well-pronounced secondary relaxation is observed. A prominent example is the archetypical glass-forming liquid glycerol. In the present work, by performing dielectric spectroscopy under superhigh pressures up to 6 GPa, we show that in glycerol a significant secondary relaxation peak appears in the dielectric loss at P > 3 GPa. We identify this beta-relaxati…
We present nonlinear dielectric measurements of glass-forming 1-propanol, a prototypical example for the monohydroxy alcohols that are known to exhibit unusual relaxation dynamics, namely an additional Debye relaxation, slower than the structural alpha relaxation. Applying high ac fields of 468 kV/cm allows for a detailed investigation of the nonlinear properties of all three relaxation processes occurring in 1-propanol, namely the Debye, alpha, and beta relaxation. Both the field-induced variations of dielectric constant and loss are reported. Polarization saturation and the absorption of fie…
The fragile-to-strong crossover seems to be a general feature of metallic glass-forming liquids. Here, we study the behavior of shear viscosity, diffusion coefficient and vibrational density of states for Cu$_\text{x}$Zr$_\text{x}$Al$_{\text{100-2x}}$ alloy through molecular dynamics simulations. The results reveal that the fragile-to-strong temperature (T$_\text{fs}$) and the glass transition temperature (T$_\text{g}$) increase as the aluminum content becomes larger. The inverse of the diffusion coefficient as a function of temperature exhibits a dynamical crossover in the vicinity of T$_\tex…
Molecular motion at the experimental glass transition
Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS（蒙彼利埃大学，法国国家科学研究中心）；Univ. Grenoble Alpes, CNRS, LIPhy（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心）；Gulliver, CNRS UMR 7083, ESPCI Paris, PSL Research University（巴黎高等物理化工学院，巴黎文理研究大学，法国国家科学研究中心）
We present quasi-elastic light scattering (LS) and dielectric (DS) spectra of the glass former alpha-picoline (13K < T < 320K). At high temperatures the evolution of the susceptibility minimum is well described by mode coupling theory (MCT) yielding a critical temperature T_c = 162K +- 5K. At T_c > T > T_g the excess wing of the alpha-process identified in the DS spectra and characterized by a power-law exponent c is rediscovered in the LS spectra. Introducing a universal evolution for c = c[lg(tau_{alpha})] as suggested by DS data of several glass formers, the fast dynamics spectrum is single…
The physical origin of dielectric loss is shown to be sum of n number of subunits relaxation of a molecule, where n=1,2,3.. For each subunit relaxation, the idea of intermolecular dipole-dipole interactions triggered non-Debye dipole, ($\bf G$)$_{n}$=((1-g$_d$)$\bf G$$_{0}$)$_{n}$, and the ensuing dual dipole ($\bf G$$_{\pm}$)$_n$=($\bf G$$_0$$\pm$$\bf G$)$_n$, relaxation processes is proposed, where $\bf G$$_{-}$=g$_{d}$$\bf G$$_{0}$, $\bf G$$_{+}$=(2-g$_{d}$)$\bf G$$_{0}$, and $\bf G$$_{0}$ is a Debye dipole. Each subunit motion is statistically highly independent process and discriminated b…
The relaxation dynamics of glass forming liquids and their structure are influenced in the vicinity of confining walls. In view of the great potential of this effect for applications in those fields of science and industry, where liquids occur under strong confinement (e.g., nano-technology), the number of researchers studying various aspects and consequences of this non-monotonic behaviour has been rapidly growing. This review aims at providing an overview of the research activity in this newly emerging field. We first briefly discuss how competing mechanisms such as packing effects and short…
