Glass-forming Liquids Research Articles

SOME COMMENTS ON THE NATURE OF GLASSES

ABSTRACT I undertake a brief presentation of the early history of the development of our modern understanding of glass-forming liquids that provides a look at how the scientific and technological communities were viewing the state of the art and how the knowledge in the field developed. I discuss aspects of our understanding from how the Vogel–Fulcher–Tammann (VFT) equation became known to questions about the development of the concept of the “ideal” glass transition. The framework for this history leads us to ask whether some of the cautions that the pioneering researchers provided should have been taken more seriously by the community. I discuss, in particular, the view presented by Tammann and Hesse [Z. Anorg. Allg. Chem. 156, 245 (1926)] cautioning that the apparent singularity of the viscosity at a finite temperature was not physical and how the, now famous, VFT equation is accurate for interpolation rather than for extrapolation. The other point is the strong sense by much of the glass community that the so-called Kauzmann paradox [Chem. Rev. 43, 219 (1948)] is fundamental to glass-formation despite the comment by Kauzmann himself that the extrapolation of the entropy to negative values is “operationally meaningless.” I build on these ideas through a presentation of my own data and that of others that addresses the Tammann and Hesse comment through experiments that show that there is not a viscosity (or relaxation time) divergence near to the Kauzmann or VFT temperatures, and I show that the equilibrium entropy of a polymer that cannot crystallize shows no evidence of an ideal glass transition that is often invoked as a means of avoiding the Kauzmann paradox. In addition to providing some sense of the history of time (or a brief history of time and temperature in glass-forming liquids, with apologies to Stephen Hawking) and viscosity, I think that the data presented lead to the conclusion that much of our understanding of the problem of glass-formation is based on misleading interpretations of the original works as well as being inconsistent with the newer data that have been published over that past 25 yr or so. On an optimistic note, there are newer models that do not rely on the VFT divergence or the Kauzmann paradox to account for glass-formation in supercooled or equilibrium liquids. In addition, the experimental situation clearly leads to the possibility of deeper investigations into the “deep glassy state” through “finessing” the geological timescale issue of creating equilibrium glasses. Such investigations are ultimately important to understanding behavior of glassy materials, especially polymers, that are used deep in the glassy state, but still close enough to the glass temperature that models able to reliably predict their behavior require better representations of glass-formation to engineer their performance.

Uniqueness of glasses prepared via x-ray induced yielding

Abstract The yield point marks the beginning of plastic deformation for a solid subjected to sufficient stress,
but it can alternatively be reached by x-ray irradiation. We characterize this latter route in terms
of thermodynamics, structure and dynamics for a series of GeSe3 chalcogenide glasses with different
amount of disorder. We show that a sufficiently long irradiation at room temperature results in
a stationary and unique yielding state, independent of the initial state of the glass. The glass at
yield is more disordered and has higher enthalpy than the annealed glass, but its properties are not
extreme: they rather match those of a glass instantaneously quenched from a temperature 20% higher than the glass-transition temperature. This is a well-known, key temperature for glass-forming liquids
which marks the location of a dynamical transition, and it’s remarkable that different glasses upon
irradiation head all there.

Selecting relevant structural features for glassy dynamics by information imbalance

We numerically investigate the identification of relevant structural features that contribute to the dynamical heterogeneity in a model glass-forming liquid. By employing the recently proposed information imbalance technique, we select these features from a range of physically motivated descriptors. This selection process is performed in a supervised manner (using both dynamical and structural data) and an unsupervised manner (using only structural data). We then apply the selected features to predict future dynamics using a machine learning technique. One of the advantages of the information imbalance technique is that it does not assume any model a priori, i.e., it is a non-parametric method. Finally, we discuss the potential applications of this approach in identifying the dominant mechanisms governing the glassy slow dynamics.

Understanding Relaxation in the Kob-Andersen Liquid Based on Entropy, String, Shoving, Localization, and Parabolic Models.

We assess the validity of a range of models of glass formation based on molecular dynamics simulation results of the Kob-Andersen (KA) model system under a wide range of constant volume and constant pressure conditions. These models include the Adam-Gibbs model emphasizing configurational entropy, the string model emphasizing collective particle exchange motion, the shoving model emphasizing material elasticity, the localization model emphasizing dynamical free volume, and parabolic models based on the ideas of dynamic facilitation and, alternatively, the hypothesis that glass formation involves an avoided critical point. We demonstrate that these seemingly disparate models all provide a reasonable description of structural relaxation and diffusion data for the KA model system under all simulation conditions considered. Hence, the present study points to some unity in our understanding of the relationship between leading models of glass formation, supporting inferences drawn from previous studies of polymeric glass-forming liquids.

Relaxation dynamics of a liquid in the vicinity of an attractive surface: The process of escaping from the surface.

We analyze the displacements of the particles of a glass-forming molecular liquid perpendicular to a confining solid surface using extensive molecular dynamics simulations with atomistic models. In the vicinity of an attractive surface, the liquid molecules are trapped. Transient localization of liquid molecules near the surface introduces a relaxation process related to the escape of molecules from the surface into the dynamics of the interfacial liquid layer. To describe this process, we analyze several dynamical observables of the confined liquid. The self-intermediate scattering function and the mean-squared displacement of the particles located in the interfacial layer are dominated by the process of escaping from the surface. This relaxation process is also associated with a strong heterogeneity in the mobility of the interfacial particles. The studied model liquid is hydrogenated methyl methacrylate. For the confining wall, we consider different models, namely a periodic single layer of graphene and a frozen amorphous configuration of the bulk liquid (frozen wall). Near graphene, where the liquid molecules form a layered structure and adopt parallel-to-surface orientation, a clear separation between small-scale movements of the molecules near the surface and the process of escaping from the surface is observed. This is reflected in the three-step relaxation of the interfacial layer. However, near the frozen wall, where the liquid molecules do not have a preferential alignment, a clear three-step relaxation is not seen, even though the dynamical quantities are controlled by the process of escaping from the surface.

Influence of Density and Pressure on Glass Formation in the Kob-Andersen Model.

We systematically study glass formation in the well-known Kob-Andersen model over a wide range of densities and pressures as a basis for judging the "universality" of glass formation through a comparison to a recent systematic study of model polymeric glass-forming liquids. Our purpose is to establish general characteristics of glass formation, to identify new relations, and to discern which properties of glass-forming liquids are material-specific and which are "universal." To this end, we analyze a number of characteristic properties of glass formation, such as the structural relaxation time, self-diffusion coefficient, viscosity, characteristic temperatures, and fragility. We also consider a suite of properties presumably related to dynamic heterogeneity in an attempt to better understand its relation to structural relaxation. We demonstrate that the glassy dynamics in the Kob-Andersen model exhibit many of the essential trends observed in polymeric glass-forming liquids, pointing to a remarkable "universality" of many aspects of glass formation.

Monte Carlo simulations of glass-forming liquids beyond Metropolis.

Monte Carlo simulations are widely employed to measure the physical properties of glass-forming liquids in thermal equilibrium. Combined with local Monte Carlo moves, the Metropolis algorithm can also be used to simulate the relaxation dynamics, thus offering an efficient alternative to molecular dynamics. Monte Carlo simulations are, however, more versatile because carefully designed Monte Carlo algorithms can more efficiently sample the rugged free energy landscape characteristic of glassy systems. After a brief overview of Monte Carlo studies of glass-formers, we define and implement a series of Monte Carlo algorithms in a three-dimensional model of polydisperse hard spheres. We show that the standard local Metropolis algorithm is the slowest and that implementing collective moves or breaking detailed balance enhances the efficiency of the Monte Carlo sampling. We use time correlation functions to provide a microscopic interpretation of these observations. Seventy years after its invention, the Monte Carlo method remains the most efficient and versatile tool to compute low-temperature properties in supercooled liquids.

In-situ scattering and calorimetric studies of crystallization pathway and kinetics in a Cu-Zr-Al bulk metallic glass

The crystallization route and kinetics of a Cu-Zr-Al bulk metallic glass (BMG), based on Cu50Zr50, were investigated using in-situ synchrotron small- and wide-angle X-ray scattering (SAXS/WAXS), in-situ high-energy X-ray diffraction (HEXRD), and differential scanning calorimetry (DSC). The acquisition of kinetic diagrams of SAXS/WAXS enables the direct construction of the overall phase transformation route from room temperature to the onset temperature of solid state phase transformation upon heating. It is revealed that the studied alloy undergoes multiple steps (at least five steps) before reaching the high-temperature thermodynamic equilibrium. This is distinct from the commonly believed simple path of glass → Cu10Zr7 + CuZr2 → B2-CuZr predicted by the Cu-Zr equilibrium phase diagram. In addition to thermodynamics, we emphasize that kinetic factors play a prominent role in the phase transformation process of Cu-Zr-Al BMGs. Furthermore, isothermal crystallization kinetics analyses conducted by in-situ HEXRD and DSC indicate that the formation of the initial crystalline phase, specifically the Cu10Zr7, follows an interface-controlled quasi-polymorphic process with an increasing nucleation rate. The findings of this study may provide novel insights into the crystallization mechanism of glass-forming supercooled liquids from a thermophysical perspective.

Normalizing flows as an enhanced sampling method for atomistic supercooled liquids

Abstract Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an atomistic model for glass-forming liquids. This is a notoriously difficult task, as it amounts to ergodically exploring the complex free energy landscape of a disordered and frustrated many-body system. We optimize a normalizing flow model to successfully transform high-temperature configurations of a dense liquid into low-temperature ones, near the glass transition. We perform a detailed comparative analysis with established enhanced sampling techniques developed in the physics literature to assess and rank the performance of normalizing flows against state-of-the-art algorithms. We demonstrate that machine learning methods are very promising, showing a large speedup over conventional molecular dynamics. Normalizing flows show performances comparable to parallel tempering and population annealing, while still falling far behind the swap Monte Carlo algorithm. Our study highlights the potential of generative machine learning models in scientific computing for complex systems, but also points to some of its current limitations and the need for further improvement.

Specific line shape of the lowest frequency Raman scattering modes of triethylene glycol.

For both dielectric spectroscopy and light scattering spectra, the relaxation modes in the microwave region have been characterized by the Debye relaxation model, which is determined by the peak frequency, or by an empirically extended model (e.g., Cole-Davidson and Kohlrausch-Williams-Watts), which has the appropriate line shape. For light scattering from glass-forming liquids, the general line shape is a broader high frequency side in comparison with Debye relaxation. However, for triethylene glycol (TEG) in liquid form at room temperature, the lowest frequency Raman scattering (LFR) mode shows a peak at about 3.0GHz, which is narrower than that expected for the Debye relaxation. With increasing temperature, this peak exhibits a significant blueshift and begins to resemble the Debye relaxation shape, indicating that the LFR mode of TEG is also a relaxation mode. The narrowing of the LFR mode of TEG is suggested to be caused from the increased non-whiteness of the fluctuation correlations due to increased hydrogen bonding. This is a consequence of breaking the Debye relaxation model's approximation of the overdamping and narrowing limits in the GHz region, which was found in this study by analyzing the relaxation modes of Raman scattering using the multiple random telegraph model for evaluating thermal bath correlation. The analysis results show that the LFR relaxation times of TEG and the main dielectric relaxation overlap only by 333K. However, the second LFR mode and β-relaxation at higher frequencies coincide over a wide temperature range, suggesting that they are corresponding modes.

Unusual dynamics of tetrahedral liquids caused by the competition between dynamic heterogeneity and structural heterogeneity.

Tetrahedral liquids exhibit intriguing thermodynamic and transport properties because of the various ways tetrahedra can be packed and connected. Recently, an unusual temperature dependence of the stretching exponent β in a model tetrahedral liquid ZnCl2 from Tm + 85K to Tm + 35K has been reported using neutron-spin echo spectroscopy. This discovery stands in sharp contrast to other glass-forming liquids. In this study, we conducted neural network force field driven molecular dynamic simulations of ZnCl2. We found a non-monotonic temperature dependence of β from liquid to supercooled liquid temperatures. Further structural decomposition and dynamic analysis suggest that this unusual dynamic behavior is a result of the competition between the decrease in the diversity of tetrahedra motifs (structural heterogeneity) and the increase in glassy dynamic heterogeneity. This result may contribute to new understandings of the structural relaxation of other network liquids.

Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test.

It has been recognized of late that even amorphous, glass-forming materials in two dimensions (2D) are affected by Mermin-Wagner-type long wavelength thermal fluctuation, which is inconsequential in three dimensions (3D). We consider the question of whether the effect of spatial dimension on dynamics is only limited to such fluctuations or if the nature of glassy dynamics is intrinsically different in 2D. To address it, we study the relationship between dynamics and thermodynamics using the Adam-Gibbs (AG) relation and the random first order transition (RFOT) theory. Using two model glass-forming liquids, we find that even after removing the effect of long wavelength fluctuations, the AG relation breaks down in two dimensions. Next, we consider the effect of anharmonicity of vibrational entropy-a second factor that affects the thermodynamics but not dynamics. Using the potential energy landscape formalism, we explicitly compute the configurational entropy, both with and without the anharmonic correction. We show that even with both the corrections, the AG relation still breaks down in 2D. The extent of deviation from the AG relation crucially depends on the attractive vs repulsive nature of interparticle interactions, choice of representative timescale (diffusion coefficient vs α-relaxation time), and implies that the RFOT scaling exponents also depend on these factors. Thus, our results suggest that some differences in the nature of glassy dynamics between 2D and 3D remain that are not explained by long wavelength fluctuations.

Proof of concept for a nonadditive stochastic model of supercooled liquids.

The recently proposed nonadditive stochastic model (NSM) offers a coherent physical interpretation for diffusive phenomena in glass-forming systems. This model presents nonexponential relationships between viscosity, activation energy, and temperature, characterizing the non-Arrhenius behavior observed in supercooled liquids. In this work, we fit the NSM viscosity equation to experimental temperature-dependent viscosity data corresponding to 25 glass-forming liquids and compare the fit parameters with those obtained using the Vogel-Fulcher-Tammann (VFT), Avramov-Milchev (AM), and Mauro-Yue-Ellison-Gupta-Allan (MYEGA) models. The results demonstrate that the NSM provides an effective fitting equation for modeling viscosity experimental data in comparison with other established models (VFT, AM, and MYEGA), characterizing the activation energy in fragile liquids, presenting a reliable indicator of the degree of fragility of the glass-forming liquids.

Mold material and dimension effects on the microstructural gradient in a glass-ceramic

Microstructural gradients can significantly affect the properties of glass-ceramics (GCs). Such spatial variations in glass-ceramic (GC) microstructure may result from a non-uniform cooling rate when the glass-forming liquid is cast into a mold. This study investigates the material and mold size influence on the cooling process, leading to a non-uniform distribution of crystalline nuclei in the parent glass. We used a high-nucleation rate, non-stoichiometric, lithium metasilicate GC as a model. Initially, the glass-forming liquid was cooled in cylindrical molds with diameters of 7 and 14 mm, made from copper and 304 stainless steel – materials with distinct thermal diffusivities. Simulated thermography, validated by thermocouple data, showed contrasting cooling profiles across the samples. Our key findings are: i) cooling rate: faster cooling in the smaller mold resulted in a lower crystal number density and a reduced crystallized volume fraction (αv) as expected; ii) mold material: surprisingly, copper molds led to quicker glass shrinkage, which facilitated the earlier formation of air gaps with reduced heat transfer and slower cooling than steel, favoring incipient crystallization during the cooling path; iii) microstructure: samples cooled in both molds exhibited higher αv in the central and upper (mold contact-free) regions due to slower cooling compared to the mold base and edges. Therefore, this study reveals how mold material and size affect microstructural gradients in GCs, paving the way for tailoring crystallization and microstructure through strategic mold design.

Direct Numerical Analysis of Dynamic Facilitation in Glass-Forming Liquids.

We propose a computational strategy to quantify the temperature evolution of the timescales and length scales over which dynamic facilitation affects the relaxation dynamics of glass-forming liquids at low temperatures, which requires no assumption about the nature of the dynamics. In two glass models, we find that dynamic facilitation depends strongly on temperature, leading to a subdiffusive spreading of relaxation events which we characterize using a temperature-dependent dynamic exponent. We also establish that this temperature evolution represents a major contribution to the increase of the structural relaxation time.

Trends in the temperature dependence of dynamical heterogeneity in strong and fragile supercooled liquids

The temperature dependence of the Kohlrausch-Williams-Watts (KWW) stretching exponent β of shear relaxation kinetics is determined for a wide variety of deeply supercooled glass-forming liquids with fragility index m ranging between ∼ 30 and 90 using small amplitude oscillatory shear parallel plate rheometry. Intriguingly, and contrary to conventional wisdom, β and m are observed to be uncorrelated at temperatures close to the glass transition Tg. However, a clear pattern emerges when the variation of β is considered as a function of the α-relaxation timescale τα. In particular, β is observed to increase rapidly (slowly) for relatively strong (fragile) liquids with decreasing τα upon increasing temperature above Tg. Consequently dβ/d(log τα) is found to be negatively correlated with m near and above Tg. A possible origin of this intriguing trend is discussed within the frameworks of the energy landscape and the elastic facilitation models of relaxation of supercooled liquids.

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel–Fulcher–Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

Stringlet excitation model of the boson peak.

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

Dipolar Order Controls Dielectric Response of Glass-Forming Liquids.

The dielectric response of liquids reflects both reorientation of single molecular dipoles and collective modes, i.e., dipolar cross-correlations. A recent theory predicts the latter to produce an additional slow peak in the dielectric loss spectrum. Following this idea we argue that in supercooled liquids the high-frequency power law exponent of the dielectric loss β should be correlated with the degree of dipolar order, i.e., the Kirkwood correlation factor g_{K}. This notion is confirmed for 25 supercooled liquids. While our findings support recent theoretical work the results are shown to violate the earlier Kivelson-Madden theory.

A model of heterogeneous undercooled liquid and glass accounting for temperature-dependent nonexponentiality and enthalpy fluctuation.

Dynamic heterogeneity is a fundamental characteristic of glasses and undercooled liquids. The heterogeneous nature causes some of the key features of systems' dynamics such as the temperature dependence of nonexponentiality and spatial enthalpy fluctuations. Commonly used phenomenological models such as Tool-Narayanaswamy-Moynihan (TNM) and Kovacs-Aklonis-Hutchinson-Ramos fail to fully capture this phenomenon. Here we propose a model that can predict the temperature-dependent nonexponential behavior observed in glass-forming liquids and glasses by fitting standard differential scanning calorimetry curves. This model extends the TNM framework of structural relaxation by introducing a distribution of equilibrium fictive temperature (Tfe) that accounts for heterogeneity in the undercooled liquid. This distribution is then frozen at the glass transition to account for the heterogeneous nature of the glass dynamics. The nonexponentiality parameter βKWW is obtained as a function of temperature by fitting the Kohlrauch-Williams-Watts (KWW) equation to the calculated relaxation function for various organic and inorganic undercooled liquids and glasses. The calculated temperature dependent βKWW shows good agreement with the experimental ones. We successfully model the relaxation dynamics far from equilibrium for two silicate systems that the TNM model fails to describe, confirming that temperature dependent nonexponentiality is necessary to fully describe these dynamics. The model also simulates the fluctuation of fictive temperature δTf during isothermal annealing with good qualitative agreement with the evolution of enthalpy fluctuation reported in the literature. We find that the evolution of enthalpy fluctuation during isothermal annealing heavily depends on the cooling rate, a dependence that was not previously emphasized.