Fragile Glass-forming Liquids Research Articles

Quantification of the volume-fraction reduction of sheared fragile glass-forming liquids and its impact on rheology

Quantification of the volume-fraction reduction of sheared fragile glass-forming liquids and its impact on rheology

Understanding the Fragile-to-Strong Transition in Silica from Microscopic Dynamics.

In this work, we revisit the fragile-to-strong transition (FTS) in the simulated BKS silica from the perspective of microscopic dynamics in an effort to elucidate the dynamical behaviors of fragile and strong glass-forming liquids. Softness, which is a machine-learned feature from local atomic structures, is used to predict the microscopic activation energetics and long-term dynamics. The FTS is found to originate from a change in the temperature dependence of the microscopic activation energetics. Furthermore, results suggest there are two diffusion channels with different energy barriers in BKS silica. The fast dynamics at high temperatures is dominated by the channel with small energy barriers (<∼1 eV), which is controlled by the short-range order. The rapid closing of this diffusion channel when lowering temperature leads to the fragile behavior. On the other hand, the slow dynamics at low temperatures is dominated by the channel with large energy barriers controlled by the medium-range order. This slow diffusion channel changes only subtly with temperature, leading to the strong behavior. The distributions of barriers in the two channels show different temperature dependences, causing a crossover at ∼3100 K. This transition temperature in microscopic dynamics is consistent with the inflection point in the configurational entropy, suggesting there is a fundamental correlation between microscopic dynamics and thermodynamics.

A perspective on the fragility of glass-forming liquids

We discuss possible extraneous effects entering in the conventional measures of "fragility" at atmospheric pressure that may obscure a characterization of the genuine super-Arrhenius slowdown of relaxation. We first consider the role of density, which increases with decreasing temperature at constant pressure, and then the potential influence of the high-temperature dynamical behavior and of the associated activation energy scale. These two effects involve both thermodynamic parameters and the strength of the "bare" activation energy reflecting the specific bonding between neighboring molecules. They vary from system to system with, most likely, little connection with any putative collective behavior associated with glass formation. We show how to scale these effects out by refining the definition of fragility and modifying the celebrated Angell plot. We dedicate this note to our great and so inspiring friend, Austen Angell, and associate in this tribute another dear colleague who died too soon, Daniel Kivelson.

Crystallization and relaxation dynamics of glass-forming liquids at the Kauzmann temperature

If the entropy extrapolation of supercooled liquids (SCL) suggested by Kauzmann was correct, then they would have the same entropy as their stable crystalline phase at a certain low temperature, below the laboratory glass transition (Tg), known as the Kauzmann temperature (TK). Extrapolating even further, the liquid entropy would be null at a temperature above absolute zero, violating the Third Law of Thermodynamics and constituting a paradox. Several possibilities have been proposed over the past 70 years to solve this paradox with different degrees of success. Our objective here is to access liquid dynamics at deep supercoolings to test the so-called crystallization solution to the paradox. By comparing the relaxation and crystallization kinetics determined above Tg and extrapolated down to TK, a possible solution would be that the crystallization time is shorter than the relaxation time, which would mean that a SCL cannot reach the TK. In this case, the liquid stability limit or kinetic spinodal temperature (Tks) should be higher than TK. We tested two fragile glass-forming liquids (diopside and wollastonite) and two strong liquids (silica and germania). For the fragile substances, Tks ≫ TK, hence such a supercooled liquid cannot exist at TK, and the entropy crisis is averted. On the other hand, the results for the strong liquids were inconclusive. We hope the findings of this work encourage researchers to further investigate the liquid dynamics of different strong glass-forming systems at deep supercoolings.

The emergence of cooperativity accompanying vitrification: insights from density fluctuation dynamics

We discuss the emergence and growth of the cooperativity accompanying vitrification based on the density fluctuation dynamics for fragile glass-forming liquids. (i) The relaxation of density fluctuations proceeds by the particle (density) exchange process, and is diffusive; that is, the allowable kinetic paths are strongly restricted by the local conservation law. (ii) In normal liquid states, this exchange process is less cooperative, and the diffusion coefficient of density fluctuations Dc is given as , where is the particle size and is the structural relaxation time. On the other hand, in supercooled states the restriction on the kinetic path is more severe with increasing the degree of supercooling, which makes the exchange process more cooperative, resulting in with being the cooperative length scale. (iii) The molecular dynamics simulation results show that the self-diffusion coefficient of the tagged particle, Ds, almost coincides with Dc, suggesting that the collective density diffusion and the particle diffusion closely share the same mechanism: in normal states Ds determines Dc, but vice versa in supercooled states. This immediately leads to the idea that the breakdown of the Stokes–Einstein relation is not the anomaly in the single-particle dynamics but reflects the increase in the cooperativity in the density diffusion at the length scale of .

Relaxation kinetics in fragile glass-forming liquids: a dispersive kinetics view of Vogel–Tammann–Fulcher behaviour in o-terphenyl

Relaxation kinetics in fragile glass-forming liquids: a dispersive kinetics view of Vogel–Tammann–Fulcher behaviour in o-terphenyl

Analysis and characterization of the transition from the Arrhenius to non-Arrhenius structural relaxation in fragile glass-forming liquids

We have studied the transition from an Arrhenius-like to a non-Arrhenius-like structural relaxation behavior in fragile glass-forming liquids. This transition is denoted by the temperature TA that usually occurs above the melting point Tm and the dynamic crossover temperature TB. Recent studies reveal that TA is a characteristic temperature related with the dynamical properties of the system. However, its unambiguous determination is not easy. In this work, a method to obtain the temperature TA from the experimental data of α-relaxation time is presented. The obtained TA is compared with the cooperativity onset temperature Tx extracted from the bond strength–coordination number fluctuation model. The result reveals that TA is close to Tx for fragile liquids. From the result of the present analyses combined with the linear relation Tx $$\propto$$ T0, where T0 is the Vogel temperature, the Arrhenius crossover phenomenon in fragile liquids is linked to the low-temperature structural relaxation dynamics.

Molecular simulations of fragility of linear and ring polymers

Nowadays, investigation on fragility in glass-forming liquids is a hot topic in the field of condensed matter physics, since the understanding of its microscopic mechanism is useful to uncover the underlying mechanism of the glass transition. In the present paper, we performed dynamic Monte Carlo simulations to explore the correlations between fragility index and conformational changes in linear and ring polymer chains. Compared with ring chains, linear chains exhibit a higher fragility index. In addition, for both ring and linear chains, during approaching the glass transition temperature (Tg), the fraction of segments with trans-conformation increased significantly. To reveal the effect of conformational changes on segmental dynamics during relaxation, a new parameter, the aggregation region of segments with trans-conformation (ARST), is proposed. The maximum ARST has the lowest mobility, which determines the relaxation time of polymers. The fragility index has a strong relationship with the maximum ARST. For linear chains, during approaching Tg, the maximum ARST grew more abruptly, resulting in the larger fragility index.

The kinetic fragility of Pt-P- and Ni-P-based bulk glass-forming liquids and its thermodynamic and structural signature

The thermodynamic and kinetic properties of Pt-P- and Ni-P-based bulk glass-forming liquids are investigated using differential scanning calorimetry and three-point beam bending. The kinetic fragility of the alloys is determined by measuring relaxation times and equilibrium viscosities. In the Pt-P-based alloy family a Pt-rich alloy is one of the most fragile bulk glass-forming liquids in the vicinity of the glass transition reported so far. The fragility parameter D∗ increases significantly with decreasing Pt-content, which is due to a more pronounced loss of excess entropy upon undercooling for the fragile liquids. Relying on previous observations made for Pd-P-based alloys, it is argued that a bifurcation of the P environment into Pt-Ni-P and Pt-Cu-P structural units stabilizes the deeply undercooled liquid due to formation of medium range order (MRO). This is supported by synchrotron X-ray scattering experiments, which reveal the formation of a pre-peak in the total structure factor with increasing fragility. Adapting a previously reported empirical correlation, we show that the more fragile liquid alloys are characterized by a more pronounced dilatation of atomic pair correlations on the length scale of 1 nm, corroborating the idea that the observed fragility behavior of Pt-P-based bulk glass-forming liquids is inherently related to structural changes on the length scale of MRO.

The impact of the stretching exponent on fragility of glass-forming liquids

The paper compared two factors governing fragility. The first one is thermodynamic, depending on the change in configurational entropy. The second one is kinetic and is determined by the stretching exponent β. Using a simple mathematical development, we show that the kinetic term $$m_{\text{K}} = f( {\beta_{{T_{\text{g}} }} } )\partial \ln \beta \left( T \right)/\partial \ln T|_{{T = T_{\text{g}} }}$$ is always smaller than 1, where T g is the glass transition temperature and $$f( {\beta_{{T_{\text{g}} }} } )$$ is the given functions of the stretching exponent at T = T g. As a result, the contribution of the kinetic term on the fragility of strong glasses is <6 %. Fragile glasses have a larger value of fragility index m, and for them, the influence of the kinetic term is significantly smaller. In any case, the thermodynamic term plays the main role in fragility and the kinetic one can be neglected.

Observation of distinct atomic relaxation process in a phase-separated metallic glass-forming melt

We have investigated the atomic relaxation processes in phase-separated alloy melts using quasielastic neutron scattering. Among the three alloy melts studied (i.e., Al30Cu20Sn50, Al30Cu30Sn40 and Y28Ti28Al24Co20), Y28Ti28Al24Co20 is not only a phase-separated melt but also vitrified upon quenching. In this glass-forming melt, we have observed dissimilar relaxation processes in the different phases of the melt: a collective atomic transport process in the phase that exhibits a slow relaxation process and an atomic jump diffusion process in the phase that displays a fast relaxation process. Interestingly, the temperature dependence of the diffusion process in the former phase is a non-Arrhenius process, which is similar to that observed in many fragile glass-forming liquids. In contrast, the temperature dependence of the diffusion process is an Arrhenius process in the later phase, which is a characteristic of non–glass-forming simple liquids.

Percolative heterogeneous topological constraints and fragility in glass-forming liquids

We present a precise atomic scale approach to topological rigidity theory of sodium silicate glasses and liquids which contain temperature-dependent constraints. Using molecular dynamics simulations, the spatial distribution of such constraints is followed as a function of temperature and pressure. Results show that the distribution of constraints broken by thermal activation is not homogeneous in the system. The spatial extent of these flexible regions shows a percolative behavior at a characteristic temperature which is deeply connected to flexible-to-rigid transitions, and influences the fragility of the glass-forming liquid.

Molecular Dynamics of the Supercooled Pharmaceutical Agent Posaconazole Studied via Differential Scanning Calorimetry and Dielectric and Mechanical Spectroscopies

This paper presents comprehensive studies on the molecular dynamics of a pharmaceutically important substance, posaconazole. In order to characterize relaxation dynamics in the supercooled liquid and glassy states, dielectric and mechanical spectroscopies were applied. Dielectric data have indicated multiple relaxation processes that appear above and below the glass transition temperature Tg (τα=100 s) of posaconazole. From the curvature of the dielectric log10(τα) versus inverse of temperature dependence, we determine so-called "fragility", being a very popular parameter for classifying the structural dynamics of supercooled liquids and polymers. From the calculations, we get m=150, which means that is one of the most fragile glass-forming liquids. In this paper, the relaxation dynamics of supercooled posaconazole extracted from the dielectric response function was also confronted with shear-mechanical relaxation. Finally, we have also presented a direct comparison of the fragility and the number of dynamically correlated molecules Nc determined from dynamic calorimetry curves and dielectric and mechanical spectroscopies, showing a clear deviation in the picture of glass-transition dynamics generated by calorimetric and spectroscopic techniques.

Slow relaxations and stringlike jump motions in fragile glass-forming liquids: Breakdown of the Stokes-Einstein relation

We perform molecular dynamics simulation on a glass-forming liquid binary mixture with the soft-core potential in three dimensions. We investigate crossover of the configuration changes caused by stringlike jump motions. With lowering the temperature T, the motions of the particles composing strings become larger in sizes and displacements, while those of the particles surrounding strings become smaller. Then the contribution of the latter to time-correlation functions tends to be long-lived as T is lowered. As a result, the relaxation time τ(α) and the viscosity η grow more steeply than the inverse diffusion constant D(-1) at low T, leading to breakdown of the Stokes-Einstein relation. At low T, the diffusion occurs as activation processes and may well be described by short-time analysis of rare jump motions with broken bonds and large displacements. Some characteristic features of the Van Hove self-correlation function arise from escape jumps over high potential barriers. We also visualize the particle motions at string formation taking place in a very short time.

Erratum: “Universality of the onset of activated transport in Lennard-Jones liquids with tunable coordination: Implications for the effects of pressure and directional bonding on the crossover to activated transport, configurational entropy, and fragility of glassforming liquids” [J. Chem. Phys. 136, 084504 (2012)

Erratum: “Universality of the onset of activated transport in Lennard-Jonesliquids with tunable coordination: Implications for the effects of pressureand directional bonding on the crossover to activated transport,configurational entropy, and fragility of glassforming liquids” [J. Chem.Phys. 136, 084504 (2012)]

Universality of the onset of activated transport in Lennard-Jones liquids with tunable coordination: Implications for the effects of pressure and directional bonding on the crossover to activated transport, configurational entropy, and fragility of glassforming liquids

We establish, via classical density functional theory, that the crossover to activated transport in liquids takes place when the depth of the metastable minimum in the free energy corresponding to long-lived aperiodic structures reaches a certain near universal value. We show that the particle vibrational displacement is strongly correlated with this depth in a broad range of pressure and temperature, thus providing basis for a Lindemann-like criterion for the onset of activated transport in liquids. The configurational entropy at the crossover temperature T(cr), too, is found to be nearly system-independent, consistent with the random first order transition theory. We show that to reproduce existing data for the pressure dependence of T(cr), the liquid must increase its coordination with pressure. Upon increasing pressure at fixed coordination, the liquid's fragility is predicted to exhibit re-entrant behavior. This prediction is consistent with glycerol data but is in contrast with data in several organic liquids and polymers, whose fragility monotonically decreases with pressure in the so far accessed pressure range. Allowing for increase in coordination with pressure mitigates the disagreement, owing to the resulting decrease in the thermal expansivity. Finally, we rationalize the correlation between the isobaric and isochoric fragilities put forth by Casalini and Roland [Phys. Rev. E 72, 031503 (2005)] and make predictions on the limiting behavior of the fragility at high pressure.

Enthalpy and Dielectric Relaxations of Triacetin in the Vicinity of Glass Transition

To understand the experimental observation that the dynamic parameters determined for enthalpy and dielectric relaxation might differ in fragile glass-forming molecular liquids, a fragile molecular liquid, triacetin, was chosen for the study of the two relaxation dynamics. The non-Arrhenius and nonexponential characters were focused, and the kinetic fragility and non-exponential parameter determined from the two relaxation measurements were found to be remarkably similar. Experimental results indicate that the degree of correlation in the molecular motions involved in the two relaxations depends on molecular flexibility. The dependence of the dynamic parameters on molecular structures in the glass forming liquids is discussed.

Compositional dependence of thermal stability, glass-forming ability and fragility index in some Se–Te–Sn glasses

Non-isothermal DSC thermograms were obtained for the ternary Se 90Te 10− x Sn x ( x = 2, 4, 6 and 8) chalcogenide glasses in order to determine the melting temperature T m, glass transition temperature T g, onset T c and peak T p temperatures of crystallization. These temperatures were utilized to investigate the thermal stability through the calculations of temperature difference ( T c − T g), the glass transition activation energy E t, the parameter S and the average value of crystallization rate factor 〈 K p〉. In addition, the glass forming ability was estimated by the criteria of reduced glass transition temperature, T rg and Hruby parameter H R. The fragility index m for the present glasses was determined in order to see whether these materials are obtained from strong or fragile glass-forming liquid. Results reveal that, both thermal stability and glass forming ability exhibit a maximum at x = 4 at.% of Sn. Meanwhile, the prepared glasses were obtained from strong glass-forming liquid as evident from the fragility index calculations. The compositional dependence of the above parameters was discussed on the basis of Philips and Thorpe topological model and the critical composition occurs at an average coordination number 〈 r〉 = 2.16 but not 2.40. This is due to the formation of iono-covallent bonds when the glass doped with heavy elements like Sn.

An upper limit to kinetic fragility in glass-forming liquids

The kinetic fragility of a liquid is correlated to the magnitude of enthalpy hysteresis in various glass-forming materials during thermal cycling across the glass transition. While the lower bound of liquid fragility is well known, there has been little research into the possibility of an inherent upper limit to fragility. In this paper, we present a theoretical argument for the existence of a maximum fragility and show that the correlation between fragility and enthalpy hysteresis allows for an empirical evaluation of the upper limit of fragility. This upper limit occurs as the enthalpy hysteresis involved in thermal cycling about the glass transition approaches zero, leading to m(max)≈175. This result agrees remarkably well with our previous estimate. The dynamics of maximum fragility liquids are discussed, and a critical temperature of ∼1.5 T(g) (where T(g) is the glass transition temperature) is revealed where a transition from nonexponential to exponential structural relaxation occurs.

Does viscosity describe the kinetic barrier for crystal growth from the liquidus to the glass transition?

An analysis of the kinetic coefficient of crystal growth U(kin), recently proposed by Ediger et al. [J. Chem. Phys. 128, 034709 (2008)], indicates that the Stokes-Einstein/Eyring (SE/E) equation does not describe the diffusion process controlling crystal growth rates in fragile glass-forming liquids. U(kin) was defined using the normal growth model and tested for crystal data for inorganic and organic liquids covering a viscosity range of about 10(4)-10(12) Pa s. Here, we revisit their interesting finding considering two other models: the screw dislocation (SD) and the two-dimensional surface nucleated (2D) growth models for nine undercooled oxide liquids, in a wider temperature range, from slightly below the melting point down to the glass transition region T(g), thus covering a wider viscosity range: 10(1)-10(13) Pa s. We then propose and use normalized kinetic coefficients (M(kin)) for the SD and 2D growth models. These new kinetic coefficients restore the ability of viscosity to describe the transport part of crystal growth rates (M(kin)∼1/η and ξ∼1) from low to moderate viscosities (η<10(6) Pa s), and thus the SE/E equation works well in this viscosity range for all systems tested. For strong glasses, the SE/E equation works well from low to high viscosities, from the melting point down to T(g)! However, for at least three fragile liquids, diopside (kink at 1.08T(g), η=1.6×10(8) Pa s), lead metasilicate (kink at 1.14T(g), η=4.3×10(6) Pa s), and lithium disilicate (kink at 1.11T(g), η=1.6×10(8) Pa s), there are clear signs of a breakdown of the SE/E equation at these higher viscosities. Our results corroborate the findings of Ediger et al. and demonstrate that viscosity data cannot be used to describe the transport part of the crystal growth (via the SE/E equation) in fragile glasses in the neighborhood of T(g).