On the correlation between fragility and stretching in glass-forming liquids

High-pressure X-ray photon correlation spectroscopy at fourth-generation synchrotron sources

A new experimental setup combining X-ray photon correlation spectroscopy (XPCS) in the hard X-ray regime and a high-pressure sample environment has been developed to monitor the pressure dependence of the internal motion of complex systems down to the atomic scale in the multi-gigapascal range, from room temperature to 600 K. The high flux of coherent high-energy X-rays at fourth-generation synchrotron sources solves the problems caused by the absorption of diamond anvil cells used to generate high pressure, enabling the measurement of the intermediate scattering function over six orders of magnitude in time, from 10-3 s to 103 s. The constraints posed by the high-pressure generation such as the preservation of X-ray coherence, as well as the sample, pressure and temperature stability, are discussed, and the feasibility of high-pressure XPCS is demonstrated through results obtained on metallic glasses.

High-pressure studies in the supercooled and glassy state of the strongly associated active pharmaceutical ingredient-ticagrelor

In this paper, the molecular dynamics at different thermodynamic conditions of hydrogen-bonded (H-bonded) active pharmaceutical ingredient-ticagrelor (TICA) have been investigated. Extensive high-pressure (HP) dielectric studies revealed surprising high sensitivity of the structural (α)-relaxation to compression. They also showed that unexpectedly the shape of the α-peak remains invariable at various temperature (T) and pressure (p) conditions at constant α-relaxation time. Further infrared measurements on the ordinary and pressure densified glasses of the examined compound indicated that the hydrogen-bonding pattern in TICA is unchanged by the applied experimental conditions. Such behavior was in contrast to that observed recently for ritonavir (where the organization of hydrogen bonds varied at high p) and explained the lack of changes in the width of α-dispersion with compression. Moreover, HP dielectric measurements performed in the glassy state of TICA revealed the high sensitivity of the slow secondary (β)-relaxation (Johari-Goldstein type) to pressure and fulfillment of the isochronal superpositioning of α- and JG-β-relaxation times. Additionally, it was found that the activation entropy for the β-process, estimated from the Eyring equation (a high positive value at 0.1 MPa) slightly increases with compression. We suggested that the reason for that are probably small conformational variations of TICA molecules at elevated p.

Relaxation Dynamics of Biomass-Derived Copolymers With Promising Gas-Barrier Properties

This article presents an experimental study on the relaxation dynamics of a series of random copolymers based on bio-friendly comonomers with interesting gas barrier properties. We analyze the relaxation response in the glassy and ultraviscous regime of poly (trimethylene furanoate/sebacate) random copolymers via dielectric spectroscopy. We report lower values of dynamic fragility [a dimensionless index introduced in 1985 (Angell, Relaxations in Complex Systems, 1985)] in comparison to popular polyesters widely used in industry, such as poly (ethylene terephthalate), suggesting that the amorphous phase of these furanoate-based polyesters adopt an efficient chain packing. This is consistent with their low permeability to gases. We also discuss on different equations (phenomenological and theory-based approaches) for fitting the temperature-evolution of the alpha relaxation time.

A density scaling conjecture for aging glasses

The aging rate of glasses has traditionally been modeled as a function of temperature, T , andfictive temperature, while density, ρ, is not explicitly included as a parameter. However, this de-scription does not naturally connect to the modern understanding of what governs the relaxationrate in equilibrium. In equilibrium it is well known that the relaxation rate, γeq , depends on tem-perature and density. In addition a large class of systems obey density scaling which means therate specifically depends on the scaling parameter, Γ = e(ρ)/T , where e(ρ) is a system specificfunction. This paper present a generalization of the fictive temperature concept in terms of a fic-tive scaling paramter, Γfic , and a density scaling conjecture for aging glasses in which the agingrate depends on Γ and Γfic .

Connecting real glasses to mean-field models

We propose a novel model for a glass-forming liquid, which allows us to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle interactions, which thus augments the effective number of neighbors of each particle. Our computer simulations of this system show that the structure of the liquid does not change with the introduction of these pseudo-neighbors and by means of analytical calculations, and we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with the increase in k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the mode-coupling theory power law behavior for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with the increase in k, whereas the non-Gaussian parameter is independent of it. Thus, we conclude that with the increase in the number of pseudo-neighbors, the system becomes more mean-field-like. By comparing our results with previous studies on mean-field-like systems, we come to the conclusion that the details of how the mean-field limit is approached are important since they can lead to different dynamical behavior in this limit.

On the experimental determination of the repulsive component of the potential from high pressure measurements: What is special about twelve?

In this paper, we present an overview of results in the literature regarding the thermodynamical scaling of the dynamics of liquids and polymers as measured from high-pressure measurements. Specifically, we look at the scaling exponent γ and argue that it exhibits the limiting behavior γ → 4 in regimes for which molecular interactions are dominated by the repulsive part of the intermolecular potential. For repulsive potentials of the form U(r) ∝ r^-n, γ has been found to be related to the exponent n via the relation γ = n/3. Therefore, this limiting behavior for γ would suggest that a large number of molecular systems may be described by a common repulsive potential U(r) ∝ r^-n with n ≈ 12.

Correlating fragility and heterogeneous dynamics in polystyrene through single molecule studies

Many macroscopic properties of polymers depend on their molecular weight, with one notable example being glass transition temperature: polymers with higher molecular weights typically have higher glass transition temperatures than their lower molecular weight polymeric and oligomeric counterparts. Polymeric systems close to their glass transition temperatures also exhibit interesting properties, showing both high (and molecular weight dependent) fragility and strong evidence of dynamic heterogeneity. While studies have detailed the correlations between molecular weight and fragility, studies clearly detailing correlations between molecular weight and degree of heterogeneous dynamics are lacking. In this study, we use single molecule rotational measurements to investigate the impact of molecular weight on polystyrene's degree of heterogeneity near its glass transition temperature. To this end, two types of fluorescent probes are embedded in films composed of polystyrene ranging from 0.6 to 1364.0 kg mol^-1. We find correlation between polystyrene molecular weight, fragility, and degree of dynamic heterogeneity as reported by single molecule stretching exponents but do not find clear correlation between these quantities and time scales associated with dynamic exchange.

Spectral shape simplicity of viscous materials

A broad survey of viscoelastic data demonstrates that van der Waals, hydrogen-bonded, and ionic liquids, as well as polymeric, inorganic, and metallic melts share a structural relaxation pattern virtually insensitive to their morphological details. This mechanical simplicity is connected with that characterizing the fast reorientation dynamics prevailing in liquids devoid of a distinguishable secondary susceptibility peak. By these means one is able to uncover a generic spectral pattern which rationalizes the recently reported "universality" of relaxation strength vs stretching of the dielectric response of viscous liquids, significantly broadening the framework in which their relaxation behavior is assessed.

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics

A large class of liquids obey density scaling characterized by an exponent, which quantifies the relative roles of temperature and density for the dynamics. We present experimental evidence that the density-scaling exponent γ is state-point dependent for the glass formers tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl ether (5PPE). A method is proposed that from dynamic and thermodynamic properties at equilibrium estimates the value of γ. The method applies at any state point of the pressure-temperature plane, both in the supercooled and the normal liquid regimes. We find that γ is generally state-point dependent, which is confirmed by reanalyzing data for 20 metallic liquids and two model liquids.

Perspective: Searching for simplicity rather than universality in glass-forming liquids

This article gives an overview of experimental results on dynamics in bulk glass-forming molecular liquids. Rather than looking for phenomenology that is universal, in the sense that it is seen in all liquids, the focus is on identifying the basic characteristics, or "stylized facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner.

High-pressure dielectric studies on 1,6-anhydro-β-D-mannopyranose (plastic crystal) and 2,3,4-tri-O-acetyl-1,6-anhydro-β-D-glucopyranose (canonical glass)

Broadband Dielectric Spectroscopy was applied to investigate molecular dynamics of two anhydrosaccharides, i.e., 1,6-anhydro-β-D-mannopyranose, anhMAN (hydrogen-bonded system) and 2,3,4-tri-O-acetyl-1,6-anhydro-β-D-glucopyranose, ac-anhGLU (van der Waals material), at different thermodynamic conditions. Moreover, the reported data were compared with those recently published for two other H-bonded systems, i.e., 1,6-anhydro-β-D-glucopyranose (anhGLU) and D-glucose (D-GLU). A direct comparison of the dynamical behavior of the materials with a similar chemical structure but significantly differing by the degrees of freedom, complexity, and intermolecular interactions made it possible to probe the impact of compression on the fragility, Temperature-Pressure Superpositioning and pressure coefficient of the glassy crystal/glass transition temperatures (dT_gc/dp ; dT_g/dp). Moreover, the correlation between dT_gc/dp determined experimentally from the high-pressure dielectric data and the Ehrenfest equation has been tested for the plastic crystals (anhGLU and anhMAN) for the first time. Interestingly, a satisfactory agreement was found between both approaches. It is a quite intriguing finding which can be rationalized by the fact that the studied materials are characterized by the low complexity (lower degrees of freedom with respect to the molecular mobility) as well as ordered internal structure. Therefore, one can speculate that in contrast to the ordinary glasses the dynamics of the plastic crystals might be described with the use of a single order parameter. However, to confirm this thesis further, pressure-volume-temperature (PVT) experiments enabling calculations of the Prigogine Defay ratio are required.

Correlation between Fragility and the Arrhenius Crossover Phenomenon in Metallic, Molecular, and Network Liquids

We report the observation of a distinct correlation between the kinetic fragility index m and the reduced Arrhenius crossover temperature θ_{A}=T_{A}/T_{g} in various glass-forming liquids, identifying three distinguishable groups. In particular, for 11 glass-forming metallic liquids, we universally observe a crossover in the mean diffusion coefficient from high-temperature Arrhenius to low-temperature super-Arrhenius behavior at approximately θ_{A}≈2 which is in the stable liquid phases. In contrast, for fragile molecular liquids, this crossover occurs at much lower θ_{A}≈1.4 and usually in their supercooled states. The θ_{A} values for strong network liquids spans a wide range higher than 2. Intriguingly, the high-temperature activation barrier E_{∞} is universally found to be ∼11k_{B}T_{g} and uncorrelated with the fragility or the reduced crossover temperature θ_{A} for metallic and molecular liquids. These observations provide a way to estimate the low-temperature glassy characteristics (T_{g} and m) from the high-temperature liquid quantities (E_{∞} and θ_{A}).

Communication: High pressure specific heat spectroscopy reveals simple relaxation behavior of glass forming molecular liquid

The frequency dependent specific heat has been measured under pressure for the molecular glass forming liquid 5-polyphenyl-4-ether in the viscous regime close to the glass transition. The temperature and pressure dependences of the characteristic time scale associated with the specific heat is compared to the equivalent time scale from dielectric spectroscopy performed under identical conditions. It is shown that the ratio between the two time scales is independent of both temperature and pressure. This observation is non-trivial and demonstrates the existence of specially simple molecular liquids in which different physical relaxation processes are both as function of temperature and pressure/density governed by the same underlying "inner clock." Furthermore, the results are discussed in terms of the recent conjecture that van der Waals liquids, like the measured liquid, comply to the isomorph theory.

Cooperativity length scale in nanocomposites: interfacial and confinement effects

Interfacial and confinement effects on the evolution of cooperativity on approaching the glass transition have been studied in poly(propylenecoethylene) functionalized with diethylmaleate, polyethylene 1,4-cyclohexylenedimethylene terephthalate glycol and their nanocomposites with montmorillonite. A small increase of the structural dynamic cooperativity, a weak alteration of the temperature dependence of the characteristic relaxation frequency, and no changes in the glass transition temperature observed in poly(propylenecoethylene)-based samples can be rationalized in terms of interfacial interactions between polymer and exfoliated clay. On the other hand, confinement of polymer chains in the galleries of clay (intercalated nanocomposite) produces a strong reduction of cooperativity, of the temperature dependence of the characteristic relaxation frequency, and of the glass transition temperature in polyethylene 1,4-cyclohexylenedimethylene terephthalate glycol samples. Finally, by investigating the temperature dependence of a generalized fragility and of cooperativity, we evidenced that fragility of glass formers is determined not only by cooperativity.

Isomorphs, hidden scale invariance, and quasiuniversality

This paper first establishes an approximate scaling property of the potential-energy function of a classical liquid with good isomorphs (a Roskilde-simple liquid). This "pseudohomogeneous" property makes explicit that-and in which sense-such a system has a hidden scale invariance. The second part of the paper gives a potential-energy formulation of the quasiuniversality of monatomic Roskilde-simple liquids, which was recently rationalized in terms of the existence of a quasiuniversal single-parameter family of reduced-coordinate constant-potential-energy hypersurfaces [J. C. Dyre, Phys. Rev. E 87, 022106 (2013)]. The new formulation involves a quasiuniversal reduced-coordinate potential-energy function. A few consequences of this are discussed.

NVU perspective on simple liquids' quasiuniversality

The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.

Correlating the stretched-exponential and super-Arrhenius behaviors in the structural relaxation of glass-forming liquids

Following the report of a single-exponential activation behavior behind the super-Arrhenius structural relaxation of glass-forming liquids in our preceding paper, we find that the non-exponentiality in the structural relaxation of glass-forming liquids is straightforwardly determined by the relaxation time, and could be calculated from the measured relaxation data. Comparisons between the calculated and measured non-exponentialities for typical glass-forming liquids, from fragile to intermediate, convincingly support the present analysis. Hence the origin of the non-exponentiality and its correlation with liquid fragility become clearer.

Bond Strength-Coordination Number Fluctuation Model of Viscosity: An Alternative Model for the Vogel-Fulcher-Tammann Equation and an Application to Bulk Metallic Glass Forming Liquids

The Vogel-Fulcher-Tammann (VFT) equation has been used extensively in the analysis of the experimental data of temperature dependence of the viscosity or of the relaxation time in various types of supercooled liquids including metallic glass forming materials. In this article, it is shown that our model of viscosity, the Bond Strength-Coordination Number Fluctuation (BSCNF) model, can be used as an alternative model for the VFT equation. Using the BSCNF model, it was found that when the normalized bond strength and coordination number fluctuations of the structural units are equal, the viscosity behaviors described by both become identical. From this finding, an analytical expression that connects the parameters of the BSCNF model to the ideal glass transition temperature T₀ of the VFT equation is obtained. The physical picture of the Kohlrausch-Williams-Watts relaxation function in the glass forming liquids is also discussed in terms of the cooperativity of the structural units that form the melt. An example of the application of the model is shown for metallic glass forming liquids.

Single-exponential activation behavior behind the super-Arrhenius relaxations in glass-forming liquids

The reported relaxation time for several typical glass-forming liquids was analyzed by using a kinetic model for liquids which invoked a new kind of atomic cooperativity--thermodynamic cooperativity. The broadly studied 'cooperative length' was recognized as the kinetic cooperativity. Both cooperativities were conveniently quantified from the measured relaxation data. A single-exponential activation behavior was uncovered behind the super-Arrhenius relaxations for the liquids investigated. Hence the mesostructure of these liquids and the atomic mechanism of the glass transition became clearer.

Connection between slow and fast dynamics of molecular liquids around the glass transition

The mean-square displacement (MSD) was measured by neutron scattering at various temperatures and pressures for a number of molecular glass-forming liquids. The MSD is invariant along the glass-transition line at the pressure studied, thus establishing an "intrinsic" Lindemann criterion for any given liquid. A one-to-one connection between the MSD's temperature dependence and the liquid's fragility is found when the MSD is evaluated on a time scale of ∼4 ns , but does not hold when the MSD is evaluated at shorter times. The findings are discussed in terms of the elastic model and the role of relaxations, and the correlations between slow and fast dynamics are addressed.

Two factors governing fragility: stretching exponent and configurational entropy

We derive an analytical expression showing that the fragility of a supercooled liquid is a result of (i) a thermodynamic term depending on change in configurational entropy and (ii) a kinetic term depending on change in the nonexponentiality or "stretching" of the relaxation function, as quantified by the exponent beta of the Kohlrausch-Williams-Watts (KWW) relaxation function. Our expression indicates that there is not a direct correlation between the non-Arrhenius scaling of liquid viscosity and the nonexponential nature of glassy relaxation. Rather, the temperature dependence of the stretching exponent beta provides a lower limit for fragility, which can be increased through changes in the configurational entropy. Our result explains the apparent contradiction between those researchers showing a correlation between beta and fragility and those who question such a correlation due to the spread of the data.

Suppression of the rate of growth of dynamic heterogeneities and its relation to the local structure in a supercooled polydisperse liquid

The relationship between the microscopic arrangement of molecules in a supercooled liquid and its slow dynamics at low temperature near glass transition is studied by molecular dynamics simulations. A Lennard-Jones liquid with polydispersity in size and mass of constituent particles is chosen as the model system. Our studies reveal that the local structure (that varies with polydispersity) plays a crucial role both in the slowing down of dynamics and in the growth of the dynamic heterogeneities, besides determining the glass forming ability of the system. Increasing polydispersity at fixed volume fraction is found to suppress the rate of growth of dynamic correlations, as detected by the growth in the peak of the nonlinear density response function, chi4(t). The growth in dynamical correlation is manifested in a stronger than usual breakdown of Stokes-Einstein relation at lower polydispersity at low temperatures and also leads to a decrease in the fragility of the system with polydispersity. We show that the suppression of the rate of growth of the dynamic heterogeneity can be attributed to the loss of structural correlations (as measured by the structure factor and the local bond orientational order) with polydispersity. While a critical polydispersity is required to avoid crystallization, we find that a further increase in polydispersity lowers the glass forming ability.

Idealized glass transitions under pressure: dynamics versus thermodynamics

The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic behavior leaves the dynamics unchanged, with important consequences for high-pressure experiments on glassy liquids. Numerical results are obtained within mode-coupling theory (MCT), but the qualitative features are argued to hold more generally. A simple square-well model can be used to explain generic features found in experiment.

Impact of fragility on enthalpy relaxation in glass

The macroscopic properties of a glass are continually relaxing toward their equilibrium supercooled liquid values. Experimentally, the shape of the relaxation function in a glass is known to depend on the fragility of the supercooled liquid. In this paper, we investigate the impact of fragility on the relaxation behavior of glasses in the enthalpy landscape framework. We show that the fragility of a supercooled liquid is a direct result of the interplay of enthalpic and entropic effects in the enthalpy landscape. Through proper adjustment of the transition barriers in an enthalpy landscape, the fragility of a system can be adjusted while maintaining the same glass transition temperature. By modeling a set of systems with identical glass transition temperatures but varying values of fragility, we show that supercooled liquid fragility has a significant impact on the enthalpy relaxation behavior of a glass. In particular, the magnitude of enthalpy relaxation decreases dramatically with increasing fragility. Finally, we discuss how in the limit of infinite fragility the glass transition becomes an ideal second-order phase transition where no relaxation is possible in the glassy state.

Energy landscape, antiplasticization, and polydispersity induced crossover of heterogeneity in supercooled polydisperse liquids

Polydispersity is found to have a significant effect on the potential energy landscape; the average inherent structure energy decreases with polydispersity. Increasing polydispersity at a fixed volume fraction decreases the glass transition temperature and the fragility of glass formation analogous to the antiplasticization seen in some polymeric melts. An interesting temperature dependent crossover of heterogeneity with polydispersity is observed at low temperature due to the faster buildup of dynamic heterogeneity at lower polydispersity.

Understanding fragility in supercooled Lennard-Jones mixtures. I. Locally preferred structures

The existence of systematic variations of isobaric fragility in different supercooled Lennard-Jones binary mixtures is revealed by molecular dynamics simulations. The connection between fragility and local structures in the bulk is analyzed by means of a Voronoi construction. It is found that clusters of particles belonging to locally preferred structures form slow, long-lived domains, whose spatial extension increases with decreasing temperature. As a general rule, a more rapid growth, upon supercooling, of such domains is associated with a more pronounced super-Arrhenius behavior, and hence to a larger fragility.