Length Scale of Dynamic Heterogeneity in Supercooled d-Sorbitol: Comparison to Model Predictions

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

We analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call "complexity reduction". In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature Tg of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2-6 nm at Tg. Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

An Ising Model for Supercooled Liquids and the Glass Transition

We describe the behavior of an Ising model with orthogonal dynamics, where changes in energy and changes in alignment never occur during the same Monte Carlo (MC) step. This orthogonal Ising model (OIM) allows conservation of energy and conservation of (angular) momentum to proceed independently, on their own preferred time scales. The OIM also includes a third type of MC step that makes or breaks the interaction between neighboring spins, facilitating an equilibrium distribution of bond energies. MC simulations of the OIM mimic more than twenty distinctive characteristics that are commonly found above and below the glass temperature, Tg. Examples include a specific heat that has hysteresis around Tg, out-of-phase (loss) response that exhibits primary (α) and secondary (β) peaks, super-Arrhenius T dependence for the α-response time (τα), and fragilities that increase with increasing system size (N). Mean-field theory for energy fluctuations in the OIM yields a critical temperature (Tc) and a novel expression for the super-Arrhenius divergence as T→Tc: ln(τα)~1/(1−Tc/T)2. Because this divergence is reminiscent of the Vogel-Fulcher-Tammann (VFT) law squared, we call it the “VFT2 law”. A modified Stickel plot, which linearizes the VFT2 law, shows that at high T where mean-field theory should apply, only the VFT2 law gives qualitatively consistent agreement with measurements of τα (from the literature) on five glass-forming liquids. Such agreement with the OIM suggests that several basic features govern supercooled liquids. The freezing of a liquid into a glass involves an underlying 2nd-order transition that is broadened by finite-size effects. The VFT2 law for τα comes from energy fluctuations that enhance the pathways through an entropy bottleneck, not activation over an energy barrier. Values of τα vary exponentially with inverse N, consistent with the distribution of relaxation times deduced from measurements of α response. System sizes found via the T dependence of τα from simulations and measurements are similar to sizes of independently relaxing regions (IRR) measured by nuclear magnetic resonance (NMR) for simple-molecule glass-forming liquids. The OIM elucidates the key ingredients needed to interpret the thermal and dynamic properties of amorphous materials, while providing a broad foundation for more-detailed models of liquid-glass behavior.

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Glassy dynamics in polyalcohols: intermolecular simplicity vs. intramolecular complexity

Using depolarized light scattering, we have recently shown that structural relaxation in a broad range of supercooled liquids follows, to good approximation, a generic line shape with high-frequency power law ω^-1/2. We now continue this study by investigating a systematic series of polyalcohols (PAs), frequently used as model-systems in glass-science, i.a., because the width of their respective dielectric loss spectra varies strongly along the series. Our results reveal that the microscopic origin of the observed relaxation behavior varies significantly between different PAs: while short-chained PAs like glycerol rotate as more or less rigid entities and their light scattering spectra follow the generic shape, long-chained PAs like sorbitol display pronounced intramolecular dynamic contributions on the time scale of structural relaxation, leading to systematic deviations from the generic shape. Based on these findings we discuss an important limitation for observing the generic shape in a supercooled liquid: the dynamics that is probed needs to reflect the intermolecular dynamic heterogeneity, and must not be superimposed by effects of intramolecular dynamic heterogeneity.

Network Formation and Physical Properties of Epoxy Resins for Future Practical Applications

Epoxy resins are used in various fields in a wide range of applications such as coatings, adhesives, modeling compounds, impregnation materials, high-performance composites, insulating materials, and encapsulating and packaging materials for electronic devices. To achieve the desired properties, it is necessary to obtain a better understanding of how the network formation and physical state change involved in the curing reaction affect the resultant network architecture and physical properties. However, this is not necessarily easy because of their infusibility at higher temperatures and insolubility in organic solvents. In this paper, we summarize the knowledge related to these issues which has been gathered using various experimental techniques in conjunction with molecular dynamics simulations. This should provide useful ideas for researchers who aim to design and construct various thermosetting polymer systems including currently popular materials such as vitrimers over epoxy resins.

Molecular Cross-correlations Govern Structural Rearrangements in a Nonassociating Polar Glass Former

Self- and cross-correlation dynamics of deeply supercooled liquids were recently identified using photon correlation spectroscopy on the one hand and dielectric investigations on the other. These results fueled a controversial discussion whether the "generic" response identified by photon correlation spectroscopy, or rather the nonuniversal dielectric response, reflect the liquid's structural relaxation. The present study employs physical aging and oscillatory shear rheology to directly access the structural relaxation of a nonassociating glass-forming liquid and reveals that collective equilibrium fluctuations of simple liquids and not single-particle dynamics govern their structural relaxation. The present results thus challenge recent views that the glassy response of polar supercooled liquids can generically be decomposed into a Debye-type, supramolecular response and a single-particle dynamics with the latter reflecting the "true" structural relaxation. Furthermore, the current findings underscore the pivotal role dielectric spectroscopy plays in glass science as one of the rare molecular-level reorientation techniques that senses dynamical cooperativity directly.

Q-dependent collective relaxation dynamics of glass-forming liquid Ca0.4K0.6(NO3)1.4 investigated by wide-angle neutron spin-echo

The relaxation behavior of glass formers exhibits spatial heterogeneity and dramatically changes upon cooling towards the glass transition. However, the underlying mechanisms of the dynamics at different microscopic length scales are not fully understood. Employing the recently developed wide-angle neutron spin-echo spectroscopy technique, we measured the Q-dependent coherent intermediate scattering function of a prototypical ionic glass former Ca_0.4K_0.6(NO₃)_1.4, in the highly viscous liquid state. In contrast to the structure modulated dynamics for Q < 2.4 Å⁻¹, i.e., at and below the structure factor main peak, for Q > 2.4 Å⁻¹, beyond the first minimum above the structure factor main peak, the stretching exponent exhibits no temperature dependence and concomitantly the relaxation time shows smaller deviations from Arrhenius behavior. This finding indicates a change in the dominant relaxation mechanisms around a characteristic length of 2π/(2.4 Å⁻¹) ≈ 2.6 Å, below which the relaxation process exhibits a temperature independent distribution and more Arrhenius-like behavior.

Length scale dependence is important for understanding the collective relaxation dynamics in glass-forming liquids. Here, the authors find in liquid Ca_0.4K_0.6(NO₃)_1.4 a change in the dominant relaxation mechanisms around 2.6 Å, below which the relaxation process exhibits a temperature independent distribution and more Arrhenius-like behavior.

Glassy dynamics predicted by mutual role of free and activation volumes

Broadband Dielectric Spectroscopy (BDS) at elevated pressures and Positron Annihilation Lifetime Spectroscopy (PALS) are employed to elucidate the importance of the ratio of activation and free volumes during vitrification. We show that this ratio has a linear correlation with the structural relaxation of glass forming liquids in a wide temperature range hence engendering it as a vital input in the description of the dynamic glass transition.

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.

Crossover between cooperative and fractal relaxation in complex glass-formers

Kinetics of physical aging at different temperatures is studied in situ in arsenic selenide glasses using high-precision differential scanning calorimetry technique. A well-expressed step-like behaviour in the enthalpy recovery kinetics is recorded for low aging temperatures. These fine features disappear when the aging temperature (T a) approaches the glass transition temperature (T g). The overall kinetics is described by stretched exponential function with stretching exponent close to 3/5 at T a  >  ~0.95 T g almost independent on glass composition, and 3/7 when the aging temperature drops to ~0.9 T g. These values are consistent with the prediction of Phillips' diffusion-to-traps model. Further decrease in aging temperature to ~0.85 T g leads to the appearance of step-like behaviour and stretching exponent of 1/3 for the overall kinetics, which is the limiting value predicted by random walk on the fractal model. Such behavior is explained as crossover from homogeneous cooperative relaxation of non-percolating structural units to high-dimensional fractal relaxation within hierarchically-arranged two-stage physical aging model.

Ionic liquids and their bases: Striking differences in the dynamic heterogeneity near the glass transition

Ionic liquids (ILs) constitute an active field of research due to their important applications. A challenge for these investigations is to explore properties of ILs near the glass transition temperature Tg, which still require our better understanding. To shed a new light on the issues, we measured ILs and their base counterparts using the temperature modulated calorimetry. We performed a comparative analysis of the dynamic heterogeneity at Tg for bases and their salts with a simple monoatomic anion (Cl(-)). Each pair of ionic and non-ionic liquids is characterized by nearly the same chemical structure but their intermolecular interactions are completely different. We found that the size of the dynamic heterogeneity of ILs near Tg is considerably smaller than that established for their dipolar counterparts. Further results obtained for several other ILs near Tg additionally strengthen the conclusion about the relatively small size of the dynamic heterogeneity of molecular systems dominated by electrostatic interactions. Our finding opens up new perspectives on designing different material properties depending on intermolecular interaction types.

Protein dynamics: from rattling in a cage to structural relaxation

We present an overview of protein dynamics based mostly on results of neutron scattering, dielectric relaxation spectroscopy and molecular dynamics simulations. We identify several major classes of protein motions on the time scale from faster than picoseconds to several microseconds, and discuss the coupling of these processes to solvent dynamics. Our analysis suggests that the microsecond backbone relaxation process might be the main structural relaxation of the protein that defines its glass transition temperature, while faster processes present some localized secondary relaxations. Based on the overview, we formulate a general picture of protein dynamics and discuss the challenges in this field.

Two glass transitions of polyurea networks: effect of the segmental molecular weight

Polymer-nanoparticle composites (PNCs) play an increasing role in technology. Inorganic or organic nanoparticles are usually incorporated into a polymer matrix to improve material properties. Polyurea is a spontaneously occurring PNC, exhibiting a phase segregated structure with hard nanodomains embedded in a soft (elastically compliant) matrix. This system shows two glass transitions at Tg1 and Tg2. It has been argued that they are related to the freezing of motion of molecular segments in the soft matrix (usual polymer α-glass transition at Tg1) and to regions of restricted mobility near the hard nanodomains (α'-process) at Tg2, respectively. We present detailed dynamic mechanical analysis (DMA) measurements for polyurea networks with different segmental lengths l(c) (2.5, 12.1, 24.5 nm) of the polymer chains, i.e. different volume fractions ϕ(x) (0.39, 0.12, 0.07) of the hard domains. The two glass transitions show up in two distinct peaks in tan δ at Tα and Tα'. Analysing the data using a Havriliak-Negami term for the α- and α'-relaxation, as well as Vogel-Fulcher dependencies for the corresponding relaxation times, it is found that the α-glass transition at Tg1 increases strongly (up to ΔT = 70 K) with increasing ϕ(x), whereas the α'-transition at Tg2 remains unchanged. At ϕ(x)(c) ≈ 0.19 the two curves intersect, i.e. Tg1 = Tg2. This value of ϕ(x)(c) is very close to the percolation threshold of randomly oriented overlapping ellipsoids of revolution with an aspect ratio of about 1 : 4-1 : 5. We therefore conclude that around 19% of the hard nanodomains polyurea changes from a system of hard nanoparticles embedded in a soft matrix (ϕ(x) ≤ ϕ(x)(c)) to a system of soft domains confined in a network of percolated hard domains at ϕ(x) ≥ ϕ(x)(c).

Characteristic Length of the Glass Transition in Isochorically Confined Polymer Glasses

We report the effect of isochoric confinement on the characteristic length of the glass transition (ξ_α) for polystyrene (PS) and poly(4-methylstyrene) (P4MS). Utilizing silica-capped PS and P4MS nanoparticles as model systems, ξ_α values are determined from the thermal fluctuation model and calorimetric data. With decreasing nanoparticle diameter, ξ_α decreases, suggesting a reduction in the number of segmental units required for cooperative motion at the glass transition under confinement. Furthermore, a direct correlation is observed between ξ_α and the isochoric fragility (m_v) in confined polymers. Due to a nearly constant ratio of the isochoric to isobaric fragility in confined polymer nanoparticles, a correlation between ξ_α and m_v also implies a correlation between ξ_α and the volume contribution to the temperature dependence of structural relaxation. Lastly, we observe that when the fragility and characteristic length are varied in the same system the relationship between the two properties appears to be more correlated than that of across different bulk glass-formers.

Heterogeneity in Single-Molecule Observables in the Study of Supercooled Liquids

Bulk approaches to studying heterogeneous systems obscure important details, as they report average behavior rather than the distribution of behaviors in such environments. Small-molecule and polymeric supercooled liquids, which display heterogeneity in their dynamics without an underlying structural heterogeneity that sets those dynamics, are important constituents of this category of condensed matter systems. A variety of approaches have been devised to unravel ensemble averaging in supercooled liquids. This review focuses on the ultimate subensemble approach, single-molecule measurements, as they have been applied to the study of supercooled liquids. We detail how three key experimental observables (single-molecule probe rotation, translation, and fluorescence lifetime) have been employed to provide detail on dynamic heterogeneity in supercooled liquids. Special attention is given to the potential for, but also the challenges in, discriminating spatial and temporal heterogeneity and detailing the length scales and timescales of heterogeneity in these systems.

Length and time scales of structural heterogeneities in deeply supercooled propylene carbonate

Deactivation of excited phenanthrene by molecular oxygen is utilized to probe the structural heterogeneity of supercooled propylene carbonate. The diffusion rate of oxygen molecules in different regions varies over two orders of magnitude. The size of the regions of different oxygen mobility was determined to be 1.5 nm. Values from 0.2 to 30 s have been obtained for the lifetime of these regions over a temperature range from T(g)-1 to T(g)+4 K (T(g)=158 K). The heterogeneity lifetime is in close agreement with the α-relaxation time determined by dielectric spectroscopy. The obtained results argue in favor of the statement that the heterogeneous cooperative dynamics of host molecules (so-called dynamical heterogeneity) is of structural origin.

Kinetics of azobenzene nitrene oxidation by molecular oxygen in glassy propylene carbonate

The kinetics of azobenzene nitrene oxidation by molecular oxygen dissolved in a matrix was studied in glassy propylene carbonate. The reaction was carried out in excess oxygen within its concentration range 0.008 to 0.048 M. The oxidation kinetics, controlled by oxygen diffusion, is not described by the exponential function. A specific reaction rate decreases in the course of the process. The higher the oxygen concentration in the matrix, the sharper is the decrease in the reaction rate. It is shown that at all concentrations, the oxidation kinetics is described in the framework of the model of heterogeneous matrix with a characteristic size of heterogeneities of 1.5 nm and a dispersion of the activation energy of oxygen molecule jump of 4 kJ/mol. The reaction radius is about 0.5 nm.

Manifestations of probe presence on probe dynamics in supercooled liquids

Experimental studies that follow behavior of single probes embedded in heterogeneous systems are increasingly common. The presence of probes may perturb the system, and such perturbations may or may not affect interpretation of host behavior from the probe observables typically measured. In this study, the manifestations of potential probe-induced changes to host dynamics in supercooled liquids are investigated via molecular dynamics simulations. It is found that probe dynamics do not necessarily mirror host dynamics as they exist either in the probe-free or probe-bearing systems. In particular, for a binary supercooled liquid, we find that smooth probes larger than the host particles induce increased translational diffusion in the host system; however, the diffusion is anisotropic and enhances caging of the probe, suppressing probe translational diffusion. This in turn may lead experiments that follow probe diffusion to suggest Stokes-Einstein behavior of the system even while both the probe-free and probe-bearing systems exhibit deviations from that behavior.

Comparing dynamic correlation lengths from an approximation to the four-point dynamic susceptibility and from the picosecond vibrational dynamics

Recently an alternative approach to the determination of dynamic correlation lengths ξ for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [Hong, Novikov, and Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, the liquid is frozen at T(g), whereby structural correlations, density variations, etc., manifested at low temperatures as spatial fluctuations of local elastic constants, can be related to a dynamic heterogeneity length scale for the liquid state. We compare ξ from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, ξ from Boson peak measurements above T(g) have a different, and unrealistic, temperature dependence.

On the decoupling of relaxation modes in a molecular liquid caused by isothermal introduction of 2 nm structural inhomogeneities

To support a new interpretation of the origin of the dynamic heterogeneity observed pervasively in fragile liquids as they approach their glass transition temperatures T(g), we demonstrate that the introduction of ~2 nm structural inhomogeneities into a homogeneous glass former leads to a decoupling of diffusion from viscosity similar to that observed during the cooling of orthoterphenyl (OTP) below T(A,) where Arrhenius behavior is lost. Further, the decoupling effect grows stronger as temperature decreases (and viscosity increases). The liquid is cresol, and the ~2 nm inhomogeneities are cresol-soluble asymmetric derivatized tetrasiloxy-based (polyhedral oligomeric silsesquioxane (POSS)) molecules. The decoupling is the phenomenon predicted by Onsager in discussing the approach to a liquid-liquid phase separation with decreasing temperature. In the present case the observations support the notion of a polyamorphic transition in fragile liquids that is hidden below the glass transition. A similar decoupling can be expected as a globular protein is dissolved in dilute aqueous solutions or in protic ionic liquids.

Dynamic heterogeneities, boson peak, and activation volume in glass-forming liquids

There are various arguments and models connecting the characteristic length associated with the boson peak vibrations ξ to the length scale of dynamical heterogeneity L(het). ξ is usually defined as the ratio of the transverse sound velocity to the boson peak frequency. Here we present pressure, temperature, and molecular weight dependencies of ξ, estimated using light scattering, in a few molecular and polymeric glass formers. These dependencies are compared with respective dependencies of the activation volume ΔV(#) in the same materials. Good agreement is found for the pressure and molecular weight dependencies of ξ and ΔV(#) measured at the glass transition temperature T(g). These results provide more evidence for a possible relationship between the sensitivity of structural relaxation to density (activation volume) and the heterogeneity volume. However, contrary to the expectations for L(het), ξ does not decrease with temperature above T(g) in most of the studied materials. The temperature dependence of ξ is compared to that of L(het) in glycerol and orthoterphenyl (OTP) estimated from literature data. The analysis shows a clear difference in the behavior of ξ(T) and ΔV(#)(T) at temperatures above T(g), although ΔV(#)(T)(1/3) and L(het)(T) have similar temperature dependence. Possible reasons for the observed difference are discussed.

Length scale of heterogeneities in glassy propylene carbonate probed by oxygen diffusion

A new method using the quenching of guest molecule phosphorescence by molecular oxygen is proposed for determination of heterogeneity size in glassy matrixes. The method is based on the high sensitivity of the diffusion of oxygen molecules to spatial density fluctuations. Phenanthrene phosphorescence decay was monitored at different concentrations of molecular oxygen in propylene carbonate below T(g). An unusual dependence of the phosphorescence decay on oxygen concentration was observed: an increase in the concentration leads to anomalously large increase in the quenching rate at short times. This dependence is considered to be caused by matrix heterogeneity. To describe the phosphorescence decay, we use a model of glass as a heterogeneous medium where oxygen jump rates are spatially correlated. The length of spatial correlation for the jump rates is taken as heterogeneity size. Using the model, the value of 1.5+/-0.5 nm was obtained for the size of structural heterogeneities in glassy propylene carbonate. The dispersion of barriers for oxygen jumps is estimated to be 4+/-1 kJ/mole and the average barrier energy is found to be 50 kJ/mole.

Subdiffusive motion in kinetically constrained models

We discuss a kinetically constrained model in which real-valued local densities fluctuate in time, as introduced recently by Bertin, Bouchaud, and Lequeux. We show how the phenomenology of this model can be reproduced by an effective theory of mobility excitations propagating in a disordered environment. Both excitations and probe particles have subdiffusive motion, characterized by different exponents and operating on different time scales. We derive these exponents, showing that they depend continuously on one of the parameters of the model.