Ideal Glass Research Articles

Hypernetted-chain investigation of the random first-order transition of a Lennard-Jones liquid to an ideal glass.

The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its random first-order transition (RFOT) to an ideal glass is investigated, using a system of two weakly coupled replicas and the hypernetted chain integral equation for the pair structure of this symmetric binary system. A systematic search in the density-temperature plane points to the existence of two glass branches below a density-dependent threshold temperature. The branch of lower free energy exhibits a rapid growth of the structural overlap order parameter upon cooling and may be identified with the ideal glass phase conjectured by several authors for both spin and structural glasses. The RFOT, signaled by a sharp discontinuity of the order parameter, is predicted to be weakly first order from a thermodynamic viewpoint. The transition temperature T(cr) increases rapidly with density and approximately obeys a scaling relation valid for a reference system of particles interacting via a purely repulsive 1/r(18) potential.

Suppression of β Relaxation in Vapor-Deposited Ultrastable Glasses.

Glassy materials display numerous important properties which relate to the presence and intensity of the secondary (β) relaxations that dominate the dynamics below the glass transition temperature. However, experimental protocols such as annealing allow little control over the β relaxation for most glasses. Here we report on the β relaxation of toluene in highly stable glasses prepared by physical vapor deposition. At conditions that generate the highest kinetic stability, about 70% of the β relaxation intensity is suppressed, indicating the proximity of this state to the long-sought "ideal glass." While preparing such a state via deposition takes less than an hour, it would require ~3500 years of annealing an ordinary glass to obtain similarly suppressed dynamics.

Performance analyses of building energy on phase transition processes of VO2 windows with an improved model

A new model is established to obtain the building energy with a gradual change process of VO2 optical properties. Based on this method, three types of existing VO2 films are employed to simulate the heating and cooling energy consumptions in five typical Chinese cities. The results show that the smart characteristic is not evident in VO2 glasses because these films are almost in the cold state or cold transition state in the entire year. To improve this situation, the concept of an ideal thermochromic intelligent glass is put forward. Unexpectedly, the level of energy consumption increases with the film phase transition temperature decreasing in the heating period. However, the energy-saving effects will be effectivelyimproved both in the cooling and heating periods when the phase transition process interval is shortened. The cooling energy consumptions for the ideal glass decrease by at most 81.7% and 70.5% compared with white glass and Low-E glass, respectively. In the heating period, the level of energy consumption for the ideal glass is better than Low-E glass.

Statistical mechanics of hard spheres: the theory of hard sphere glasses revisited

In a previous article (1995 J. Math. Phys. 36 201) a new theoretical equation of state for the hard sphere fluid was found. It contains two parameters which could be calculated, not only for the fluid state, but also for the known glassy states. In the latter case the calculation of the parameters was possible by making use of a specific model (1997 Z. Phys. B 102 255). The resulting equations of state are in good agreement with the simulation data. Yet the theory of the glassy states is highly inconsistent. In this paper it will be reformulated—still making use of the above mentioned model—so that consistency is realized approximately to within small deviations. Furthermore, three new simulated hard sphere glasses are reported. Not only the earlier simulated glasses, but also the new ones, can accurately be described by the theory presented here. In section the concepts of random close packing and ideal glass are discussed.It should be emphasized that this paper is partly based on some ideas which appear in a former article about the hard sphere crystal, although the main purpose of the latter was different—namely to calculate the pressure and the densities of the transition fluid-crystal (2011 J. Stat. Phys. 145 1640).

Thermodynamic Comparison and the Ideal Glass Transition of Antiferromagnetic Ising Model on Multi-branched Husimi and Cubic Recursive Lattice with the Identical Coordination Number**Supported by National Natural Science Foundation of China under Grant No. 11505110

Two types of recursive lattices with the identical coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states. A multi-branched structure of the 2-D plaquette model, which we introduced in this work, makes it possible to be an analog to the cubic lattice. Two solutions of each model can be found to exhibit the crystallization of liquid, and the ideal glass transition of supercooled liquid respectively. Based on the solutions, the thermodynamics on both lattices, e.g. the free energy, energy density, and entropy of the supercooled liquid, crystal, and liquid state of the model are calculated and compared with each other. Interactions between particles farther away than the nearest neighbor distance and multi-spins interactions are taken into consideration, and their effects on the thermal behavior are examined. The two lattices show comparable properties on the thermodynamics, which proves that both of them are practical to describe the regular 3-D case, especially to locate the ideal glass transition, while the 2-D multi-branched plaquette model is less accurate with the advantage of simpler formulation and less computation time consumption.

One-dimensional Kac model of dense amorphous hard spheres

We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is a one-dimensional chain of the d-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite-dimensional limit of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scales at the glass transition. The divergence of the lengths are characterized by the two exponents, for the dynamical transition and −1 for the ideal glass transition, which are consistent with those of the p-spin mean-field spin glass model. We also show that the model is useful for the study of the growing length scale at the jamming transition.

How to predict the ideal glass transition density in polydisperse hard-sphere packings.

The formula for the entropy s of the accessible volume of the phase space for frictionless hard spheres is combined with the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state for polydisperse three-dimensional packings to obtain an analytical expression for s as a function of packing density φ. Polydisperse hard-sphere packings with log-normal, Gaussian, and Pareto particle diameter distributions are generated to estimate their ideal glass transition densities φg. The accessible entropy s at φg is almost the same for all investigated particle diameter distributions. We denote this entropy as sg and can predict φg for an arbitrary particle diameter distribution through an equation s(φ) = sg. If the BMCSL equation of state is used for s(φ), then φg is found to depend only on the first three moments of a particle diameter distribution.

Atomistic Molecular Insight into the Time Dependence of Polymer Glass Transition.

The most atomistic molecular details of polymer glass transition were analyzed through the frozen torsions in our molecular dynamics simulations. Different observation times were used to determine the frozen fractions and frozen chain lengths. The glass transition temperature was found to coincide well with the temperature at which the frozen fractions were reduced to 1/e. The frozen chain segments grow as the temperature decreases in a similar way with that of linear polymerization, and the inverse number-average frozen chain length leads to the formulation of configuration entropy during glass transition. The ideal glass transition temperature extrapolated to zero configuration entropy corresponds well with those reported in the literature, and the relation between the relaxation time and the configuration entropy shows perfect agreement with the Adam-Gibbs theory around the glass transition temperature. Volume spanning clusters are formed at the low temperature end, which might serve as a premature prototype for the formation of the "ideal glassy state" with limited accessible configurations.

Novel Ge–Ga–Te–CsBr glass system with ultrahigh resolvability of halide

CO2 molecule, one of the main molecules to create new life, should be probed accurately to detect the existence of life in exoplanets. The primary signature of CO2 molecule is approximately 15μm, and traditional S- and Se-based glass fibers are unsuitable. Thus, Te-based glass is the only ideal candidate glass for far-infrared detection. In this study, a new kind of Te-based chalcohalide glass system was discovered with relatively stable and large optical band gap. A traditional melt-quenching method was adopted to prepare a series of (Ge15Ga10Te75)100−x (CsBr)x chalcogenide glass samples. Experiment results indicate that the glass-forming ability and thermal properties of glass samples were improved when CsBr was added in the host of Ge–Ga–Te glass. Ge–Ga–Te glass could remarkably dissolve CsBr content as much as 85at.%, which is the highest halide content in all reports for Te-based chalcohalide glasses. Moreover, ΔT values of these glass samples were all above 100°C. The glass sample (Ge15Ga10Te75)65 (CsBr)35 with ΔT of 119°C was the largest, which was 7°C larger than that of Ge15Ga10Te75 host glass. The infrared transmission spectra of these glasses show that the far-infrared cut-off wavelengths of (Ge15Ga10Te75)100−x (CsBr)x chalcogenide glasses were all beyond 25μm. In conclusion, (Ge15Ga10Te75)100−x (CsBr)x chalcogenide glasses are potential materials for far-infrared optical application.

Jamming in hierarchical networks

We study the Biroli–Mezard model for lattice glasses on a number of hierarchical networks. These networks combine certain lattice-like features with a recursive structure that makes them suitable for exact renormalization group studies and provide an alternative to the mean-field approach. In our numerical simulations here, we first explore their equilibrium properties with the Wang–Landau algorithm. Then, we investigate their dynamical behavior using a grand-canonical annealing algorithm. We find that the dynamics readily falls out of equilibrium and jams in many of our networks with certain constraints on the neighborhood occupation imposed by the Biroli–Mezard model, even in cases where exact results indicate that no ideal glass transition exists. But while we find that time-scales for the jams diverge, our simulations cannot ascertain such a divergence for a packing fraction distinctly above random close packing. In cases where we allow hopping in our dynamical simulations, the jams on these networks generally disappear.

Equilibrium phase diagram of a randomly pinned glass-former

We use computer simulations to study the thermodynamic properties of a glass-former in which a fraction c of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature [Formula: see text] at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, i.e., [Formula: see text] is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, i.e., the order parameter that signals the glass state. We find that the transition line obtained from the overlap coincides with that obtained from the thermodynamic integration, thus showing that the two approaches give the same transition line. Finally, we determine the geometrical properties of the potential energy landscape, notably the T- and c dependence of the saddle index, and use these properties to obtain the dynamic transition temperature [Formula: see text]. The two temperatures [Formula: see text] and [Formula: see text] cross at a finite value of c and indicate the point at which the glass transition line ends. These findings are qualitatively consistent with the scenario proposed by the random first-order transition theory.

Colloquium: Random first order transition theory concepts in biology and physics

The routine transformation of a liquid, as it is rapidly cooled, resulting in glass formation, is remarkably complex. A theoretical explanation of the dynamics associated with this process has remained one of the major unsolved problems in condensed matter physics. The random first order transition (RFOT) theory, which was proposed over 25 years ago, provides a theoretical basis for explaining much of the phenomena associated with glass forming materials. It links or relates multiple metastable states, slow or glassy dynamics, dynamic heterogeneity, and both a dynamical and an ideal glass transition. Remarkably, the major concepts in the RFOT theory can also be profitably used to understand many spectacular phenomena in biology and condensed matter physics, as illustrated here. The presence of a large number of metastable states and the dynamics in such complex landscapes in biological systems from molecular to cellular scale and beyond leads to behavior, which is amenable to descriptions based on the RFOT theory. Somewhat surprisingly even intratumor heterogeneity arising from variations in cancer metastasis in different cells is hauntingly similar to glassy systems. There are also deep connections between glass physics and electronically disordered systems undergoing a metal-insulator transition, aging effects in which quantum effects play a role, and the physics of superglasses (a phase that is simultaneously a superfluid and a frozen amorphous structure). It is argued that the common aspect in all these diverse phenomena is that multiple symmetry unrelated states governing both the equilibrium and dynamical behavior---a lynchpin in the RFOT theory---controls the behavior observed in these unrelated systems.

Understanding the ideal glass transition: lessons from an equilibrium study of hard disks in a channel.

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter σ confined to a two-dimensional channel of width 1.95σ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction ϕ(K) that is less than the maximum possible ϕ(max), the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any real divergence of the pressure at ϕ(K). We give arguments that this avoided phase transition is a structural feature, the remnant in our narrow channel system of the hexatic to crystal transition, but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale ξ̃(3) as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around 15σ at ϕ(K), which is larger than the penetration lengths that have been reported for three-dimensional systems. It is argued that the α-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches ϕ(K).

An investigation of the liquid to glass transition using integral equations for the pair structure of coupled replicae.

Extensive numerical solutions of the hypernetted-chain (HNC) and Rogers-Young (RY) integral equations are presented for the pair structure of a system of two coupled replicae (1 and 2) of a "soft-sphere" fluid of atoms interacting via an inverse-12 pair potential. In the limit of vanishing inter-replica coupling ɛ12, both integral equations predict the existence of three branches of solutions: (1) A high temperature liquid branch (L), which extends to a supercooled regime upon cooling when the two replicae are kept at ɛ12 = 0 throughout; upon separating the configurational and vibrational contributions to the free energy and entropy of the L branch, the Kauzmann temperature is located where the configurational entropy vanishes. (2) Starting with an initial finite coupling ɛ12, two "glass" branches G1 and G2 are found below some critical temperature, which are characterized by a strong remnant spatial inter-replica correlation upon taking the limit ɛ12 → 0. Branch G2 is characterized by an increasing overlap order parameter upon cooling, and may hence be identified with the hypothetical "ideal glass" phase. Branch G1 exhibits the opposite trend of increasing order parameter upon heating; its free energy lies consistently below that of the L branch and above that of the G2 branch. The free energies of the L and G2 branches are found to intersect at an alleged "random first-order transition" (RFOT) characterized by weak discontinuities of the volume and entropy. The Kauzmann and RFOT temperatures predicted by RY differ significantly from their HNC counterparts.

Thermodynamic Transitions of Antiferromagnetic Ising Model on the Fractional Multi-branched Husimi Recursive Lattice

The multi-branched Husimi recursive lattice is extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi lattice. The Ising spins of antiferromagnetic interaction on such a set of lattices are calculated to check the critical temperatures (Tc) and ideal glass transition temperatures (Tk) variation with fractional branch numbers. Besides the similar results of two solutions representing the stable state (crystal) and metastable state (supercooled liquid) and indicating the phase transition temperatures, the phase transitions show a well-defined shift with branch number variation. Therefore the fractional branch number as a parameter can be used as an adjusting tool in constructing a recursive lattice model to describe real systems.

Glass transition, kinetics of crystallization and anomalous phase transformations in tellurite melts

A lead-tellurite (0.3PbO:0.7TeO2) eutectic glass was investigated through a combination of thermal, structural and vibrational spectroscopic studies to examine the kinetics of crystallization and phase transformations during the heating of the glass and the cooling of the liquid. A linear relation was found to correlate the glass transition and crystallization temperatures, from which the ideal glass transition was determined. Among the several kinetic models that were analyzed, the primary crystallization was found to agree most to the Johnson–Mehl–Avrami model, suggesting the microstructural evolution as a two-dimensional crystallization and growth. The complexity of the transformation process was evidenced from the dependence of activation energy (E) on the crystallized fraction (α) using model-free isoconversional methods. The decreasing trend of E(α) was found to be characteristic of a reversible process followed by an irreversible one. Furthermore, nucleation was found to maximize at a temperature much lower than the experimentally observed crystallization onset. The structural evolution of the devitrified phases depicted the coexistence of phases (PbTeO3 and α-TeO2) during the two-stage crystallization. Anomalous crystallization into the Pb2Te3O8 phase was observed when the devitrified melt was cooled. Such an anomaly is explained using amorphous phase separation, which is inherent to the tellurite glass system owing to the presence of unique asymmetric structural units in the corresponding melts.

Empirical study on the effects of screen inclination and feed loading on size classification of solids by gravity

This study explored the insights into the theory of dry solids classification, in particular the classical dynamics aspects related to the mass loading of particles, deck inclination of the screen, and resulting measures of flowability. Prototype screening equipment was fabricated and experiments were carried out with ideal rounded mono-shaped glass beads. The overall performance of the prototype was assessed in relation to two screen design variables, the tilt angle of inclination and the mass throughput of the feed, which affects particles flow. Mathematical models relating to the classification process were developed, simulated and compared to the results obtained from the experiments. Important parameter ranges within which equipment may be operated with minimal malfunctioning were approximated from the models. Screen loading, bulk flow velocity, and screen inclination angles determine flowability of powders and particles in gravity classification; these parameters were used in this study to assess how well the particles flowed over the screens. A close correlation was found between theory, simulation models and the experimental results, which facilitated development of empirical models that may be used to predict and estimate the classification rates, efficiencies and flowability for such systems. Dense screen loading improved the classification rates, but hampered flowability, and consequently the efficiency. Increase in deck inclinations improved flowability and efficiency, but only to a certain optimum point after which it led to excessive overflow.

On the uncertain distinction between fast landscape exploration and second amorphous phase (ideal glass) interpretations of the ultrastable glass phenomenon

This paper is written as a challenge to the ultrastable glass community to distinguish phenomenologically between the fast landscape searching scenario under discussion in the ultrastable glass community, and the alternative scenario in which the material in the ultrastable state is actually an attempted realization of the low temperature ideal glass phase of the system that can be reached in some systems, like ST2 water and amorphous silicon, and model systems like the attractive Jagla model, by a first order thermodynamic transition. These are special in that they exhibit first order phase transitions to the ground state that are accessible above the normal Tg of the high temperature phase — and in consequence exhibit vanishingly small excess entropies over crystal, and none of the “ubiquitous” glassy state cryogenic anomalies. In particular we show how, near a liquid–liquid critical point, the diffusivity can decrease arbitrarily rapidly over several orders of magnitude and that a growth front transformation from ultraslow phase to normal viscous liquid will be very difficult to distinguish from nucleation and growth of a new phase of different mobility.

On the jamming phase diagram for frictionless hard-sphere packings

We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10(4) particles with log-normal particle diameter distributions in a wide range of packing densities φ (for monodisperse packings φ = 0.46-0.72). We equilibrated these packings and searched for their inherent structures, which for hard spheres we refer to as closest jammed configurations. We found that the closest jamming densities φ(J) for equilibrated packings with initial densities φ ≤ 0.52 are located near the random close packing limit φ(RCP); the available phase space is dominated by basins of attraction that we associate with liquid. φ(RCP) depends on the polydispersity and is ∼ 0.64 for monodisperse packings. For φ > 0.52, φ(J) increases with φ; the available phase space is dominated by basins of attraction that we associate with glass. When φ reaches the ideal glass transition density φ(g), φ(J) reaches the ideal glass density (the glass close packing limit) φ(GCP), so that the available phase space is dominated at φ(g) by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation σ = 0.1, φ(GCP) ≈ 0.655 and φ(g) ≈ 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density φ(m) and ends at the crystallization offset density φ(off). For monodisperse packings, φ(m) ≈ 0.54 and φ(off) ≈ 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for φ ≤ φ(g).

Potential improvements in the optical and thermal efficiencies of parabolic trough concentrators

A detailed 3D heat transfer model is used to analyze the improvement potential of a typical parabolic trough concentrator (PTC) system with step-wise idealizations of system components. Sigmoid functions are used to idealize and optimize the optical behavior of the absorber tube selective coating. Reflectance, absorptance, and transmittance behavior is evaluated for the glass envelope, assessing the potential performance of a system with an ideal selective glass. Optical properties of the primary concentrator mirror, such as reflectivity as well as tracking and surface errors, are successively idealized to reveal the differences between ideal and real concentrators. In addition, the effect of the supporting structure is analyzed by reducing the number of heat collection elements (HCE) per mirror module, lowering the shaded area between HCEs, and removing the structure altogether. Applying these component idealizations individually yielded increases in thermal efficiency between 4.3% and 7.3% compared to a selected benchmark PTC design, while a combination of all idealizations resulted in an increase of 23%. The analysis of an alternative PTC design has shown that the idealization approach is robust in that it predicts similar increases in thermal efficiency. In a second step, several secondary mirror designs are evaluated and optimized, including a partially reflective glass surface, insulation in the vacuum annulus with reflective surfaces, as well as aplanatic mirror and tailored secondary designs. The analysis of systems with secondary optics revealed potential increases in thermal efficiencies between 0.8% and 1.6% compared to the benchmark design.