Ideal Glass Transition Research Articles

Structural properties and electrical conductivity mechanisms of semiconducting quaternary nanocomposites: Effect of two transition metal oxides

Several quaternary nanocomposites, doped with two transition metal oxides, of the generalised composition formula 0.4ZnO–0.1P2O5–0.5[xV2O5–(1-x) MoO3] were prepared via the melt quenching process. We investigated the microstructural and conductivity properties of two ternary systems and four quaternary systems to determine the better semiconductor nanocomposite system for wider application purposes. The X-ray diffraction results showed the presence of superposed nanocrystallites within amorphous networks or matrices. Analysis of ultraviolet–visible absorption spectra showed that optical bandgap energy (Eopt) values varied with V2O5 concentration, and there was an inverse relationship between Eopt and average nanocrystallite size. The responsible mechanisms of ac conductivity were examined using the model of Jonscher's universal power-law and Almond–West formalism, and it was found that ac conductivity increased as temperature rose, exhibiting semiconducting features. All the ternary (two examples) and quaternary (four examples) nanocomposite systems established non-linearity in dc conductivity, caused by the small polaron hopping process with dissimilar activation energies at different temperature regions. The power-law exponent (s) of Jonscher's universal power-law revealed that the ac conductivity mechanism could be described by correlated barrier-hopping (CBH) or non-overlapping small polaron tunnelling (NSPT) models for different samples due to major structural alterations. We applied modified CBH and NSPT models (as s > 0.8) to get realistic values of different fitting parameters, and in this process, we also obtained the values of ideal or hypothetical glass transition temperature from the theoretical models. The different activation energies associated with ac conductivity and for the small polaron migration process diminished with an increment in conductivity. Scaled ac conductivity spectra demonstrated that the conductivity relaxation process relied upon the composite structural features and did not depend on temperature. These materials can be used for such applications as gas sensors, even at higher temperatures due to their semiconducting nature and the different valence states of transition metal ions.

Role of many-body correlation in slow dynamics of glass-forming liquids: intrinsic or perturbative

Upon cooling or densification, a supercooled liquid shows drastic slowing down toward its glass-transition point. The physical mechanism behind this slow glassy dynamics has been a matter of discussion for a long time, but there has still been no consensus on its origin. Recently, we have found that for systems mainly interacting with steric repulsions, glassy structural order (or, angular order) generally develops upon cooling and its correlation length, , grows as ( is the bare correlation length, T is the temperature, T0 is the hypothetical ideal glass transition, and d is the spatial dimensionality). This ordering is difficult to detect by two-body density correlation since it is a consequence of sterically-induced (entropically-driven) many-body correlation that lowers local free energy. Interestingly, the power-law growth of with the exponent of 2/d is reminiscent of the Ising criticality. We also find that the structural relaxation time diverges as (: the microscopic relaxation time, K is a fragility index, is the Boltzmann constant), suggesting that glass transition is a consequence of Ising-like criticality with growing activation energy. Unlike ordinary critical phenomena, the activation energy of particle motion increases in proportion to the root of the correlation volume of , implying that the particle motion is strongly correlated in that volume. This relation indicates that the impact of spatial fluctuations of the order parameter on slow dynamics is not perturbative but intrinsic. Although we need further study to confirm our claim, we hope that the discussion in this article would provide a good starting point for further consideration of the physical nature of glass transition.

Relaxation times, jamming densities, and ideal glass transition densities for hard spheres in a wide range of polydispersities

We computationally study the behavior of asymptotic alpha-relaxation times τα as well as jamming densities for equilibrated frictionless polydisperse hard spheres in wide ranges of particle volume fractions φ. Log-normal particle radii distribution (r) with polydispersities δ=⟨Δr2⟩/⟨r⟩=0.1−0.3 in steps of 0.05 is used. We discover that τα(φ) can be fitted well with the Vogel–Fulcher–Tammann (VFT) form. Through the VFT fits, we estimate positions of the ideal glass transition densities φg. For each equilibrated configuration, we calculate equilibrium kinetic pressure Z. Equilibrium pressures can be well described by the Boublík–Mansoori–Carnahan–Starling–Leland fluid equation of state. For each equilibrated configuration, a jammed particle configuration, which is the closest one in the configuration space, is determined. We measure jamming densities φEJ of these configurations and present plots φEJ(φ) for all polydispersities. We demonstrate that the lines τα(φ), φEJ(φ), and Z(φ), as well as values φg, depend significantly on δ. These results show that φg is, in general, distinct from the random close packing limit (φEJ at φ = 0). We plan to use these data in the future to estimate glass equations of state and the configurational entropy for these hard-sphere systems.

LOOKING AT THE GLASS TRANSITION: CHALLENGES OF EXTREME TIME SCALES AND OTHER INTERESTING PROBLEMS

ABSTRACTThe behavior of glass-forming materials is examined with emphasis on the below-glass transition behavior. A major question that is related to the super-Arrhenius behavior of the dynamics of glass-forming systems is whether the apparent divergence at finite temperature continues below the kinetic or laboratory glass transition that is related to the limits of measurement and is standardized so that the material relaxation time is near 100 s. The problem arises because as the temperature decreases, the time scales required to reach equilibrium (or metastable equilibrium) become geologically long. Yet the apparent finite temperature divergence is fundamental to many theories of glasses; therefore, it becomes essential to find ways to finesse the extreme time scales related to the so-called Kauzmann paradox to bring new information to the ongoing conversation concerning the existence or not of an ideal glass transition at either the Kauzmann temperature or the Vogel–Fulcher–Tammann temperature. After describing the framework of the glassy state that is formed by the early ideas of a fictive temperature, we examine the use of extremely low fictive temperature glasses as a means to potentially get around the long time-scale problem. The challenge is to find ways to create such glasses and measure their properties. In addition to looking at the dynamic behavior of a 20-million-year-old amber and a vapor-deposited amorphous perfluoropolymer whose fictive temperature was the same as the Kauzmann temperature for the material, we also examine the possibility of directly testing the thermodynamics of an ideal glass transition by making athermal solutions of a poly(α-methyl styrene) and its pentamer, where we find that the entropy surface determined from extrapolation of the heat capacity to zero pentamer shows no distinct transition at as much as 180 K below the Kauzmann temperature. The significance of the dynamics of the stable glasses and the thermodynamics of the polymer solutions is discussed in terms that challenge the idea of an ideal glass transition. We also look in more detail at the ability to use vapor deposition to make ethylbenzene, a small-molecule organic, into an ultra-stable glass with a fictive temperature that is possibly below the Kauzmann temperature of this material. We end with remarks on the question of decoupling of different relaxation mechanisms as something not treated by current theories of glass, and we consider some open questions related to the fact that the glass transition remains an unresolved and important problem.

Measured and ideal glass transition temperatures of glass-forming liquids

Herein, measured and ideal glass transition temperatures of glass-forming liquids have been investigated. The value of T0/Tg increases with increasing fragility parameter m or decreasing strength parameter D (where Tg and T0 are the measured and ideal glass transition temperatures, respectively). We utilize T0/Tg values to classify various glass-forming liquids into three broad categories, which are strong, metallic glass-forming (intermediate) and fragile liquids. The result reveals that strong liquids with 15.25 < m ≤ 30 (or 37.3 ≤ D) have 0 < T0/Tg ≤ 0.49. By contrast, fragile liquids obtain 0.82 ≤ T0/Tg ≤ 0.94 when m values lie in 100 ≤ m ≤ 214 (or 1.8 ≤ D ≤ 9.1). Metallic glass-forming liquids have 0.52 ≤ T0/Tg ≤ 0.77 when m values have 32 ≤ m ≤ 66 (or 10.8 ≤ D ≤ 32.8).

The Effect of the Nature of Cation on Transport Properties of Bis(trifluoromethylsulfonyl)imide Ionic Liquids

The methods of viscosimetry, conductometry, densimetry, and differential scanning calorimetry are used for studying the physicochemical properties of cations (1-butyl-3-methylimidazolium [BuMeIm]+, N-butylmethylpyrrolidinium [BuMePyrr]+, and methytrioctylammonium [MeOc3Am]+) and their effect on the transport properties of bis(trifluoromethylsulfonyl)imide ionic liquids (IL). It is shown that ILs formed by cyclic amines ([BuMeIm]+ and [BuMePyrr]+) as the cations demonstrate the close values and temperature dependences of viscosity and conductivity. The cation [MeOc3Am]+ predetermines the difference in the IL structure and, thus, a substantial difference in the transport properties of the melt. For salts [BuMeIm][Tf2N], [BuMePyrr][Tf2N], and [MeOc3Am][Tf2N] at 293 К, the following transport characteristics are observed: viscosity 57.7, 88.1, and 726.5 mPa s; specific conductivity 0.376, 0.252, and 0.005 S m–1; activation energy of conductivity 21, 21, and 35 kJ mol–1; degree of “ionicity” 0.92, 0.94, and 1.00, respectively. Using the equation of Vogel–Fulcher–Tammann and based on the temperature dependences of specific conductivity and viscosity, the ideal glass transition temperatures are calculated for liquids under study. In the positive temperature range, a linear correlation is observed between the conductivity and the cation volume in these ionic liquids.

Cluster approach to phase transitions from fluid to amorphous solids: gels, glasses and granular materials

Based on various results present in the literature, we elaborate a unifying cluster percolation approach to interpret the dynamical arrest occurring in amorphous materials such as those of the gel, glass and granular variety. In the case of the sol-gel transition, this cluster approach predicts scaling laws relating dynamical exponents to critical random percolation exponents. Interestingly, in the mean-field such relations coincide with those predicted by the schematic continuous mode coupling theory, known as model A. More appropriate to describe the molecular glass transition is the schematic discontinuous mode coupling theory known as model B. In this case a similar cluster approach and a diffusing defect mechanism predicts scaling laws, relating dynamical exponents to the static critical exponents of the bootstrap percolation. In finite dimensions, the glass theory based on the random first order transition suggests that the mode coupling theory transition is only a crossover towards an ideal glass transition characterised by the divergence of cooperative rearranging regions. Interestingly, this scenario can also be mapped onto a mixed order percolation transition, where the order parameter jumps discontinuously at the transition, while the mean cluster size and the linear cluster dimension diverge. A similar mixed order percolation transition seems to apply to the jamming transition as well.

Structural characterization and electrical conductivity analysis of MoO3–SeO2–ZnO semiconducting glass nanocomposites

A series of glass nanocomposite samples of the general composition formula xMoO3–(1-x) (0.5SeO2–0.5ZnO) for x = 0.05, 0.1, 0.2, and 0.3 have been prepared by solid-state reaction, i.e., slow cooling process. The structural characteristics have been explored by analyzing X-ray diffraction patterns, Fourier-transform infrared, and UV–Vis spectra. The superposition of different nanophases SeO2, SeO3, ZnO, MoO3, Zn (SeO3), Zn (SeO4), Zn(MoO4), Zn2Mo3O8 and ZnMo8O10 over the amorphous glassy matrices have been identified, and their crystallite sizes have been evaluated as well. Fourier transform infrared (FTIR) spectra reveal different types of bonding like Zn–O–Se type and stretching vibrations of MoO6 octahedral units. It is observed that with increasing MoO3 concentration, the estimated values of optical bandgap energy, Urbach energy, and average crystallite size reduce. The dependency of electrical conductivity on frequency and temperature have been analyzed using Almond-West formalism and Jonscher's universal power-law. The non-linear character of DC conductivity and different activation energies at low and high-temperature regions affirm that the present glassy systems exhibit semiconducting nature. Moreover, DC conduction process is due to small polaron hopping through localized or defect states. The decreasing trend of power-law exponent (s) with temperature rise reveals that AC conduction mechanism is consistent with the correlated barrier-hopping (CBH) model. The existing correlated barrier-hopping model has been modified to attain reasonable values of fitting parameters and to obtain theoretical values of ideal thermodynamic glass transition temperature. The AC conductivity activation energy and free energy required for small polaron migration reduce with increasing conductivity. The scaling property emphasizes that conductivity relaxation process is subjected to the structure of the composition and does not depend on temperature.

Revisiting the replica theory of the liquid to ideal glass transition.

The replica theory of the "Random First Order Transition" (RFOT) from a supercooled liquid to an "ideal" glass of a system of "soft spheres" is revisited. Following the seminal work of Mézard and Parisi [J. Chem. Phys. 111, 1076 (1999)], the number m of weakly interacting replicas of the system is varied continuously from m = 2 to m < 1. Relevant order parameters and the free energy of the liquid and glass phases are calculated using the hypernetted chain (HNC) approximation for the pair correlation functions. The scenario observed for all m confirms the existence of two glass branches G1 and G2. The latter has the lowest free energy for all m > 1, while the former has a lower free energy for m < 1 but is shown to be unstable against spinodal decomposition for any nonzero value of the attractive inter-replica coupling. The critical temperature Tcr of the RFOT turns out to depend on m, which may be a by-product of the approximation inherent in the HNC closure. The RFOT is predicted to be weakly first order, characterized by a small jump in density between the coexisting liquid and G2 phases for all m > 1. Estimating Tcr in the limit m → 1 requires a proper extrapolation of high resolution HNC calculations. The present protocol explores the behavior of the free energy of the ideal glass phase below Tcr as a function of m.

A Husimi rhombus lattice with random angles to present the configurational stochasticity in exact thermodynamic calculation

Abstract The square unit in Husimi lattice is generalized to be rhombus with random angles. The independence feature of unit cells in recursive lattice makes the random conformation possible, which is unfeasible in conventional lattices. Since the randomness of conformations in real system is naturally introduced into the model, this new lattice can describe the off-crystal metastable states without artificial randomness. With reasonable simplification, a coefficient A ( θ ) is formulated to present the effect of angle in the rhombus unit. A “visit and count” recursive calculation is developed to numerically approach the thermodynamics. The critical temperature T c of spontaneous magnetization is lowered with the presence of angle randomness, implying a less stable system. Besides consistent results to the regular lattice, the random-angled model features a distribution of solutions and thermal fluctuation with exact calculation. The Kauzmann paradox and ideal glass transition due to the off-crystal metastable portion are identified by the appearance of negative entropy. The effects of energy parameters on thermodynamics and the ground states are investigated.

Testing the paradigm of an ideal glass transition: Dynamics of an ultrastable polymeric glass.

A major challenge to understanding glass-forming materials is obtaining equilibrium data far below the laboratory glass transition temperature T g. The challenge arises because it takes geologic aging times to achieve the equilibrium glassy state when temperatures are well below T g. Here, we finesse this problem through measurements on an ultrastable amorphous Teflon with fictive temperature T f near to its Kauzmann temperature T K. In the window between T f and T g, the material has a lower molecular mobility than the equilibrium state because of its low specific volume and enthalpy. Our measurements show that the determined scaled relaxation times deviate strongly from the classical expectation of divergence of time scales at a finite temperature. The results challenge the view of an ideal glass transition at or near to T K.

Ideal Glass States Are Not Purely Vibrational: Insight from Randomly Pinned Glasses.

We use computer simulations to probe the thermodynamic and dynamic properties of a glass former that undergoes an ideal glass transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass state, the system relaxes to some extent because of the presence of localized excitations that allow the system to access different inherent structures, thus giving rise to a nontrivial contribution to the entropy. By calculating with high accuracy the vibrational part of the entropy, we show that also in the equilibrium glass state thermodynamics and dynamics give a coherent picture, and that glasses should not be seen as a disordered solid in which the particles undergo just vibrational motion but instead as a system with a highly nonlinear internal dynamics.

The Temperature Effect on the Transport Properties of 1-Alkyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide Ionic Liquids

The temperature dependences of specific and equivalent conductivities, viscosity, density, and crystallization temperature are determined for three 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide ([C n MeIm] [Tf2N], n = 2, 3, 4) ionic liquids saturated with water vapor at room temperature. It is established that in the area of positive temperatures, the relationship between viscosity and conductivity obeys the fractional Walden rule with exponents of 0.97, 0.92, and 0.92 for ionic liquids with ethyl-, propyl-, butylradicals, respectively. The temperature dependences of conductivity and viscosity are approximated using the Vogel–Fulcher–Tammann equation (R2 > 0.999), and ideal glass transition temperatures T0 are calculated for the investigated liquids. The obtained values of T0 depend largely on the chosen range of temperatures. It is shown that [C2MeIm][Tf2N] occupies a separate position with regard to [C3MeIm][Tf2N] and [C4MeIm][Tf2N].

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.

Calorimetric study on Ge23Se67Sb10–0.5CsCl glass

The mechanical behavior of Ge23Se67Sb10 glass can be improved by adding CsCl facilitating the nano-crystaline formation. Understanding the crystallization mechanism of chalcogenide glass can help in directing the subsequent annealing processing and tuning the microstructure and physical properties. In this work, 99.5Ge23Se67Sb10–0.5CsCl glass was prepared and its transformation kinetics was investigated under non-isothermal conditions with heating rate up to 400 K min−1. Using Vogel–Fulcher–Tammann equation, the ideal glass transition temperature was determined as T 0g = 434.1 K. Using the classical JMA theory, the average activation energy and average growth exponent were determined as 135.0 and 2.4 kJ mol−1, while using the model considering impingements (MCI), the two parameters were determined as 120.9 and 3.2 kJ mol−1, respectively. Compared to JMA theory, the MCI model can fit the transition curves better, and it shows that the growth mode of the present glass is between two-dimension and three-dimension. By comparing with the result of Ge23Se67Sb10 glass, it is found that addition of CsCl can reduce the growth dimension and activation energy during crystallization.

Frequency and temperature dependent conductivity spectra of mixed transition metal oxide doped semiconducting glassy system

Frequency and temperature dependent conductivity of mixed transition metal oxide (TMO) doped semiconducting glassy system, xV2O5–(1−x) (0.05MoO3–0.95ZnO) have been investigated in the wide range of frequency and temperature. The dc conductivity (σdc), crossover frequency (ωH), frequency exponent (n) and power law exponent (s) have been computed from the best fitted plots of experimental data. We have estimated the values of activation energy of ac conduction (Eac) and free energy of polaron migration (EH). Dc conductivity of the as-prepared samples shows thermally activated non–linear nature, which has been interpreted with Vogel–Tammann–Fulcher (VTF) model. From the fitting, pseudo activation energy (Ea) and thermodynamic ideal glass transition temperature (T0) have been estimated. Nature of variation of conductivity and the power law exponent (s) data exhibit that non–overlapping small polaron tunnelling (NSPT) model is suitable to interpret these data for compositions x=0.3, 0.5 and 0.7. On the other hand, correlated barrier hopping (CBH) model is most applicable mechanism for ac conduction for compositions x=0.9 and 0.93. Formation of some complex Mo-O-V structures may be possible reason for applicability of CBH model for composition x=0.9, 0.93. It is also observed that conductivity relaxation process of charge carriers (polarons) is independent of temperature, but depends upon composition.

Calorimetric studies on Ge23Se67Sb10-0.5%RbI glass

Understanding the crystallization mechanism of chalcogenide glass can help in directing the subsequent annealing processing, thus tuning the microstructures and physical properties. In this work, the transformation kinetics of Ge23Se67Sb10-0.5%RbI was investigated under non-isothermal conditions. From VFT equation, the ideal glass transition temperature was determined as T0g=427.74K. The fragility index m was estimated to be 64.74, indicating a relatively fragile liquid. From the classical JMA theory, the activation energy was determined as 222.9kJ/mol, growth index was 1.26, while from the model considering the impingement modes(MCI) activation energy was determined as 90.99kJ/mol and growth index was 1.38, which indicated that the growth mode of crystallization of the present glass was between one dimension and two dimension. The result shows that addition of RbI can reduce the growth dimension and activation energy.

Kinetics and thermal stability of the Ni62Nb38–x Ta x (x=5, 10, 15, 20 and 25) bulk metallic glasses

We studied thermal stability and its relationship to the glass-forming ability (GFA) of the Ni62Nb38–xTax (x=5, 10, 15, 20, 25) bulk metallic glasses (BMG) from a kinetic point of view. By fitting the heating-rate dependence of glass transition temperature (Tgonset) and crystallization temperatures (Txonset and Txpeak) of the Ni62Nb38–xTax BMG using the Vogel-Fulcher-Tammann (VFT) equation, we obtained the ideal glass transition and crystallization temperatures (Tg0 and Tx0) and the fragility parameter (m), and also constructed continuous heating transition (CHT) diagrams for crystallization of the BMG. The CHT diagrams of the BMG indicate enhanced thermal stability by Ta addition; the Tg0 as well as the Tx0 also illustrates this improved stability limit. The compositional dependence of m, which agrees well with that of the reduced glass-transition temperature, indicates a strong correlation between liquid fragility and glass-forming ability in the present alloy system. These results provide new evidence for understanding thermal stability, liquid fragility, and GFA in BMG.

Study on glass transition temperature and kinetics of Cu–Zr glassy alloys

Ideal glass transition temperatures and transition activation energies of Cu46Zr45Al9 metallic glass was investigated using differential scanning calorimetry (DSC). The Vogel–Fulcher–Tammann temperature T 0 and Kauzmann temperature T k were determined, respectively, and T 0 is greater than T k. Meanwhile, activation energies of glass transition E g, onset crystallization E x and crystallization peak E p were deduced to be 634.2 ± 15, 444 ± 16.1 and 366.8 ± 25.1 kJ mol−1, which indicates that glass transition is harder than crystallization process to proceed.

Exact Calculation of Antiferromagnetic Ising Model on an Inhomogeneous Surface Recursive Lattice to Investigate Thermodynamics and Glass Transition on Surface/Thin Film**Supported by the National Natural Science Foundation of China under Grant No. 11505110, the Shanghai Pujiang Talent Program under Grant No. 16PJ1431900, and the China Postdoctoral Science Foundation under Grant No. 2016M591666

An inhomogeneous 2-dimensional recursive lattice formed by planar elements has been designed to investigate the thermodynamics of Ising spin system on the surface/thin film. The lattice is constructed as a hybrid of partial Husimi square lattice representing the bulk and 1D single bonds representing the surface. Exact calculations can be achieved with the recursive property of the lattice. The model has an anti-ferromagnetic interaction to give rise to an ordered phase identified as crystal, and a solution with higher energy to represent the amorphous/metastable phase. Free energy and entropy of the ideal crystal and supercooled liquid state of the model on the surface are calculated by the partial partition function. By analyzing the free energies and entropies of the crystal and supercooled liquid state, we are able to identify the melting and ideal glass transition on the surface. The results show that due to the variation of coordination number, the transition temperatures on the surface decrease significantly compared to the bulk system. Our calculation qualitatively agrees with both experimental and simulation works on the thermodynamics of surfaces and thin films conducted by others. Interactions between particles farther than the nearest neighbor distance are taken into consideration, and their effects are investigated.