Ideal Glass Transition Temperature Research Articles

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.

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.

Diffusion and interdiffusion in binary metallic melts

We discuss the dependence of self- and interdiffusion coefficients on temperature and composition for two prototypical binary metallic melts, Al-Ni and Zr-Ni, in molecular-dynamics computer simulations and the mode-coupling theory of the glass transition (MCT). Dynamical processes that are mainly entropic in origin slow down mass transport (as expressed through self-diffusion) in the mixture as compared to the ideal-mixing contribution. Interdiffusion of chemical species is a competition of slow kinetic modes with a strong thermodynamic driving force that is caused by nonentropic interactions. The combination of both dynamic and thermodynamic effects causes qualitative differences in the concentration dependence of self-diffusion and interdiffusion coefficients. At high temperatures, the thermodynamic enhancement of interdiffusion prevails, while at low temperatures, kinetic effects dominate the concentration dependence, rationalized within MCT as the approach to its ideal-glass transition temperature ${T}_{c}$. The Darken equation relating self- and interdiffusion qualitatively reproduces the concentration dependence in both Zr-Ni and Al-Ni, but quantitatively, the kinetic contributions to interdiffusion can be slower than the lower bound suggested by the Darken equation. As temperature is decreased, the agreement with Darken's equation improves, due to a strong coupling of all kinetic modes that is a generic feature predicted by MCT.

Probing the pair structure of supercooled fluids by integral equations: Evidence for an equilibrium liquid-ideal glass transition?

We solve the hypernetted-chain (HNC) and Rogers-Young (RY) integral equations for the pair structure of a system of two weakly coupled replicæ of a soft-sphere fluid, in order to detect signatures of an equilibrium transition to an “ideal glass”. Both integral equations predict, in addition to the supercooled-liquid branch, the appearance of a new disordered state characterized by different pair correlations, over a range of temperatures. The ideal-glass transition temperature , identified by a discontinuous jump in the inter-replica pair correlation function, is predicted to be substantially higher with RY compared to HNC theory. The internal energy is predicted to undergo a weak discontinuity at .

Comparative study on transport properties for LiFAP and LiPF6 in alkyl-carbonates as electrolytes through conductivity, viscosity and NMR self-diffusion measurements

We present in this work a comparative study on density and transport properties, such as the conductivity (σ), viscosity (η) and self-diffusion coefficients (D), for electrolytes based on the lithium hexafluorophosphate, LiPF6; or on the lithium tris(pentafluoroethane)-trifluorophosphate, LiFAP dissolved in a binary mixture of ethylene carbonate (EC) and dimethylcarbonate (DMC) (50:50 wt%). For each electrolyte, the temperature dependence on transport properties over a temperature range from 10 to 80 °C and 20 to 70 °C for viscosity and conductivity, respectively, exhibits a non-Arrhenius behavior. However, this dependence is correctly correlated by using the Vogel-Tamman-Fulcher (VTF) type fitting equation. In each case, the best-fit parameters, such as the pseudo activation energy and ideal glass transition temperature were then extracted. The self-diffusion coefficients (D) of the Li+ cation and PF6− or FAP− anions species, in each studied electrolyte, were then independently determined by observing 3Li, 19F and 31P nuclei with the pulsed-gradient spin-echo (PGSE) NMR technique over the same temperature range from 20 to 80 °C. Results show that even if the diffusion of the lithium cation is quite similar in both electrolytes, the anions diffusion differs notably. In the case of the LiPF6-based electrolyte, for example at T ≈ 75 °C (high temperature), the self-diffusion coefficients of Li+ cations in solution (D (Li+) ≈ 5 × 10−10 m2 s−1) is 1.6 times smaller than that of PF6− anions (D (PF6−) = 8.5 × 10−10 m2 s−1), whereas in the case of the LiFAP-based electrolyte, FAP− anions diffuse at same rate as the Li+ cations (D (FAP−) = 5 × 10−10 m2 s−1). Based on these experimental results, the transport mobility of ions were then investigated through Stokes–Einstein and Nernst–Einstein equations to determine the transport number of lithium tLi+, effective radius of solvated Li+ and of PF6− and FAP− anions, and the degree of dissociation of these lithium salts in the selected EC/DMC (50:50 wt%) mixture over a the temperature range from 20 to 80 °C. This study demonstrates the conflicting nature of the requirements and the advantage of the well-balanced properties as ionic mobility and dissociation constant of the selected electrolytes.

Glass forming ability, thermodynamics and mechanical properties of novel Ti–Cu–Ni–Zr–Hf bulk metallic glasses

Novel, pentabasic Ti–Cu–Ni–Zr–Hf bulk metallic glasses (BMGs), with critical diameters of 2–4mm, were successfully developed through the proportional mixing of the binary eutectic compositions of Ti27Cu73, Ti76Ni24, Zr76Ni24 and Hf84Ni16. According to the concept of binary eutectic units, five Ti–Cu–Ni–Zr–Hf BMGs were fabricated, of which the Ti29.44Cu46.72Ni7.88Zr7.6Hf8.4 alloy had the lower glass forming ability, and the smallest reduced ideal glass transition temperature δ and ΔCpm/ΔSm values, where ΔCpm and ΔSm represent the specific heat and entropy differences at the melting temperature (Tm), respectively. The Ti29.44Cu46.72Ni7.88Zr7.6Hf8.4 alloy also showed good mechanical properties, i.e., good plastic strain and relatively high compressive strength.

The Correlation between Reduced Glass Transition Temperature and Glass Forming Ability of Undercooled Polymeric Glasses

The thermodynamic behaviour of glass forming undercooled melt have been studied by analysing the temperature dependence of the Gibbs free energy difference (Δ<i>G</i>) for six polymeric glass forming materials[O-terphenyl, Tri-α-naphthyl benzene, Glycerol, Ethanol, 2-methylpentane and Phenyl salicylate (salol)] between the undercooled melt and the corresponding equilibrium solid phases. The expression obtained by expanding free energies of the undercooled liquid and solid phases of the materials in the form of Taylor’s series expansion. The procedure for the estimation of the ideal glass transition temperature has been reviewed together its importance in the glass forming ability of materials. The glass forming ability of undercooled materials is also explained in terms of ratio of reduced glass transition temperature and ideal glass transition temperature. It has also reported that Glycerol has the largest melting interval with the poorest glass forming ability among these six polymers. It has also been found that the best polymeric glass forming materials are at near eutectic composition. There is a strong correlation between glass forming ability of these polymeric materials.

Density, conductivity, viscosity, and excess properties of (pyrrolidinium nitrate-based Protic Ionic Liquid + propylene carbonate) binary mixture

Density, ρ, viscosity, η, and conductivity, σ, measurements of binary mixtures containing the pyrrolidinium nitrate Protic Ionic Liquid (PIL) and propylene carbonate (PC), are determined at the atmospheric pressure as a function of the temperature from (283.15 to 353.15)K and within the whole composition range. The temperature dependence of both the viscosity and conductivity of each mixture exhibits a non-Arrhenius behaviour, but is correctly fitted by using the Vogel–Tamman–Fulcher (VTF) equation. In each case, the best-fit parameters, such as the pseudo activation energy, Ea∗ and ideal glass transition temperature, T0 are then extracted. The excess molar volumes VE, and viscosity deviations from the ideality, Δη, of each investigated mixture were then deduced from the experimental results, as well as, their apparent molar volumes, Vϕ, thermal expansion coefficients αp, and excess Gibbs free energies (ΔG∗E) of activation of viscous flow. The VE, αpE, Δη values are negative over the whole composition range for each studied temperature therein. According to the Walden rule, the ionicity of each mixture was then evaluated as a function of the temperature from (283.15 to 353.15)K and of the composition. Results have been then discussed in terms of molecular interactions and molecular structures in this binary mixture.

Simulation study on thermodynamic, dynamic and structural transition mechanisms during the formation of Ca70Mg30 metallic glass

The rapid quenching process of Ca70Mg30 alloy is simulated by using the molecular dynamics method. During the liquid-glass transition process, the thermodynamic, dynamic and structural transition mechanisms are investigated deeply, and the relations between glass transition temperatures determined by different methods are discussed. It is found that both the simulated structural factor of Ca70Mg30 metallic glass and glass transition temperature are consistent with the experimental results, and the icosahedral local configuration plays a critical role in the formation of Ca70Mg30 metallic glass. The dynamic property of supercooled liquid gradually deviates from the Arrhenius law and satisfies the MCT power law due to the cage effect formed by neighbor atoms. It is also found that the structural glass transition temperature is close to the dynamic one, and they are higher than the calorimetric glass transition temperature. The relationship between them and the ideal dynamic glass transition temperature satisfies the Odagaki relation.

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.

Vogel–Fulcher–Tammann plot for viscosity scaled with temperature interval between actual and ideal glass transitions for metallic glasses in liquid and supercooled liquid states

The glass transition temperature- ( T g-) scaled Arrhenius plot (Angell plot) has been modified by considering viscosity ( η) of metallic glasses in a liquid and supercooled liquid state with absolute temperature ( T). The log η−( T g/ T) relationships in Angell plot were modified as log η−[( T g− T 0)/( T− T 0)] relationships where T 0 is the ideal glass transition temperature from Vogel–Fulcher–Tammann (VFT) parameters. Introducing Δ T g−0 (≡ T g− T 0) makes it possible to regard the modified plot as Δ T g−0-scaled VFT plot. Using B from VFT parameters provides a relationship D* VFT = B/Δ T g−0 ∼38, in which T g was principally measured at a heating rate of 0.333 K s −1. The analyses revealed that Δ T g−0-scaled VFT plot reflects α relaxation due to a motion of groups of atoms, and that Δ T g−0/( T l− T 0) where T l is the liquidus temperature can be a glass-forming parameter.

Glass forming ability of materials: A thermodynamic approach

The glass forming ability of materials has been studied on the basis of the critical cooling rate ( R c ) for the glass formation. The study is made by obtaining an analytical expression for the nose temperature ( T n ) of the time–temperature–transformation ( T–T–T) diagram using the expressions for the thermodynamic quantities Gibbs free energy difference (Δ G), entropy difference (Δ S) and enthalpy difference (Δ H) between the undercooled liquid and solid phases obtained on the basis of Taylor’s series expansion. The study is made for oxide as well as for polymeric glasses by calculating R c for SiO 2, B 2O 3, O-terphenyl, 2-methylpentane, glycerol and ethanol. The variations of R c with the reduced ideal glass transition temperature ( T K / T m ) as well as with the ratio of specific heat and entropy differences ( Δ C p m / Δ S m ) at the melting temperature ( T m ) have been analyzed, where T K is the ideal glass transition temperature. It is found that material having a large value of the reduced ideal glass transition temperature ( T K / T m ) results a lower value of R c . It is also found that R c decreases with increasing Δ C p m / Δ S m . Attempt has also been made to study the glass forming ability of materials on the basis of reduced residual entropy ( Δ S R / Δ S m ) and ( T g - T K ) / T m , where T g is the glass transition temperature and it is found that the material having a lower reduced residual entropy ( Δ S R / Δ S m ) requires a lower R c to convert into a glassy structure. It is also found that the materials having low ( T g - T K ) / T m require low R c and consequently such materials can be said as a good glass former.

Dielectric Properties of Nanocomposites Based on Polyethylene and Layered Double Hydroxide

Nanocomposites with a predominantly exfoliated morphology were prepared by melt blending of organically modified doubled layered hydroxide (LDH) and low density polyethylene (PE). The prepared materials were investigated by differential scanning calorimetry (DSC) and in detail by dielectric spectroscopy. The DSC experiments show that the degree of crystallinity decreases linearly with increasing content of the LDH. The extrapolation of this dependence to zero results in a limiting concentration of ca. 50 wt % LDH were the crystallization of PE is completely suppressed by the nanofiller. The dielectric response of pure polyethylene shows different weak relaxation processes. The intensity of dynamic glass transition (β-relaxation) increases with the concentration of LDH. This is attributed to the increasing concentration of the exchanged anion dodecyl benzene sulfonate (SDBS). The SDBS molecules are strongly adsorbed at the exfoliated LDH layers. Therefore, a detailed analysis of the β-relaxation provides information about the structure and the molecular dynamics in the interfacial region between the exfoliated LDH layers and the polyethylene matrix. This analysis shows that the β-relaxation region consists of two processes: both of them obey glassy dynamics. The difference in corresponding Vogel (ideal glass transition) temperatures is about 30 K. The relaxation process at lower frequency is assigned to polyethylene segments with a reduced molecular mobility close to LDH layers. The process at higher frequencies is related to polyethylene segments in a farer distance for the surface of the nanofiller. In the nanocomposite materials an additional process due to Maxwell−Wagner−Sillars (MWS) polarization was observed. The time constant of this MWS process can be correlated with characteristic length scales in nanocomposites and therefore provides additional information on dispersion and delamination/exfoliation of the LDH layers in these materials.

Physicochemical properties of ZnCl 2–NaCl–KCl eutectic melt

Physicochemical properties of ZnCl 2–NaCl–KCl eutectic melt were studied at 200–300 °C for the first time. Firstly, it was reconfirmed that the eutectic composition is ZnCl 2:NaCl:KCl = 0.6:0.2:0.2 in mole fraction, and that the eutectic temperature is 203 °C. Then, the density, viscosity, and ionic conductivity of the ZnCl 2–NaCl–KCl eutectic melt were measured at 200–300 °C. At 250 °C, the density was 2.43 g cm −3, the viscosity was 42.0 cP and the ionic conductivity was 8.53 S m −1. The temperature dependencies of density and ionic conductivity were well fitted by the VTF equations with the same ideal glass transition temperature of 283 K (10 °C). It was found that the melt obeys the fractional Walden's rule which is explained by the decoupling effect. The electrochemical window of the melt was determined to be 1.7 V at 250 °C with the cathode limit being zinc metal deposition and the anode limit being chlorine gas evolution.

Solvents in salt electrolyte: Benefits and possible use as electrolyte for lithium-ion battery

An EC/DEC [40:60% (v/v)] solvent mixture has been added in various amounts to the ionic liquid (IL) hexyltrimethylammonium bis(trifluoromethylsulfonyl)imide (N 1116-NTf 2) in the presence of LiNTf 2 (lithium bis(trifluoromethylsulfonyl)imide) as lithium salt for possible use as electrolytes in lithium-ion batteries. These electrolytes exhibit a larger thermal stability than the reference electrolyte EC/DEC [40:60] + LiNTf 2 1 M when the percentage of the IL exceeds 30% (v/v). All studied electrolytes are glass forming ones with an ideal glass transition temperature of ca. −85 °C(±5 °C), which has been determined by application of the VTF theory to conductivity and viscosity measurements and confirmed by DSC ( T g = −90 ± 5 °C). An electrochemical window of about 5 V versus Li/Li + was measured at a glassy carbon electrode. The cycling ability of the optimized electrolyte N 1116-NTf 2/EC:DEC (40/60% (v/v)) + 1 M LiNTf 2 has been investigated at a titanate oxide (Li 4Ti 5O 12) and a cobalt oxide (Li x CoO 2) electrodes. Cycling the positive and the negative electrodes was conducted successfully with a high capacity and without any significant fading.

An extended criterion for estimation of glass-forming ability of metals

If a metal contracts upon solidification, the specific volume of a metallic liquid phase must not be smaller than that of the corresponding crystal. As molten metals have higher thermal expansion coefficients compared with those of the corresponding crystals, the intersection point of two specific-volume–temperature plots of the liquid and the corresponding solid crystalline phase by analogy with Kauzmann’s paradox for entropy could be treated as an ideal glass-transition temperature. This paper describes this phenomenon observed for a number of pure metals and gives a semiempirical criterion for the achievement of a good glass-forming ability.

Theoretical Study of Glass Transition Based on Cluster Variation Method

Modeling of Glass transition is attempted based on the Cluster Variation Method. Free energy functional of an L10 ordered phase is employed to describe the first order nature of the transition. Free energy contour surface calculated as a function of temperature and an order parameter which simulates an amount of defects provides a generalized stability diagram in which the ideal glass transition temperature is identified as a critical point. Transition kinetics is investigated by Path Probability Method which is the kinetics version of the CVM to time domain. Continuous cooling behavior is calculated by explicitly incorporating the temperature dependent viscosity term based on VFT (Vogel-Fulcher-Tamman) formula. The glass transition is realized as the freezing of the order parameter due to the enhanced viscosity. The extension of the present theoretical scheme to non-Bravais lattice is attempted by Continuous Cluster Variation Method.

Structural relaxation and rheological response of a driven amorphous system

The interplay between the structural relaxation and the rheological response of a simple amorphous system {a 80:20 binary Lennard-Jones mixture [W. Kob and H. C. Andersen, Phys. Rev. Lett. 73, 1376 (1994)]} is studied via molecular dynamics simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of Tc=0.435 has been identified in the previous studies via the analysis of the system's dynamics in the framework of the mode coupling theory of the glass transition [W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995)]. In the present work, we focus on the question whether a signature of this ideal glass transition can also be found in the case where the system's dynamics is driven by a shear motion. Indeed, the following distinction in the structural relaxation is found: In the supercooled state, the structural relaxation is dominated by the shear at relatively high shear rates gamma, whereas at sufficiently low gamma the (shear-independent) equilibrium relaxation is recovered. In contrast to this, the structural relaxation of a glass is always driven by shear. This distinct behavior of the correlation functions is also reflected in the rheological response. In the supercooled state, the shear viscosity eta decreases with increasing shear rate (shear thinning) at high shear rates, but then converges toward a constant as the gamma is decreased below a (temperature-dependent) threshold value. Below Tc, on the other hand, the shear viscosity grows as eta proportional, etax 1/gamma, suggesting a divergence at gamma=0. Thus, within the accessible observation time window, a transition toward a nonergodic state seems to occur in the driven glass as the driving force approaches zero. As to the flow curves (stress versus shear rate), a plateau forms at low shear rates in the glassy phase. A consequence of this stress plateau for Poiseuille-type flows is demonstrated.

Thermal Stability and Kinetics of Binary Cu65Hf35Bulk Metallic Glass

We investigate the thermal stability and kinetics ofCu65Hf35 bulk metallic glass (BMG).Cu65Hf35 glassy rods in diameter up to 2 mm are preparedby a conventional copper mould suction casting. Kinetics of glasstransition and crystallizations are investigated and the ideal glasstransition temperature of the alloy is obtained. It is found that thedependence of crystallization temperature of the BMG on the heatingrates follows the Vogel–Fulcher–Tammann (VFT) non-linear relationshiprather than the Kissinger and Lasocka linear fittings. The long-termthermal stability of the BMG is investigated by means of continuouscrystallization diagrams obtained from the extension of VFT analysis.It is suggested that ideal glass transition and crystallizationtemperatures can also be regarded as the long-term stability criteriaof the BMG.

KINETICS AND THERMAL STABILITY OF Nd55Al20Fe25 BULK METALLIC GLASS

In this work, we studied the thermal stability and kinetics of Nd 55 Al 20 Fe 25 bulk metallic glass (BMG) with distinct glass transition and multistage crystallizations. The kinetics of glass transition and crystallizations were investigated using the Kissinger method and the ideal glass transition temperature of the alloy was obtained via Lasoka's equation. The thermal stability of the BMG was investigated by means of continuous transformation diagrams obtained from the extension of Kissinger analysis. It is suggested that the stability limit of the supercooled liquid, i.e. Kauzmann temperature, could also be regarded as the long-term stability criteria of the BMG.