Isobaric thermal behavior of glasses during uniform cooling and heating. III. Predictions from the multiparameter KAHR model

The behavior of the multiparameter KAHR model (put forward by Kovacs, Aklonis, Hutchinson, and Ramos) has been investigated using a single-box retardation spectrum to describe the kinetics of volume and enthalpy recovery of glasses in three-step thermal cycles involving colling, isothermal annealing, and subsequent reheating. It has been shown that during the heating stage, the system may display up to three peaks in the expansion coefficient and the specific heat. The shifts of the peak temperatures T_p with respect to each of the four experimental variables Y_i defining the thermal history are analyzed systematically in terms of a set of reduced variables, scaled by two of the material constants of the system. These shifts, from which the various partial derivatives (?T_p/?Y_i)_j≠i are estimated, are determined for five values of another material parameter x, which characterizes the relative contributions (O ≤ x ≤ 1) of temperature and structure to the retardation times. the results show that the upper peak is always small and is insensitive to the characteristics of the spectrum and to the value of x, while the relevant peak temperature depens only slightly on the cooling and heating rates. On the Other hand, the magnitude and the shifts of the main peak depend on all the experimental variables and the material constants in a rather complex manner. It is shown, however, that in limiting situations, involving fast heating of well-stabilized glasses, the shifts of the relevant peak temperature T?all reduce to a linear function of x^?1. since this relationship is rather insensitive to the shape of the spectrum, the experimental determination of any one of the nonzero partial derivatives of T? provides a simple means for an independent estimate of the value of the important material constant x. Finally, the shifts of the upper and main peaks relative to each other will be analyzed in terms of the pertinent experimental variables and compared with actual data reported in the literature for polymer glasses.     

Investigations on the Thermal and Elastic Properties of ZnO-Incorporated Phosphate Glasses and Glass Ceramics

Abstract

Glasses of the 45P₂O₅-(40-x)CaO-15Na₂O-xZnO system with increasing zinc oxide (ZnO) concentrations within the ranges of 3 ≤ x ≤ 12 mol% were obtained by employing the melt-quench technique. ZnO inclusions in the phosphate glass network lead to increases in its density and, conversely, a decrease in its molar volume. On the basis of the obtained thermal analysis data, the glasses underwent thermal treatment, which helped to derive their glass ceramic equivalents. The evaluations of structural and elastic properties of glasses before and after thermal treatments were made using X-ray diffraction (XRD) studies and ultrasonic nondestructive testing. The differential thermal analysis data show the reduction in the crystallization tendency and increase in thermal properties, such as crystallization temperature (T _P), thermal stability

(T _c – T _g) (where T_c is crystallization onset temperature and T _g is glass transition temperature), thermal stability parameter (S), and degree of glassification (D _g) of phosphate glasses against the progressive additions of ZnO. The XRD of glass ceramics confirmed the dominance of metaphosphate, pyrophosphate, and ZnO-related crystalline features. The measured elastic moduli, such as longitudinal (L), shear (G), Young's (Y), and bulk (K), and Vicker's microhardness values increased in both glass and glass ceramics with an increase in ZnO incorporation.     

Effect of MoO<Subscript>3</Subscript> additions on the thermal stability and crystallization kinetics of PbO–Sb<Subscript>2</Subscript>O<Subscript>3</Subscript>–As<Subscript>2</Subscript>O<Subscript>3</Subscript> glasses

The present paper reports on the effect of MoO₃ on the glass transition, thermal stability and crystallization kinetics for (40PbO–20Sb₂O₃–40As₂O₃)_100−x –(MoO₃) _x (x = 0, 0.25, 0.5, 0.75 and 1 mol%) glasses. Differential scanning calorimetry (DSC) results under non-isothermal conditions for the studied glasses were reported and discussed. The values of the glass transition temperature (T _g) and the peak temperature of crystallization (T _p) are found to be dependent on heating rate and MoO₃ content. From the compositional dependence and the heating rate dependence of T _g and T _p, the values of the activation energy for glass transition (E _g) and the activation energy for crystallization (E _c) were evaluated and discussed. Thermal stability for (40PbO–20Sb₂O₃–40As₂O₃)_100−x –(MoO₃) _x glasses has been evaluated using various thermal stability criteria such as ΔT, H _r , H _g and S. Moreover, in the present work, the K _r(T) criterion has been considered for the evaluation of glass stability from DSC data. The stability criteria increases with increasing MoO₃ content up to x = 0.5 mol%, and decreases beyond this limit.     

Thermal coefficient of linear expansion of non-crystalline chalcogenides in the As-S-Se-Te-I system

The object of the paper is an investigation of the glasses of the (As₂S₃)_x(AsSe_0.5Te_0.5I)_100-x. type for 65≤;x≤;95, using methods of thermomechanical analysis. Values of the thermal coefficients of linear expansion in solid and visco-plastic phase were determined. it was shown that introducing arsenic-sulfide in glass-matrix AsChI, i.e. (AsSe_0.5Te_0.5I), leads to an increasing stability of these glasses. The characteristic temperatures of softening Tg and the temperature of the beginning of deformation t_w increase by increasing content of As₂S₃. The analytical forms of dependence of four significant physical values α_g, α_l, Tg, Tw, as a function of As₂S₃ content in the structure of glasses were fitted. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetic Studies of Bulk Ge22Se78−xBix (x=0, 4 and 8) Semiconducting Glasses

Results of phase transformations, enthalpy released and specific heat of Ge₂₂Se_78–xBi_x(x=0, 4 and 8) chalcogenide glasses, using differential scanning calorimetry (DSC), under non-isothermal condition have been reported and discussed. The glass transition temperature, T _g, is found to increase with an average coordination number and heating rates. Following Gibbs—Dimarzio equation, the calculated values of T _g (i.e. 462.7, 469.7 and 484.4 K) and the experimental values (i.e. 463.1, 467.3 and 484.5 K) increase with Bi concentration. Both values of T _g, at a heating rate of 5 K min^–1, are found to be in good agreement. The glass transition activation energy increases i.e. 102±2, 109±3 and 115±8 kJ mol^–1 with Bi concentration. The demand for thermal stability has been ensured through the temperature difference T _c–T _g and the enthalpy released during the crystallization process. Below T _g, specific heat has been observed to be temperature independent but highly compositional dependent. The growth kinetic has been investigated using the Kissinger, Ozawa, Matusita and modified JMA equations. Results indicate that the crystallization ability is enhanced, the activation energy of crystallization increases with increasing the Bi content and the crystal growth of these glasses occur in 3 dimensions.This revised version was published online in November 2005 with corrections to the Cover Date.     

Application of the “Tg-Δ rule” to the local structural study of ferrate glasses

A linear relationship exists between the glass transition temperature (T _g) and the quadrupole splitting (Δ) of Fe(III). The linear relationship, termed ‘T _g-Δ rule’, has been verified in 60CaO·(40-x)Al₂O₃·xFe₂O₃, 60CaO·10BaO·(30-x) Al₂O₃·xFe₂O₃, 60CaO·(40-x)Ga₂O₃·xFe₂O₃, and 50CaO·(50-x)Ga₂O₃·xFe₂O₃ glasses. In these glasses, both theT _g and Δ decrease linearly with an increasing content of Fe₂O₃ (≈40 mol%). The slope of the straight line, obtained from the plot of theT _g vs. Δ, was calculated to be 670≈700, °C/(mm·s⁻¹), revealing that the Fe(III) constitutes the skeleton of aluminoferrate and galloferrate glasses.     

Studies of the amorphous region of polymers. II. Relationship between change of structure and glass-transition temperature in polycarbonate

A study of the effect of drawing on the glass transition temperature T_g of amorphous polycarbonate was carried out. The T_g attains a maximum at a draw ratio in the range from 1.6 to 2.0. The relationship between the change of structure and T_g is discussed in terms of the configurational entropy and the rate of molecular motion in local mode relaxation. The variation of T_g with drawing may be explained by using the iso-entropy theory. The frequency of the maximum in the dielectric loss f_max and the dielectric relaxation strength Δε of the β mechanism changed with drawing in the same way as that of T_g. Based on the parallel behavior in these results, it is reasonable to consider that the β process of local mode relaxation of polyesters such as PC and PET reflects the structure of the glassy state.     

Evidence of two relaxation processes in the photon correlation spectra of poly(methyl methacrylate) above Tg

Photon correlation functions of a high-molecular-weight PMMA (M_w = 1.06 × 10⁷, M_n = 2.2 × 10⁶, T_g = 103°C) have been studied in the temperature range 98 ? 149°C. In contrast to previous results, two relaxation modes are observed in relaxation functions. The observed relaxation functions of PMMA are analyzed for the first time in terms of a continuous spectrum representing the distribution of retardation times. Using a modified computer program originally developed by Provencher, we have computed the spectrum of retardation times at various temperatures. The appearance of two distinct relaxation modes is clearly evident in the distribution of the retardation times and in the time correlation functions below 123°C.     

Effect of composition on the width of the calorimetric glass transition in polymer–solvent and solvent–solvent mixtures

The calorimetric glass‐transition temperature (T_g) and transition width were measured over the full composition range for solvent–solvent mixtures of o‐terphenyl with tricresyl phosphate and with dibutyl phthalate and for polymer–solvent mixtures of polystyrene with three dialkyl phthalates. T_g shifted smoothly to higher temperatures with the addition of the component with the higher T_g for both sets of solvent–solvent mixtures. The superposition of the differential scanning calorimetry traces showed almost no composition dependence for the width of the transition region. In contrast, the composition dependence of T_g in polymer–solvent mixtures was different at high and low polymer concentrations, and two distinct T_g's were observed at intermediate compositions. These results were interpreted in terms of the local length scale and associated local composition variations affecting T_g. The possible implications of these results for the dynamics of miscible polymer blends were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1155–1163, 2004     

Determination of thermal parameters of glasses from the system Bix(As2S3)100?x based on DSC curves

Thermal properties of glasses from the system Bi _x (As₂S₃)_100−x were studied by differential scanning calorimetry of a representative series of samples with x = 0.5, 2, 4, 6, 8, and 10 at.% Bi by determining the characteristic temperatures (T _g, T _onset, T _c, T _m) and enthalpies (H _c, H _m) of the processes taking place in the samples during their thermal treatment. Analysis of DSC recordings for the samples at the same heating rate allowed characterization of the phase transition temperature T _g as a function of the content of doping atoms in accordance with the criteria of chemical bonds formation in amorphous materials. Samples with 4 and 6 at.% Bi were thermally treated at different heating rates with the aim of determining, among the others, the parameters of their thermal stability. The assessment was done based on three different criteria. A higher tendency toward crystallization was observed with the glasses having a higher Bi content. Also, a trend of T _g shifting toward higher values, observed with increase in the heating rate, is in concordance with the Lasocka equation.     

Radiation-induced polymerization of glass-forming systems. III. Effect of melting point and glass transition temperature on the formation of the glassy phase

The general empirical rules about glass formation of organic compounds including monomers were studied. It was found that the difference of T_m (melting point) and T_g (glass transition temperature) was the most important factor in glass formation, that is, the glass-forming property of organic systems, mono- or multicomponent, could be expressed as a function of T_m and T_m – T_g at the cooling temperature ?196°C. The glassforming property was further divided into four classes according to the relation between T_m and T_m – T_g, and each class was related to several patterns in DTA curves. From these results it was clarified that the phases are completely or partially glassified depending on the different values of T_m – T_g in eutectic and noneutectic compositions. The overall phase diagrams covering the whole composition with the variation of T_m and T_g were determined, and they also supported the relationship between T_m – T_g and the glass-forming property. The distinct glass-forming property of binary systems with large molecular interaction was attributed to the great lowering of T_m and elevation of T_g in those systems. The effect of the number of components on glass formation was also studied; it was shown that if T_m, T_g, and ΔH (sum of heat of melting and of mixing) are given, the number of components necessary to glassification can be estimated.     

Sodium and silver phosphate glasses doped with chlorides of Fe,Mn and Zn

A number of samples of sodium and silver phosphate glasses doped with various compositions of some transition metals viz. iron, manganese and zinc chlorides alongwith undoped samples of sodium and silver phosphate glasses were synthesized and characterized by X-ray diffraction, IR spectral, electrical conductivity and differential scanning calorimetry (DSC). The glass transition temperature (T _g) and crystallization temperature (T _c) values obtained from DSC curves were found to increase with increasing concentration of the dopant Fe/Mn/Zn chlorides in both sodium and silver phosphate glasses and the following sequence is observed: T _g(–FeCl₃)>T _g(–MnCl₂)>T _g(–ZnCl₂) T _c(–FeCl₃)>T _c(–MnCl₂)>T _c(–ZnCl₂) The increase in T _g and T _c values indicate enhanced chemical durability of the doped glasses. The electrical conductivity values and the results of FTIR spectral studies have been correlated with the structural changes in the glass matrix by the addition of different transition metal cations as dopants.     

Mobile ion transport pathways in (LiBr) x [(Li2O)0.6(P2O5)0.4](1−x) glasses

(LiBr) _x [(Li₂O)_0.6(P₂O₅)_0.4]_{(1 − x)} glasses with 0 ≤ x ≤ 0.2 are prepared by melt quenching. Glass transition temperature (T _g), ionic conductivity (σ), and its activation energy (E _a) are determined experimentally and correlated to molecular dynamics (MD) simulations with an optimized potential, fitted to match bond lengths, coordination numbers, and ionic conductivity. Based on equilibrated MD configurations, ion transport pathways are modelled in detail by the bond valence approach to clarify the influence of the halide dopant concentration on the glass structure and its consequence for Li ion mobility. Results of experimental and computational studies are compared with our previous report on the (LiCl) _x [(Li₂O)_0.6(P₂O₅)_0.4]_{(1 − x)} system. Both T _g and σ values are higher for LiBr-doped glasses than for LiCl-doped glasses, but the effect of halide doping is unusually small.     

General formulation of HDMR component functions with independent and correlated variables

The High Dimensional Model Representation (HDMR) technique decomposes an n-variate function f (x) into a finite hierarchical expansion of component functions in terms of the input variables x = (x ₁, x ₂, . . . , x _n ). The uniqueness of the HDMR component functions is crucial for performing global sensitivity analysis and other applications. When x ₁, x ₂, . . . , x _n are independent variables, the HDMR component functions are uniquely defined under a specific so called vanishing condition. A new formulation for the HDMR component functions is presented including cases when x contains correlated variables. Under a relaxed vanishing condition, a general formulation for the component functions is derived providing a unique HDMR decomposition of f (x) for independent and/or correlated variables. The component functions with independent variables are special limiting cases of the general formulation. A novel numerical method is developed to efficiently and accurately determine the component functions. Thus, a unified framework for the HDMR decomposition of an n-variate function f (x) with independent and/or correlated variables is established. A simple three variable model with a correlated normal distribution of the variables is used to illustrate this new treatment.     

Kinetics of crystallization of Zr52Cu18Ni14Al10Ti6 metallic glass

Metallic glasses have received considerable attention in comparison to normal metallic materials due to their superior physical and mechanical properties. These systems possess large under cooled region, ∆T (∆T = T _x − T _g where, T _x is crystallization temperature and T _g is glass transition temperature) and hence increased thermal stability against crystallization. Due to this, the study of their crystallization kinetics is important and interesting. It is interesting because of the fact that, crystallization becomes multi-step process due to several components present in these systems. In this paper, we report the experimental investigations of crystallization of Zr₅₂Cu₁₈Ni₁₄Al₁₀Ti₆ glassy alloy system, which is among the best non-beryllium containing glasses, using differential scanning calorimetry (DSC). The crystallization, as expected, consists of multiple steps. Interestingly, the peak heights of these steps vary with heating rate. At lower heating rates, first peak is most prominent and subsequently diminishes with increase in heating rate with last peak prominence visible at highest heating rate. Both, iso-kinetic and iso-conversional methods of analysis of kinetics of crystallization have been used to evaluate the activation energy and Avrami exponents and consistent results are obtained.     

Thermal stability and crystallization kinetics of Pb and Bi borate-based glasses

Glasses with compositions 60B₂O₃–40PbO, 60B₂O₃–40Bi₂O₃, and 60B₂O₃–30Bi₂O₃–10PbO have been prepared and studied by differential thermal analysis. The crystallization kinetics of the glasses was investigated under non-isothermal conditions. From dependence of the glass transition temperature (T _g) on the heating rate, the activation energy for the glass transition was derived. Similarly the activation energy of the crystallization process was determined. Thermal stability of these glasses were achieved in terms of the characteristic temperatures, such as the glass transition temperature, T _g, the onset temperature of crystallization, T _in , the temperature corresponding to the maximum crystallization rate, T _p, beside the kinetic parameters, K(T _g) and K(T _p). The results revealed that the 60B₂O₃–40PbO is more stable than the others. The crystallization mechanism is characterized for glasses. The phases at which the glass crystallizes after the thermal process have been identified by X-ray diffraction.     

Effect of crosslink density on the pressure relaxation response of polycyanurate networks

The effect of crosslink density on the pressure-volume-temperature (PVT) behavior and on the pressure relaxation response for two polycyanurate networks is investigated using a custom-built pressurizable dilatometer. Isobaric cooling measurements were made to obtain the pressure-dependent glass transition temperature (T_g). The pressure relaxation studies were carried out as a function of time after volume jumps at temperatures in the vicinity of the pressure-dependent T_g, and the pressure relaxation curves obtained were shifted to construct master curves by time-temperature superposition. The reduced pressure relaxation curves are found to be identical in shape and placement, independent of crosslink density, when T_g is used as the reference temperature. The horizontal shift factors used to create the master curves are plotted as a function of the temperature departure from T_g (T − T_g), and they agree well with their counterparts obtained from the shear response. Moreover, the retardation spectra are derived from bulk compliance and compared to those from the shear. The results, similar to our previous work on polystyrene, indicate that at short times, the bulk and shear responses have similar underlying molecular mechanisms; however, the long-time mechanisms available to the shear response, which increase with decreasing crosslink density, are unavailable to the bulk response. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2477–2486, 2009     

Dielectric relaxations in the liquid and glassy states of 47% polypropylene oxide in toluene as diluent

Molecular relaxations in 47-wt % polypropylene oxide of molecular weight 4000 in toluene as diluent have been studied by dielectric permittivity and loss measurements from 77 to 320 K, in the frequency range 1 Hz to 2 × 10⁵ Hz. One relaxation process (β process) is observed in the glassy state below T_g (= 148 K), and two processes are observed in the supercooled liquid at T > T_g. Relative to the amplitude of the fast relaxation process (i.e., the local segmental motions of the polymer chain), the amplitude of the slow process is increased and that of the β process decreased on dilution of the pure polymer. The β process has an Arrhenius energy of 17 kJ mol^?1. The rates of the two relaxations at T > T_g follow the Vogel–Fulcher–Tamman equation and seem to merge on cooling the liquid towards T_g. The relative temperatures at which the three relaxation processes occur at the rate of 1 kHz remain largely unaffected on dilution. The increase in static permittivity of the solution on cooling is more than anticipated from the temperature effects alone. It is suggested that the increase is due to the enhanced short-range orientational correlation of the dipoles, which may involve H bonding.     

Simultaneous kinetic and microdielectric studies of some epoxy–amine systems

Three reactive epoxy–amine systems based on diglycidyl ether of bisphenol A (DGEBA) with 4,4′-diaminodiphenylsulfone (DDS), 4,4′-methylenebis [3-chloro 2,6-diethylaniline] (MCDEA), and 4,4′-methylenebis [2,6-diethylaniline] (MDEA), were studied during isothermal curings at 140 and 160°C. The simultaneous kinetic and dielectric studies allow to express conductivity, σ, in terms of conversion, x, and of glass transition temperature, T_g. The conductivity, σ₀, of the initial monomer mixture and, σ_∞ of the fully cured network are measured. It is found that:

• The glass transition temperature, T_g, versus conversion, x, curves follows the equation of Di Benedetto modified by Pascault and Williams
• There exists a linear relation between log σ/log σ₀ and T_g.

So, it is possible to predict both kinetic and dielectric behaviors of these epoxy-amine systems by the knowledge of T_g0, ΔC_p0, and σ₀, respectively, glass transition temperature, heat capacity, and conductivity of initial monomer mixture, T_g∞ and ΔC_p∞, and σ_∞, respectively, glass transition temperature and heat capacity and conductivity of fully cured network. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2911–2921, 1998     

Thermodynamic study of glasses in Ag-As-Se system using EMF method with Ag<Subscript>4</Subscript>RbI<Subscript>5</Subscript> solid electrolyte

The EMF method with Ag₄RbI₅ solid electrolyte was used to study silver solubility in Ag-As-Se glasses on the basis of the cross-sections of (I) Ag-As_0.25Se_0.75, (II) Ag-As_0.33Se_0.67, (III) Ag-As_0.4Se_0.6, and (IV) Ag-As_0.5Se_0.5. It is found that silver solubility reaches 30 and 40 at % in sections (I), (IV) and (II), (III), accordingly. The data of EMF measurements were used as a basis for calculation of partial polar functions of Ag in glasses. The Gibbs-Duhem equations were integrated to calculate thermodynamic functions of silver dissolution in vitreous As _x Se_{1 − x} (x = 0.25; 0.33; 0.4; 0.5), from which the corresponding data for the latter were used to obtain the standard integral thermodynamic functions of the mixing of glasses. The obtained results were compared with the thermodynamic data for crystalline silver selenoarsenites.