Kissinger equation versus glass transition phenomenology

The applicability of the Kissinger equation for the evaluation of apparent activation energy corresponding to glass transition kinetics is examined. Theoretically simulated data based on the generally accepted Tool–Narayanaswamy–Moynihan model were used to represent relevant cases of structural relaxation behavior. The values of the apparent activation energy determined by the Kissinger equation were, despite the linearity of the dependencies, in major disagreement with the original values of ?h ^* used for the simulation of the source data. Furthermore, a large dependence of the ?h _Kis ^* evaluation (performed using the Kissinger equation) on the thermal history of the glass was found. The latter represents an unacceptable systematic error in the methodology, implying the incorrectness of the Kissinger equation usage for the evaluation of “glass transition activation energy”. This study addresses the currently widespread (incorrect) usage of the Kissinger equation for the above-mentioned purpose.     

Simple relaxation model of the reversible part of the StepScan® DSC record of glass transition

The results of the StepScan® DSC obtained for 15Na₂O?xMgO?(10–x)CaO?75SiO₂ glasses were described in the frame of the commonly accepted theory of the glass transition. A new simplified model of the reversible part of StepScan® DSC record was developed on the basis of the Tool Narayanaswamy Moynihan relaxation theory. Equivalence between the formal activation energy of enthalpy relaxation process on one side, and the viscous flow activation enthalpy on the other side, was found.     

Thermal stability and crystallization kinetics of Se–Te–Sn alloys using differential scanning calorimetry

The present article deals with the differential scanning calorimetric (DSC) study of Se?CTe glasses containing Sn. DSC runs are taken at four different heating rates (10, 15, 20 and 25?K?min^?1). The crystallization data are examined in terms of modified Kissinger, Matusita equations, Mahadevan method and Augis and Bennett approximation for the non-isothermal crystallization. The activation energy for crystallization (E _c) is evaluated from the data obtained at different heating rates. Activation energy of glass transition is calculated by Kissinger??s relation and Moynihan theory. The glass forming tendency is also calculated for each composition. The glass transition temperature and peak crystallization temperature increases with the increase in Sn % as well as with the heating rate.     

Enthalpy relaxation of an epoxy–anhydride resin by temperature‐modulated differential scanning calorimetry

The enthalpy relaxation of an epoxy–anhydride resin was studied by physical aging and frequency‐dependence experiments with alternating differential scanning calorimetry (ADSC), which is a temperature‐modulated differential scanning calorimetry technique. The samples were aged at 80 °C, about 26 K below the glass‐transition temperature, for periods up to 3800 h and then scanned under the following modulation conditions: underlying heating rate of 1 K min⁻¹, amplitude of 0.5 K, and period of 1 min. The enthalpy loss was calculated by the total heat‐flow signal, and its variation with the log (aging time) gives a relaxation rate (per decade), this value being in good agreement with that calculated by conventional DSC. The enthalpy loss was also analyzed in terms of the nonreversing heat flow, revealing that this property is not suitable for calculating enthalpy loss. The effect of aging on the modulus of the complex heat capacity, |Cp*|, is shown by a sharper variation on the low side of the glass transition and an increase in the inflexional slope of |Cp*|. Likewise, the phase angle also becomes sharper in the low‐temperature side of the relaxation. The area under the corrected out‐phase heat capacity remains fairly constant with aging. The dependence of the dynamic glass transition, measured at the midpoint of the variation of |Cp*|, on ln(frequency) allows one to determine an apparent activation energy, Δh*, which gives information about the temperature dependence of the relaxation times in equilibrium over a range close to the glass transition. The values of Δh*, determined from ADSC experiments in a range of frequencies between 4.2 and 33 mHz and at an amplitude of 0.5 K, and an underlying heating rate of 1 K min⁻¹, were analyzed and compared with that obtained by conventional DSC from the dependence of the fictive temperature on the cooling rate. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2272–2284, 2000     

Effect of antimony on glass transition and thermal stability of Se<Subscript>78−x</Subscript>Te<Subscript>18</Subscript>Sn<Subscript>2</Subscript>Sb<Subscript>x</Subscript> (<Emphasis Type="Italic">x</Emphasis> = 0, 2, 4 and 6 at.%) multicomponent glassy alloys

Multicomponent glassy alloys Se_78?xTe₁₈Sn₂Sb_x (x?=?0, 2, 4 and 6) have been synthesized using melt quench technique. The prepared samples have been characterized by X-ray diffraction technique and differential scanning calorimetry (DSC). Glass transition kinetics of Se_78?xTe₁₈Sn₂Sb_x (x?=?0, 2, 4 and 6 at.%) glassy alloys has been examined using DSC. DSC runs have been recorded at different heating rates (5, 10, 15 and 20 K min^?1) for each sample under investigation. Heating rate dependence of glass transition temperature (T_g) has been studied using Lasocka empirical relation. The activation energy of glass transition has been evaluated using Kissinger and Moynihan’s relation. The effect of antimony concentration on glass transition temperature and activation energy has been investigated in the prepared samples. Glass-forming ability and thermal stability of Se_78?xTe₁₈Sn₂Sb_x (x?=?0, 2, 4 and 6) glassy alloys have been monitored through the evaluation of thermal stability using Dietzal relation, Hurby parameter, and Saad and Poulin parameter. The above-mentioned parameters are found to be compositionally dependent, which indicates that among the studied glass samples the stability is maximum for Sb at 2% content.     

Non-isothermal crystallisation kinetics study on Se90−xIn10Sbx (x = 0, 1, 2, 4, 5) chalcogenide glasses

The non-isothermal crystallisation kinetics of Se_90?xIn₁₀Sb_x (x = 0, 1, 2, 4, 5) chalcogenide glasses prepared by a conventional melt quenching technique was studied using the differential scanning calorimetry (DSC) measurement at different heating rates 5, 7, 10 and 12 °C min^?1. The values of the glass transition temperature T _g and the crystallisation temperature T _c are found to be composition and heating rate dependent. The activation energy of glass transition E _g, Avrami index n, dimensionality of growth m and activation energy of crystallisation E _c have been determined from different models.     

Slow molecular mobility in the amorphous thermoplastic polysulfone

The thermally stimulated depolarization current (TSDC) technique has been used to study the slow molecular mobility of polysulfone in the glassy state and in the glass transformation region, i.e., in the temperature ranging from ?155 to 183 °C. Since the polysulfone is a rigid polymer without polar side-groups, a broad and low-intensity secondary relaxation was detected in the temperature region from ?120 °C up to the glass transition; the activation energy of the motional modes of this secondary relaxation is in the range between 35 and 100 kJ mol^?1. The glass transition temperature of polysulfone provided by the TSDC technique is T _M = T _g = 176 °C (at 4 °C min^?1). The relaxation time at this temperature is τ(T _g) = 33 s and the fragility index was found to be m = 91. Our results are compared with literature values obtained by dynamic mechanical analysis and by dielectric relaxation spectroscopy. The amorphous polysulfone was also characterized by DSC; a glass transition signal with an onset at T _on = 185.5 ± 0.3 °C (heating rate 10 °C min^?1) was detected, with ΔC _p = 0.21 ± 0.01 J g^?1 °C^?1.     

The kinetics of phase transitions in vitreous chalcogenide semiconductors As10.2Se89.8 and As9Se90Bi in early stage of physical ageing process

The kinetics of glass transition in selenide glasses As_10.2Se_89.8 and As₉Se₉₀Bi in early stage of physical ageing process has been investigated by parallel differential scanning calorimetry (DSC) and exoelectron emission (EEE). It has been found that the glass transition process occurring in investigated glasses is evidenced by peaks on EEE intensity and DSC curves. Admixture of bismuth causes a distinct lowering of the temperature of glass transitions process both in the surface layer and in the volume. The addition of Bi causes a decrease in the value of the activation energy for glass transition process in both the volume and in the surface layer, thus reducing the thermal stability of investigated glasses. Physical ageing in Se-rich chalcogenide glasses leads to a significant increase of endothermic peak area A, temperature of glass transition T _g and decrease of the activation energy value E. All these effects are strongly dependent on glass composition.     

Thermal transformations of selected transition metals oxyhydroxides

We investigated the features of the glass transition relaxation of two room temperature ionic liquids using DSC. An important observation was that the heat capacity jump, that is the signature of the glass transition relaxation, shows a particularly strong value in this type of new and promising materials, candidates for a range of applications. This suggests a high degree of molecular mobility in the supercooled liquid state. The study of the influence of the heating rate on the temperature location of the glass transition signal, allowed the determination of the activation energy at the glass transition temperature, and the calculation of the fragility index of these two ionic glass-formers. It was concluded that this kind of materials belong to the class of relatively strong glass-forming systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study of the physical aging of an epoxy/cycloaliphatic amine resin modified with abs

Using differential scanning calorimetry (DSC) we have studied the physical aging of an epoxy resin based on the diglycidyl ether of bisphenol A (DGEBA) modified by two different contents of an acrylonitrile-butadiene-styrene (ABS) and cured with 1,3-bisaminomethylcyclohexane (1,3-BAC). Samples fully cured were annealed at temperature of 125°C for periods of time of 72 and 120 h, to determine the process of physical aging. The apparent activation energy for the enthalpy relaxation, Dh*, is determined as the sample is heated at 10°C min^-1 following cooling at various rates through the glass transition region. DSC studies suggested that the presence of thermoplastic inhibits the process of relaxation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Glass transition behavior and crystallization kinetics of Cu0.3(SSe20)0.7 chalcogenide glass

The glass transition behavior and crystallization kinetics of Cu_0.3(SSe₂₀)_0.7 chalcogenide glass were investigated using differential scanning calorimetry (DSC), X-ray diffraction (XRD). Two crystalline phases (SSe₂₀ and Cu₂Se) were identified after annealing the glass at 773 K for 24 h. The activation energy of the glass transition (E_g), the activation energy of crystallization (E_c), the Avrami exponent (n) and the dimensionality of growth (m) were determined. Results indicate that this glass crystallizes by a two-stage bulk crystallization process upon heating. The first transformation, in which SSe₂₀ precipitates from the amorphous matrix with a three-dimensional crystal growth. The second transformation, in which the residual amorphous phase transforms into Cu₂Se compound with a two-dimensional crystal growth.     

Studies of molecular dynamics of carboxylated acrylonitrile-butadiene rubber composites containing in situ synthesized silica particles

The molecular dynamics of carboxylated acrylonitrile-butadiene rubber - silica hybrid materials was investigated. Silica hybrids were formed in situ rubber matrix using varied amounts of N-(2-aminoethyl)-3-aminopropyltrimethoxysilane (DAMS), serving also as a cross-linker. Filler-filler and filler-rubber interactions were present, due to the specific nature of these materials. It was found that the amounts of added aminosilane determined the cross-linking density of obtained materials and was the highest with 20 phr DAMS used. The cross-links had ionic nature. Dielectric relaxation spectroscopy (DRS) revealed β, α and α′ relaxation processes. The β relaxation, correlated with the mobility of polymer side groups, was influenced by the weak interaction between both acrylonitrile and carboxylic groups of the rubber and silanol groups of silica. The activation energy for that relaxation was similar for all materials (∼32 kJ mol⁻¹). Both DRS and dynamical mechanical analysis (DMA) demonstrated that the amount of in situ formed silica filler did not significantly influence either the temperature of the α relaxation (correlated with glass transition) or its activation energy. Therefore, that relaxation was caused by free polymer chains, not attached to the silica particles. Similar values of glass transition temperature (T_g) for all hybrids were confirmed by DSC. It appeared that the amplitude of tangent delta (DMA) within T_g was dependent on silica amount. Detected at higher temperature α′ relaxation resulted from the presence of domains, where polymer chains were affected by silica network, geometrical restrictions and morphology of the silica-rich domains.     

Preparation of nano poly(phenylsilsesquioxane) spheres and the influence of nano-PPSQ on the thermal stability of poly(methyl methacrylate)

The nano poly(phenylsilsesquioxane) spheres (nano-PPSQ) were prepared by the sol?Cgel method and incorporated into poly(methyl methacrylate) (PMMA) by in situ bulk polymerization of methyl methacrylate. The structure of nano-PPSQ was confirmed by transmission electron microscope and thermogravimetry analysis (TG). The interaction between nano-PPSQ and PMMA was investigated by Fourier transform infrared spectra (FT-IR). The influence of nano-PPSQ on the thermal stability of PMMA was investigated by TG and differential scanning calorimetry (DSC) measurements. The results indicated that nano-PPSQ enhanced the thermal stability and the temperatures of glass transition (T _g) of nanocomposites. The effect of the heating rate in dynamic measurements (5?C30?°C?min^?1) on kinetic parameters such as activation energy by TG both in nitrogen and air was investigated. The Kissinger method was used to determine the apparent activation energy for the degradation of pure PMMA and nanocomposites. The kinetic results showed that the apparent activation energy for degradation of nanocomposites was higher than that of pure PMMA under air.     

Effect of Molecular Weight on Enthalpy Relaxation in Syndiotactic Poly(Methyl-Methacrylate)

The structural relaxation behaviour of narrow fractions (M_w/M_n < 1.1) of syndiotactic poly(methyl methacrylate) with molecular masses ranging from 2,000 to 200,000 Daltons have been studied by DSC with two classical procedures, namely: the rate of cooling and the isothermal approaches. The apparent activation energy (Δh*) of enthalpy relaxation was evaluated from the dependence of the glass transition temperature on the cooling rate while a comparison of the apparent relaxation rates was appraised from the enthalpy loss by annealing the different samples at the same level of undercooling (T_a = T_g − 10 °C). As expected, the increase of molecular weights gives rise to both a continuous increase of Δh* and a decrease of the apparent isothermal relaxation rate. More interestingly, both Δh* and the apparent isothermal relaxation rate showed abrupt changes around the syndiotactic PMMA entanglement mass (M_e ).     

Thermal stability and crystallization kinetics of ternary Se–Te–Sb semiconducting glassy alloys

This paper presents the results of kinematical studies of glass transition and crystallization in glassy Se_85?x Te₁₅Sb _x (x = 2, 4, 6 and 8) using differential scanning calorimetry (DSC). From the dependence on heating rates of, the glass transition temperatures (T _g), and temperature of crystallization (T _p) the activation energy for glass transition (E _g) and the activation energy for crystallization (E _c) are calculated and their composition dependence can be discussed in term of the average coordination number and cohesive energy. The thermal stability of Se_85?x Te₁₅Sb _x was evaluated in terms of criterion ΔT = T _c ? T _g and kinetic criteria K(T _g) and K(T _p). By analyzing the crystallization results, the crystallization mechanism is characterized. Two (two- and three-dimensional growth) mechanisms are working simultaneously during the amorphous–crystalline transformation of the Se₈₃Te₁₅Sb₃ alloy while only one (three-dimensional growth) mechanism is responsible for the crystallization process of the chalcogenides Se_85?x Te₁₅Sb _x (x = 4, 6 and 8) glass. The phases at which the alloy crystallizes after the thermal process have been identified by X-ray diffraction.     

Kinetics of phase transition and thermal stability in Se80?x Te20Zn x (x?=?2, 4, 6, 8, and 10) glasses

Se_80?x Te₂₀Zn _x (x?=?2, 4, 6, 8, and 10) glasses have been prepared using conventional melt quenching technique. The kinetics of phase transformations (glass transition and crystallization) have been studied using differential scanning calorimetry (DSC) under non-isothermal condition at five different heating rates in these glasses. The activation energy of glass transition (E _t), activation energy of crystallization (E _c), Avrami exponent (n), dimensionality of growth (m), and frequency factor (K _o) have been investigated for the better understanding of growth mechanism using different theoretical models. The activation energy is found to be highly dependent on Zn concentration. The rate of crystallization is found to be lowest for Se₇₀Te₂₀Zn₁₀ glassy alloy. The thermal stability of these glasses has been investigated using various stability parameters. The values of these parameters were obtained using characteristic temperatures, such as glass transition temperature T _g, onset crystallization temperature T _c, and peak crystallization temperature T _p. In addition to this, enthalpy-released during crystallization has also been determined. The values of stability parameters show that the thermal stability increases with the increase in Zn concentration in the investigated glassy samples.     

Determination of Activation Energy for Glass Transition of an Epoxy Adhesive Using Dynamic Mechanical Analysis

The activation energy associated with the glass transition relaxation of an epoxy system has been determined by using the three-point bending clamp provided in the recently introduced TA Instruments DMA 2980 dynamic mechanical analyzer. A mathematical expression showing the dependency of modulus measurements on the sample properties and test conditions has also been derived. The experimental results showed that the evaluation of activation energy is affected by the heating rate and test frequency, as well as the criterion by which the glass transition temperature (T _g) is established. It has been found that the activation energy based on the loss tangent (tanδ) peak is more reliable than on the loss modulus (E ₂) peak, as long as the dynamic test conditions do not cause excessive thermal lags. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of crosslink length on the enthalpy relaxation of fully cured epoxy–diamine resins

Enthalpy relaxation of epoxy–diamine thermosets of different crosslink lengths (CLL) has been studied by DSC. The epoxy resins based on diglycidyl ether of bisphenol A were cured with ethylenediamine (FEDA), and diamines of polyoxypropylene of 2.6 and 5.6 oxypropylene units, named FJ230 and FJ400, respectively. As was expected, increasing the CLL decreases the glass transition temperature T_g from 121°C (FEDA) to 47°C (FJ400). Aging experiments at T_g − 20 K for each resin permit the determination of the enthalpy loss, the relaxation rate per decade (β_H), and the nonlinearity parameter, x. The apparent activation energy, Δh*, and the nonexponentiality parameter β are found for each resin from intrinsic cycles in which the sample is heated at 10 K min⁻¹ following cooling at various rates through the glass transition region. An increase of CLL is related to an increase of β_H, and of the nonlinearity parameter. In agreement with the general trend for thermoplastic polymers, the increase of the parameter x is correlated with a decrease of Δh* and with an increase in the nonexponentiality parameter. Application of the Adam–Gibbs (AG) theory reveals that the parameters B and T_f/T₂ increase with CLL, corresponding to a decrease of the nonlinear behavior of the glassy epoxies. However, the T₂ values calculated in this way appear unrealistic, and the alternative assumption that T₂ = T_g −51.6 K, making use of the “universal” WLF constant, leads to a much smaller variation of B, which nevertheless still increases with CLL. From a consideration of the minimum number of configurations required for a cooperative rearrangement, it is argued that the elementary activation energy Δμ increases, and the minimum size of the cooperatively rearranging region decreases as CLL increases. This is consistent with the relaxation process becoming more cooperative as the CLL decreases, as is suggested by the decrease in the value of β. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 456–468, 2000     

Synthesis and thermal characterization of sulfur containing methionine bridged cobalt(III) and copper(II) complex

The sulfur containing amino acid bridging polynuclear transition metal complex has been synthesized and characterized by different measurements such as UV?CVis, FT?CIR, C?CH?CN?CS, TG?CDTA, ICP-AES, differential scanning calorimeter (DSC), and XRD. DSC has showed negative specific heat of this polynuclear system and has used to evaluate some thermodynamic constants like activation energy (E _a), frequency factor (A), enthalpy, and entropy of that system. The specific heat capacity is measured at heating rate of 10?°C?min^?1 in room atmosphere of this polynuclear complex. The characterization of this complex has showed five Co(III) and four Cu(II) atoms and this complex contained ten sulfur containing methionine amino acid units.