On the use of Diefallah's composite integral method for the non-isothermal kinetic analysis of heterogeneous solid-gas reactions

The paper contains an analysis of the used of Diefallah's composite integral method of kinetic parameters evaluation. It is shown that the application of this method should be preceded by the application of an isoconversional method through which the dependence of the activation energy, E, on the conversion degree,<span style='font-size:10.0pt; font-family:"SymbolProp BT";mso-bidi-font-family:"SymbolProp BT"'>a, should be established. If Edepends on<span style='font-size:10.0pt;font-family:Symbol;mso-bidi-font-family:Symbol'>a, Diefallah's composite integral method leads to erroneous results. If Edoes not depend on<span style='font-size: 10.0pt;font-family:"SymbolProp BT";mso-bidi-font-family:"SymbolProp BT"'>a, the true kinetic model should be comprised in the pre-established set of kinetic models. These observations were checked for two sets of non-isothermal data, namely: (a) the TG curves corresponding to the dehydration of CaC₂O4·H₂O; (b) the TG curves corresponding to the thermal decomposition of polyvinyl chloride (PVC).     

Activation energy of Se2Ge0.2Sb0.8 chalcogenide glass by differential scanning calorimetry

Results of differential scanning calorimetry (DSC) at different heating rates on Se₂Ge_0.2Sb_0.8 chalcogenide glass are reported and discussed. As the heating rate () changed, also the glass transition temperature (T _g) and onset temperature of crystallization (T _c) changed. As the value of the transition activation energyE _t changed, the crystallization fraction (), heat flow (_q and the crystallization peak temperature (T _p) also changed. The value of the effective activation energy of crystallizationE _c was calculated by means of six different methods. The Se₂Ge_0.2Sb_0.8 chalcogenide glass has two crystallization mechanisms, a one-dimensional and an other surface crystallization growth. The average value ofE _t for Se₂Ge_0.2Sb_0.8 is equal to 194.95±3.9 kJ·mol^–1 and the average value ofE _c is equal to 164±3.3 kJ·mol^–1.     

Derivation of the Kissinger equation for non-isothermal glass transition peaks

A brief derivation of the Kissinger’s equation for analysis of experimental data of non-isothermal glass transition peaks based on the free volume model is given. This equation was applied successfully to Cu_0.3(SSe₂₀)_0.7 chalcogenide glass for different heating rates. For granted this model, the obtained glass transition activation energy, E _g must be constant throughout the whole glass transition temperature range. This required that T _g to be determined for three characteristic temperature points for each DSC curve.     

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.     

Glass transition temperature and thermal decomposition of cellulose powder

Cellulose powder and cellulose pellets obtained by pressing the microcrystalline powder were studied using differential scanning calorimetry (DSC), differential thermal analysis (DTA), and thermal gravimetry (TG). The TG method enabled the assessment of water content in the investigated samples. The glass phase transition in cellulose was studied using the DSC method, both in heating and cooling runs, in a wide temperature range from −100 to 180 °C. It is shown that the DSC cooling runs are more suitable for the glass phase transition visualisation than the heating runs. The discrepancy between glass phase transition temperature T _g found using DSC and predictions by Kaelbe’s approach are observed for “dry” (7 and 5.3% water content) cellulose. This could be explained by strong interactions between cellulose chains appearing when the water concentration decreases. The T _g measurements vs. moisture content may be used for cellulose crystallinity index determination.     

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.     

The effect of gamma irradiation on glass transition temperature and thermal stability of Se96Sn4 chalcogenide glass

Se₉₆Sn₄ chalcogenide glass was prepared by melt quenching technique and exposed, at room temperature, to different doses of 4, 8, 12, 24 and 33 kGy of high-energy ⁶⁰Co gamma irradiation. Differential scanning calorimeter (DSC) was used under non-isothermal condition to determine the glass transition temperature T_g, onset T_c and peak T_p temperatures of crystallization, of un-irradiated and γ-irradiated samples, at four different heating rates. The variation of T_g with heating rates was utilized to calculate the glass transition activation energy E_t for un-irradiated and γ-irradiated glass, using the methods suggested by Kissinger and Moynihan. Based on the obtained values of the characteristic temperatures T_g, T_c and T_p, thermal stability was monitored through the calculation of the S parameter and the crystallization rate factor 〈K_p〉 for irradiated and un-irradiated glass. Results reveal that, as γ-dose increases T_g increases up to 12 kGy then decreases at higher doses but remains more than that of un-irradiated glass. Meanwhile, both E_t and 〈K_p〉 attain their minimum values at the same dose of 12 kGy and the glass is thermally stable at this particular dose.     

Measuring the Glass Transition of Thermosets by Alternating Differential Scanning Calorimetry

The glass transition temperature of thermosets is determined by alternating differential scanning calorimetry (ADSC), which is a temperature modulated DSC technique. The different values of the glass transition obtained from heat flow measurements (total and reversible) and heat capacity (modulus of the complex heat capacity) are analysed and compared with the values obtained by conventional DSC. The effect of the sample mass on the values of T_g, heat capacity and phase angle has been analysed. The effect of the thermal contact between sample and pan has been studied using samples cured directly inside the pan and disc-shaped samples of different thickness. The results obtained for the thermal properties and the phase angle are compared and analysed. The modulus of the complex heat capacity enables the determination of the dynamic glass transition, T_g, which is frequency dependent. The apparent activation energy ofthe relaxation process associated with the glass transition has been evaluated from the dependence of T_g on the period of the modulation.This revised version was published online in November 2005 with corrections to the Cover Date.     

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.     

Crystallization kinetics of chalcogenide glass Se0.8 Te0.2

The crystallization kinetics of the chalcogenide glass Se_0.8Te_0.2 was studied by means of differential scanning calorimetry. The variation in partial area (X) with temperature (T) revealed that the transition from the amorphous to the crystalline phase occurs in two dimensions.Activation energies were determined for both the glass transition (E _t) and the crystallization (E _c).E _t was calculated from the variation inT _g with the heating rate (a).E _c was determined by three different methods: (i) variation inX withT, (ii) variation inT _p witha, and (iii) variation inT _c witha.E _t andE _c have values of 161.01±2.75 and 84.75 ±8.21 kJ/mol, respectively.

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Zusammenfassung Mittels DSC wurde die Kristallisierungskinetik des Chalkogenidglases Se_0.8Te_0.2 untersucht. Eine Änderung partieller Gebiete (X) mit der Temperatur (T) zeigte, daß der Übergang von der amorphen zur kristallinen Phase zweidimensional verläuft.Es wurde die Aktivierungsenergie sowohl für den Glasübergang (E _t) als auch für die Kristallisierung (E _c) bestimmt.E _t wurde mittels der Abhängigkeit vonT _g von der Aufheizgeschwindigkeit (a) ermittelt.E _c wurde auf drei verschiedene Wege bestimmt: (i) Änderung vonX in Abhängigkeit vonT, (ii) Änderung vonT _p in Abhängigkeit vona und (iii) Änderung vonT _c in Abhängigkeit vona. Die Werte vonE _t undE _c betragen 161.01±2.75 bzw. 84.75±8.21 kJ/mol.

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This work was partly supported by a Grant-in-Aid for Scientific Research from the GTZ GmbH and DAAD, W. Germany.     

The glass transition in athermal poly(α‐methyl styrene)/oligomer blends

The glass transition behavior in athermal blends of poly(α‐methyl styrene) (PaMS) and its hexamer is investigated using differential scanning calorimetry (DSC). The results, along with previous data on similar blends of PaMS/pentamer, are analyzed in the context of the Lodge–McLeish self‐concentration model. A methodology is described to partition the calorimetric transition to obtain effective T_gs for each component of the blend. The dependences of these effective T_gs on overall blend composition are described by the Lodge–McLeish model, although the self‐concentration effect is less than expected based on the Kuhn length. The length scales of the cooperatively rearranging regions for the two components in the blends are also calculated adapting Donth's fluctuation model to the partitioned DSC transitions and are found to be similar for the two components and show a slight decrease at intermediate concentrations. The kinetics associated with the glass temperature, T_g, is examined by studying the cooling rate dependence of T_g for the pure components and the blends, as well as by examining the enthalpy overshoots in the heating DSC scans. It is observed that the cooling rate dependence of T_g in PaMS/hexamer blends at intermediate concentrations is similar to that of the hexamer, indicating that the kinetics of the glass transition for blends is dominated by the high mobility oligomeric component. Moreover, compared to the pure materials, the PaMS/hexamer blends exhibit a considerably depressed enthalpy overshoot, presumably resulting from their broader relaxation time distribution. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 418–430, 2008     

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.     

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.     

Twinkling fractal theory of the glass transition

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T_g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ω^df–1 exp −|ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ω^df–1, where d_f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T² − T). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near T_g. The twinkling fractal spectrum F(ω) at T_g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t^−1/3 (short times), C(t) ∼ t^−4/3 (long times) and C(t) ∼ t⁻² (ω < ω_c), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T_g. Using the Morse potential, the TFT predicts that T_g = 2D_o/9k, where D_o is the interatomic bonding energy ∼ 2–5 kcal/mol and is comparable to the heat of fusion ΔH_f. Because anharmonicity controls both the thermal expansion coefficient α_L and T_g, the TFT uniquely predicts that α_L×T_g ≈ 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T_g, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p_c as α_g ≈ p_cα_L. The change in heat capacity ΔC_p = C_pL–C_pg at T_g was found to be related to the change in dimensionality from D_f to 3 in the Debye approximation as the ratio C_pL/C_pg = 3/D_f, where D_f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T_g, the role of crosslinks on T_g, the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a_T, which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T_m and T_g as T_m/T_g = 1/[1−p_c] ≈ 2. The TFT is universal to all glass forming liquids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765–2778, 2008     

Study of glass transition kinetics of selenium matrix alloyed with up to 10% indium

Glassy selenium matrix alloyed with up to 10% indium, namely Se_0.95In_0.05 and Se_0.9In_0.1, was prepared by the melt quenching technique. Differential thermal analysis (DTA) has been used to study the glass transition kinetics of the two binary Se–In alloys in comparison with that of pure Se. DTA scans were recorded at different constant heating rates (β = 1:20 °/min). The glass transition temperature (T _g) is found to be shifting to a higher value with increasing of both β and In-content. Such a configurationally response is related to the observed increase of the stability parameters accompanied with the introduction of In into the Se matrix. The activation energy of glass transition (E _g) has been determined using two different non-isothermal models (Moynihan and Kissinger) where a good coincidence is obtained. The compositional dependence (0:10% In) of all considered parameters is discussed in terms of the introduced structural matrix.     

Glass transition in partially sulfonated polystyrene

The glass transition temperature T_g of partially sulfonated polystyrene has been measured dilatometrically as a function of degree of sulfonation. A semitheoretical relationship between T_g and degree of sulfonation has been derived by treating the strong-acid polymer as a highly polar copolymer of styrene and styrenesulfonic acid. The T_g of copolymer has been found to increase linearly up to 0.15 weight fraction of styrene-sulfonic acid w_A as given by: where T_gB is the glass transition temperature of loosely crosslined (1%) polystyrene matrix. Our experimental results agree well with theoretical relations developed on the basis of the iso-free-volume state of glass transition applied to sulfonated polystyrene. The marked linear increase in copolymer T_g with the styrenesulfonic acid is accounted for by the effect of progressively higher intermolecular forces due to the highly polar sulfonic acid substituents.     

Crystallization study of Sn additive Se–Te chalcogenide alloys

Calorimetric study of Se_85−x Te₁₅Sn _x (x = 0, 2, 4 and 6) glassy alloys have been performed using Differential Scanning Calorimetry (DSC) under non-isothermal conditions at four different heating rates (5, 10, 15 and 20 °C/min). The glass transition temperature and peak crystallization temperature are found to increase with increasing heating rate. It is remarkable to note that a second glass transition region is associated with second crystallization peak for Sn additive Se–Te investigated samples. Three approaches have been employed to study the glass transition region. The kinetic analysis for the first crystallization peak has been taken by three different methods. The glass transition activation energy, the activation energy of crystallization, and Avrami exponent (n) are found to be composition dependent. The crystallization ability is found to increase with increasing Sn content. From the experimental data, the temperature difference (T _p − T _g) is found to be maximum for Se₈₃Te₁₅Sn₂ alloy, which indicates that this alloy is thermally more stable in the composition range under investigation.     

Infrared spectroscopic studies of polymer transitions. III. Effects of sodium ion on glass transitions in styrene-based ionomers

The glass transition in styrene-based ionomers was investigated by means of infrared spectroscopy and differential scanning calorimetry (DSC). Transition temperatures were determined from the temperature dependence of the peak absorbances of the 1700 and 1745 cm^?1 bands. These transition temperatures agreed with glass transition temperatures (T_g) determined by DSC. With increasing degree of ionization, T_g and the enthalpy ΔH of the residual intermolecular hydrogen bonding increased. The values of T_g obtained were analyzed by the theory of Fox and Loshaek for the effect of crosslinks. It is concluded that sodium ions probably from ionic domains and act as crosslinks to reinforce the residual hydrogen bonding and may increase T_g. The absorbance at 1560 cm^?1 (ν_COO^?) did not change at T_g. This suggests that the glass transition observed here is not due to the onset of the mobility in ionic domains, as has been proposed for ethylene-based ionomers on the basis of dielectric measurements.     

Thermal behavior of ferroelectric Polyamide 11 in relation to pyroelectric properties

The pyroelectric properties of oriented thin films of ferroelectric Polyamide 11 have been studied in the temperature range of −100°C up to +140°C. The temperature dependence of the experimental pyroelectric coefficient has been analyzed. Three changes of slope of the pyroelectric coefficient are observed at −20, +50, and +100°C. The origin of the lower temperature event has not yet been defined. The upper transition is attributed to chain movements in crystalline regions, and more precisely, to a crystalline phase transition. The intermediate event is close to the glass transition temperature T_g observed by DSC. It is attributed to the manifestation of the glass transition. Below T_g, the variations of the pyroelectric coefficient are very small. For higher temperatures, it increases rapidly, attesting to a major contribution of secondary pyroelectricity and dimensional effects above T_g. The breaking of hydrogen bonds occurring at the glass transition temperature observed on DSC thermograms does not affect pyroelectric properties. Pyroelectric properties are mildly reduced after annealing at temperatures up to +140°C. A comparative study of oriented ferroelectric films prepared by quenching from the melt and nonoriented slowly cooled samples has been carried out by means of DSC. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 715–723, 1999     

Curing kinetics and glass‐transition temperature of hexamethylene diisocyanate‐based polyurethane

The curing process of hexamethylene diisocyanate‐based polyurethane has been monitored by applying FTIR and DSC methods. A general relationship between glass‐transition temperature (T_g) and conversion of curing process has been obtained. This suggests that the reaction path and the relative reaction rates are independent of the curing temperature. The reaction kinetics of the system is analyzed using the T_g data converted to the conversion of the curing process. A set of experimental data and one theoretical model of T_g versus chemical conversion are presented to prove the assumption where a direct one‐to‐one relationship between the T_g (as measured) and the chemical conversion is obtained. Apparent activation energies (E_a) obtained by applying three different methods suggest good agreement. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2213–2220, 2000