How to determine activation energy of glass transition

The article critically reviews the current methodologies for determination of apparent activation energy of structural relaxation, ?h*, in the glass transition range. Tool–Narayanaswamy–Moynihan phenomenological model was used to simulate data for all major types of relaxation behavior, which were consequently evaluated in terms of the tested methodologies (curve-fitting, evaluation of ?h* from intrinsic cycles and evaluation of ?h* from constant heating rate cycles). Advantages and disadvantages of particular methodologies are demonstrated and thoroughly discussed. In addition, effects of various data-distortive effects influencing determination of glass transition activation energy are demonstrated and described. The discussed data-distortive effects include presence thermal gradients, improperly designed temperature programs, incorrectly applied subtractions of the thermokinetic background, or inability of the DSC instrument to perform high cooling/heating rates. Detailed guide for correct determination of ?h* from DSC measurements is introduced.     

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.     

A model-free method for evaluating theoretical error of Kissinger equation

Kissinger equation is widely used to calculate the activation energy. However, since a number of assumptions and approximations are introduced in the derivation, the activation energy resolved by this method will have some errors. Here, we propose a model-free evaluation method to estimate the relative error of activation energy of Kissinger equation. Our work shows that the error in activation energy solved by Kissinger equation is not only related to the magnitude of x = E/RT, but also depended on the change of β and ?x = x ₁ ? x ₂. From the experimental and theoretical analysis on the degradation of polyamide-6, it can be found that the actual error and the theoretical error in the activation energy solved by Kissinger equation are almost same.     

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.     

Thermal analysis and gelation property of multifunctional epoxy resins used for pultruded composite ropes

Non-isothermal curing reactions of three different multifunctional epoxy resin systems were investigated by differential scanning calorimetry. The Kissinger equation was applied to calculate the apparent activation energy, and the Levenberg–Marquardt algorithm was used to fit the curing kinetic data. It was observed that the two-parameter model was in good match with the curing kinetics. In addition, dynamic mechanical thermal analysis was used to obtain the glass transition temperature (T _g). Furthermore, the thermal stabilities of the systems were studied by thermogravimetric (TG) analysis, the integral procedure decomposition temperature and temperature index T _s were used to characterize the thermal stability. Finally, the gelation time was measured by plate–knife method of a home-made device, and the relationship between gelation time and temperature was established, according to which the pultrusion process parameters were predicted.     

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.     

Effect of lithium-sodium mixed-alkali on phase transformation kinetics in Er/Yb co-doped aluminophosphate glasses

Er³⁺ doped aluminophosphate glasses with various Na₂O/Li₂O ratios were prepared at 1250 °C using a silica crucible to study mixed alkali effect (MAE). The effect of relative alkali content on glass transition temperature, crystallization temperature and thermal stability were investigated using differential scanning calorimetry (DSC). In addition, apparent activation energies for crystallization, E_c, were determined employing the Kissinger equation. The effect of Al₂O₃ content on the magnitude of MAE was also discussed. No mixed-alkali effect is observed on crystallization temperature.     

Non-isothermal crystallization kinetics of a Si–Ca–P–Mg bioactive glass

In this work, the crystallization process of a SiO₂–3CaO·P₂O₅–MgO glass was studied by non-isothermal measurements using differential thermal analysis carried out at various heating rates. X-ray diffraction at room and high temperature was used to identify and follow the evolution of crystalline phases with temperature. The activation energy associated with glass transition, (E _g), the activation energy for the crystallization of the primary crystalline phase (E _c), and the Avrami exponent (n) were determined under non-isothermal conditions using different equations, namely from Kissinger, Matusita & Sakka, and Osawa. A complex crystallization process was observed with associated activation energies reflecting the change of behavior during in situ crystal precipitation. It was found that the crystallization process was affected by the fraction of crystallization, (x), giving rise to decreasing activation energy values, E _c(x), with the increase of x. Values ranging from about 580 kJ mol^?1 for the lower crystallized volume fraction to about 480 kJ mol^?1 for volume fractions higher than 80 % were found. The Avrami exponents, calculated for the crystallization process at a constant heating rate of 10 °C min^?1, increased with the crystallized fraction, from 1.6 to 2, indicating that the number of nucleant sites is temperature dependent and that crystals grow as near needle-like structures.     

Iso-conversional kinetic study of non-isothermal crystallization in glassy Se98Ag2 alloy

The crystallization kinetics of glassy Se₉₈Ag₂ alloy is studied at different heating rates (5, 10, 15, and 20?K?min^?1) using differential scanning calorimetric technique. Endothermic and exothermic peaks are obtained at glass transition (T _g) and crystallization temperature (T _c). Four iso-conversional methods (Kissinger?CAkahira?CSunose (KAS), Flynn?CWall?COzawa (FWO), Tang and Straink) were used to determine the various kinetic parameters (crystallization temperature T _?? , activation energy of crystallization E _??, order parameter n) in non-isothermal mode.     

Kinetik der Diazotierung der Chloraniline in methanolischer Chlorwasserstofflösung

The kinetics of the diazotization of o-, m-, p-chloroaniline in 0.005n- to 0.4n-methanolic HCl-solution at 25, 15, 0, ?10 ?20, and ?30°C was invertigated. It was found that the nitrosation reaction (the same as in¹) $$C_6 H_4 ClNH_2 + NOCl \mathop \rightleftharpoons \limits^k C_6 H_4 ClNH_2 NO^ + + Cl^ - $$ is a proceeding advance-back-reaction. The decomposition of C₆H₄ClNH₂NO⁺ by splitting off a proton is the rate determining step. The free activation enthalpies ΔG ^* for the nitrosation reaction, the activation entropies ΔS ^*, the activation enthalpies ΔH ^* and the activation energiesE _a at the given temperatures are calculated. The experimentally found and the calculated velocities are given in Tables 1–6. The equilibrium constants of the o-, m-, p-chloroanilinium ions, and nitrosyl-chloride in methanol are indicated in Table 7, diagram 1. TheK _M values (the ionic products of methanol, extrapolated at infinite dilution) together with theK _A values of Table 7 give theK _B values (p. 2) using the table¹⁰. The ΔG _B values can be calculated using equation ΔG _B = ?RTlnK _B Fig 2 shows the linear dependance of the logarithmus of the ΔG ^* values from the logarithmus of theK _B values.     

Pressure dependence of dielectric properties of chlorinated polyethylene vulcanizate. III. β relaxation

The effects of temperature and pressure on the shift factor and the dielectric increment of the β relaxation process were measured for vulcanized chlorinated polyethylene. The isobaric and isochoric activation enthalpies, H^*_P and H^*_V, the activation volume V^*, the pressure dependence of the glass–glass transition temperature, T_gβ/dP, and the apparent extinction temperature T_0β were obtained. The pressure dependences of both V^* and the dielectric increment would reach very small values near the liquid–glass transition temperature T_g, and the β process seems to be affected by the transition near T_g. The value of H^*v/H^*p for the β process is larger than that for the α process, and it is suggested that the molecular motions pertaining to the β process are more strongly restricted than those pertaining to the α process. The ratio T_0β/T₀, where T₀ is the characteristic temperature in the Vogel–Fulcher–Tammann–Hesse equation for the α process, follows the empirical relation of Matsuoka and Ishida, T_gβ/T_g ～0.75. The value of dT_gβ/dP estimated from T_g and T_0β/T₀ is consistent with the experimental value.     

Characterization of alkyd based thermosetting resins

The rate of cure of different oxidative drying oil modified alkyd resins are investigated by DSC, when the cure is made under UV light or not. We determine, from the Kissinger equation, the apparent activation energy at different stages of the curing process. This activation energy depends on the curing conditions (temperature, illumination or not). These variations lead to the determination of a time constant, characteristic of the curing kinetics. Two particular values of the apparent activation energy are also defined. The first one called ΔE _o is a characteristic of the varnish at the liquid state, the second one called ΔE _inf characterizes the stability of the structural state of the final film.     

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 ).     

Study of catalase immobilized on a silicate matrix for non-aqueous biocatalysis

Catalytic activity of catalase (CAT) immobilized on a modified silicate matrix to mediate decomposition of meta-chloroperoxibenzoic acid (3-CPBA) in acetonitrile has been investigated by means of quantitative UV-spectrophotometry. Under the selected experimental conditions, the kinetic parameters: the apparent Michaelis constat (K _M ), the apparent maximum rate of enzymatic reaction (V _max ^app ), the first order specific rate constants (k _sp ), the energy of activation (E _a ) and the pre-exponential factor of the Arrhenius equation (Z₀) were calculated. Conclusions regarding the rate-limiting step of the overall catalytic process were drawn from the calculated values of the Gibbs energy of activation ΔG^*, the enthalpy of activation ΔH^*, and the entropy of activation ΔS^*.     

Kinetic analysis for non-isothermal decomposition of un-irradiated and gamma-irradiated potassium bromate

The thermal decomposition of un-irradiated and gamma-irradiated potassium bromate (KBrO₃) was performed under non-isothermal conditions at different heating rates (5, 10, 15 and 20 K min^?1). The data was analysed using isoconversional and non-isoconversional methods. The kinetic parameters of thermal decomposition process were obtained by three model-free isoconversional methods: Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and Friedman. Irradiation enhances the decomposition and the effect increases with the irradiation dose. The activation energy decreases on irradiation. Kinetic analysis of data in view of various solid-state reaction models showed that the decomposition of un-irradiated and irradiated anhydrous KBrO₃ is best described by the Avrami–Erofeev model equation, [?ln(l?α)]^1/2 = kt.     

DSC-TG studies on kinetics of curing and thermal decomposition of epoxy–ether amine systems

The cure behavior of diglycidyl ether of bisphenol A with a simple ether amine (4,7,10, trioxa -1,13, tridecane diamine), system I and a polyether amine (polypropylene glycol block polyethylene glycol block polypropylene glycol bis 2 amino propyl ether), system II was compared by Differential Scanning Calorimetry. The exothermicity of the curing reaction of system I is higher than that of system II (316 ± 15 J g^?1 for System I and 230 ± 15 J g^?1 for system II). Kinetic parameters viz., activation energy, pre-exponential factor, and rate constant for curing were evaluated by Kissinger method and Kissinger–Akahira–Sunose isoconversion method. Both systems showed low glass transition temperatures and System II shows a much lower T _g (?38 °C) than system I (26 °C). The thermogravimetric analysis of the two cured epoxy amine systems showed comparable thermal stability.     

Studies on an ionic compound (3-ATz)+ (NTO)–: crystal structure, specific heat capacity, thermal behaviors and thermal safety

A new ionic compound (3-ATz)⁺ (NTO)^?C was synthesized by the reaction of 3-amino-1,2,4-triazole (3-ATz) with 3-nitro-1,2,4-triazol-5-one (NTO) in ethanol. The single crystals suitable for X-ray diffraction measurement were obtained by crystallization at room temperature. The crystal is monoclinic, space group p _2(1)/c with crystal parameters of a?=?0.6519(2)?nm, b?=?1.9075(7)?nm, c?=?0.6766(2)?nm, ???=?94.236(4)°, R ₁?=?0.0305 and wR ₂?=?0.0789. The thermal behaviors were studied, and the apparent activation energy and pre-exponential constant of the exothermic decomposition stage were obtained by Kissinger??s method and Ozawa??s method. The self-accelerating decomposition temperature is 505.40?K, and the critical temperature of the thermal explosion is obtained as 524.90?K. The specific heat capacity was determined with Micro-DSC method and the theoretical calculation method, and the standard molar specific heat capacity is 221.31?J?mol^?1?K^?1 at 298.15?K. The Gibbs free energy of activation, enthalpy of activation, and entropy of activation are 151.55?kJ?mol^?1, 214.52?kJ?mol^?1 and 122.44?J?mol^?1?K^?1. The adiabatic time-to-explosion of the compound was estimated to be a certain value between 5.0 and 5.2?s, and the detonation velocity (D) and pressure (P) were also estimated using the nitrogen equivalent equation according to the experimental density.     

Crystallization Kinetics of Lithium Diborate Glass by DTA

The crystallization process of Li₂B₄O₇ in the glass of stoichiometric composition, characterized by the crystal growth of pre-existing nuclei, was analyzed kinetically by means of DTA. Because the number of pre-existing nuclei for the subsequent growth varies depending on the cooling rate of the glass-forming melt and heating rate of the as-prepared glass, a modified Kissinger plot was applied for evaluating the apparent activation energy to the crystal growth in the glass samples with three different thermal histories, i.e., the pre-annealed, slowly quenched and quickly quenched glasses. The process was characterized by the three dimensional growth of pre-existing nuclei with the apparent activation energy of ca 340 kJ mol⁻¹. This revised version was published online in August 2006 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.     

Free volumes in simple and polymeric liquids

Values of ε₀ν₀ the vaporization energy and volume in the hypothetical liquid state at 0°K., are derived for some simple polar and nonpolar molecules used as models for vinyl polymers. The following empirical relationship between the free volume fraction, f = (v ? v₀)/v, and the liquid compressibility coefficient β is demonstrated: ?f² ∝? This is applied to several vinyl polymer liquids near their glass transition temperatures, T_g, giving. f_g ? 0.17, if the “hard-core” volume v^* is considered to be independent of pressure and temperature, (i.e., v^* = v₀); or, f_g ?0.12, if the P,T dependence of v^* is considered to be the same as that of the glass. These agree with f_g values derived by Simha and Boyer from thermal expansion coefficients for the two analogous cases. An empirical viscosity-free volume equation of the Doolittle form: η = ATⁿe^b/f is applied to the glass transition, on assuming that this is an isoviscosity state and with the use of reported values for the expansion and compressibility coefficients and dT_g/dP for three polymers: polystyrene, poly(methyl methacrylate), and poly(vinyl acetate). Reasonable values of b/n are thus obtained. This viscosity equation is critically examined in the light of molecular theories of liquid viscosity.