Multiple Heating Rate Method Research Articles

Synthesis, structure analysis and thermodynamics of [Ni(H2O)4(TO)2](NO3)2·2H2O (TO = 1,2,4-triazole-5-one)

Abstract A novel complex [Ni(H2O)4(TO)2](NO3)2·2H2O (TO = 1,2,4-triazole-5-one) was synthesized and structurally characterized by X-ray crystal diffraction analysis. The decomposition reaction kinetic of the complex was studied using TG-DTG. A multiple heating rate method was utilized to determine the apparent activation energy (E a) and pre-exponential constant (A) of the former two decomposition stages, and the values are 109.2 kJ mol−1, 1013.80 s−1; 108.0 kJ mol−1, 1023.23 s−1, respectively. The critical temperature of thermal explosion, the entropy of activation (ΔS ≠), enthalpy of activation (ΔH ≠) and the free energy of activation (ΔG ≠) of the initial two decomposition stages of the complex were also calculated. The standard enthalpy of formation of the new complex was determined as being −1464.55 ± 1.70 kJ mol−1 by a rotating-bomb calorimeter.

Thermal decomposition behavior and durability evaluation of thermotropic liquid crystalline polymers

The thermal decomposition behavior and degradation characteristics of four different thermotropic liquid crystalline polymers (TLCPs) were studied. The thermal decomposition behavior was determined by means of thermogravimetric analysis (TGA) at different heating rates in nitrogen and air. The order of the thermal stability was as follows: multi-aromatic polyester > hydroxybenzoic acid (HBA)/hydroxynaphthoic acid (HNA) copolyester > HNA/hydroxyl acetaniline (HAA)/terephthalic acid (TA) copolyester > HBA/Poly(ethylene terephthalate) (PET) copolyester. The activation energies of the thermal degradation were calculated by four multiple heating rate methods: Flynn-Wall, Friedman, Kissinger, and Kim-Park. The Flynn-Wall and Kim-Park methods were the most suitable methods to calculate the activation energy. Samples were exposed to an accelerated degradation test (ADT), under fixed conditions of heat (63±3 °C), humidity (30±4%) and Xenon arc radiation (1.10 W/m2), and the changes in surface morphology and color difference with time were determined. The TLCPs decomposed, discolored and cracked upon exposure to ultraviolet radiation.

Curing Kinetics and Thermal Stability of Diglycidyl Ether of Bisphenol‐A Using Mixtures of Heterocyclic Derivatives of Stannanes and 4,4′‐Diaminodiphenylsulfone

AbstractCuring kinetics of diglycidyl ether of bisphenol‐A (DGEBA) in the presence of varying molar ratios of derivatives of stannanes to 4,4′‐diaminodiphenylsulfone (DDS) was investigated by the dynamic differential scanning calorimetry. The derivatives were synthesized by reacting 1 mole of biguanide (B) with 1 mole of phenylethyltindihydride (PETH) or phenylmethyltindihydride (PMTH) or phenylbutyltindihydride (PBTH) and designated as BPETH or BPMTH or BPBTH respectively. These derivatives were characterized by elemental analysis and spectroscopic techniques such as IR, 1H NMR, 13C NMR and 119Sn NMR. The mixtures of these derivatives to DDS at ratios of 0:1, 0.25:0.75, 0.5:0.5, 0.75:0.25 and 1:0 were used to investigate the curing behaviour of DGEBA. The multiple heating rate method (5, 10, and 15 and 20 °C·min−1) was used to study the curing kinetics of epoxy resins. The thermal stability of the isothermally cured resins was also evaluated using dynamic thermogravimetry in a nitrogen atmosphere.

Triphenyl Phosphine Catalyzed Curing of Diallyl Bisphenol A‐Novolac Epoxy Resin System—A Kinetic Study

The kinetics of triphenyl phosphine (TPP) catalyzed phenol‐epoxy reaction in the blend of 2,2′‐diallyl bisphenol A (DABA) and an epoxy novolac (EPN) was investigated using differential scanning calorimetry (DSC). The kinetic parameters viz., activation energy (E) and the pre‐exponential factor (A) were calculated by the multiple heating rate methods of Ozawa and Kissinger. The effect of catalyst concentration on the kinetic parameters of the cure reaction was studied and E and A were found to depend on catalyst concentration. The apparent activation energy values normalised to a fixed A value decreased systematically and the corresponding rates of reaction showed an increasing trend with increase in catalyst concentration. The iso‐conversional kinetic analysis done for different catalyst concentrations and for different conversion levels implied that the overall kinetics does not vary much with conversion level. The activation parameters were used to predict the cure profile of the resin under given conditions of temperature and catalyst concentration.

Curing of epoxy resin using imide‐amines

AbstractThe curing behavior of diglycidyl ether of bisphenol‐A (DGEBA) was investigated by differential scanning calorimetry, using varying molar ratios of imide‐amines and 4,4′‐diaminodiphenyl sulfone (DDS). The imide‐amines were prepared by reacting 1 mol of pyromellitic dianhydride (P) with excess (2.5 mol) of 4,4′‐diaminodiphenyl ether (E), 4,4′‐diaminodiphenyl methane (M), or 4,4′‐diaminodiphenyl sulfone (S) and designated as PE, PM, PS. Structural characterization was done using FTIR, 1H NMR, 13C NMR spectroscopic techniques and elemental analysis. The mixture of imide‐amines and DDS at ratio of 0 : 1, 0.25 : 0.75, 0.5 : 0.5, 0.75 : 0.25, and 1 : 0 were used to investigate the curing behavior of DGEBA. The multiple heating rate method (5, 10, 15, and 20°C/min) was used to study the curing kinetics of epoxy resins. The peak exotherm temperature was found to be dependent on the heating rate, structure of imide‐amine, and also on the ratio of imide‐amine : DDS used. Activation energy was highest in case of epoxy cured using a mixture of DDS : imide‐amine of a ratio of 0.75 : 0.25. Thermal stability of the isothermally cured resins was also evaluated in a nitrogen atmosphere using dynamic thermogravimetry. The char yield was highest in case of resins cured using mixture of DDS : PS (0.25 : 0.75; EPS‐3), DDS : PM (0.25 : 0.75; EPM‐3), and DDS : PE (0.75 : 0.25; EPE‐1). © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 3502–3510, 2006

Kinetic analysis of a fast reacting thermoset system

Many thermosets are rapidly mixed and processed to quickly and efficiently effect a bond or produce a protective coating or a finished part. These processes are often characterized by non-linear time–temperature profiles. While it is often desirable to model the cure it can be challenging with such highly reactive systems in rapid processes. Described here is a hybrid approach to determine the kinetic equation for such a system. DSC multiple heating rate, isothermal and simulated process methods were combined with time–temperature superposition methodology to generate a master curve for the chemically controlled cure. Analysis of the master curve showed that it could be described by a second-order kinetic equation, consistent with polyurethane cure and permitting the complete kinetic description of the system.

Grafting of Vinyl Monomers onto Sodium Salt of Partially Carboxymethylated Guar Gum: Comparison of Their Reactivity

: The optimum reaction conditions for affording maximum percentage of grafting have been established in the case of grafting of acrylonitrile (AN), methyl acrylate (MA), methyl methacrylate (MMA), and ethyl methacrylate (EMA) onto sodium salt of partially carboxymethylated guar gum (Na-PCMGG, ) using ceric ammonium nitrate (CAN) as a redox initiator in an aqueous medium by using different reaction parameters. Under the optimized reaction conditions, the following reactivity order of monomers was observed: AN > MA > MMA > EMA. The plausible explanation for this observed order of reactivity has been furnished. The thermal behavior of different graft copolymers of Na-PCMGG () has been studied at four different heating rates by thermogravimetric analysis (TGA) and the results obtained have been analyzed by employing Osawa as well as Freeman-Carroll (multiple heating rate) methods for the evaluation of activation energy (E). The values of E calculated at various constant conversions as well as the average activation energy values (for both the steps of thermal degradation) calculated according to Osawa as well as Freeman-Carroll methods, for all the four different graft copolymers of Na-PCMGG (), have been found to be in good agreement with each other. The evidence of grafting has been ascertained by spectral (IR/1H-NMR) and scanning electron microscopic (SEM) methods.

Studies on the curing kinetics of epoxy resins using silicon containing amide-amines

Curing kinetics of diglycidyl ether of bisphenol-A (DGEBA) in the presence of novel silicon containing amide-amines were investigated by the dynamic differential scanning calorimetry. Silicon containing amide-amines were prepared by reacting 2.5 moles of 4,4'-diaminodiphenyl ether (E)/4,4'-diaminodiphenyl methane (M)/3,3'-diaminodiphenyl sulfone (mS)/bis(m-aminophenyl) methyl phosphine oxide (B) with one mole of bis(4-chlorobenzoyl) dimethyl silane. The multiple heating rate method (5, 10, 15 and 20°C min-1) was used to study the curing kinetics of epoxy resins in the presence of stoichiometric amounts of amide-amines having molecular masses in the range of 660 to 760 g mol-1. The peak exotherm temperature depends on the heating rate as well as on the structure of amide-amines. Activation energy of curing reaction as determined in accordance to the Ozawa's method was found to be dependent on the structure of amine. The thermal stability of the isothermally cured resins was also evaluated using dynamic thermogravimetry in a nitrogen atmosphere. The char yield was the highest in case of resins cured with amide-amines having both phosphorus and silicon atoms.

Kinetic Model of a Methacrylate-Based Monolith Polymerization

Monolithic stationary phases are becoming more and more important in the field of liquid chromatography, because they enable extremely fast separations. Methacrylate-based monoliths are produced via a free-radical bulk polymerization of glycidyl methacrylate and ethylene dimethacrylate using a benzoyl peroxide as an initiator. Preparation of large monoliths represents a big problem because of the heat release during the polymerization, which consequently leads to the distortion of the structure. A closer investigation of the polymerization, using differential scanning calorimetry, was performed in order to determine global kinetic parameters. A multiple heating rate method, based on the work of Ozawa, Flynn, and Wall, was applied for estimation of the values of the apparent activation energy, preexponential factor, and reaction order. Global polymerization kinetics is of first order with A = 1.681 × 10 9 s -1 and E a,app = 81.5 kJ/mol, where the heat of polymerization is approximately 190 J/g. In addition, the influence of air and nitrogen atmosphere on polymerization is presented.

Thermal characterization of diglycidyl ether of bisphenol‐A/phosphorus containing amines

AbstractIn order to improve the thermal resistance of diglycidyl ether of bisphenol‐A (DGEBA), phosphorus‐containing di‐ and tri‐amines, i.e., bis (3‐aminophenyl) methyl phosphine oxide (B) and tris (3‐aminophenyl) phosphine oxide (T), were used as curing agents. The effect of phosphorus content on the curing characteristics and char residue of cured resins in nitrogen atmosphere was evaluated by using different molar ratios of conventional curing agent, i.e. 4, 4′‐diaminodiphenyl sulfone (D) and amine B or T. Activation energy of curing, as evaluated by using the multiple heating rate method, was lowest when triamine T (61.0 kJmol−1) was used as hardener and was highest when D (68.7 kJmol−1) was used. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 390–395, 2001

Thermogravimetric kinetics of thermotropic copolyesters containingp-oxybenzoate unit by multiple heating-rate methods

Two series of thermotropic liquid crystalline copolyesters containing mainly the p-oxybenzoate unit were studied by thermogravimetry to ascertain the kinetic parameters of their thermal degradation by six multiple heating-rate techniques for the first time. The two copolyesters are (1) poly(p-oxybenzoate-co-ethylene terephthalate-co-vanillate) and (2) poly(p-oxybenzoate-co-2,6-oxynaphthoate). The effect of copolymer composition, degradation stage, and test atmosphere on the three kinetic parameters of the thermal degradation in the weight loss range from 5 to 70% is discussed. Comparison of the multiple heating-rate techniques with single heating-rate techniques for calculating the kinetic parameters of thermal degradation was made. The respective activation energy, order, and natural logarithm of the frequency factor of the thermal degradation in nitrogen for the poly(p-oxybenzoate-co-ethylene terephthalate-co-vanillate)s are between 180 and 230 kJ/mol, between 2.0 and 5.0, and between 28 and 38 min−1 for the first degradation step and between 250 and 390 kJ/mol, between 6.4 and 7.6, and between 38 and 64 min−1 for the second degradation step of the poly(p-oxybenzoate-co-ethylene terephthalate-co-vanillate)s with the unit-B content in the range of 70–75 mol %. The respective activation energy, order, and natural logarithm of frequency factor of the first degradation stage for the poly(p-oxybenzoate-co-2,6-oxynaphthoate) (Vectra) are between 380 and 570 kJ/mol, between 2.0 and 3.1, and between 55 and 68 min−1 in nitrogen and between 160 and 210 kJ/mol, between 0.8 and 1.8, and between 25 and 32 min−1 in air. The best methods of calculating the kinetic parameters of the thermal degradation for the copolymers are suggested. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2016–2028, 1999

Thermal degradation kinetics of thermotropic poly(p-oxybenzoate-co-p,p?-biphenylene terephthalate) fiber

An advanced heat-resistant fiber (trade name Ekonol) spun from a nematic liquid crystalline melt of thermotropic wholly aromatic poly(p-oxybenzoate-p,p′-biphenylene terephthalate) has been subjected to a dynamic thermogravimetry in nitrogen and air. The thermostability of the Ekonol fiber has been studied in detail. The thermal degradation kinetics have been analyzed using six calculating methods including five single heating rate methods and one multiple heating rate method. The multiple heating-rate method gives activation energy (E), order (n), frequency factor (Z) for the thermal degradation of 314 kJ mol−1, 4.1, 7.02 × 1020 min−1 in nitrogen, and 290 kJ mol−1, 3.0, 1.29 × 1019 min−1 in air, respectively. According to the five single heating rate methods, the average E, n, and Z values for the degradation were 178 kJ mol−1, 2.1, and 1.25 × 1010 min−1 in nitrogen and 138 kJ mol−1, 1.0, and 6.04 × 107 min−1 in air, respectively. The three kinetic parameters are higher in nitrogen than in air from any of the calculating techniques used. The thermostability of the Ekonol fiber is substantially higher in nitrogen than in air, and the decomposition rate in air is higher because oxidation process is occurring and accelerates thermal degradation. The isothermal weight-loss results predicted based on the nonisothermal kinetic data are in good agreement with those observed experimentally in the literature. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 1923–1931, 1999

Analysis of non-isothermal reaction kinetics: Part 1. Simple reactions

Owing to the compensation effect, multiple sets of Arrhenius parameters can be obtained from non-isothermal data. This leads to non-unique results and, hence, to criticisms of the non-isothermal methods. In this paper, procedures used to analyze non-isothermal data in order to obtain reliable Arrhenius parameters for simple reactions are discussed. The integral method has been found to yield reliable Arrhenius parameters from non-isothermal data. Concurrent use of the integral and the multiple heating-rate methods has been found to be a powerful tool for obtaining reliable results for both the order of reaction and the Arrhenius parameters.

Condensation polymerization of multifunctional monomers and properties of related polyester resins. II. Thermal properties of polyester—imide varnishes

Polyester—imide prepolymers containing synthesized N,N′-bis(hydroxyethyl)pyromellitic diimide (PMDI) or N,N′-bis(hydroxyethyl)-3,3′-4,4′-benzophenone tetracarboxylic diimide (BTDI) were synthesized under conditions previously reported. One-component varnishes were obtained by mixing the synthesized prepolymers with commercial Desmodur CT-stable. Thermal behavior of these varnishes was investigated using thermogravimetric analysis. Activation energy of cured film, which was a polyester—imide varnish, was determined by using a multiple heating rate method. Polyester—imides coated copper wires were characterized, and were found to be acceptable, according to the specification of Japanese Industrial Standard (JIS-C-3214).

Addition polyimides. III. Thermal behavior of bismaleimides

AbstractThis article describes the synthesis of N,N′‐bis(3,3′‐maleimidophenyl) sulfone (S) and its Michael addition products with (4,4′‐diaminodiphenyl) methane (S‐M), 4,4′‐diaminodiphenyl ether (S‐E), (3,3′‐diaminodiphenyl) sulfone (S‐DDSm), (4,4′‐diaminodiphenyl) sulfone (S‐DDSp), (3,3′,3″‐tris aminophenyl) phosphine oxide (S‐TAP), and 9,9‐bis(p‐aminophenyl) fluorene (S‐B). Curing behavior of these bisimides was investigated by differential scanning calorimetry. Activation energy of curing reaction was determined by using isothermal and multiple heating rate method. Thermal stability of bisimides was evaluated by thermogravimetric analysis. Better char yields were obtained in S‐TAP resins.

The influence of molecular weight on the degradation of poly( N-vinylcarbazole)

The methods of isothermal and dynamic thermogravimetry have been used to study the degradation of poly( N-vinylcarbazole) (PNVC). The multiple heating rate method has been used, as a dynamic method, to obtain kinetic parameters. A linear relationship between the activation energy. E, and M w −1 ( M w being weight average molecular weight) was found. From isothermal experiments, a temperature was found for which E was independent of molecular weight. We could then refer to a degradation characteristic- temperature of the polymer. On the other hand, altering the heating rate leads to changes in the values of E for each molecular weight indicating two kinds of scission: one occurs in the backbone, producing mainly monomer; in the other, both side-group and backbone scissions occur producing different products.

Determination of kinetic parameters for the thermal decomposition of phenolic ablative materials by a multiple heating rate method

The rate of decomposition for two widely used glass- and asbestos-phenolic ablative materials were measured using standard thermogravimetric techniques. Thermograms were obtained at six heating rates ranging from 10°C min −1 to 160°C min −1. From these data the kinetic parameters were determined by a slightly modified version of Friedman's method. Fractional weight loss calculated using the derived kinetic parameters over the temperature range of decomposition agreed with measured values with a mean error of 0.33 and 0.28%, with a standard deviation of errors 0.58 and 0.84% for glass- and asbestos-phenolic, respectively. The 95% confidence for the mean error was 0.22 and 0.44% for the glass-phenolic and 0.14 and 0.42% for the asbestos-phenolic. Also, the activation energy was calculated by the method of Flynn and Wall. The average activation energy values determined by the two methods agreed within 4.6% for both materials.

Thermogravimetric investigation of the pyrolysis of pitch materials. A compensation effect and variation in kinetic parameters with heating rate

Thermogravimetric measurements of weight loss accompanying the pyrolysis of four pitches have been made over a range of linear heating rates. For three of the samples, the data at each heating rate could be described by an integral and a differential method of analysis, assuming a simple order function for f(α), with the result that the apparent activation energy increased with heating rate. The data for all four samples could also be satisfactorily described by the Ozawa or Friedman multiple heating rate methods, and these resulted in apparent activation energies ( E a) which increased with the value of β at which they were determined. It is suggested that this tendency for the apparent activation energy to increase, as the temperature is raised, is due to a change in the relative importance of the different reactions which lead to weight loss in this system. The apparent kinetic parameters all fall on a common compensation plot which is used to explain the relative magnitude of E a values from Ozawa and Doyle methods of analysis. The higher values of E a from Friedman than from Ozawa analyses are also explained.

Rapid determination of kinetic parameters for the thermal degradation of high polymers utilizing a computerized thermogravimetric analyzer‐mass spectrometer system

AbstractA thermogravimetric analyzer and a mass spectrometer are operated in a tandem mode for mass spectrometric thermal analysis (MTA) of high polymers. During the course of an analysis, the weight loss of the sample under investigation is recorded with respect to increasing sample temperature by the thermogravimetric analyzer. Simultaneously, the evolved gaseous thermal decomposition products are introduced into the mass spectrometer which records mass spectra repetitively at scan speeds of the operator's choice. The mass spectrometer is coupled to a computer for continuous on‐line data acquisition, thus producing a complete mass spectrometric record of the released breakdown products. All original data are stored on magnetic tapes for subsequent processing employing a variety of computer programs. The computerized MTA technique allows the characterization of complex and simultaneous thermal degradation reactions. The rate of evolution for identified components as measured by the mass spectrometer and the total weight of volatilized products are used in the kinetic analysis of degradation reactions. A program for a programmable calculator that permits rapid calculation for order of reaction n and activation energy E has been developed. The results of the kinetic analysis from MTA data are compared to those obtained employing the multiple heating rate method.