K. Krishnan

New approximation for the p(x) function in the evaluation of non-isothermal kinetic data

Abstract Three new approximations for the temperature integral, p(x), viz. a series, a three-term and a two-term, are proposed. The former two approximations have almost the same accuracy as the Scholmilch series, the percentage deviation being of the order of 10−6. The linear dependence of x on 1n p(x), of the slope d[1n p ( x )] d x on 1 x and of the intercept of the In p(x) versus x curve on 1n x have been established. A new equation for the evaluation of the kinetic parameters has been obtained from the above dependence which can be put in the form The validity of this equation, based on the two-term approximation for p(x), has been tested with data from a theoretical thermogravimetric curve.

New equations for kinetic analysis of non-isothermal reactions

Abstract Kinetic equations of the form ln[frsol″>; g(α)/Tc″] =ln[AE/φR] + c′ -c″ ln E - c″( E T ) are proposed for the evaluation of activation parameters from non-isothermal experiments. The values of c′, c″ and c″ have been derived using the already established linear dependence of (i) the logarithm of the Arrhenius temperature integral ln p(x) on x (= E R T ), (ii) its slope on x−1 and (iii) its intercept on In x, respectively. The ln p(x) values were computed from the recently proposed series and the closed-form three-term approximations. The kinetic parameters computed with the proposed equations show better agreement for theoretical TG curves than do the well known methods. The equations have equal practical significance in the kinetic analysis of non-isothermal processes.

Kinetics of Alder-ene reaction of Tris(2-allylphenoxy)triphenoxycyclotriphosphazene and bismaleimides — a DSC study

Tris(2-allylphenoxy)triphenoxycyclotriphosphazene was reacted with three bismaleimides (BMI), viz. bis(4-maleimido phenyl)methane (BMM), bis(4-maleimido phenyl)ether (BME) and bis(4-maleimido phenyl)sulphone (BMS) via the Alder-ene reaction. The differential scanning calorimetric analysis of the blend manifested two distinct exotherms. The low temperature exothermic reaction was attributed to the Wagner-Jauregg reaction following the ene reaction and the strong exotherms at around 250–270°C to the cross-linking Diels–Alder reactions of the initially formed adducts. The Kinetic parameters, viz. activation energy (E) and pre-exponential factor (A) of the reactions were evaluated by Kissinger and Ozawa methods using the variable heating rate method. The kinetic data revealed that the Wagner-Jauregg reaction was disfavoured by electron-withdrawing nature of the BMI. The Diels–Alder reaction was facilitated by the electron-withdrawing nature of the bismaleimide. The activation energy for the first exothermic stage decreased and for the second major step increased on enhancing the stoichiometry of BMI in the blend for a given pair. The activation parameters served to predict the isothermal cure profiles of the blends and deduce the possible network structure under the given conditions of cure temperature and stoichiometry.

Differential scanning calorimetric study on the Claisen rearrangement and thermal polymerisation of diallyl ether of bisphenols

Abstract The diallyl ethers of bisphenol A (APP), 4,4′-dihydroxy biphenyl (ABP) and bisphenol sulfone (ABS) were synthesised and the kinetics of their thermal rearrangement to the diallyl bisphenols were studied by DSC. The ethers manifested two distinct exotherms corresponding to the Claisen rearrangement of the ether and thermal polymerisation of the rearranged product. The kinetics of both reactions as estimated by the Kissinger and Ozawa methods showed that the rearrangement is disfavoured by the electron-withdrawing substituent and favoured by electron-releasing groups at the para position of the allyloxy group. The rate constants calculated from the activation parameters showed the structural dependency. Thus, the rearrangement was facilitated in the order ABP>APP>ABS. The polymerisation kinetics revealed that the polymerisability of the allyl phenols decreased due to the presence of substituent groups on the phenyl ring that can stabilise the free radical formed by way of degenerative transfer at the allylic position. Thus, the polymerisation tendency increased in the order APP>ABP>ABS.

Thermal decomposition studies. Part 19. Kinetics and mechanism of thermal decomposition of copper ammonium chromate precursor to copper chromite catalyst and correlation of surface parameters of the catalyst with propellant burning rate

Abstract The thermal decomposition of copper ammonium chromate (CAC), which is a precursor of copper chromite (CC) catalyst (used as a ballistic modifier in solid propellants), has been thoroughly studied. The DTG curves show that there are three main peaks at about 286, 440 and 740°C, whereas DTA gives peaks at 254 (endo), 278 (exo), 408 (exo) and 699°C (endo). The kinetic parameters for the prominent and clear-cut first stage in TG (DTG peak at 286°C) are E = 236 kJ mol−1, A = 1.51 × 1021 s−1, and Δ = 136 J K−1 mol−1. The mechanism of this decomposition reaction is identified as a phase boundary reaction with spherical symmetry, as per the equation g(α) = 1 − (1 − α) 1 3 . The surface parameters of the CC samples obtained by calcination of CAC, at different temperature regimes compatible with TG data, have been determined. The surface area of the CC decreases when the calcination temperature increases. The surface area also decreases when CC samples are washed with acetic acid. X-ray diffraction (XRD) patterns of CC samples obtained from higher temperature calcinations of CAC differ from those obtained at lower temperatures. The propellant burning rate is enhanced by the addition of CC and increases when the Lewis acid amounts of the catalyst sample increase. These correlations have been established for the first time for CC catalysts used in propellant technology.

A DSC Study on the Effect of RDX and HMX on the Thermal Decomposition of Phase Stabilized Ammonium Nitrate

Phase stabilized ammonium nitrate(PSAN) was prepared by incorporating copper(II) diammine nitrate in the ammonium nitrate(AN) crystal lattice. The effect of two energetic materials viz., RDX and HMX on the thermal decomposition of PSAN was investigated using DSC. The decomposition temperatures of PSAN and RDX are almost in the same temperature range. The decomposition of PSAN is endothermic and that of RDX is exothermic, while that of a 1:1 mixture of the two is exothermic with a net heat release in excess of that of the individual reactions, which is attributed to the combustion reaction among the decomposition products of PSAN and RDX. Though HMX decomposes at a higher temperature, in presence of molten PSAN a substantial portion of it decomposes at a lower temperature along with PSAN with a net excess heat release, again due to the combustion reaction. The kinetic parameters of the two exothermic decompositions were computed using two equations based on variable heating rate method viz., Kissinger and Ozawa equations. The activation energy obtained from Ozawa method was refined by an iteration procedure. There is a close agreement among the values obtained by the three methods. The kinetic parameters for PSAN-HMX mixture are lower, probably due to the effect of its higher heat release.

Thermal decomposition of tetraalkyl ammonium tetrafluoroborates

Abstract The thermal decomposition of tetraalkyl ammonium tetrafluoroborates (R 4 NBF 4 ), where R=methyl, ethyl, n -propyl and n -butyl, were studied using thermogravimetric (TG) technique in an inert atmosphere of N 2 at a heating rate of 20 K min −1 . The decreasing order of thermal stability and activation energy ( E ) with increase in size of the substituted alkyl group are consistent with each other. The probable causes for higher activation energy observed in the case of n -butyl substituted compound are discussed.

The effect of the simultaneous variation of sample mass and heating rate in DTA and DSC

Abstract Quantitative correlations between kinetic parameters (energy of activation, E), procedural factors (sample mass, m, and heating rate, φ) and the dependent variables (the temperature of inception of reaction, Ti, and temperature Tα at which a constant fraction α has decomposed) have been derived for differential thermal analysis (DTA) and differential scanning calorimetry (DSC). The relations have the same form as those derived from earlier TG studies. The dependent variables Ti and Tα are related to m, φ and E by the equations where C3 and C2 are constants, and where C4 and C5 are constants for a given α. The variation of C5 with α is given by C5 = a + b α where a and b are constants. The equations are applicable to TG, DTA and DSC.

Equations for the rapid evaluation of general temperature integrals in non-isothermal kinetic analysis

Abstract Integrals of the form ∫ O T A m T m e − E/RT T have been evaluated for integer and fractional values of m = b − 2. The results of the numerical integration are presented for Arrhenius integrals having negative as well as positive exponents. Equations have been derived which relate m to the natural logarithm of the p( x ) function. Methods for the rapid evaluation of general temperature integrals for any combination of m and x , from four different approximations, are also presented.

Effect of simultaneous variation of sample mass and heating rate on the mechanism of dehydration of zinc oxalate dihydrate

Abstract The mechanism of the single-step dehydration of ZnC 2 O 4 · 2H 2 O has been established from TG, DTA and DSC studies. The rate-controlling process for the reaction is random nucleation with the formation of one nucleus on each particle. The kinetic parameters are calculated from mechanistic as well as non-mechanistic kinetic equations. For the dehydration reaction, the activation energy and the pre-exponential factor show a systematic decrease with the simultaneous increase in sample mass and heating rate, whereas the mechanism of the process remains unaffected by these variations.