K.N. Ninan

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.

Thermal decomposition studies: Part X. Thermal decomposition kinetics of calcium oxalate monohydrate — correlations with heating rate and samples mass

Abstract Quantitative correlations between kinetic parameters (energy of activation E , pre-exponential factor A ) and procedural factors (heating rate, sample mass) in non-isothermal thermogravimetry have been made for the first time. The effect of heating rate and sample mass on the first two stages of thermal decomposition of calcium oxalate monohydrate in a nitrogen atmosphere has been evaluated in detail using non-isothermal thermogravimetry. Kinetic parameters are calculated from the TG curves using three integral methods (two “exact” and one “approximate”). The values obtained by the “approximate” method are higher than the corresponding values from the “exact” integral methods. For the decomposition of calcium oxalate to carbonate, the kinetic parameters are not much affected by heating rates or sample masses in the ranges studied. For the dehydration of CaC 2 O 4 · H 2 O, the parameters show a systematic decrease with increase in either heating rate or sample mass. The values of E and log A obtained by all three equations are best correlated to heating rate as rectangular hyperbole of the type: The best fits for correlation to sample mass are parabolae of the type E (or log A ) = constant × (mass) 2 − constant × mass ÷ constant SYMBOLS USED A = pre-exponential factor α = fraction decomposed φ = heating rate in deg min −1 E = energy of activation n = order parameter R = gas constant T i = temperature of inception of reaction T f = temperature of completion of reaction T s = DTG peak temperature Δ T = T − T s

Thermal decomposition kinetics. Part XI. Mechanism of thermal decomposition of calcium oxalate monohydrate from a thermogravimetric study — the effects of heating rate and sample mass on kinetic parameters from mechanistic equations

Abstract The mechanisms of the first two stages of the thermal decomposition of calcium oxalate monohydrate have been established from non-isothermal thermogravimetric studies. For both stages, the rate-controlling processes are phase boundary reactions; the dehydration step assumes spherical symmetry whereas the decomposition step follows cylindrical symmetry. The kinetic parameters calculated from mechanistic equations show the same trend as those from mechanism-non-invoking equations. Thus, for the decomposition of CaC 2 O 4 the kinetic parameters are not appreciably affected by heating rate or sample mass. For the dehydration step they show a systematic decrease with increase in either heating rate or sample mass. The best fit correlations can be expressed as follows E (or, log A ) = (Constant/Heating rate) + Constant, (at fixed sample mass) E (or, log A ) = (Constant) × (Mass) 2 − (Constant) × (Mass) + Constant, (at fixed heating rate)

Thermal decomposition studies. Part XII. Kinetics of dehydration of calcium oxalate monohydrate. Multiple correlation with heating rate and sample mass

Abstract The kinetic parameters (energy of activation, E , and pre-exponential factor, A ) from non-isothermal TG data have been correlated, for the first time, with simultaneous variations of both the procedural factors (heating rate and sample mass) by multiple regression analysis. The unique equation based on the mechanism of the reaction as well as three general mechanism-non-invoking integral equations were used to calculate E and A from the TG data for the dehydration of CaC 2 O 4 · H 2 O. The kinetic parameters calculated using all four equations showed a systematic trend and the results can be expressed as E (or log A ) = constant heating rate + constant mass + constant

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.

Thermal decomposition kinetics. XIII. Effect of sample mass on the thermal decomposition kinetics of CaC2O4 · H2O from isothermal mass-loss data

Abstract The kinetic parameters for the first two stages of the thermal decomposition of calcium oxalate monohydrate CaC 2 O 4 · H 2 O CaC 2 O 4 CaCO 3 have been established from isothermal mass-change studies. For the decomposition of calcium oxalate to carbonate, the kinetic parameters are not appreciably affected by the sample mass in the ranges studied. For the dehydration of CaC 2 O 4 · H 2 O, they show a systematic decrease with increase in sample mass, and the curves of E or log A vs. sample mass can be best fitted as parabolae following an equation of the type E (or log A ) = constant − (constant) × (mass) + (constant) × (mass) 2

Thermal decomposition kinetics: Part XV. Kinetics and mechanism of thermal decomposition of tetrammine copper(II) sulphate monohydrate

Abstract The kinetics and mechanism of the thermal decomposition of tetrammine copper(II) sulphate monohydrate have been studied using non-isothermal thermogravimetry. Kinetic parameters were calculated for each step in the decomposition reaction from the TG curve using four integral methods, three “exact” and one “approximate”. The rate-controlling process for all the four stages of decomposition is random nucleation with the formation of one nucleus on each particle (Mampel equation). The stages of decomposition have been identified from X-ray diffraction and independent pyrolysis.

Thermal decomposition kinetics: Part XVII. Kinetics and mechanism of thermal decomposition of bis(ethylenediamine)copper(II) halide monohydrate

Abstract The thermal decomposition studies of bis(ethylenediamine)copper(II) chloride monohydrate and bis(ethylenediamine)copper(II) bromide monohydrate were carried out using thermogravimetry (TG), derivative thermogravimetry (DTG) and differential thermal analysis (DTA). The kinetics and mechanism of the dehydration and the deamination stages of both the complexes were evaluated. The different stages of decomposition were identified from TG, DTG and DTA. The intermediate and residue analysis done using optical microscopy and X-ray diffraction showed the formation of CuCl and CuBr at about 450°C and copper as fine linear wires at about 700°C. The kinetic parameters for the dehydration and the deamination reactions were evaluated from the TG and DTA curves using four integral methods. For both the complexes the dehydration and the deamination processes follow the mechanism of random nucleation with the formation of one nucleus on each particle (Mampel equation). The heat of reaction for each stage of decomposition was determined using DTA.

Thermal decomposition kinetics: Part IX. A study of the thermal decomposition of sodium tetraphenyl borate☆

Abstract Sodium tetraphenylborate [NaB(C 6 H 5 ) 4 ] undergoes a two-stage decomposition on heating in air. The DTG peak temperatures are at about 320 and 500°C, the corresponding DTA peaks are at 330 and 520°C. The energies of activation for the two stages are ≈ 220 kJ mol −1 and ≈ 140 kJ mol −1 . The total enthalpy change for the complete decomposition (including combustion of carbonaceous decomposition products) is ≈ − 13,200 kJ mol −1 The ultimate decomposition product in air is NaBO 2 .