Estimation of the Critical Temperature of Thermal Explosion for the Highly Nitrated Nitrocellulose Using Non-isothermal DSC

Two methods for estimating the critical temperature (T_b) of thermal explosion for the highly nitrated nitrocellulose (HNNC) are derived from the Semenov's thermal explosion theory and two non-isothermal kinetic equations, d/dt=Af()e^–E/RT and d/dt=Af()[1+E/(RT)(1–T_o/T)]e^–E/RT, using reasonable hypotheses. We can easily obtain the values of the thermal decomposition activation energy (E), the onset temperature (T_e) and the initial temperature (T_o) at which DSC curve deviates from the baseline of the non-isothermal DSC curve of HNNC, and then calculate the critical temperature (T_b) of thermal explosion by the two derived formulae. The results obtained with the two methods for HNNC are in agreement to each other.This revised version was published online in November 2005 with corrections to the Cover Date.     

Numerical integration of Euler's integral and numerical relationships involving E and T

Numerical integration has been carried out for p(x) = ?^∞_xx^?2e^?xdx where x = E/RT with E = 20, 25, …, 100 kcal mole^?1 and T = 300, 350, …, 1000 K. Using the values of -log p(x), numerical equations have been obtained that enable calculations of -log p(x) at other values of E and T.     

Estimation of the critical temperature of thermal explosion for azido-acetic-acid-2-(2-azido-acetoxy)-ethylester using non-isothermal DSC

A method for estimating the critical temperatures (T _b) of thermal explosion for energetic materials is derived from Semenov’s thermal explosion theory and the non-isothermal kinetic equation dα/dt=A ₀ T ^B f(α)e^−E/RT using reasonable hypotheses. The final formula of calculating the value of T _b is $ \left( {\frac{B} {{T_b }} + \frac{E} {{RT_b^2 }}} \right) $ \left( {\frac{B} {{T_b }} + \frac{E} {{RT_b^2 }}} \right) (T _b−T _e0=1. The data needed for the method, E and T _e0, can be obtained from analyses of the non-isothermal DSC curves. When B=0.5 the critical temperature (T _b) of thermal explosion of azido-acetic-acid-2-(2-azido-acetoxy)-ethylester (EGBAA) is determined as 475.65 K.     

The absorption spectrum of carbon monoxide in the CO(3Π r,a) state between 215 nm and 285 nm

Bye-beam excitation of a He/CO mixture the CO(³Π _r ,a) state was sufficiently populated to allow the measurement of the absorption spectrum. The (0, 0), (1, 1), (2, 2) and (0, 1) bands of thec ³Π←a ³Π system of CO have been observed and the molecular constantsT _e =92036.0 cm^?1 (for the band head), ω _e =2249.5 cm^?1, ω _e x _e =29.5 cm^?1 have been derived for CO(c). A new electronic state withT _e =91854.3 cm^?1, ω _e =848.4 cm^?1, ω _e x _e =9.8 cm^?1,B _e =1.351 cm^?1, and α _e =0.021 cm^?1 was identified to be a³Σ state. It seems to be very likely that this state is the CO (3pσ,³Σ,j) state discussed in the literature. The results indicate a perturbation of the υ=1 levels of the new state by the CO (c,υ=0) levels. Another strong perturbation is found in the υ=4 levels. The three CO(³Σ,b,υ′=0,1,2)←CO (a,υ″=0) bands were also investigated yielding for CO(b):T _e =83778 cm^?1, ω _e =2335 cm^?1, ω _e x _e =59 cm^?1 andB _e =1.86 cm^?1.     

The Accuracy of Senum and Yang's Approximations to the Arrhenius Integral

The accuracy of the integral of the Arrhenius equation, as determined from the 1^st to the 4^th degree rational approximation proposed by Senum and Yang, has been calculated. The precision of the 5^th to 8^th rational approximations, here proposed for the first time, has also been analyzed. It has been concluded that the accuracy increases by increasing the order of the rational approximation. It has been shown that these approximations to the Arrhenius equation integral would allow an accuracy better than 10⁻⁸ % in the E/RT range generally observed for solid state reactions. Moreover, it has been demonstrated that errors closed to 10⁻² % can be obtained even for E/RT=1, provided that high enough degrees of rational approximation have been used. Thus, it would be reasonable to assume that high degree rational approximations for the Arrhenius integral could be used for the kinetic analysis of processes, like adsorption or desorption of gases on solid surfaces, which can take place at low temperatures with very low values of E/RT. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of climate on the weathering of polyacetal

The degrees of weathering of polyacetal specimens exposed for a year at fourteen sites throughout the world have been assessed from weight loss measurements. From a consideration of the results and meteorological data it has been shown that the extent of polyacetal degradation depends on uv dose and temperature. Moisture also affects the degree of breakdown; its effect is to inhibit the photo-oxidative process.An expression, W = 1·58 × 10⁴D e^{?10 000/RT}, is developed which enables polyacetal weight loss at a site to be estimated from a knowledge of the annual uv dose (D) as measured by the PPO film technique and the mean temperature (T) in degrees absolute.From information presented on these two climatic factors, a relationship between site latitude and the degree of polyacetal breakdown is proposed.     

A New Modified Pseudoequilibrium Calculation to Determine the Composition of Hydrogen and Nitrogen Plasmas at Atmospheric Pressure

This paper proposes a modified pseudoequilibrium calculation, which gives almost the same results as those of kinetic calculations to determine the composition of hydrogen and nitrogen plasmas at atmospheric pressure. The computing time is two to three orders of magnitude faster than that of the kinetic calculations. First, according to experimental results, a relationship between the electron temperature T_e and the heavy species one T_h has been proposed. The ratio T_e/T_h varies as a function of the logarithm of the ratio n_e/n _e ^max , _e ^max being the electron density in the plasma core for which equilibrium is achieved _e ^max ~ 10 ²³ ). The kinetic calculations have been performed assuming the microreversibility where the backward kinetic rate coefficient k_b is calculated by k_d/k_b=K_x, where k_d is the direct kinetic coefficient and K_x the molar fraction equilibrium constant. When electrons are involved in both direct and backward reactions, k_d and K_x are expressed as functions of T_e . However, when the direct reaction involves electrons while the backward one is due to collisions between heavy species (or the reverse), a temperature T* between T_e and T_h is introduced. T* is determined as a function of the ratio of the electron flux to that of neutral species in such a way that T*=T^e for n_e > 10²³ and T*=T_h for low values of n_e(n_e < 10¹⁵ m^–3). Compared to hydrogen, the nitrogen composition exhibits a very abrupt variation between 6000 and 6500 K, corresponding to a shift from the dissociation-dominated regime to that of ionization. It occurs because dissociation of nitrogen starts almost simultaneously with its ionization, which is not the case of H₂, for which dissociation is terminated long before ionization starts. If the charge transfer reaction, whose activation energy is low for both gases, is neglected, in both cases the electron density increases drastically below 9000 K. These results are quite similar to those obtained when calculating the composition with the multitemperature mass action law. The kinetic calculations are dominated by the reactions with a low activation energy: dissociation, dissociative recombination and charge transfer. Thus, a modified pseudoequilibrium calculation has been introduced, the plasma composition being calculated with the equilibrium constants corresponding to low activation energies[X₂ 2X, e+X ₂ ⁺ 2X, X ₂ ⁺ +X X⁺ + X₂ both for hydrogen (X=H) and nitrogen (X=N)] at the temperature T* between T_e and T_h. The results are in very good agreement with those of the kinetic calculations.     

Two-photon absorption spectroscopy of iodine monochloride in the 5 eV region

Two-photon high resolution sequential spectroscopy has been used to excite iodine monochloride from X¹Σ⁺ ground state to the intermediate A³Π₁ state and thence to a final electronic state at 4.82 eV. Vibrational and rotational analyses of this state have been carried out for both isotopic species. For I³⁵Cl, T_e = 38916.0 cm^?1 ω_e = 168.99 cm^?1, ω_ex_e = 0.357 cm^?1 and B_e = 0.05685 cm^?1. The state probably has Ω = 1 in case (c) coupling approximation. It is also shown how to two-photon technique enables rotational line structure of the A ← X transition to be selectively excited for either isotopic species at a resolution of 500000, from an absorption mixture containing natural iodine monochloride plus its iodine dissociation product at equilibrium vapour pressure.     

b1Σ+ Emissions from group V–VII diatomic molecules. b 0+ → X1 0+, X2 1 emissions of AsI and SbI

Chemiluminescence from the b 0⁺ → X₁ 0⁺ band system of AsI and of the b 0⁺ → X₁ 0⁺, X₂ 1 systems of SbI in the near-infrared spectral region has been observed in a discharge flow system. Analysis of the spectra led to the spectroscopic constants (in cm^?1) of AsI: ω_e(X₁, X₂) = 257 ± 2, ω_ex_e(X₁, X₂) = 0.82 ± 0.2, T_e(b 0⁺) = 11738 ± 5, ω_e(b 0⁺) = 271 ± 2, ω_ex_e(b 0⁺) = 0.66 ± 0.2, and of SbI: T_e(X₂ 1) = 965 ± 10, ω_e(X₁, X₂) = 206 ± 6, T_e(b 0⁺) = 12328 ± 10, ω_e(b 0⁺) = 211 ± 6. The intensity ratio of the two sub-systems b 0⁺ → X₂ 1 and b 0⁺→ X₁ 0⁺ was found to be ≈0.013 in the case of SbI and ? 0.01 for AsI.     

The evaluation of the Arrhenius integral with special reference to small computers

This paper discusses the factors which influence the choice and implementation of computer methods to evaluate the Arrhenius integral, I_A = ∫^Tα₀ exp(?E/RT)dT. It also identifies the sources of computational error and inefficiency. It is shown that, amongst numerical integration techniques, the classical trapezoidal and Simpson rules have little to recommend them compared with the method of Gaussian quadrature. A technique for preserving the accuracy of the Gauss method at very high values of E/RT_α is also described and evaluated. Rational (Padé) approximation is found to compare favourably with Gaussian quadrature in efficiency and accuracy, and is simpler to use. The discussion also reveals that six decimal-digit arithmetic is adequate for all practical purposes.     

Studies on the non-isothermal kinetics of thermal decomposition of the mixed ligand complex — [Fe2O(OC6H4CH=NC6H4O)2(C5H5N)4]·2H2O

The thermal decomposition of the mixed-ligand complex of iron(III) with 2-[(o-hydroxy benzylidene)amino] phenol and pyridine-[Fe₂O(OC₆H₄CH=NC₆H₄O)₂(C₅H₅N)₄]·2H₂O and its non-isothermal kinetics were studied by TG and DTG techniques. The non-isothermal kinetic data were analyzed and the kinetic parameters for the first and second steps of the thermal decomposition were evaluated by two different methods, the Achar and Coats-Redfern methods. Steps 1 and 2 are both second-order chemical reactions. Their kinetic equations can be expressed as: dα/dt=Ae^?E/RT(1-α)²     

Rate constants of the reactions of OH radicals with cyclopropane and cyclobutane

The kinetics of the reactions of hydroxy radicals with cyclopropane and cyclobutane has been investigated in the temperature range of 298–492 K with laser flash photolysis/resonance fluorescence technique. The temperature dependence of the rate constants is given by k₁ = (1.17 ± 0.15) × 10^?16 T^3/2 exp[?(1037 ± 87) kcal mol^?1/RT] cm³ molecule^?1 s¹ and k₂ = (5.06 ± 0.57) × 10^?16 T^3/2 exp[?(228 ± 78) kcal mol^?1/RT] cm³ molecule^?1 s^?1 for the reactions OH + cyclopropane → products (1) and OH + cyclobutane → products (2), respectively. Kinetic data available for OH + cycloalkane reactions were analyzed in terms of structure-reactivity correlations involving kinetic and energetic parameters.     

Synthesis,crystal structure,and kinetics of thermal decomposition of the Zn(II) complex with vanillin

A complex [Zn(C₈H₇O₃)₂(H₂O)₂] (C₈H₈O₃ is vanillin) has been synthesized and characterized by IR, elemental analysis, and X-ray diffraction single-crystal analysis. The crystals are monoclinic, space group C2/c, a = 22.236(8) Å, b = 10.594(2) Å, c = 7.8190(16) Å, α = 89.90(3)°, β = 106.87(4)°, γ = 89.99(3)°, V = 1762.6(8) ų, Z = 4, F(000) = 832, S = 1.079, ρ _c = 1.521g cm^?3, R = 0.0221, R _w = 0.0604, μ = 1.433 mm^?1. The Zn²⁺ ion is six-coordinated with a distorted octahedron geometry. The complex forms a three-dimensional network through intermolecular hydrogen bonds. The thermal decomposition kinetics of the complex for the second stage was studied under non-isothermal conditions by the TG and DTG methods. The kinetic equation can be expressed as dα/dt = Ae^?E/RT 2(1 ? α)[1 ? ln(1 ? α)]^1/2. The kinetic parameters (E, A), activation entropy ΔS ^≠, and activation free-energy ΔG ^≠ were also gained.     

Homogeneous decomposition of vinyl ethers. The heat of formation of ethanal-2-yl

The thermal unimolecular decomposition of three vinylethers has been studied in a VLPP apparatus. The high-pressure rate constant for the retro-ene reaction of ethylvinylether was fit by log k (sec^?1) = (11.47 + 0.25) - (43.4 ± 1.0)/2.303 RT at <T> = 900 K and that of t - butylvinylether by log k (sec^?1) = (12.00 ± 0.27) - (38.4 ± 1.0)/2.303 RT at <T> = 800 K. No evidence for the competition of the higher energy homolytic bond-fission process could be obtained from the experimental data. The rate constant compatible with the C? O bond scission reaction in the case of benzylvinylether was log k (sec^?1) = (16.63 ± 0.30) - (53.74 ± 1.0)/2.303 RT at <T> = 750 K. Together with ΔH_f,300⁰(benzyl·) = 47.0 kcal/mol, the activation energy for this reaction results in ΔH_f,300⁰(CH₂CHO) = +3.0 ± 2.0 kcal/mol and a corresponding resonance stabilization energy of 3.2 ± 2.0 kcal/mol for 2-ethanalyl radical.     

Gleichgewichtsmessungen an oxidischen Mehrstoffsystemen. II Gleichgewichtsmessungen an einer Me3O4-Phase im quaternären System Fe?Mn?Zn?O

The diffusion coefficients D of UCl₄ and UOCl₂ in the eutectic LiCl? KCl melt at 370–610°C have been determined, using α-active ²³³U as a tracer, to be: UCl₄/D = 1.13 · 10^?3 e^?6300/RT; UO₂Cl₂/D = 1.76 · 10^?3 e^?7500/RT cm²/sec.     

Kinetics and mechanism of the decomposition of N-brominated alanine in aqueous solution

Aqueous bromine reacts with alkyl-sidechain amino acids through a series of steps resulting in the formation of the corresponding alkyl aldelydes and nitriles. The kinetics and the mechanism of the interaction of bromine with alanine are examined. The products and the rates of this reaction are dependent in a complex way on the initial reactant concentration and pH. Acetaldeyde production is favored at low bromine-to-alanine ratios, low bromine concentrations, and pH values above 6. The first-order rate constant for the formation of acetaldelyde from alanine under these conditions is k₄ = 1.98 × 10¹⁵ e^?22,500/RT min^?1. At higher concentration the nitrile is formed through a bromoimine intermediate. Under most conditions the nitrile appears to form from a catalyzed decomposition of the bromoimine which is too fast to be followed by the methods used in this study. However, residual amounts of the bromoimine decay by a slower first-order mechanism. The rate constant for this slower reaction in the case of alanine at pH 6.8–6.9 and alanine concentrations of 1 × 10^?4M is k₆ = 1.75 × 10⁵ e^?10,400/RT min^?1.     

Kinetics and mechanism of atmospheric reactions of partially fluorinated alcohols

Gas-phase reactions typical of the Earth’s atmosphere have been studied for a number of partially fluorinated alcohols (PFAs). The rate constants of the reactions of CF₃CH₂OH, CH₂FCH₂OH, and CHF₂CH₂OH with fluorine atoms have been determined by the relative measurement method. The rate constant for CF₃CH₂OH has been measured in the temperature range 258–358 K (k = (3.4 ± 2.0) × 10¹³exp(?E/RT) cm³ mol^?1 s^?1, where E = ?(1.5 ± 1.3) kJ/mol). The rate constants for CH₂FCH₂OH and CHF₂CH₂OH have been determined at room temperature to be (8.3 ± 2.9) × 10¹³ (T = 295 K) and (6.4 ± 0.6) × 10¹³ (T = 296 K) cm³ mol^?1 s^?1, respectively. The rate constants of the reactions between dioxygen and primary radicals resulting from PFA + F reactions have been determined by the relative measurement method. The reaction between O₂ and the radicals of the general formula C₂H₂F₃O (CF₃CH₂? and CF₃?HOH) have been investigated in the temperature range 258–358 K to obtain k = (3.8 ± 2.0) × 10⁸exp(?E/RT) cm³ mol^?1 s^?1, where E = ?(10.2 ± 1.5) kJ/mol. For the reaction between O₂ and the radicals of the general formula C₂H₄FO (? HFCH₂O, CH₂F?HOH, and CH₂FCH₂?) at T = 258–358 K, k = (1.3 ± 0.6) × 10¹¹exp(?E/RT) cm³ mol^?1 s^?1, where E = ?(5.3 ± 1.4) kJ/mol. The rate constant of the reaction between O₂ and the radicals with the general formula C₂H₃F₂O (?F₂CH₂O, CHF₂?HOH, and CHF₂CH₂?) at T = 300 K is k = 1.32 × 10¹¹ cm³ mol^?1 s^?1. For the reaction between NO and the primary radicals with the general formula C₂H₂F₃O (CF₃CH₂? and CF₃?HOH), which result from the reaction CF₃CH₂OH + F, the rate constant at 298 K is k = 9.7 × 10⁹ cm³ mol^?1 s^?1. The experiments were carried out in a flow reactor, and the reaction mixture was analyzed mass-spectrometrically. A mechanism based on the results of our studies and on the literature data has been suggested for the atmospheric degradation of PFAs.     

A new equation for modeling nonisothermal reactions

Based on previously reported approximations of the temperature integral, a new approximation $$\int {\exp ( - E/RT)dT = \frac{{RT^2 }}{E}} \left[ {\frac{{1 - 2(RT/E)}}{{1 - 5(RT/E)^2 }}} \right]\exp ( - E/RT)$$ has been proposed for modeling nonisothermal reactions. It has been found that the equation of Coats and Redfern deviates by less than 1 % from the exact solution forE/RT ratio greater than 23 and by less than 10% forE/RT ratio greater than 6. The exact solution was obtained independently by solving the exponential temperature integral numerically by the Simpson's rule and the Trapezoidal rule. The Gorbachev equation deviates by less than 0.1% forE/RT ratio greater than 41 and by less than 1 % forE/RT ratio greater than 11. The Li equation deviates by less than 0.1 % forE/RT ratio greater than 21 and by less than 1% forE/RT ratio greater than 9. The proposed equation deviates by less than 0.1% forE/RT greater than 7.     

High-temperature pyrolysis of dimethyl ether

The kinetics of pyrolysis of dimethyl ether wexre studied in an adiabatic flow reactor at temperatures between 790 and 950°C. The unimolecular rate constant for the initiating step CH₃OCH₃ = CH₃O + CH₃ was found to be k₁ = 2.16 × 10¹⁵e^?76,600/RTsec^?1. Aspects of the kinetic mechanism are discussed and a system postulated to account for the high-temperature products.     

The galvanostatic double-pulse method in the study of the kinetics of stepwise electrode reactions

Analysis of the kinetics of the overall electrode reaction Me⁰ ? e^? = Me²⁺ proceeding through the three consecutive charge-transfer steps Me⁰ ? e^? = Me⁺ Me⁺ ? e^? = Me²⁺ Me²⁺ ? e^? = Me³⁺ involving non-adsorbed intermediates under transient single- and double-galvanostatic conditions has been made. Curves of η ? t were plotted and change of intermediate concentrations with time were calculated numerically for different ratios of exchange current densities. It is shown that when the time of reaching the steady-state, caused by the rate levelling of single-electron steps considerably exceeds the time of double-layer charging by the short duration current impulse, the employment of the galvanostatic double-pulse method allows the stepwise electrode process under non-stationary conditions to be investigated and information about the kinetics of the fastest steps in the reaction sequence to be obtained. Comparison of the conclusions of the analysis and experiment has been carried out by the galvanostatic double-pulse method in the stepwise electrode reaction Bi⁰ ?3 e^? = Bi(III) on an amalgam electrode in 2 M HClO₄ solutions.