The mechanism of thermal decomposition of ionic oxalates

A mechanism for the thermal decomposition of ionic oxalates has been proposed on the basis of three quantitative relationships linking the quantitiesr _c/r _i (the ratio of the Pauling covalent radius and the cation radius of the metal atom in hexacoordination) andΣI _i (the sum of the ionization potentials of the metal atom in kJ mol^?1) with the onset oxalate decomposition temperature (T _d) (Eq. 1) the average C-C bond distance (¯d) (Eq. 2), and the activation energy of oxalate decomposition (E _a) (Eq. 3): (1) $$T_d = 516 - 1.4006\frac{{r_c }}{{r_i }}(\sum I_i )^{\frac{1}{2}}$$ (2) $$\bar d = 1.527 + 5.553 \times 10^{ - 6} \left( {122 - \frac{{r_c }}{{r_i }}(\sum I_i )^{\frac{1}{2}} } \right)^2$$ (3) $$E_a = 127 + 1.4853 \times 10^{ - 6} \left( {\left( {\frac{{r_c }}{{r_i }}} \right)^2 \sum I_i - 9800} \right)^2$$ On the basis of these results it is proposed that the thermal decomposition of ionic oxalates follows a mechanism in which the C-O bond ruptures first. From Eq. 3 it is further proposed that strong mutual electronic interactions between the oxalate and the cations restrict the essential electronic reorganization leading to the products, thereby increasingE _a.     

DSC study of the decomposition of azodicarbonamide in different media

The decomposition of azodicarbonamide (Genitron AC-2) in the solid state was investigated by DSC. It was found that the decomposition under non-isothermal conditions can be described by the autocatalytic reaction scheme $$X\xrightarrow{{k_1 }}Y,X + Y\xrightarrow{{k'_2 }}2Y$$ where the following dependences hold for the rate constants: $$k_1 = 4.8 \times 10^{19} e - {{243 600} \mathord{\left/ {\vphantom {{243 600} {RT_s - 1}}} \right. \kern-\nulldelimiterspace} {RT_s - 1}}$$ and $$k'_2 = 1.0 \times 10^{13} e - {{133 500} \mathord{\left/ {\vphantom {{133 500} {RT_s - 1}}} \right. \kern-\nulldelimiterspace} {RT_s - 1}}$$ The first pre-exponential factor includes the thermal history of the sample, especially the quick heating to a certain temperature, from which normal slow heating starts. Due to this fast heating, the decomposition reaction of AZDA may be understood as the collapse of its crystal lattice into nucleation centres with critical dimensions.     

Bounds for the Kirchhoff index via majorization techniques

Using a majorization technique that identifies the maximal and minimal vectors of a variety of subsets of ${\mathbb{R}^{n}}$ , we find upper and lower bounds for the Kirchhoff index K(G) of an arbitrary simple connected graph G that improve those existing in the literature. Specifically we show that $$K(G) \geq \frac{n}{d_{1}} \left[ \frac{1}{1+\frac{\sigma}{\sqrt{n-1}}} + \frac{(n-2)^{2}}{n-1-\frac{\sigma}{\sqrt{n-1}}}\right] ,$$ where d ₁ is the largest degree among all vertices in G, $$\sigma ^{2} = \frac{2}{n} \sum_{(i, j) \in E} \frac{1}{d_{i}d_{j}} = \left( \frac{2}{n}\right) R_{-1}(G),$$ and R _?1(G) is the general Randi? index of G for ${\alpha =-1}$ . Also we show that $$K(G) \leq \frac{n}{d_{n}}\left( \frac{n-k-2}{1-\lambda _{2}}+\frac{k}{2}+\frac{1}{\theta}\right) ,$$ where d _n is the smallest degree, ${\lambda _{2}}$ is the second eigenvalue of the transition probability of the random walk on G, $$k = \left \lfloor \frac{\lambda _{2} \left( n-1\right) +1}{\lambda _{2}+1}\right\rfloor {\rm and}\quad\theta = \lambda _{2} \left( n-k-2\right) -k+2.$$      

Supersymmetry and the Hartmann potential of theoretical chemistry

An exactly solvable ring-shaped potential in quantum chemistry given by $$V = \eta \sigma ^2 \varepsilon _{\text{o}} \left( {\frac{{2a_{\text{O}} }}{r} - \frac{{\eta a_{\text{O}}^2 }}{{r^2 {\text{sin}}^{\text{2}} \theta }}} \right)$$ was introduced by Hartmann in 1972 to describe ring-shaped molecules like benzene. In this article, the supersymmetric features of the Hartmann potential are discussed, We first review the results of a previous paper in which we rederived the eigenvalues and radial eigenfunctions of the Hartmann potential using a formulation of one-dimensional supersymmetric quantum mechanics (SUSYQM) on the half-line [0, ∞). A reformulation of SUSYQM in the full line (? ∞, ∞) is subsequently developed. It is found that the second formulation makes a connection between states having the same quantum number L but different values of ησ2 and quantum number N. This is in contrast to the first formulation, which relates states with identical values of the quantum number N and ησ2 but different values of the quantum number L.     

New approximate formula for the generalized temperature integral

A new procedure to approximate the generalized temperature integral $ \int_{0}^{T} {T^{m} {\text{e}}^{ - E/RT} } {\text{d}}T, $ which frequently occurs in non-isothermal thermal analysis, has been developed. The approximate formula has been proposed for calculation of the integral by using the procedure. New equation for the evaluation of non-isothermal kinetic parameters has been obtained, which can be put in the form: $$ \ln \left[ {{\frac{g(\alpha )}{{T^{(m + 2)0.94733} }}}} \right] = \left[ {\ln {\frac{{A_{0} E}}{\beta R}} - (m + 2)0.18887 - (m + 2)0.94733\ln {\frac{E}{R}}} \right] - (1.00145 + 0.00069m){\frac{E}{RT}} $$ The validity of the new approximation has been tested with the true value of the integral from numerical calculation. Compared with several published approximation, the new one is simple in calculation and retains high accuracy, which indicates it is a good approximation for the evaluation of kinetic parameters from non-isothermal kinetic analysis.     

Half-width and asymmetry of glow peaks and their consistent analytical representation

The kinetic equation which describes many electronic as well as atomic or chemical reactions under the condition of a steadily linear raise of the temperature, is considered in a mathematically exact and straightforward way. Therefore, the equation has been transformed into a dimensionsless form, using with profit the maximum condition for the intensity peak. The two temperatures T₁ and T₂, corresponding to the half-height of the intensity peak, are found as unique polynomials of the small argument \(\bar y \equiv {{k\bar T} \mathord{\left/ {\vphantom {{k\bar T} E}} \right. \kern-0em} E}\) only ( \(\bar T\) =temperature of peak maximum). Thereupon, further combinations give half-widthδ, peak asymmetryA=δ₂/δ₁ or \(\tilde A = {{\bar C} \mathord{\left/ {\vphantom {{\bar C} {(1 - \bar C)}}} \right. \kern-0em} {(1 - \bar C)}}\) and the maximum of the intensity peakJ; they again all depend only on¯y. In some cases this dependence is weak, so that e.g. it is deduced that the half-width energy product divided by \(\bar T^2 \) is an invariant, different for every kinetic orderπ: $$\frac{{\delta \cdot E[eV]}}{{\bar T^2 }} = \left\{ {\begin{array}{*{20}c} {{1 \mathord{\left/ {\vphantom {1 {4998 K for monomolecular process}}} \right. \kern-\nulldelimiterspace} {4998 K for monomolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {3542 K for bimolecular process}}} \right. \kern-\nulldelimiterspace} {3542 K for bimolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {2872 K for trimolecular process}}} \right. \kern-\nulldelimiterspace} {2872 K for trimolecular process}}} \\ \end{array} } \right.$$ By means of these correlations, activation energy valuesE [eV] can be determined accurately to within 0.5 %, so that for most experiments the inaccuracy of theδ values becomes dominant and limiting. A special nomogram for the express estimation ofE from experimentally observedδ and \(\bar T\) is demonstrated.     

Special features of the compensation effect in non-isothermal kinetics of solid-phase reactions

The appearance of the compensation effect (logA=a+bE) in non-isothermal kinetics of solid-phase reactions is discussed. An analytical expression of the compensation effect is derived in the form $$InA = In\frac{{E\left( {\frac{{dT}}{{dt}}} \right)_s }}{{RT_s^2 }} + \frac{E}{{RT_s }}$$ It is demonstrated that the compensation effect appears in a number of chemical reactions if theT _s and rate constant values are close. Experimental data confirm the theoratical discussion.     

A solution of the exponential integral in the non-isothermal kinetics for linear heating

A simple and satisfactorily accurate solution of the exponential integral in the nonisothermal kinetic equation for linear heating is proposed: $$\mathop \smallint \limits_0^T e^{ - E/RT} dT = \frac{{RT^2 }}{{E + 2RT}}e^{ - E/RT} $$      

A contribution to Semenov's general theory of thermal ignition regarding thermal analysis

The general theory of thermal ignition under the conditions of thermal analysis of flammable substances is discussed. For a linear heating rate of the specimen the ignition temperature is obtained from the relationship $$(dT/dt)_b - \frac{q}{{(dT/dt)_b }} = \frac{E}{{RT_b^2 }}(T_b - T_c^\prime )$$ whereT′_c is the temperature of the reactor wall (heated at the rateq) at the starting moment of the development of the thermal explosion.     

Effects of washing conditions on the thermal decomposition behaviour of gelled UO3 microspheres

DTA, TG and DTG curves obtained in various atmospheres using different heating rates were used together with X-ray examinations to study the thermal decomposition mechanisms of two types of gelled UO₃ microspheres: ammonia-washed (UN) and hot water-washed (UH) microspheres. The kinetics of the thermal decompositions were studied. The specific reaction rate constantk _r for the decomposition of UO₃ to U₃O₈ could be expressed in terms of the activation energy and the pre-exponential factor by the expressions: $$\begin{gathered} K_r (s^{ - 1} ) = 1.277 \times 10^{18} \exp \frac{{ - 295.4}}{{RT}}for the UN spheres, \hfill \\ K_r (s^{ - 1} ) = 8.406 \times 10^{19} \exp \frac{{ - 263.2}}{{RT}}for the UH spheres. \hfill \\ \end{gathered} $$      

Synthesis,thermal behavior,and application of 4-amino-3,5-dinitropyrazole lead salt

Lead salt of 4-amino-3,5-dinitropyrazole (PDNAP) was synthesized from 4-amino-3,5-dinitropyrazole by the process of metathesis reaction, and its structure was characterized by IR, element analysis, TG, and DSC. The thermal decomposition kinetics and mechanism were studied by means of different heating rate differential scanning calorimetry (DSC) and thermolysis in situ rapid-scan FTIR simultaneous. The effects of PDNAP as an energetic combustion catalyst on the combustion performance of the solid propellant were studied. The results show that the peak temperature is 319.2 °C on DSC curve. The kinetic equation of major exothermic decomposition reaction is $ \frac{{\text{d}}\alpha}{{\text{d}}T} = \frac{{10^{15.45} }}{\beta }4(1 - \alpha )[ - \ln \left( {1 - \alpha } \right)]^{{{3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-0pt} 4}}} \exp ({{ - 1.972 \times 10^{5} } \mathord{\left/ {\vphantom {{ - 1.972 \times 10^{5} } {RT}}} \right. \kern-0pt} {RT}}). $ The PDNAP is shown by IR spectroscopy to convert to PbO during the decomposition process. Combustion experiments show PDNAP can reduce the burning rate pressure exponent of the double-base or composite-modified double-base propellant.     

Thermochemische und kinetische Untersuchungen der endothermen Umbildungsreaktionen des Epsomits (MgSO4 · 7H2O)

Heterogeneous decompositions of MgSO₄ · 7H₂O (Epsomite) monocrystals were studied with thermal (DTA, DSC, TG) and thermo-optical methods. The polythermal reaction is controlled by nucleation of the reactant. This process has been considered by the Avrami-Erofe'ev equation: $$kt = [ - \ln (1 - \alpha )]^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$3$}}} $$ The plots and the slope which give the activation energyE+=23.5 kcal/mole (760 Torr N₂, 50–100°), are obtained from the Freeman-Carroll equation. The DSC technique was used to determine the heat of decomposition (ΔH=42.3 kcal/mole, 760 Torr N₂, 50–100°). The heat of transformation for the reaction 39–47° $$MgSO_4 \cdot 7H_2 O\xrightarrow{{39 - 47^ \circ }}MgSO_4 \cdot 6H_2 O + H_2 O$$ wasΔH=2.8 kcal/mole. The isothermal reaction (20°, 10^?6 Torr) is controlled by first-order kinetic.     

Determination of the kinetic constants of endothermic decompositions of the type Asol f Bsol + Cgas

The present work describes the endothermic decompositions of calcium carbonate and nickel carbonate, recorded on a MOM derivatograph in the non-isothermal mode at different heating rates. The possibility and advantages of determining the kinetic parametersE, Z, andn for reactions proceeding in one step, as well as the detection of simultaneous (parallel or concurrent) reactions in the decomposition process, are discussed. The results obtained permit the conclusion that the thermal decomposition of calcite occurs in one step. In this case, the kinetic equation has the following form: $$\lg \left[ {\frac{{d\alpha }}{{(1 - \alpha )^n }}} \right] = \lg \frac{Z}{q} - \frac{E}{{2.3R}} \cdot \frac{1}{T}$$ where f(α)=(1?α)ⁿ,n=0.3, andE=176.8 kJ/mol. In the case of nickel carbonate the results of treating the experimental data have been obtained only in the graphical form. From the shape of the curves obtained, it is clearly seen that the decomposition of nickel carbonate in open air proceeds in several steps (i.e. several simultaneous reactions take place), which cannot be described by the equations for a one-step reaction.     

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.     

Determination of kinetics of supercooled Β-phase decomposition in cast ZnAl8Cu2 alloy

Temperature changesT ₁ (Τ) of a sample during the decomposition of theΒ-phase of ZnAl8Cu2 alloy supercooled from 360?, and the cooling curveT ₂ (Τ) from about 100? were determined. The cooling curve shows temperature changes of the sample in which no transformation proceeds. From the heat balance and courses of the curvesT ₁ (Τ) andT ₂ (Τ), the temperature changesT ₃ (Τ) of the sample were determined, under adiabatic conditions. On the assumption that the capacity is constant, the following relationship arises: $$T_3 (\tau ) = T_1 (\tau ) - \int\limits_0^\tau {\left( {\frac{{dT_2 }}{{d\tau }}} \right)d\tau } T_2 = T_1 (\tau )$$ The degree of transformationx (Τ) was determined from the temperature changesT ₃ (Τ). The transformation rate constantK and transformation enthalpy were calculated. A valueδH=34.0 J/g was obtained. The method used seems to be of value for phase changes characterized by a relatively large heat effect and an intensive course.     

Densities,Refractive Indices,Ultrasonic Speeds and Excess Properties of Acetonitrile + Poly(ethylene glycol) Binary Mixtures at Temperatures from 298.15 to 313.15 K

The densities, ρ, refractive indices, n _D, and ultrasonic speeds, u, of binary mixtures of acetonitrile (AN) with poly(ethylene glycol) 200 (PEG200), poly(ethylene glycol) 300 (PEG300) and poly(ethylene glycol) 400 (PEG400) were measured over the entire composition range at temperatures (298.15, 303.15, 308.15 and 313.15) K and at atmospheric pressure. From the experimental data, the excess molar volumes, \( V_{\text{m}}^{\text{E}} \) , deviations in refractive indices, \( \Delta n_{\text{D}} \) , excess molar isentropic compressibility, \( K_{{s , {\text{m}}}}^{\text{E}} \) , excess intermolecular free length, \( L_{\text{f}}^{\text{E}} \) , and excess acoustic impedance, Z ^E, have been evaluated. The partial molar volumes, \( \overline{V}_{\text{m,1}} \) and \( \overline{V}_{\text{m,2}} \) , partial molar isentropic compressibilities, \( \overline{K}_{{s , {\text{m,1}}}} \) and \( \overline{K}_{{s , {\text{m,2}}}} \) , and their excess values over whole composition range and at infinite dilution have also been calculated. The variations of these properties with composition and temperature are discussed in terms of intermolecular interactions in these mixtures. The results indicate the presence of specific interactions among the AN and PEG molecules, which follow the order PEG200 < PEG300 < PEG400.     

Electron capture by protons from theK-shell of H and Ar

Whenever a collision takes place between charged particles, the first Born approximation for electron capture from hydrogenlike ions (Z _T ,e) by a bare nucleusZ _P , must be modified in order to account for the long-range Coulomb effects. One of the simplest ways to fulfill this requirement is provided by theT-matrix of the following form: $$T_{if}^{(1)} = \left\langle {\Phi _f exp\left\{ { - i\frac{{Z_T (Z_p - 1)}}{\upsilon } ln (\upsilon R + v \cdot R)} \right\}\left| {\frac{{Z_P }}{R} - \frac{{Z_P }}{{r_P }}} \right| exp\left\{ {i\frac{{Z_P (Z_T - 1)}}{\upsilon } ln (\upsilon R + v \cdot R)} \right\}\Phi _i } \right\rangle $$ where Φ's are the usual unperturbed channel states andZ's are the nuclear charges. In this transition amplitude, both initial and final scattering states satisfy the correct asymptotic boundary conditions in their respective channels. In the present paper, detailed computation of theK-shell cross sections is carried out for charge exchange in H⁺-H and H⁺-Ar collisions. The results are in good agreement with experimental data.     

Formalkinetische Behandlung des Masseverlustes bei thermischen Abbauprozessen von Polymeren unter nichtisothermen Bedingungen

On the basis of the formal basic relation $$\frac{{d\alpha }}{{dt}} = A \cdot e^ - \frac{E}{{RT}}(1 - \alpha )^n $$ methods of calculating kinetic values from non-isothermal thermogravimetric curves have been critically evaluated. It has been established that in general integral methods are preferable to differential methods. Methods basing on a series expansion of the exponential integral $$\int\limits_0^T {e^ - \frac{{ET}}{{RT}}} dT$$ are applicable without limitations to any cases. It has been concluded that the integral method suggested by Zsakó is the most reliable.     

Improved approximations of the exponential integral in tempering kinetics

The exponential integral in non-isothermal kinetic equations for tempering with linear heating can be represented in the following analytical form $$\int\limits_0^T {e^{ - E/kT'} dT'} = \frac{{kT^2 /E}}{{\sqrt {1 + 4kT/E} }}e^{ - E/kT} ,$$ which is one order inkT/E?1 more accurate than two other representations recently proposed in this journal [1, 2]. A few variants of approximated forms for the exponential integral are compared with regard to the error due to the kind of approximation, which appears when activation energies are evaluated from experimental non-isothermal kinetic curves.