On the Separation of Timescales in Chemically Activated Reactions

Chemically activated reactions are important in describing the composition of reactive gases including flames, planetary atmospheres, and the interstellar medium (ISM). In a chemically activated reaction, two reactants combine to populate a vibrationally excited well that can undergo unimolecular transformations (isomerization, dissociation) or be thermalized through collisions with the bath gas. Once a well has been thermalized, it may still have sufficient energy to undergo further unimolecular reaction, in a purely thermal process. If the timescale for the thermally activated process is sufficiently short, such that it approaches that of the chemically activated reaction, the two concurrent processes become inseparable and the value of the phenomenological rate coefficient is no longer obvious. Here, we introduce the thermal decay (TD) procedure to determine phenomenological rate coefficients for chemically activated reactions proceeding on timescales approaching those of thermal reaction, principally for use in stochastic master equation simulations of multiple‐well multiple‐channel unimolecular reaction processes. By fitting the thermal decay of the initially activated well to a first‐order kinetic model, the would‐be thermal yield can be eliminated so as to arrive at the chemically activated component in a reliable and objective fashion. This technique is demonstrated here for the reaction of 1,3,6‐heptatriyne with H using the MultiWell code and a 16‐well 33‐channel C₇H₅ reaction model. A computer program implementing the TD method and for postprocessing of MultiWell output data, PPM, is provided.     

Correlation of thermal and spectral properties of chromium(III) picolinate complex and kinetic study of its thermal degradation

Chromium(III) picolinate complex, namely [Cr(pic)₃]·H₂O, was prepared and characterized by the methods of the elemental analysis, infrared spectroscopy, X-ray diffraction, and thermal analysis (TG/DTG, DTA). The correlation of the thermal and spectral properties of the complex with its structure is discussed in the study. The correlation of the spectral data with the structure leads to the accord, and coherence was found between thermal properties and structure of the complex for both steps of the thermal decomposition (dehydration and pyrolysis of organic ligand). Activation parameters were evaluated using the theory of absolute reaction rate.     

The diffusion coefficient of H2S in liquid sulfur

The diffusion coefficient of H₂S in liquid sulfur is a key kinetic parameter that has been missing in literature. In this paper, a pressure decay method was applied to measure the diffusion coefficients of H₂S in liquid sulfur at 403 and 423 K. This pressure decay process was then modeled by taking the simultaneous diffusion and reversible chemical reactions between H₂S and liquid sulfur into consideration. The diffusion coefficients and reaction rate constants were numerically determined by fitting theoretical curves to experimental data using Finite Element Method and Genetic Algorithm. The solubility of H₂S in liquid sulfur at 403 and 423 K was also calculated and the results agreed with the semi-empirical correlation lately reported in literature. This study further extended the validity of the correlation to higher partial H₂S pressure conditions.     

Thermochemistry and Kinetics of the Thermal Decomposition of 1‐Chlorohexane

A theoretical kinetic study of the thermal decomposition of 1‐chlorohexane in gas phase between 600 and 1000 K was performed. Transition‐state theory and unimolecular reaction rate theory were combined with molecular information provided by quantum chemical calculations. Particularly, the B3LYP, BMK, M05–2X, and M06–2X formulations of the density functional theory (DFT) and the high‐level ab initio methods G3B3 and G4 were employed. The possible reaction channels for the thermal decomposition of 1‐chlorohexane were investigated, and the reaction takes place through the elimination of HCl with the formation of 1‐hexene. The derived high‐pressure limit rate coefficients are k _∞(600–1000 K) = (8 ± 5) × 10¹³ exp[‐((56.7 ± 0.4) kcal mol⁻¹/RT )] s⁻¹. The pressure effect over the reaction was analyzed from the calculation of the low‐pressure limit rate coefficients and the falloff curves. In addition, the standard enthalpies of formation at 298 K of −46.9 ± 1.5 kcal mol⁻¹ for 1‐chlorohexane and 5.8 ± 1.5 kcal mol⁻¹ for C₆H₁₃ radical were derived from isodesmic and isogiric reactions at high levels of theory.     

Some remarks on equilibrium state in dynamic condition

For dehydration of CaC₂O₄·H₂O and thermal dissociation of CaCO₃ carried out in Mettler Toledo TGA/SDTA-851^e/STAR^e thermobalance similar experimental conditions was applied: 9–10 heating rates, q = 0.2, 0.5, 1, 2, 3, 6, 12, 24, 30, and 36 K min⁻¹, for sample mass 10 mg, in nitrogen atmosphere (100 ml min⁻¹) and in Al₂O₃ crucibles (70 μl). There were analyzed changes of typical TGA quantities, i.e., T, TG and DTG in the form of the relative rate of reaction/process intended to be analyzed on-line by formula (10). For comparative purposes, the relationship between experimental and equilibrium conversion degrees was used (for P = P^\ominus P = P^{{\ominus}} ). It was found that the solid phase decomposition proceeds in quasi-equilibrium state and enthalpy of reaction is easily “obscured” by activation energy. For small stoichiometric coefficients on gas phase side (here: ν = 1) discussed decomposition processes have typical features of phenomena analyzable by known thermokinetic methods.     

Kinetics and dynamics study of the H + CCl4?��?HCl(v��, j��)?+?CCl3 reaction

Based on a previous potential energy surface describing the H?+?CCl₄ reaction, a new analytical surface named PES-2010 was developed modifying both the functional form to give it more flexibility, and the calibration process in which exclusively theoretical information was used. Thus, the surface is completely symmetric with respect to the permutation of the four methane chlorine atoms, and no experimental information is used in the process. For the kinetics, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 300?C2,500?K. The theoretical results reproduce the experimental variation with temperature. The influence of the tunneling factor is small, since the abstraction reaction involves the motion of a heavy particle (a chlorine atom) that cannot easily tunnel through the reaction barrier. The coupling between the reaction coordinate and the vibrational modes shows qualitatively that the HCl stretching mode in the products appears vibrationally excited. The dynamics study was performed using quasi-classical trajectory calculations, including corrections to avoid the zero-point energy problem. First, we found that the HCl(????, j??) product mostly appears with small rotational energy and vibrational population inversion. Second, the state-specific scattering distributions show backward scattering, which becomes more noticeable as the HCl(????) vibrational state increases. Unfortunately, no experimental dynamics data are available for the title reaction, but the comparison with the kinematically similar and well-studied H?+?Cl₂ reaction shows good agreement, indicative of similar mechanisms. These kinetics and dynamics results seem to indicate that the potential energy surface is adequate to describe this reaction, and the reasonable agreement with experiment lends further confidence to this new surface.     

Rate constant estimation for C1 to C4 alkyl and alkoxyl radical decomposition

Rate coefficients for alkyl and alkoxy radical decomposition are important in combustion, biological, and atmospheric processes. In this paper, rate constant expressions for C₁? C₄ alkyl and alkoxy radicals decomposition via β‐scission are recommended based on the reverse, exothermic reaction, the addition of a hydrogen atom or an alkyl radical to an olefin or carbonyl species with the decomposition reaction calculated using microscopic reversibility. The rate expressions have been estimated based on a wide‐range study of available experimental data. Rate coefficients for hydrogen atom and alkyl radical addition to an olefin show a strong temperature curvature. In addition, it is found that there is a correlation between the activation energy for addition and (i) the type of atom undergoing addition and (ii) whether this radical adds to the internal or terminal carbon atom of the olefin. Rate coefficients for alkoxy radical decomposition show a strong correlation to the ionization potential of the alkyl radical leaving group and on the enthalpy of reaction. It is shown that the activation energy for alkyl radical addition to a carbonyl species can be estimated as a function of the alkyl radical ionization potential and enthalpy of reaction. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 250–275, 2006     

The influence of the effective potential on the strong collision limiting low–pressure rate coefficients

The influence of the effective potential energy curves on the calculation of the strong collision limiting low-pressure rate coefficients of thermal dissociation-recombination reactions was analyzed in terms of the factorized formalism of Troe. An analysis of 26 reactions employing a Morse potential coupled with a quasitriatomic molecular model and an explicit account of the adiabatic zero-point barriers, as originallyproposed by Troe, was performed. A comparison between calculations realizedwith an exactly fitted looseness parameter, α, and with a standard value of α = 1.0 Å^?1, indicates that the use of this last value is satisfactorily justified in the evaluation of thestrong collision limiting low-pressure rate coefficients. A study interms of restrictive relationships between the looseness and Morse parameters and ab initio, radial potentials (for CH₄, CH₃O₂, and HO₂) was also realized. The uncertainties in the evaluation of termolecular rate coefficients due to the lack of a complete knowledge of the long-range potentials are also briefly discussed.     

Study on Apparent Kinetics of the Reaction between Sulfuric and Hydriodic Acids in the Iodine–Sulfur Process

The iodine–sulfur (IS) thermochemical process for hydrogen production is one of the most promising approaches in using high‐temperature process heat supplied by a nuclear reactor. This process includes three reactions that form a closed cycle: the Bunsen reaction, in which iodine, water, and sulfur dioxide react to form sulfuric acid and hydriodic acid (HI); HI decomposition; and sulfuric acid decomposition. However, the side reactions between H₂SO₄ and HI may disturb the operation of the IS closed cycle. For optimal process conditions, the reaction kinetics between H₂SO₄ and HI should be examined. In this work, a preliminary kinetic study was conducted. Using the initial reaction rate method, the kinetic parameters of the reaction between sulfuric acid and HI, such as the apparent reaction orders and rate constant were determined. For I^?, the apparent reaction order was approximately 1.77, whereas the orders for H⁺ and SO₄^2? were 7.78 and 1.29, respectively. The apparent rate constant at 85 ± 1°C was approximately 2.949 × 10^?11 min^?1 (mol/L)^?9.84. The H⁺ concentration had more significant influence on the reaction rate than those of SO₄^2? and I^?. Such basic data provide useful information for related process design and further kinetics study.     

Kinetics of non-isothermal decomposition of three IRGANOX-type antioxidants

In the present work a comparative kinetic study was performed on the thermal behavior of three antioxidants of IRGANOX-type (L101, L109 and L115) in dynamic air atmosphere under non-isothermal conditions. The TG-DTG data were obtained at heating rates of 5, 7, 10 and 15 K min⁻¹. The kinetic parameters were obtained by processing these data with strategies corresponding to Flynn-Wall-Ozava (FWO), Friedman (FR), Budrugeac-Segal (BS) and non-parametric kinetic (NPK) methods. The thermal degradation by all the three compounds take place in melted state, so that any kinetic models regarding the decomposition of solids are inapplicable. Only with the NPK method it was possible a separation between the two functions of the reaction rate. For the temperature dependence, f(T), an Arrhenius-type model was searched; for the conversion dependence, the Ŝestak-Berggren equation was suggested in order to discriminate between physical (m) and chemical (n or p) steps of a complex thermodegradation process.     

Designing a safer process for the reaction of TFA with sodium borohydride in THF by calorimetric technique

Reaction of TFA with sodium borohydride in THF is a loss of thermal control involving the evolution of Hydrogen gas. The investigation of the process by RC1e and ARSST showed that the criticality class of the reaction is dependant on the addition of TFA. Heat of reaction (Q _r), adiabatic temperature rise (ΔT _ad), and MTSR data are obtained from RC1e experiment. Exothermic onset temperature, Pressure rise, and self heat rate data are obtained from ARSST experiments. The correlation of these data was utilized to define the criticality class of the reaction under different conditions. The reaction with uncontrolled addition of TFA falls in the undesirable criticality class 5. Vent size data are obtained from the adiabatic calorimeter for undesirable reaction. The criticality class can be changed to class 2 with controlled addition. Accordingly, interlock system to control the undesired reaction and appropriate vent relief system are provided.     

Simulation approach to decomposition kinetics and thermal hazards of hexamethylenetetramine

The thermal stability of HMT under dynamic, isothermal and adiabatic conditions was investigated using differential scanning calorimeter (DSC) and accelerating rate calorimeter (ARC), respectively. It is found from the dynamic DSC results that the exothermic decomposition reaction appears immediately after endothermic peak, a coupling phenomenon of heat absorption and generation, and the endothermic peak and exothermic peak were indentified at about 277–289 and 279–296 °C (T_peak) with the heating rates 1, 2, 4 and 8 °C min⁻¹. The ARC results reveal that the initial decomposition temperature of HMT is about 236.55 °C, and the total gas production in decomposition process is 6.9 mol kg⁻¹. Based on the isothermal DSC and ARC data, some kinetic parameters have been determined using thermal safety software. The simulation results show that the exothermic decomposition process of HMT can be expressed by an autocatalytic reaction mechanism. There is also a good agreement between the kinetic model and kinetic parameters simulated based on the isothermal DSC and ARC data. Thermal hazards of HMT can be evaluated by carrying out thermal explosion simulations, which were based on kinetic models (Isothermal DSC and ARC) to predict several thermal hazard indicators, such as T_D24, T_D8, TCL, SADT, ET and CT so that we can optimize the conditions of transportation and storage for chemical, also minimizing industrial disasters.

     

Variations of Rate Coefficients and Termination Mechanism During the After‐Effects of a Light‐ Induced Polymerization of a Dimethacrylate Monomer

This work was aimed at studying variations in the termination mechanism occurring during the after‐effects of a light‐induced polymerization of a dimethacrylate monomer after the irradiation had been discontinued. The experimental method was based on differential scanning calorimetry. The initiation was stopped at various moments of the reaction corresponding to different degrees of double‐bond conversion (starting conversions). Three termination models: monomolecular, bimolecular, and mixed were used to calculate the ratio of the bimolecular termination and propagation rate coefficients k_t^b/k_p and/or the monomolecular termination rate coefficient k_t^m. The models were determined over short time intervals (conversion increments) of the dark reaction giving different values of rate coefficients for each time interval (interval approximation method). Two‐stage statistical analysis was used to find the model that best reproduced the experimental data obtained for each conversion increment. This enabled variations in the termination mechanism during the after‐effects to be followed. It was found that the termination mechanism changed with the time of the dark reaction from the bimolecular reaction to the mixed reaction when the light was cut off at low and medium double‐bond conversions. At higher starting conversions a monomolecular termination mechanism dominated from the beginning of the dark reaction. The mixed termination model was the only model to describe correctly the variations of rate coefficients in the dark, i. e., the increase in k_t^m and the decreasein the k_t^b/k_p ratio.     

Effect of gamma-radiation on thermal decomposition of bis(diethylene triamine)cobalt(II) nitrate and bis(diethylene triamine)zinc(II) nitrate

Effect of γ-radiation on non-isothermal decomposition kinetics of bis(diethylene triamine)cobalt(II) nitrate and bis(diethylene triamine)zinc(II) nitrate have been studied in nitrogen atmosphere at a heating rate of 10 °C/minute. The data were analyzed by Coats- Redfern, Freeman-Caroll and Horowitz-Metzeger methods. The result showed that irradiation enhanced thermal decomposition in both the complexes. Activation energy and associated kinetic parameters are lowered upon irradiation and the extent of lowering is higher in cobalt complex compared to zinc complex. Order of the reaction for each step was found to be unity. The mechanism for deamination and decomposition is controlled by R₂ function except for the deamination of unirradiated cobalt complex where the process is governed by R₃ function.     

Formation of H‐atoms in the pyrolysis of cyclohexane and 1‐hexene: A shock tube and modeling study

Cyclohexane (cC₆H₁₂) plays an important role in the combustion of practical liquid fuels, as a major component of naphthenic compounds. Therefore, the pyrolysis of cyclohexane was investigated by measuring the formation of H‐atoms. The thermal decomposition of 1‐hexene (1‐C₆H₁₂) was also studied, because of the assumption that 1‐hexene is the sole initial product of cyclohexane decomposition. For cyclohexane, the measurements were performed over a temperature range of 1320–1550 K, at pressures ranging from 1.8 to 2.2 bar; 1‐hexene experiments were done at temperatures between 1250 and 1380 K and pressures between 1.5 and 2.5 bar. For each experiment, the time‐dependent formation of H‐atoms was measured behind reflected shock waves by using the method of atomic resonance absorption spectrometry. For the dissociation of 1‐hexene to n‐propyl (C₃H₇) and allyl (C₃H₅) radicals, the following Arrhenius expression was derived: k_R2(T) = 2.3 × 10¹⁶ exp(?36,672 K/T) s^?1. For cyclohexane, overall rate coefficients (k_ov) were deduced for the global reaction cC₆H₁₂ → products + H from the H‐atom time profiles; the following temperature dependency was obtained: k_ov(T) = 4.7 × 10¹⁶ exp(?44,481 K/T) s^?1. For both sets of rate coefficient values, an uncertainty of ±30% is estimated. Especially concerning the isomerization cC₆H₁₂ → 1‐C₆H₁₂, our experimental results are in excellent agreement with the rate coefficient values given by Tsang (Tsang, W. Int J Chem Kinet 1978, 10, 1119–1138). A reaction model was assembled that is able to reproduce the H‐atom profiles measured for both sets of experiments. According to this model, H‐atoms are mostly stemming from the thermal decomposition of allyl radicals (C₃H₅), which arise from the decomposition of 1‐hexene. Furthermore, it will be shown that the recombination of allyl radicals with H‐atoms to propene (C₃H₆) also represents a very important subsequent reaction. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 43: 107–119, 2011     

Adsorption of U (VI) ions from aqueous solution using silicon dioxide nanopowder

The adsorption kinetics for removal of uranium (V1) from aqueous solution using silicon dioxide nanopowder (nano-SiO₂) was investigated in batch and continuous techniques. Pseudo-first order and pseudo-second order were used to analyze the kinetics of batch experiments. In continuous technique the important parameters (initial concentration, flow rate and bed height) on the breakthrough curves were studied and the adsorption kinetics was analyzed using Thomas and Yoon and Nelson kinetic models. The comparison between the kinetic models was evaluated by the correlation coefficients (r²). The results indicated that the batch experiments fitted well with pseudo second-order kinetic model. The comparison of the experimental breakthrough curve to the breakthrough profile obtained from Thomas and Yoon and Nelson methods showed a satisfactory fit for silicon dioxide nanopowder.     

Structural characterization and prediction of Kovats retention indices (RI) for alkylbenzene compounds

A new molecular structural characterization (MSC) method called the molecular vertex eigenvalue correlative index (MVECI) is constructed and used to describe the structures of 122 alkylbenzene compounds. Through multiple linear regression (MLR) and stepwise multiple regression (SMR), a quantitative structure-retention relationship (QSRR) model with correlation coefficient (R) of 0.995 is obtained. Through partial least-square regression (PLS), another QSRR model with correlation coefficient (R) of 0.991 is obtained. The estimation stability and prediction ability of the two models are strictly analyzed by both internal and external validations. For the internal validation, the cross-validation (CV) correlation coefficients (R _CV) of the two models are 0.993 and 0.988. For the external validation, the correlation coefficients (R _test) of the two models are 0.996 and 0.995, respectively. The results show that the stability and predictability of the models are good, and the molecular vertex eigenvalue correlative index can successfully describe the structures of alkylbenzene compounds.     

Effect of oxygen activity in the gaseous phase on the mechanism of reactions in the solid-state synthesis of In<Subscript>2</Subscript>(WO<Subscript>4</Subscript>)<Subscript>3</Subscript> and In<Subscript>6</Subscript>WO<Subscript>12</Subscript>

The effect of oxygen’s activity on the rate of In₂(WO₄)₃ and In₆WO₁₂ formation reactions was studied to determine the reaction mass transfer mechanism. It was established that the formation of In₂(WO₄)₃ in a model reaction cell is due to the transfer of WO ₄ ^2? components and electrons moving in opposite directions through the reaction product. The relation between the diffusion coefficients of the carriers was found. The rate of electron diffusion and the reaction rate were shown to vary according to the law \(K_p \approx D_{\lim } = D_e \sim a_{O_2 }^{ - 1/4} \). We conclude that the formation of electronic conductor In₆WO₁₂ is a two-region process: at the In₂(WO₄)₃ | In₆WO₁₂ interface, the product is formed on the In₂(WO₄)₃ surface due to {WO₃} escaping toward In₂O₃, and at the In₆WO₁₂ | In₂O₃ interface, the product is formed on the In₂O₃ surface via the reaction of diffuse {WO₃} with In₂O₃. The probable relationship between the diffusion coefficients of the In₆WO₁₂ components was obtained. A relation was developed for the process rate. The diffusion coefficients for the limiting component were calculated using the data on the estimated thickness of the product layers.     

Spontaneous Thiono-Thiolo Isomerization of Thiono-Phosphates. Does it Appear without Impurities?

Abstract

Thiono-thiolo isomerization of 0-alkyl esters of thiophosphoric acids to corresponding S-alkyl isomers has been extensively studied because of high biological acivity of both esters. Such an isomerization proceeding without other reactants initially added is called thermal isomerization. Kinetic studies of this process allow to distinguish between reaction pathways of methyl esters A₂P(S)OMe leading only to S-methyl esters and of diesters AP(S)(OMe)₂, which give also other products. It is well known that the isomerization can be effected by organic bases (amines, phosphines), corresponding alkylonium thiophosphates, and protic acids. We decided to investigate the kinetics of thermal isomerization in solutions, to examine the influence of impurities of reactants or solvents for thiophosphates studied up to now appear to be not thoroughly purified. O,O-Diphenyl-0-methylthiophosphate, 5,5-dimethyl-2-methoxy-2-thio-l,3,2-dioxaphos-phosphorinane and O,O-dimethyl-O-(4-nitro)phenylthiophosphate as model reactants and benzonitrile or 1-methylnaphtalene as solvents were chosen. We have found that the observed first-order rate constants k of the isomerization reaction significantly decreases (even 1000 times) with improving the purity of either the reactant or the solvent. The k values we could obtained may be considered to be the rate constant of either the thermal isomerization or the isomerization caused by residual impurities. For all the thiono-phosphate studied the activation energies of the thermal isomerization and the isomerization reaction with corresponding tetramethylammonium thiophosphates are practically the same. We believe that our findings may be of significant importance against the spontaneous isomerization of the thionophosphates studied.