非等温反应过程中新的动力学方程

对于非等温过程中的动力学方程，正确的Arrhenius方程的温度积分应该是从T₂到T₁，但是许多动力学方程中的温度积分是从T到0 K，例如Ozawa等方程。我们的研究指出对于某些反应，这些方程中的活化能存在较大的误差，因此我们提出了一个新的动力学方程。凭借等转化率法，应用新的方程可以精确求解线性或非线性加热过程中化学反应的活化能。用新方程对2个经典反应（聚酰胺的热裂解和一水草酸钙的热分解）的研究表明：Ozawa方程的活化能有时是精确的，有时偏差太大。     

Kinetics and Mechanism of the Reactions Between Triphenylphosphine,Dialkyl Acetylenedicarboxilates and a NH-Acid,Pyrazole, by UV Spectrophotometry

Kinetic studies were made of the reactions between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of a NH-acid such as pyrazole. To determine the kinetic parameters of the reactions, the reaction progress was monitored by UV spectrophotometry. The second-order fits were automatically drawn and the values of the second-order rate constant (k ₂) were automatically calculated using standard equations. In the temperature range studied, the dependence of ln k ₂ on the reciprocal temperature was consistent with the Arrhenius equation. Furthermore, useful information was obtained from studies of the effect of solvent, structure of the reactants (different alkyl groups within the dialkyl acetylenedicarboxylates), and also the concentration of reactants on the rate of reaction. The mechanism was confirmed to involve a steady-state condition with the first step of the reaction being the rate-determining step.     

Checking of mathematical calculation methods for the determination of kinetic parameters from non-isothermal measurements by test functions

The applied computing programs are checked by means of test values from theoretical models. First-order kinetics, the Avrami equation and the 2-dimensional diffusion equation have been calculated as theoretical values. The computer calculation was carried out both for the total reaction and for individual reaction intervals.For the calculation of kinetic parameters and the distinction between the various models, in principle, the integral method should be used. The calculation does not give any answer to the question whether there exists another equation not involved in the models selected, which describes the processes better. If there is no indication of the reaction, it should first be checked by the differential method. The correlation coefficient does not allow the individual model equations to be distinguished with statistical significance.     

大柴旦富硼浓缩盐卤中硼酸镁盐稀释结晶动力学

采用动力学法研究了富硼浓缩盐卤稀释过程硼酸镁盐的结晶动力学,重点探讨了温度、稀释比和硼浓度对结晶过程的影响。利用单纯形优化法配合Runge-Kutta微分方程组数值解法对实验数据进行拟合,给出了结晶动力学方程和结晶速率。结果表明,低温、高硼浓度和中间稀释比有利于硼酸镁盐的结晶析出,最优条件下析硼率(以B_2O_3计)高达88%;结晶速率随硼浓度的增加和温度的降低快速增大;反应级数表明稀释结晶过程硼酸镁盐结晶主要受多核表面反应控制,同时提出了结晶相转化机理。     

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

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 CaC₂O₄ · H₂O. The kinetic parameters calculated using all four equations showed a systematic trend and the results can be expressed as E(or log A) = $\text{constant}\text{heating rate}$ + $\text{constant}\text{mass}$ + constant     

Enzymatic hydrolysis of protein: Mechanism and kinetic model

The bioreaction mechanism and kinetic behavior of protein enzymatic hydrolysis for preparing active peptides were investigated to model and characterize the enzymatic hydrolysis curves. Taking into account single-substrate hydrolysis, enzyme inactivation and substrate or product inhibition, the reaction mechanism could be deduced from a series of experimental results carried out in a stirred tank reactor at different substrate concentrations, enzyme concentrations and temperatures based on M-M equation. An exponential equation dh/dt = aexp(-bh) was also established, where parameters a and b have different expressions according to different reaction mechanisms, and different values for different reaction systems. For BSA-trypsin model system, the regressive results agree with the experimental data, i.e. the average relative error was only 4.73%, and the reaction constants were determined as K _m = 0.0748 g/L, K _s = 7.961 g/L, k _d = 9.358/min, k ₂ = 38.439/min, E _a = 64.826 kJ/mol, E _d = 80.031 kJ/mol in accordance with the proposed kinetic mode. The whole set of exponential kinetic equations can be used to model the bioreaction process of protein enzymatic hydrolysis, to calculate the thermodynamic and kinetic constants, and to optimize the operating parameters for bioreactor design. __________ Translated from Journal of Tianjin University, 2005, 38(9) (in Chinese)     

Finite-difference model for the reaction sintering of oxide ceramics by direct oxidation of intermetallic powder compacts

A kinetic model for the reaction sintering of oxide ceramics in the system Al₂O₃–SiO₂–ZrO₂ using mixtures of intermetallic compounds is presented. A 2D finite-difference model is developed to describe the exothermic gas-solid reactions taking place during the firing of ZrAl₃/ZrSi₂ powder compacts. The model accounts for the oxidation kinetics of the powder particles, as well as the consumption and diffusion of gaseous oxygen through the porous matrix. Additionally, possible changes in the pore structure of the green body due to the oxidation reactions and sintering effects are incorporated in the model. The resulting differential equations are coupled with a two-dimensional Fourier heat balance equation leading to a system of nonlinear partial differential equations, which is solved by the numerical method of lines. The influence of different processing parameters like sample composition and heating cycle on the reaction sintering process is investigated and the model-predicted reaction behaviour is compared to experimental results.     

Kinetics of the exothermic decomposition of 1-nitro-3-(β,β,β-trinitroethyl)-4,5-dinitroiminoimidazolidine-2-one

The kinetic parameters of the exothermic decomposition of the title compound in a temperatureprogrammed mode have been studied by means of DSC. The DSC data obtained are fitted to the integral, differential, and exothermic rate equations by the linear least-squares, iterative, combined dichotomous, and least-squares methods, respectively. After establishing the most probable general expression of differential and integral mechanism functions by the logical choice method, the corresponding values of the apparent activation energy (E _a), preexponential factor (A), and reaction order (n) are obtained by the exothermic rate equation. The results show that the empirical kinetic model function in differential form and the values of E _a and A of this reaction are (1 − α)^−4.08, 149.95 kJ mol⁻¹, and 10^14.06 s⁻¹, respectively. With the help of the heating rate and kinetic parameters obtained, the kinetic equation of the exothermic decomposition of the title compound is proposed. The critical temperature of thermal explosion of the compound is 155.71°C. The above-mentioned kinetic parameters are quite useful for analyzing and evaluating the stability and thermal explosion rule of the title compound. The text was submitted by the authors in English.     

Kinetics of metal exchange in Cd(II) octa(4-bromophenyl)porphyrinate with <Emphasis Type="Italic">d</Emphasis>-metal salts in organic solvents

The reaction of metal exchange between Cd(II) octa(4-bromophenyl)porphyrinate with СuCl₂ and ZnCl₂ in DMFA and DMSO is studied by means of spectrophotometry. The kinetic parameters of the metal exchange reaction are calculated, a stoichiometric reaction mechanism is proposed. The effect the natures of the solvent, salt solvate, and the chemical modification of tetrapyrrole macrocycle have on the kinetic parameters of the metal exchange reaction are revealed.     

Curing reaction of biphenyl epoxy resin with different phenolic functional hardeners

The investigation of cure kinetics and relationships between glass transition temperature and conversion of biphenyl epoxy resin (4,4′-diglycidyloxy-3,3′,5,5′-tetramethyl biphenyl) with different phenolic hardeners was performed by differential scanning calorimeter using an isothermal approach over the temperature range 120–150°C. All kinetic parameters of the curing reaction including the reaction order, activation energy, and rate constant were calculated and reported. The results indicate that the curing reaction of formulations using xylok and dicyclopentadiene type phenolic resins (DCPDP) as hardeners proceeds through a first-order kinetic mechanism, whereas the curing reaction of formulations using phenol novolac as a hardener goes through an autocatalytic kinetic mechanism. The differences of curing reaction with the change of hardener in biphenyl epoxy resin systems were explained with the relationships between T_g and reaction conversion using the DiBenedetto equation. A detailed cure mechanism in biphenyl-type epoxy resin with the different hardeners has been suggested. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 773–783, 1998     

Curing reaction of o-cresol novolac epoxy resin according to hardener change

The investigations of cure kinetics and glass transition temperature (T_g) versus reaction conversion (α) of o-cresol novolac epoxy resin with the change of hardener were performed. All kinetic parameters of the curing reaction such as the reaction rate order, activation energy, and frequency factor were calculated. The curing mechanisms were classified into two types. One was an autocatalytic mechanism and the other was a nth order kinetic mechanism. The constants related to the chain mobility of polymer segments were obtained by using the DiBenedetto equation. We have tried to correlate the relationships between curing mechanism and molecular structures of hardeners from these results. © 1993 John Wiley & Sons, Inc.     

The Kinetic Study of Copolymerization of Acrylonitrile with Allyl Alcohol in Concentrated Zinc Chloride Aqueous Solution with the Aid of a Computer

This paper presents a kinetic study of the copolymerization of acrylonitrile (AN, M₂) with allyl alcohol (AOH, M₂) in zinc chloride aqueous solution. The monomer reactivity ratios, r₁ and r₂, determined by application of the Lewis-Mayo equation to the system, are 1.60 and 0.01, respectively. The observed value of copolymer composition agrees well with one calculated by use of computer up to higher conversion. This means that the Lewis-Mayo equation may be applicable to the present system. The possibility of homopolymerization of AOH, confirmed empirically, is also sustained by numerical calculation.     

UV spectrophotometric study of the kinetics and mechanism of the reactions between triphenylphosphine, dialkyl acetylenedicarboxylates and NH-acid

To determine the kinetic parameters of the reactions between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of an NH-acid, such as 2,3-di-hydroxybenzaldehyde, the reactions were monitored by UV spectrophotometry. The second order fits were automatically drawn and the values of the second order rate constants (k₂) were calculated using standard equations as part of the program. The dependence of the second order rate constant (lnk₂) on the reciprocal temperature was in agreement with the Arrhenius equation, in the temperature range studied, providing the relevant plots to calculate the activation energy of all reactions. Furthermore, we evaluated the effects of solvent, structure of different alkyl groups within the dialkyl acetylenedicarboxylates, and their concentration on the rates of reactions. The proposed mechanism was confirmed by experimental results and steady-state approximation. The first step (k₂) of the reaction was recognized as the rate determining step on the basis of experimental data.     

Kinetic Analysis of Thermal Decomposition of Ca(OH)2 Formed During Hydration of Commercial Portland Cement by DSC

In this paper, evaluation of kinetic parameters (the activation energy – E,the pre-exponential factor – A and the reaction order – n) with simultaneous determination of the possible reaction mechanism of thermal decomposition of calcium hydroxide (portlandite), Ca(OH)₂ formed during hydration of commercial Portland-slag cement, by means of differential scanning calorimetry (DSC) in non-isothermal conditions with a single heating–rate plot has been studied and discussed. The kinetic parameters and a mechanism function were calculated by fitting the experimental data to the integral, differential and rate equation methods. To determine the most probable mechanism, 30 forms of the solid-state mechanism functions, f(α_c) have been tried. Having used the procedure developed and the appropriate program support, it has been established that the non-isothermal thermal decomposition of calcium hydroxide in the acceleratory period (0.004<α_c<0.554) can be described by the rate equation: d α_c/dT=A/βexp(−E/RT)f(α_c), which is based on the concept of the mechanism reaction:f(α_c)=2(α_c)^1/2. The mechanism functions as well as the values of the kinetic parameters are in good agreement with those given in literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal and kinetic analysis of uranium salts

The thermal decomposition kinetics of UO₂C₂O₄·3H₂O were studied by TG method in a flowing nitrogen, air, and oxygen atmospheres. It is found that UO₂C₂O₄·3H₂O decomposes to uranium oxides in four stages in all atmosphere. The first two stages are the same in the whole atmosphere that correspond to dehydration reactions. The last two stages correspond to decomposition reactions. Final decomposition products are determined with X-Ray powder diffraction method. Decomposition mechanisms are different in nitrogen atmosphere from air and oxygen atmosphere. The activation energies of all reactions were calculated by model-free (KAS and FWO) methods. For investigation of reaction models, 13 kinetic model equations were tested and correct models, giving the highest linear regression, lowest standard deviation, and agreement of activation energy value to those obtained from KAS and FWO equations were found. The optimized value of activation energy and Arrhenius factor were calculated with the best model equation. Using these values, thermodynamic functions (??H ^*, ??S ^*, and ??G ^*) were calculated.     

Mechanism of transannular bromination reactions of diolefins of the bicyclo[3.3.1]nonane series

Mechanisms of reactions of brominated diolefins of the bicyclo[3.3.1]nonane series were studied. The reaction of transannular cyclization into adamantane derivatives proceeds by a molecular-ionic mechanism, and the rate of reaction obeys a third-order kinetic equation. An analysis of the calculated thermodynamic parameters of the transition state shows that intermediate complexes with charge transfer of the diolefin...Br₂ and diolefin...Br₄ type are formed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 1, pp. 52–56, January–February, 1985.     

Kinetik und Mechanismus der α/β-Umwandlung von Li2ZnGe

Kinetics and Mechanism of the α/βαTransformation of Li₂ZnGe The α/β-transformation of Li₂ZnGe was investigated by differential thermal analysis under nearly isothermal conditions. The possible mechanisms of solid state reactions are represented using the integrated and differentiated kinetic equations. For the investigation of DTA curves soft ware is developed to calculate the activation parameters and to find an adequate kinetic equation. A mechanism for the α/β-transformation of Li₂ZnGe is proposed and discussed.     

Thermal and kinetic analysis of uranium salts

In this study the thermal decomposition kinetics of uranyl acetate dehydrate [UO₂(CH₃COO)₂·2H₂O] were studied by thermogravimetry method in flowing nitrogen, air, and oxygen atmospheres. Decomposition process involved two stages for completion in all atmosphere conditions. The first stage corresponded to the removal of two?moles of crystal water. The decomposition reaction mechanism of the second stage in nitrogen atmosphere was different from that in air and oxygen atmospheres. Final decomposition products were determined with X-ray powder diffraction method. According to these data, UO₂ is the final product in nitrogen atmosphere, whereas U₃O₈ is the final product in air and oxygen atmospheres. The calculations of activation energies of all reactions were realized by means of model-free and modeling methods. Kissinger?CAkahira?CSunose (KAS) and Flynn?CWall?COzawa (FWO) methods were selected for model-free calculations. For investigation of reaction models, 13 kinetic model equations were tested. The model, which gave the highest linear regression, the lowest standard deviation, and an activation energy value which was close to those obtained from KAS and FWO equations, was selected as the appropriate model. The optimized value of activation energy and Arrhenius factor were calculated using the selected model equation. Using these values, thermodynamic functions (??H*, ??S*, and ??G*) were calculated.     

Kinetic and mechanistic study of micellar effect of hydrolytic reaction of Di-2-methoxy-4-nitroaniline phosphate

The effect of anionic surfactant (sodium dodecyl sulphate) and nonionic surfactant (Brij-35) on the hydrolysis of di-2-methoxy-4-nitroaniline phosphate was studied spectrophotometrically at 303 K. The influence of salts on the reaction rate was studied. The presence of inorganic salts (KCl, KNO₃, and K₂SO₄) exhibited positive effect on the reaction rate. The thermodynamic activation parameters were calculated from Arrhenius equation. On the basis of the experimental findings a suitable mechanism has been proposed. The binding constants between the reactants and the surfactants evaluated from the kinetic models proposed by Menger-Portnoy, Piszkiewicz, and Berezin have been found in good agreement.     

Kinetic, mechanistic and spectral investigation of ruthenium (III)-catalysed oxidation of atenolol by alkaline permanganate (stopped-flow technique)

Kinetics of ruthenium (III) catalyzed oxidation of atenolol by permanganate in alkaline medium at constant ionic strength of 0.30 mol dm³ has been studied spectrophotometrically using a rapid kinetic accessory. Reaction between permanganate and atenolol in alkaline medium exhibits 1 : 8 stoichiometry (atenolol : KMnO₄). The reaction shows first-order dependence on [permanganate] and [ruthenium (III)] and apparently less than unit order on both atenolol and alkali concentrations. Reaction rate decreases with increase in ionic strength and increases with decreasing dielectric constant of the medium. Initial addition of reaction products does not affect the rate significantly. A mechanism involving the formation of a complex between catalyst and substrate has been proposed. The active species of ruthenium (III) is understood as [Ru(H₂O)₅OH]₂₊. The reaction constants involved in the different steps of mechanism are calculated. Activation parameters with respect to the slow step of the mechanism are computed and discussed and thermodynamic quantities are also calculated.