Classic and multivariate modeling treatment of the kinetics and mechanism of isomerization of 5‐cholesten‐3‐one catalyzed by sodium ethoxide

A classic kinetic methodology including the treatment of the steady‐state method and a multivariate modeling kinetic treatment were applied to the kinetics and mechanism of the isomerization reaction of 5‐cholesten‐3‐one to 4‐cholesten‐3‐one catalyzed by EtO⁻ in ethanol absolute. The rate constants, thermodynamic parameters of activation, equilibrium constant, and the isomerization enthalpy were determined. The multivariate modeling kinetic treatment allows us to calculate the concentrations of the species, in which the 3,5‐dienolate is included as a highly reactive intermediate species and was able to discriminate among several applicable mechanisms validating the one comprising two reversible steps. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 38: 38–47, 2006     

Influence of the ionic strength in the heterocoagulation process between bare and surfactant-coated latexes

A novel and useful process of heterocoagulation between bare and surfactant-coated latexes is studied. Basically, this process consists of the heterocoagulation of two identical latexes, i.e. of the same size and with charges of the same sign, but distinguished by the degree of coverage by a nonionic surfactant (Triton X-100). The different critical coagulation concentrations (ccc) of this type of sample permitted us to analyze the influence of the ionic strength in the heterocoagulation process between both colloidal samples. Different ratios (2:1, 1:1 and 1:2) of the bare and surfactant-coated latexes were used during the experiments. In all cases, the heterocoagulation rate constants were lower than the homocoagulation rate constant in diffusion conditions; however, for an ionic strength higher than the ccc of both systems, similar values were found for the rate constants. Received: 18 January 1999 Accepted in revised form: 14 April 1999     

Kinetic analysis of sequential multistep reactions

Many processes in biology and chemistry involve multistep reactions or transitions. The kinetic data associated with these reactions are manifested by superpositions of exponential decays that are often difficult to dissect. Two major challenges have hampered the kinetic analysis of multistep chemical reactions: (1) reliable and unbiased determination of the number of reaction steps, and (2) stable reconstruction of the distribution of kinetic rate constants. Here, we introduce two numerically stable integral transformations to solve these two challenges. The first transformation enables us to deduce the number of rate-limiting steps from kinetic measurements, even when each step has arbitrarily distributed rate constants. The second transformation allows us to reconstruct the distribution of rate constants in the multistep reaction using the phase function approach, without fitting the data. We demonstrate the stability of the two integral transformations by both analytic proofs and numerical tests. These new methods will help provide robust and unbiased kinetic analysis for many complex chemical and biochemical reactions.     

A linear solvation energy relationship study for the reactivity of 2‐(4‐substituted phenyl)‐cyclohex‐1‐enecarboxylic, 2‐(4‐substituted phenyl)‐benzoic,and 2‐(4‐substituted phenyl)‐acrylic acids with diazodiphenylmethane in various solvents

The reactivities of 2‐(4‐substituted phenyl)‐cyclohex‐1‐enecarboxylic acids, 2‐(4‐substituted phenyl)‐benzoic acids, and 2‐(4‐substituted phenyl)‐acrylic acids with diazodiphenylmethane in various solvents were investigated. To explain the kinetic results through solvent effects, the second‐order rate constants of the examined acids were correlated using the Kamlet–Taft solvatochromic equation. The correlations of the kinetic data were carried out by means of multiple linear regression analysis, and the solvent effects on the reaction rates were analyzed in terms of initial and transition state contributions. The signs of the equation coefficients support the proposed reaction mechanism. The solvation models for all investigated carboxylic acids are suggested. The quantitative relationship between the molecular structure and the chemical reactivity is discussed, as well as the effect of geometry on the reactivity of the examined molecules. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 430–439, 2010     

Solvent and structural effects on the kinetics of the reactions of 2‐substituted cyclohex‐1‐enylcarboxylic and 2‐substituted benzoic acids with diazodiphenylmethane

The rate constants for the reaction of 2‐methyl‐cyclohex‐1‐enylcarboxylic, 2‐phenylcyclohex‐1‐enylcarboxylic, and 2‐methylbenzoic and 2‐phenylbenzoic acids with diazodiphenyl‐methane were determined in 14 various solvents at 30°C. To explain the kinetic results through solvent effects, the second‐order rate constants of the examined acids were correlated using the Kamlet–Taft solvatochromic equation. The correlations of the kinetic data were carried out by means of multiple linear regression analysis, and the solvent effects on the reaction rates were analyzed in terms of initial and transition state contributions. The quantitative relationship between the molecular structure and the chemical reactivity has been discussed, as well as the effect of geometry on the reactivity of the examined molecules. The geometric data of all the examined compounds corresponding to the energy minima in solvent, simulated as dielectric continuum, obtained using semiempirical MNDO‐PM3 energy calculations. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 664–671, 2007     

A comparative LSER study of the reactivity of 2‐substituted cyclohex‐1‐eneacetic and 2‐substituted phenylacetic acids with diazodiphenylmethane in various solvents

The rate constants for the reaction of 2‐substituted cyclohex‐1‐eneacetic and 2‐substituted phenylacetic acids with diazodiphenylmethane were determined in various aprotic solvents at 30°C. To explain the kinetic results through solvent effects, the second‐order rate constants of the examined acids were correlated using the Kamlet–Taft solvatochromic equation. The correlations of the kinetic data were carried out by means of multiple linear regression analysis, and the solvent effects on the reaction rates were analyzed in terms of initial and transition state contributions. The opposite signs of the electrophilic and the nucleophilic parameters are in agreement with the well‐known mechanism of the reaction of carboxylic acids with diazodiphenylmethane. The quantitative relationship between the molecular structure and the chemical reactivity is discussed, as well as the effect of the molecular geometry on the reactivity of the examined compounds. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 613–622, 2009     

A Multivariate Curve Resolution Approach to the Study of the Degradation Kinetics of Valsartan under Photolytic and Acid Conditions

The analysis of UV‐spectrophotometric data with second‐order chemometrics techniques, including multivariate curve resolution with alternating least‐squares (MCR‐ALS) and hybrid hard‐ and soft MCR (HS‐MCR), was examined as an alternative tool for studying the kinetics of drug degradation under stress conditions, employing valsartan (VAL) as a model drug. Despite small structural and spectroscopic differences between VAL and its degradation products, MCR‐ALS and HS‐MCR were able to detect the generation of two photoneutral degradation products (DP‐1 and DP‐2) and a single acid hydrolysis product (DP‐3), providing good approximations to their pure spectra and concentration profiles, from which estimations of the kinetic profiles and rate constants were obtained. Kinetic models based on first‐order reactions explained the degradation processes. MCR‐ALS and HS‐MCR analyses yielded similar rate constants; however, the latter was capable of more properly fitting the experimental data to a kinetic model in the case of drug photolysis. The results were confirmed by comparison with data obtained by HPLC analysis of the degraded samples.     

典型燃料点火延迟时间的一阶和二阶局部和全局敏感度分析

Sensitivity analysis is an important tool in model validation and evaluation that has been employed extensively in the analysis of chemical kinetic models of combustion processes. The input parameters of a chemical kinetic model are always associated with some uncertainties, and the effects of these uncertainties on the predicted combustion properties can be determined through sensitivity analysis. In this work, first- and second-order global and local sensitivity coefficients of ignition delay time with respect to the scaling factor for reaction rate constants in chemical kinetic mechanisms for combustion of H₂, methane, n-butane, and n-heptane are examined. In the sensitivity analysis performed here, the output of the model is taken to be natural logarithm of ignition delay time and the input parameters are the natural logarithms of the factors that scale the reaction rate constants. The output of the model is expressed as a polynomial function of the input parameters, with up to coupling between two input parameters in the present sensitivity analysis. This polynomial function is determined by varying one or two input parameters, and allows the determination of both local and global sensitivity coefficients. The order of the polynomial function in the present work is four, and the factor that scales the reaction rate constant is in the range from 1/e to e, where e is the base of the natural logarithm. A relatively small number of sample runs are required in this approach compared to the global sensitivity analysis based on the highly dimensional model representation method, which utilizes random sampling of input (RS-HDMR). In RS-HDMR, sensitivity coefficients are determined only for the rate constants of a limited number of reactions; the present approach, by contrast, affords sensitivity coefficients for a larger number of reactions. Reactions and reaction pairs with the largest sensitivity coefficients are listed for ignition delay times of four typical fuels. Global sensitivity coefficients are always positive, while local sensitivity coefficients can be either positive or negative. A negative local sensitivity coefficient indicates that the reaction promotes ignition, while a positive local sensitivity coefficient suggests that the reaction actually suppresses ignition. Our results show that important reactions or reaction pairs identified by global sensitivity analysis are usually rather similar to those based on local sensitivity analysis. This finding can probably be attributed to the fact that the values of input parameters are within a rather small range in the sensitivity analysis, and nonlinear effects for such a small range of parameters are negligible. It is possible to determine global sensitivity coefficients by varying the input parameters over a larger range using the present approach. Such analysis shows that correlation effects between an important reaction and a minor reaction can have relatively sizable second-order sensitivity coefficient in some cases. On the other hand, first-order global sensitivity coefficients in the present approach will be affected by coupling between two reactions, and some results of the first-order global sensitivity analysis will be different from those determined by local sensitivity analysis or global sensitivity analysis under conditions where the correlation effects of two reactions are neglected. The present sensitivity analysis approach provides valuable information on important reactions as well as correlated effects of two reactions on the combustion characteristics of a chemical kinetic mechanism. In addition, the analysis can also be employed to aid global sensitivity analysis using RS-HDMR, where global sensitivity coefficients are determined more reliably.     

Solvent and structural effects on the kinetics of the reactions of cycloalkenylcarboxylic and cycloalkenylacetic acids with diazodiphenylmethane

The rate constants for the reaction of different cycloalkenylcarboxylic, cycloalkenylacetic acids, and phenylacetic acid with diazodiphenylmethane were determined in 12 aprotic solvents at 30°C. In order to explain the kinetic results through solvent effects, the second‐order rate constant of the examined acids was correlated using the Kamlet–Taft solvatochromic equation. The correlations of the kinetic data were carried out by means of multiple linear regression analysis, and the solvent effects on the reaction rates were analyzed in terms of initial and transition state contributions. The opposite signs of the electrophilic and the nucleophilic parameters are in agreement with the well‐known mechanism of the reaction of carboxylic acids with diazodiphenylmethane. The quantitative relationship between the molecular structure and the chemical reactivity is also discussed. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 361–367, 2005     

Description of the shape of thermoanalytical curves : Part 3. A Method for estimating kinetic constants from parameters characterizing peak shape

The relationships between empirical parameters characterizing the shape of thermo-analytical curves and the constants of the kinetic equation, dα/dt = A exp (?E/RT)(1 ? α)ⁿ, are studied. A procedure is developed for the estimation of the three constants of this equation from the empirical parameters. The efficiency of this method is compared to that of model fitting. In evaluation of the confidence intervals of estimated constants and in the case of identification, least-squares (or similar) fitting is shown to be inferior because of its low sensitivity to properties other than the position of the peak along the temperature axis. This lack of sensitivity may be a major cause of the apparent kinetic compensation effect often encountered in the field of thermal analysis.     

Effect of Intramolecular Transfer to Polymer on Stationary Free Radical Polymerization of Alkyl Acrylates, 2

Summary: Procedures are developed to estimate kinetic rate coefficients from available rate data for the free radical solution polymerization of butyl acrylate at 50 °C. The analysis is based upon a complete mechanistic set that includes the formation of mid‐chain radicals through backbiting and their subsequent reaction, and contains no assumptions on how the rate coefficient for cross‐termination of mid‐chain and end‐chain radicals is related to the two homo‐termination rate coefficients. After a thorough statistical analysis, the results of the fitting are combined with other recent literature data to provide a complete set of individual rate coefficients for the butyl acrylate system. Monomer addition to a mid‐chain radical is estimated to be slower than addition to a chain‐end radical by a factor of more than 400. The termination of two mid‐chain radicals is estimated to be two orders of magnitude slower than termination of two end‐chain radicals, with the cross‐termination rate coefficient close to the geometric mean.

Formation of a mid‐chain radical by intramolecular chain transfer to polymer by a chain‐end radical.     

Temperature‐dependent feature sensitivity analysis for combustion modeling

Sensitivity analysis is one of the most widely used tools in kinetic modeling. Typically, it is performed by perturbing the A‐factors of the individual reaction rate coefficients and monitoring the effect of these perturbations on the observables of interest. However, the sensitivity coefficients obtained in this manner do not contain direct information on possible temperature‐dependent effects. Yet, in many combustion processes, especially in premixed flames, the system undergoes substantial temperature changes, and the relative importance of individual reaction rates may vary significantly within the flame. An extension of conventional sensitivity analysis developed in the present work provides the means of identifying the temperatures at which individual reaction rate coefficients are most important as a function of input parameters and specific experimental conditions. The obtained information is demonstrated to be of critical relevance in optimizing complex reaction schemes against multiple experimental targets. Applications of the presented approach are not limited to sensitivities with respect to reaction rate coefficients; the method can be used for any temperature‐dependent property of interest (such as binary diffusion coefficients). This application is also demonstrated in this paper. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 282–295, 2005     

Cure kinetics of biphenyl epoxy‐phenol novolac resin system using triphenylphosphine as catalyst

The effects of the concentration of triphenylphosphine as a catalyst on the cure reaction of the biphenyl epoxy/phenol novolac resin system were studied. The kinetic study was carried out by means of the analysis of isothermal experiments using a differential scanning calorimeter. All kinetic parameters including the reaction orders, activation energy and kinetic rate constants were evaluated. To describe the cure reaction with the catalyst concentration, the normalized kinetic model was developed. The suggested kinetic model with a diffusion term was successfully able to describe and predict the cure reaction of epoxy resin compositions as functions of the catalyst content and temperature. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 713–720, 1999     

Sol MWD During Styrene,Vinyl Acetate,Methyl Methacrylate,and Butyl Acrylate Homopolymerization: A Numerical Study Using the NFT Approach

Complete parameter sensitivity analyses using the numerical fractionation technique are presented for the cases of homopolymerization with chain transfer to polymer and termination by combination. Also, using reported values for the kinetic rate constants associated with the linear and non‐linear homopolymerizations of styrene, vinyl acetate, methyl methacrylate and butyl acrylate, overall molecular weight distributions and averages of the MWD were calculated using the NFT. Good agreement with the expected behavior, with MMA and STY not gelling while BA and VAc do, was obtained. It is concluded that the NFT produces coherent and reliable performance for known polymerization systems, whether linear or non‐linear.

     

Analysis of the thermal decomposition of azo-peroxyesters by Arrhenius-type and three-parameter equations

Thermogravimetric analysis of azo-peroxyesters revealed two decomposition stages on TG curves. Molecular nitrogen is released in the first stage and carbon dioxide in the second. Fitting the thermogravimetric data by means of the three-parameter model and a classic one based on an Arrhenius-type kinetic equation showed that the former approach satisfactorily describes the process within the wide range of the extent of decomposition. It was found that two coefficients of the three-parameter equation are related to the temperature of maximum reaction rate. One of the coefficients of the three-parameter equation is also related to the activation energy. The compounds investigated can be grouped with respect to their kinetic characteristics, structure and stage of decomposition.     

Sensitivity analysis of the two kinetic states of the Belousov-Zhabotinsky reaction

A recently published kinetic model of the Belousov-Zhabotinsky reaction was studied by the feature sensitivity analysis of the slow bromide consumption and slow bromide production periods of the relaxing-type oscillatory system. The computed sensitivities allowed us to reveal the kinetic importance of the 17 individual reactions during the two, “kinetically homogeneous” states of the oscillation. Similarities and differences in the relative kinetic importances of the reaction steps were carefully studied when changing the magnitude of the rate constants (high set and low set). Of the 17 reactions examined, the attack of Ce⁴⁺ on malonic acid proved to be an essential step of the mechanism. Using the low set, there emerge more reactions which significantly affect the length of the two kinetic states.     

Determination of the kinetic constants of the reversible opening of a triazolo‐1,4‐thienodiazepine in water at different pH values: A striking example of the determination of intimately intricate kinetic and equilibrium constants

Apparent kinetic constants of the reversible opening of a triazolo‐1,4‐thienodiazepine were determined by UV‐spectrophotometry and by polarography in water at several pH values assuming as a hypothesis a stationary state for the carbinolamine intermediate. Both the apparent kinetic constants, k_f and k_r, exhibited a maximum for the values H₀ = −0.25 and pH = 6.07. A possible determination of the elementary kinetic constants of the several acido‐basic species which may be involved in the opening and closing process according to the pH and pKa values was studied and is discussed. The results are consistent with the hypothesis that both the opening of the diazepine cycle and the closing of the opened form proceed through a mechanism suggesting that the protonated form of the carbinolamine function of the intermediate is involved. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 826–834, 1999     

Estimation of kinetic rate constants by turbidity and nephelometry techniques in a homocoagulation process with different model colloids

 In this work turbidimetric and nephelometric techniques have been used to study the homocoagulation of aqueous dispersions of uniform spherical particles of surfactant-free latexes. Cationic and anionic latexes of similar particle sizes (361 and 370 nm) and different surface charge densities (+16.4 and −3.6 μC/cm²) were used throughout. The kinetic constants which control the aggregation processes when the electrical repulsion disappears were estimated by both techniques at different particle concentration and wavelength in order to establish the experimental conditions which provided reliable and similar values for the coagulation rate constant. Both experimental techniques (turbidity and nephelometry) and two ways of fitting the data have been used with both latexes. For the first method, the initial slope of turbidity or total scattered intensity versus time curves were used to calculate the kinetic constants. In the second method, the whole turbidity or total scattered intensity versus time curves were fitted and the kinetic constants calculated. An unambiguous experimental value for the doublet rate constant in diffusion conditions is obtained by turbidity and nephelometry techniques. By nephelometry both data treatments have permitted a distinction between the doublet rate constant and the global rate constant in diffusion conditions. Received: 2 June 1997 Accepted: 14 August 1997     

Kinetic Analysis of a Two‐Phase EC Mechanism with Concomitant Lateral Processes

Electrochemical transfer of azo dye fast red TR across the water/1,2 – dichloroethane (DCE) interface followed by the coupling reaction with 1‐naphthylamine in the organic phase is studied. Pseudo first order rate constants of this reaction were obtained by fitting the experimental I_p?/I_p+ ratio under different experimental conditions with the theoretical values reported by Nicholson and Shain. The occurrence of lateral processes is demonstrated (partition of the azo dye non assisted by potential and electrochemical transfer of the protons generated in the coupling reaction), which constrains the accurate determination of the kinetic parameters.     

Determination of Solvatochromic Regression Coefficients for the Molybdenum(VI) Complex with Ethylenediamine‐N,N′‐diacetic Acid by Using Kamlet‐Abboud‐Taft Equation

The Solver, Microsoft Excel 2000 powerful optimization package, has been used to perform non‐linear least‐squares curve fitting on the basis of Gauss‐Newton method for the calculation of solvatochromic regression coefficients for the complexation of molybdenum(VI) with ethylenediamine‐N,N′‐diacetic acid and dissociation constants at 25°C and constant ionic strength 0.1 mol·L⁻¹ sodium perchlorate in different aqueous solutions of methanol. A combination of potentiometric and UV spectrophotometric methods have been used for experimental studies. Non specific and specific solute‐solvent interactions were interpreted by correlating the equilibrium data with solvent parameters using the Kamlet‐Abboud‐Taft solvatochromic equation. Finally the influence of the solvent on the stability of the complex was discussed on the basis of the correlation results and the contribution of α (hydrogen‐bond donor acidity), β (hydrogen‐bond acceptor basicity) and π* (dipolarity/polarizability) parameters.