Rank annihilation factor analysis method for spectrophotometric study of second-order reaction kinetics

In this study several methods are described to determine the rate constant of a second-order reaction in the form of A+B→C. These approaches allow circumventing a rank deficiency inherent of a second-order reaction when the spectroscopic data is influenced by additional source of variance. Classically, to determine the unknown rate constant in this kind of systems, one needs to have extra knowledge about the system, including the spectra of the reactants or product and the exact kinetics. In the case of the presence of an unknown phenomenon in the data set that cannot be explained by the model, such as baseline drift, the estimated rate constant might be erroneous. Present work is a modification of the rank annihilation factor analysis (RAFA) algorithm by inclusion of I) pure spectra of reactants, or IIA) mean centering step, or IIB) mean spectrum. The proposed methods can interestingly be applied on a single kinetic run. The performances of the new methods have been evaluated by applying them to analysis of simulated and experimental data.     

Application of simplified complementary tristimulus colorimetry to chemical kinetics in solution-I: analysis of reaction mixtures and determination of first- or pseudo first-order rate constants

A graphical method is described which allows estimation of the number of reacting light-absorbing species from the plots of complementary colour points which are obtained with the use of simplified complementary tristimulus colorimetry (SCTS method) from absorption spectra of a series of kinetics solutions. It is shown that the mole function of the reactant or the product at any time can be calculated from the complementary colour points, so that the rate constant can also be determined. The present method has some advantages over the common approach to the determination or reaction rates in presence of a colour impurity.     

Extraction of the contribution of kinetic profile for reaction of a chemical species in unknown matrices by standard addition method

A new and simple strategy is applied to resolve kinetic profile for the reaction of an analyte in unknown matrices, using standard addition method (SAM). The proposed method uses kinetic spectrophotometric data obtained by standard addition of analyte into unknown mixtures followed by the reaction of analyte with a proper reagent. The proposed method extracts kinetic profile for the reaction of an analyte by averaging the kinetic profiles obtained by subtraction of kinetic profiles after and before standard addition. The rate constant can be obtained using computational curve fitting. The performance of method was evaluated by using synthetic data as well as several experimental data sets. The proposed method can be applied to obtain kinetic profiles of the reactions in the presence of additive interference as well as multiplicative interferences. Hydroxylation reaction of diphenylcarbazide (DPCI) in the presence of diphenylcarbazone (DPCO) as a real system at various pHs was also studied by the present method. The rate constant and the order of the hydroxylation reaction were determined from extracted kinetic profiles.     

Derivation of rate constant ratios for consecutive second‐order irreversible reactions

The determination of rate constants for consecutive irreversible reactions is a difficult and time‐consuming problem, especially when the research extends up to many subsequent products. Thus, the derivation of proper mathematical expressions would greatly facilitate the determination of these rate constants when only the rate constant of the first consecutive reaction is known. Many authors have dealt with this problem in the past but the issue is still of interest to the scientific community judging from recent publications. This paper aims at extending our knowledge of mathematical expressions for rate constant ratios of consecutive reactions to more than three reactions, as is the situation now, and offering a simple graphical estimation of the rate constant ratios exploiting the maxima of each intermediate product. Furthermore, the method extends to the derivation of a generic formula for the estimation of the rate constant ratios based on this graphical approach. This approach for the estimation of rate constant ratios based on mathematical expressions and graphical estimations was validated against experimental data found in the literature.     

速率常数-秩分析法在化学反应过程分析中的应用

针对化学反应动力学谱-吸收光谱组成的两维数据,提出了以优化速率常数而消去反应物波谱信息为减秩手段的速率常数-秩分析法(RCRA).结果表明,RCRA在一次优化过程中可同时获得两个最优解,分别对应于两步速率常数.在获得动力学参数的前提下,利用最小二乘回归可解出包括中间体在内的各组分的吸收光谱.该方法用于处理苯胺电解降解的两维数据,发现苯胺降解过程中有一种表观中间体存在,降解过程符合一级连串反应模型.     

Spectrophotometric investigation of the effect of beta-cyclodextrin on the intramolecular cyclization reaction of catecholamines using rank annihilation factor analysis

The catalytic effect of β-cyclodextrin (β-CD) on the intramolecular cyclization reaction of catecholamines dopamine, methyldopa and levodopa after their oxidation with periodate was investigated spectrophotometrically using rank annihilation factor analysis (RAFA). The method was based on the effect of β-CD concentration on the intramolecular cyclization reaction of the investigated catecholamines after their oxidation with potassium periodate. In order to perform RAFA, concentration profiles were calculated by optimizing the value of formation constant. The rank of original data matrix can be reduced by one by annihilating the information of the cyclization reaction in the absence of β-CD. The rate constant for the reactions in the presence and absence of β-CD was also determined. The best estimation of rate constant in the presence of β-CD reduces the rank of the system to zero (noise level). The method was evaluated using synthetic data as well as experimental data and good results were obtained.     

Estimation of second order rate constants using chemometric methods with kinetic constraints

Several methods are described for determining rate constants for second order reactions of the form U + V --> W using chemometrics and hard modelling to analyse UV absorption spectroscopic data, where all species absorb with comparable concentrations and extinctions. An interesting feature of this type of reaction is that the number of steps in the reaction is less than the number of absorbing species, resulting in a rank-deficient response matrix. This can cause problems when using some of the methods described in the literature. The approaches discussed in the paper depend, in part, on what knowledge is available about the system, including the spectra of the reactants and product, the initial concentrations and the exact kinetics. Sometimes some of this information may not be available or may be hard to estimate. Five groups of methods are discussed, namely use of multiple linear regression to obtain concentration profiles and fit kinetics information, rank augmentation using multiple batch runs, difference spectra based approaches, mixed spectral approaches which treat the reaction as two independent pseudospecies, and principal components regression. Two datasets are simulated, one where the spectra are quite different and the other where the spectrum of one reactant and the product share a high degree of overlap. Three sources of error are considered, namely sampling error, instrumental noise and errors in initial concentrations. The relative merits of each method are discussed.     

Application of chemometrics methods with kinetic constraints for estimation of rate constants of second order consecutive reactions.

To determine the rate constants for the second order consecutive reactions of the form U + V -(k1)--> W -(k2)--> P, a number of chemometrics and hard modeling-based methods are described. The absorption spectroscopic data from the reaction were utilized for performing the analysis. Concentrations and extinctions of components were comparable, and all of them were absorbing species. The number of steps in the reaction was less than the number of absorbing species, which resulted in a rank-deficient response matrix. This can cause difficulties for some of the methods described in the literature. The standard MATLAB functions were used for determining the solutions of the differential equations as well as for finding the optimal rate constants to describe the kinetic profiles. The available knowledge about the system determines the approaches described in this paper. The knowledge includes the spectra of reactants and products, the initial concentrations, and the exact kinetics. Some of this information is sometimes not available or is hard to estimate. Multiple linear regression for fitting the kinetic parameters to the obtained concentration profiles, rank augmentation using multiple batch runs, a mixed spectral approach which treats the reaction using a pseudo species concept, and principal components regression are the four groups of methods discussed in this study. In one of the simulated datasets the spectra are quite different, and in the other one the spectra of one reactant and of the product share a high degree of overlap. Instrumental noise, sampling error are the sources of error considered. Our aim was the investigation of the relative merits of each method.     

Estimation of first-order kinetic parameters by using the extended kalman filter

A model for first-order kinetics is derived for spectra obtained while a reaction is taking place. A technique for nonlinear-regression analysis known as the extended Kalman filter is used to estimate the initial concentrations of the reactants and the rate constant from the spectral data. The effects of the magnitude of the rate constant and the identity of the absorbing species are examined for synthetic spectra containing overlapped responses. The technique is used successfully to obtain the rate constant for the dissociation reaction of a praseodymium complex. The filter is also shown to be useful for the detection of erros in the kinetic model employed to fit the data. The extended Kalman filter can be used to fit kinetic models other than the one discussed here, and may prove to be a valuable technique for estimation of kinetic parameters.     

Multi-structural variational transition state theory: kinetics of the 1,5-hydrogen shift isomerization of the 1-butoxyl radical including all structures and torsional anharmonicity

We investigate the statistical thermodynamics and kinetics of the 1,5-hydrogen shift isomerization reaction of the 1-butoxyl radical and its reverse isomerization. The partition functions and thermodynamic functions (entropy, enthalpy, heat capacity, and Gibbs free energy) are calculated using the multi-structural torsional (MS-T) anharmonicity method including all structures for three species (reactant, product, and transition state) involved in the reaction. The calculated thermodynamic quantities have been compared to those estimated by the empirical group additivity (GA) method. The kinetics of the unimolecular isomerization reaction was investigated using multi-structural canonical variational transition state theory (MS-CVT) including both multiple-structure and torsional (MS-T) anharmonicity effects. In these calculations, multidimensional tunneling (MT) probabilities were evaluated by the small-curvature tunneling (SCT) approximation and compared to results obtained with the zero-curvature tunneling (ZCT) approximation. The high-pressure-limit rate constants for both the forward and reverse reactions are reported as calculated by MS-CVT/MT, where MT can be ZCT or SCT. Comparison with the rate constants obtained by the single-structural harmonic oscillator (SS-HO) approximation shows the importance of anharmonicity in the rate constants of these reactions, and the effect of multi-structural anharmonicity is found to be very large. Whereas the tunneling effect increases the rate constants, the MS-T anharmonicity decreases them at all temperatures. The two effects counteract each other at temperatures 385 K and 264 K for forward and reverse reactions, respectively, and tunneling dominates at lower temperatures while MS-T anharmonicity has a larger effect at higher temperatures. The multi-structural torsional anharmonicity effect reduces the final reverse reaction rate constants by a much larger factor than it does to the forward ones as a result of the existence of more low-energy structures of the product 4-hydroxy-1-butyl radical than the reactant 1-butoxyl radical. As a consequence there is also a very large effect on the equilibrium constant. The neglect of multi-structural anharmonicity will lead to large errors in the estimation of reverse reaction rate constants.     

A statistical/collisional approach to rates of bimolecular reactions at low pressure

An expression for the rate constant of gas‐phase bimolecular reactions at low pressure is derived in the framework of collisional theory. The key feature of the proposed model is the calculation of the energy‐dependent rate constant in terms of the collisional cross section and the probability of reaction, expressed as the ratio of the volume in phase space that leads to product over the total volume. The contribution of the internal energy of the reacting fragments is taken into account, as well as the relative translational energy. The resulting formulation is able to account for both negative and positive temperature dependences of the rate constants of neutral and charged species. The dependence of temperature of the bimolecular rate constant is given both for reactions with and without potential energy barriers. The performance of the proposed model is tested against experimental rate constant for three well‐studied reactions by fitting the parameters of the model to experimental data at various temperatures. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 233–242, 2005     

The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics

The rates of formation and concentration distributions of a dimer reaction showing hysteresis behavior are examined in an ab initio chemical reaction designed as elementary and where the hysteresis structure precludes the formation of transition states (TS) with pre-equilibrium and internal sub-reactions. It was discovered that the the reactivity coefficients, defined as a measure of departure from the zero density rate constant for the forward and backward steps had a ratio that was equal to the activity coefficient ratio for the product and reactant species. This surprising result, never formally incorporated in elementary rate expressions over approximately one and a half centuries of quantitative chemical kinetics measurement and calculation is accepted axiomatically and leads to an outline of a theory for the form of the rate constant, in any one given substrate—here the vacuum state. A major deduction is that the long-standing definition of the rate constant for elementary reactions is not complete and is nonlinear, where previous works almost always implicitly refer to the zero density limit for strictly irreducible elementary reactions without any attending concatenation of side-reactions. This is shown directly from MD simulation, where for specially designed elementary reactions without any transition states, density dependence of reactants and products always feature, in contrast to current practice of writing rate equations. It is argued that the rate constant expression without reactant and product dependence is due to historical conventions used for strictly elementary reactions. From the above observations, a theory is developed with the aid of some proven elementary theorems in thermodynamics, and expressions under different state conditions are derived whereby a feasible experimental and computational method for determining the activity coefficients from the rate constants may be obtained under various approximations and conditions. Elementary relations for subspecies equilibria and its relation to the bulk activity coefficient are discussed. From one choice of reaction conditions, estimates of activity coefficients are given which are in at least semi-quantitative agreement with the data for non-reacting Lennard-Jones (LJ) particles for the atomic component. The theory developed is applied to ionic reactions where the standard Brönsted-Bjerrum rate equation and exceptions to this are rationalized.     

Mean centering of ratio kinetic profiles for the simultaneous kinetic determination of binary mixtures in electroanalytical methods

In this work, the applicability of mean centering (MC) of ratio kinetic profiles method to the kinetic voltammetry data is verified. For this purpose, a procedure is described for the determination of Sb(III) and Sb(V) by adsorptive linear sweep voltammetry using pyrogallol (py) as a complexing agent. The method is based on the differences between the rate of complexation of pyrogallol with Sb(V) and Sb(III) at pH 1.2. The results show that the mean centering of ratio kinetic profiles method is suitable for the speciation of antimony. Sb(III) and Sb(V) can be determined in the ranges of 3.0-120.0 and 10.0-240.0 ng mL⁻¹, respectively. Moreover, the solution is analyzed for any possible effects of foreign ions. The obtained results show that the method of MC in combination to electroanalytical techniques is a powerful method with high sensitivity and selectivity. The procedure is successfully applied to the speciation of antimony in pharmaceutical preparations.     

THE REGIOSPECIFICITY OF INTRAMOLECULAR N-3-BUTENYL NITRONE CYCLOADDITION

The reaction mechanism of the intramolecular cycloaddition ofN-3-butenyl nitrone has been investigated theoretically by using AM1 MOmethod and transition state theory.There are two parallel reactionsleading to two different regioisomers.The ratio of the rate constantsof these two reactions was calculated to be 124.1(at 383.75 K).Theobtained results can be used to explain the high regiospecificity ofthe reaction product.     

Rate-determining cooperative effects of bimolecular reactions in solution

An expression for the rate constant of condensed-phase bimolecular reactions is derived. The key feature of the proposed model is the formulation of the energy-dependent rate constant in terms of the diffusion rate and the ratio of the volume in phase space that leads to product over the total volume. The dependence of the bimolecular rate constant by the reduced barrier x = E thermod/kT is given in explicit form in terms of the incomplete and the complete gamma functions of Euler. The performance of the proposed model is tested against the experimental rate constants for the Menschutkin reaction by fitting the parameters of the expression for the rate constant to experimental data at various temperatures. The potential energy barrier obtained from the regression (16.75 kcal mol-1) is close to the independently computed value at the CPCM B3LYP/CRENBL.6-311(+)G(d) level of theory (16.84 kcal mol-1). The corresponding fitting to the transition state theory expression affords the lower value of 14.65 kcal mol-1.     

Analysis of nonlinear reactions in modulated molecular beam surface experiments

An approximate method of analyzing nonlinear reaction models in modulated molecular beam surface kinetic studies is developed. The exact method for treating nonlinear surface mechanisms is tedious and almost always requires computer analysis. The proposed approximate method is a simple extension of the Fourier expansion technique valid for linear surface reactions; it quickly provides analytical expressions for the phase lag and amplitude of the reaction product for any type of nonlinear surface mechanism, which greatly facilitates comparison of theory and experiment. The approximate and exact methods are compared for a number of prototypical adsorption–desorption reactions which include coverage-dependent adsorption and desorption kinetics of order greater than unity. Except for certain extreme forms of coverage-dependent adsorption, the approximate method provides a good representation of the exact solution. The errors increase as the nonlinearities become stronger. Fortunately, when the discrepancy between the two methods is substantial, the reaction product signal is so highly demodulated that reliable experimental data usually cannot be obtained in these regions anyway.     

Analysis of gamma-ray spectra by using fast Fourier transform (author's transl)]

In order to simplify the mass data processing in a response matrix method for gamma-ray spectral analysis, a method using a Fast Fourier Transform devised. The validity of the method was confirmed by a computer simulation for spectra of a NaI detector. The method uses the fact that spectral data can be represented by Fourier series with reduced number of terms. The estimation of intensities of gamma-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of gamma-ray energies is also easy. Several features in the method and a general problem to be solved in a response matrix method are described.     

聚苯胺在有机溶剂中掺杂质子酸的In-site UV-Vis光谱及其因子分析法解谱

对聚苯胺在有机溶剂中掺杂质子酸的反应进行了in-situ UV-Vis光谱跟踪,用因子分析法对掺杂反应机理进行了研究.结果表明,聚苯胺在有机溶剂中掺杂质子酸的过程可能存在着两个并行反应:一个是掺杂与脱掺杂的动态平衡过程,在实验条件下反应的平衡常数约为k=5.16(24℃);另一个反应为副反应,生成的产物结构介于本征态与平衡掺杂态之间,很可能是反应过程中形成的包含不同掺杂形态的混合体.     

Off-line form of the Michaelis-Menten equation for studying the reaction kinetics in a polymer microchip integrated with enzyme microreactor

We firstly transformed the traditional Michaelis-Menten equation into an off-line form which can be used for evaluating the Michaelis-Menten constant after the enzymatic reaction. For experimental estimation of the kinetics of enzymatic reactions, we have developed a facile and effective method by integrating an enzyme microreactor into direct-printing polymer microchips. Strong nonspecific adsorption of proteins was utilized to effectively immobilize enzymes onto the microchannel wall, forming the integrated on-column enzyme microreactor in a microchip. The properties of the integrated enzyme microreactor were evaluated by using the enzymatic reaction of glucose oxidase (GOx) with its substrate glucose as a model system. The reaction product, hydrogen peroxide, was electrochemically (EC) analyzed using a Pt microelectrode. The data for enzyme kinetics using our off-line form of the Michaelis-Menten equation was obtained (K(m) = 2.64 mM), which is much smaller than that reported in solution (K(m) = 6.0 mM). Due to the hydrophobic property and the native mesoscopic structure of the poly(ethylene terephthalate) film, the immobilized enzyme in the microreactor shows good stability and bioactivity under the flowing conditions.     

A density functional study of propylene glycol conversion to propanal and propanone of various acid-catalyzed reaction models: a water-addition effect

The acid-catalyzed models on reaction mechanisms of pinacol rearrangement of propylene glycol conversion to propanal and propanone have been investigated using the density functional method at 298.15 K. Thermodynamic quantities of activation steps of four water-addition models were obtained. The number of added water interacting with the transition states of three concerted pathways has obviously affected the product ratio. The relative energetic profiles of the conversion reactions of all solvation models have been comparatively displayed. Estimation of the percent ratio of product composition computed from activation free energies of each acid-catalyzed reaction model was carried out. The percent ratios of propanal and propanone were decreased as the number of added water increased.