Comparison of PLS and kinetic models for a second-order reaction as monitored using ultraviolet visible and mid-infrared spectroscopy

A second-order reaction between benzophenone and phenylhydrazine to give benzophenone phenylhydrazone was followed using UV/vis and mid-infrared spectroscopic probes. Established kinetic (hard) and partial least squares (soft) modelling chemometrics methods were applied to both datasets in order to compare the information acquired with each probe. To this purpose, an experimental design with 25 samples and a test set with 5 samples were used to build a partial least squares calibration model to predict the concentration profiles of the compounds present in the reaction vessel. In addition, multivariate kinetic modelling was also performed on the spectroscopic data. Using a guess of the rate constant, concentration profiles were estimated. The profiles are then used to calculate the estimated spectroscopic profile, which is compared to the data acquired experimentally. The residual is minimised and the rate constant estimated; this procedure is iterated until convergence. A total of four profiles were obtained for each compound, corresponding to two sets of probes and two sets of models. The results were compared and discussed. It is shown that several different spectroscopic techniques can be used in reaction monitoring, with increasing benefits in terms of information and interpretation of the results. The profiles obtained agreed well which was also demonstrated when comparing the different rate constants obtained.     

A simple method for analysis of consecutive reactions with a second order formation and a first order decay of an intermediate

A simple method is developed to evaluate rate constants from absorbance-time traces for a pair of consecutive reactions consisting of a second order formation and a first order decay of an intermediate. Initially, a first order profile is simulated utilizing the data near the end of the reaction. The difference between this simulated and observed profiles provides the absorbance-time data for the initial phase from which a second order rate constant is evaluated. These rate constants were used to simulate composite kinetic curves which were then compared with experimental curves. This method was used to test the reaction between cis-Pt(NH₃)₂(H₂O)₂ ²⁺ and a nonapeptide, ERFKCPCPT. The reaction proceeds through a cysteine coordinated intermediate formed in a second order process (first order with respect to each reactant). The intermediate is then converted to a product through a first order process, in which both cysteines are coordinated to platinum(II).     

Detection and use of selective ions for providing initial estimates of the concentration vectors in iterative target transformation factor analysis

The characteristic of discreteness in mass spectral direction distinguishes GC/MS from other spectral techniques. Based on this feature, we propose a new method to construct the initial concentration vectors for iterative target transformation factor analysis (ITTFA). For each chemical component, a search for a selective ion with good signal-to-noise ratio is first conducted using evolving factor analysis (EFA) and information entropy. The corresponding chromatogram of the selective ion is subsequently applied to construct an initial concentration vector for ITTFA. Special strategies are developed to cope with chromatographic patterns with embedded peaks and complex multicomponent structure. Results from three simulated and one real mixture and comparison with results from heuristic evolving latent projections (HELP) and a previously published method for definition of the initial profiles for ITTFA, indicate that selective ion chromatogram (SIC) ITTFA represents a fast, automatic and accurate method for resolution of GC/MS data.     

Algorithm for error-compensated kinetic determinations without prior knowledge of reaction order or rate constant

The development and evaluation of a new algorithm for error-compensating predictive kinetic determinations are described. With the new algorithm it is possible to fit kinetic data without prior knowledge of the rate constant, reaction order or initial and final values of the detector signal. A curve-fitting method is used to obtain values of these parameters that give the best fit of the model to the data. Although intended to be used primarily to compute signal changes between t=0 and ∞, the method can also be used to determine reaction orders. Although the algorithm fails for reaction orders of zero and unity, it works well for orders between these values and orders greater than unity. Simulated data are used to evaluate the effects of reaction order, signal noise and data range on computed values of signal change and, to a lesser extent, reaction order.     

Kinetic analyses of consecutive solid-state decompositions illustrated with iron(II) sulfate

Use of consecutive reaction analysis for the derivation of kinetic parameters is demonstrated for the solid state decompositions which often include fractional orders of reaction. The differential equations describing the relative amounts of reactants and products during an isothermal decomposition are solved numerically by machine. Unlike previously used methods for solid-state decompositions there is no need to assume that the rate constant of the first step is much greater than that of the second. Also, the technique allows the interpretation of experimental data throughout the entire range of the reaction. The treatment was applied to the two-step decomposition of iron(II) sulfate in a dry nitrogen atmosphere. The results show the data to fit consecutive half-order reactions.     

Rheological studies of the gelation kinetics of Cr+3-polyacrylamide solutions

A new rheological approach for the study of the gelation kinetics of aqueous Cr⁺³ polyacrylamide solutions has been investigated which relies on the assumption that at the gel point, GP, a constant amount of Cr⁺³ will have reacted, independent of the initial Cr⁺³ concentration. From this, a kinetic expression relating GP to the initial concentrations of Cr⁺³ and reactive groups on the polymer has been derived for the case of a crosslinking reaction first order in Cr⁺³ and polymer. Experimental evidence that the amount of Cr⁺³ reacted at the GP is constant for a given polymer and solution pH has been obtained. The good fit of the kinetic expression to the rheological data provides new evidence that the gelation reaction is first order in Cr⁺³ rather than second order as claimed previously.     

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.     

Resolving co-eluting chromatographic patterns by means of dissimilarity analysis in iterative target transformation factor analysis

The initialization of concentration vector for iterative target transformation factor analysis (ITTFA) and identification of pure or key variables are the important issue in MCR. In this study, dissimilarity analysis and evolving factor analysis (EFA) are combined to find the selective or key variables and subsequently obtain initial estimates of the concentration vectors for resolution of gas chromatography/mass spectrometry (GC/MS) data by ITTFA. For systems containing components with highly similar mass spectra, a new constraint setting the elements out of elution window to 0 is used to improve convergence rate and accuracy of results. Tested by standard mixture of two wax esters and real GC/MS data of gasoline 97#, dissimilarity based ITTFA could obtain accurate results (average Dot product of concentration vectors, average deviation of peak area ratio and average similarity of mass spectra are 0.9929, 0.0228 and 981.0, respectively).     

Spectroelectrochemical study of the oxidative doping of polydialkylphenyleneethynylene using iterative target transformation factor analysis

Iterative target transformation factor analysis (ITTFA) was used to determine the spectra of the individual species generated during the oxidative p-doping of films of poly(para-phenyleneethynylene) (PPE). UV-visible spectra of PPE films on transparent electrodes were obtained in-situ during an anodic sweep. ITTFA identified 4 species present during the oxidation, which we assign as neutral polymer, polaron species, bipolaron species, and a species formed by further bipolaron reaction. The region of electrochemical stability for each of these species was identified and their potential-dependent profiles were obtained. This work is the first deconvolution of conjugated polymer spectroelectrochemistry.     

Poly(phenylene sulfide): Synthesis from 1,4-dibromobenzene and sodium sulfide

A new route to synthesize poly(p-phenylene sulfide) by nucleophilic substitution of 1,4-dibromobenzene with sodium sulfide in N-methylpyrrolidone is described. Kinetic evaluation shows the reaction to be of second order with two distinctive rate constant regimes. The first rate constant is higher and is operative until 50% conversion, whereas in the second regime (between 50 and 92% conversion) the rate is slower. The kinetics of this route is compared under identical conditions with the conventional synthesis based on 1,4-dichloro benzene and sodium sulfide.     

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.     

Analytical solutions for the rate equations of irreversible two-step consecutive processes with second order later steps

Analytical solutions are presented for four consecutive two-step kinetic schemes, which involve a first reaction with zeroth, first, second or mixed second order dependence and a second step, which is second order with respect to the intermediate formed in the first step. Two of the analytical solutions found use elementary functions not very commonly encountered in chemistry, as the rate equations are shown to be related to the Legendre or modified Bessel differential equations. The solutions are analyzed not only as a function of time, but by plotting two concentrations as a function of each other as well. The dependence of the kinetic traces on the parameter values is also investigated. In all cases, two scaling parameters are identified. Three of the four cases are characterized by a single shape parameter, which is basically the ratio of the rate constant scaled with a suitable concentration unit if necessary. The mixed second order–second order scheme has an additional shape parameter, which is the ratio of the initial concentrations of the two reactants.     

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.     

Development of kinetic models for acid‐catalyzed methyl acetate formation reaction: Effect of catalyst concentration and water inhibition

The reaction kinetics of reversible liquid‐phase esterification of acetic acid with methanol is investigated in the temperature range 26–50°C using sulfuric acid catalyst. The main goal of this work is to study the effect of catalyst concentration and sensitivity to the presence of water on the rate expression of this industrially important reaction. Experiments are conducted in an isothermal batch reactor and a second‐order kinetic model is used to correlate the experimental data, which are found to fit well with the assumed kinetic model in terms of the concentrations of reactants and products. Furthermore, an activity‐based kinetic model is also developed employing the UNIQUAC (universal quasi‐chemical equation) model to compute the activities. It is observed that the rate constant is influenced by the concentration of catalyst, and the reaction rate increased with an increase in the catalyst concentration. It is also observed that the catalyst activity is slightly inhibited by the water present in the reaction mixture. The performance of the proposed models is compared with that of other models reported in the literature, and it is found that the proposed models outperformed all the other models reported in the literature. © 2011 Wiley Peiodicals, Inc. Int J Chem Kinet 43: 263–277, 2011     

Theoretical evaluation of methods for extracting retention factors and kinetic rate constants in liquid chromatography

A three-dimensional stochastic simulation is used to provide a detailed understanding of mass transfer processes in liquid chromatography. In this simulation, the migration of individual molecules is established through diffusion and laminar convection within the mobile phase. The molecules interact with the stationary phase by a partition (absorption) mechanism. For these studies, the column length, linear velocity, stationary-phase diffusion coefficient, interfacial mass transfer coefficient, and equilibrium constant are varied in a system with a homogeneous surface. Heterogeneous surfaces are also investigated by having multiple types of interaction sites that are equally or unequally distributed. For each simulation, the molecular distribution is examined and characterized at specified times or column lengths. Five individual methods are then applied to extract the thermodynamic and kinetic information for transport between the mobile and stationary phases. In the first method, all of the molecules are initially distributed in the mobile phase and the fraction remaining is monitored as a function of time. These simulation data are fit to a single exponential decay by nonlinear regression to determine the "true" retention factors and rate constants. The other methods rely on evaluating the shape of the zone profiles along the column. The statistical moments of the profiles are used to calculate the mean and the variance, which are related to the retention factors and the rate constants, respectively. The profiles are also fit to the exponentially modified Gaussian equation, the Giddings equation, and the Thomas equation. The fitting parameters from these equations are then used to calculate the retention factors and rate constants. Comparisons of the accuracy relative to the "true" retention factors and "true" rate constants, as well as the advantages and limitations of each method are discussed.     

Time shift correction in second-order liquid chromatographic data with iterative target transformation factor analysis

When the generalized rank annihilation method (GRAM) is applied to liquid chromatographic data with diode-array detection, an important problem is the time shift of the peak of the analyte in the test sample. This problem leads to erroneous predictions. This time shift can be corrected if a time window is selected so that the chromatographic profile of the analyte in the test sample is trilinear with the peak of the analyte in the calibration sample. In this paper we present a new method to determine when this condition is met. This method is based on the curve resolution with iterative target transformation factor analysis (ITTFA). The calibration and test matrices are independently decomposed into profiles and spectra, and aligned before GRAM is applied. Here we study two situations: first, when the calibration matrix has one analyte and second, when it has two analytes. When the calibration matrix has two analytes, we selectively determine the time window for the analyte to be quantified. There were considerably fewer prediction errors after correction.     

Kinetic Treatments for Catalyst Activation and Deactivation Processes based on Variable Time Normalization Analysis

Progress reaction profiles are affected by both catalyst activation and deactivation processes occurring alongside the main reaction. These processes complicate the kinetic analysis of reactions, often directing researchers toward incorrect conclusions. We report the application of two kinetic treatments, based on variable time normalization analysis, to reactions involving catalyst activation and deactivation processes. The first kinetic treatment allows the removal of induction periods or the effect of rate perturbations associated with catalyst deactivation from kinetic profiles when the quantity of active catalyst can be measured. The second treatment allows the estimation of the activation or deactivation profile of the catalyst when the order of the reactants for the main reaction is known. Both treatments facilitate kinetic analysis of reactions suffering catalyst activation or deactivation processes.     

Thermal and kinetic evaluation of biodiesel derived from soybean oil and higuereta oil

The purpose of this work is to evaluate the thermal and kinetic behavior of biodiesel derived from soybean and higuereta oils. The thermogravimetric profiles of biodiesels indicated one step associated with decomposition of the ethyl esters. The thermal profiles were compared with reference diesel. Kinetic parameters were obtained by thermal analysis, estimating reaction order, pre-exponential factor and activation energy. For estimation of the kinetic parameters the Coats & Redfern method was used. The selection criterion of best fit was based on the correlation coefficient of the linear regression and the compensation effect of the kinetic parameters.     

液相法苯选择加氢制环己烯催化反应动力学方程

 测定了Ru－M－B／ZrO2催化剂上选择加氢制环己烯反应过程中苯、环己烯及环己烷浓度随时间变化的c～t曲线，获得了苯选择加氢制环己烯反应中各步反应的级数和速率常数等动力学参数．结果给出，苯转化的反应级数对苯为1，对氢低压下为2，高压下为0；环己烯继续加氢生成环己烷的反应级数对环己烯为0，对氢低压下为2，高压下为0．在此基础上建立了苯选择加氢制环己烯各步反应的动力学方程，并对动力学方程进行了验证．     

Chemometrics study of the kinetics of the Griess reaction

The kinetics of the Griess reaction in which 3‐nitroaniline acts as a nitrosation agent and 1‐naphtylamine as a coupling reagent was studied by chemometrics methods. The kinetic reaction was investigated under pH 1.0 and 25°C by UV‐vis spectrophotometry. The concentrations of nitrite, 3‐nitroaniline and 1‐naphtylamine were such that a second‐order kinetic reaction took place. Data explorations based on principal component analysis and multivariate curve resolution–alternating least squares were performed to obtain information about the reaction. Calculation of band boundaries of the multivariate curve resolution–alternating least squares solutions showed that the rotational ambiguities associated with the calculation of spectra and concentration profiles have been completely removed. The decrease in the ambiguity of the recovered solutions was closely related to the application of the equality constraint. The results of the exploratory data analysis showed that the kinetic reaction proceeds through a two‐step mechanism. Moreover, the two‐steps are second order. Data analysis approaches based on hard modeling and global hard modeling were used to resolve profiles of the reactants, intermediates and products and to evaluate the rate constants. Copyright © 2013 John Wiley & Sons, Ltd.