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.     

Kinetic analysis of nonisothermal solid-state reactions: determination of the kinetic parameters by means of a nonlinear regression method

A nonlinear regression method has been proposed for a simultaneous calculation of the activation energy, frequency factor, and reaction order from a single TG curve. This method was based on the new temperature integral approximation proposed in this paper and the Levenberg–Marquardt method. The newly proposed nonlinear regression method was applied for determining the kinetic parameters from two simulated TG curves. The results of the calculations were compared with values obtained by the traditional method. It can be concluded from this comparison that the new nonlinear regression method is more accurate than the traditional method for the determination of the kinetic parameters of solid-state heterogeneous reactions.     

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.     

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.     

Detection limit estimator for multivariate calibration by an extension of the IUPAC recommendations for univariate methods

A methodology is proposed to estimate the limit of detection (LOD) of analytical methods when multivariate calibration is applied. It tries to follow the same premises as the IUPAC methodology for univariate calibration. The mathematical support is given and algorithms such as partial least squares (PLS) regression, PLS2 and principal component regression (PCR) are used. Only multivariate raw data are used; that is, no surrogate univariate signal is deduced. Non-linearities are allowed. Near infrared (NIR) data of 5 component pseudo-gasoline samples together with simulated fluorescence synchronous spectra of binary mixtures (first order data) are used for evaluation. Experimental verification is performed using different kinds of data, namely: binary mixtures of bentazone and fenamiphos (very overlapped spectra, second order data) obtained by sequential injection (SI), and kinetic data of the reaction between the Fenton's reagent (FR) and pesticides such as atrazine, bentazone and alachlor (individual or binary mixtures, second order data). Results are always compared with independent methods previously proposed in the literature, based in the use of surrogate univariate signals. In general, similar results are found and no statistically significant differences seem to be present, except in a few cases when complex chemical systems are involved.     

根据动力学-光谱数据解析高锰酸钾氧化草酸钠的反应过程

通过在线测量硫酸介质中高锰酸钾氧化草酸钠反应过程的光谱变化，获得了动力学—光谱二维数据。借助主成分分析法，确定了高锰酸钾的单信息区，并确认反应过程中产生了一种有吸收的中间体。根据最小二乘回归等化学计量学方法，结合相关组分间存在等吸收点这一光谱特征及质量平衡原理，成功地解折出反应体系中相关组分的实际动力学谱及纯光谱。根据Savitsky-Golay求导法，获得了各组分的速率曲线。对解析结果的进一步研究表明，该反应符合自催化模式。     

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.     

Determination of kinetic parameters of polymerizations by differential scanning calorimetry

Differential scanning calorimetry is well suited to record heat productions of chemical and physical processes as data for the following kinetic analysis. To obtain kinetic parameters of complex reactions, nonlinear optimization methods have to be used. Such complex reaction systems are polymerizations. We tried to evaluate measurements of the epoxy cure and the polymerization of β-propiolactame with simple and complex models. In both cases the simple models did not produce satisfactory results. But by using complex models a successful fitting of the measured data was possible. Our investigation shows that the combination of DSC and modern nonlinear evaluation methods presents a suitable tool for the kinetic investigation of polymerizations.     

聚乙烯熔体的离散松弛时间谱与熔融指数的关系

该文通过动态线性小振幅剪切震荡实验所得的聚乙烯熔体储能模量Ｇ′（ω）和耗能模量Ｇ″（ω）数据,采用最小二乘法线性回归、正则法和非线性回归法分别计算得到离散松弛时间谱,比较三种方法得到结果的差别,讨论计算参数、温度和材料对离散松驰时间谱影响．     

连串反应速差动力学分析中的数据处理方法的研究

连串反应速差动力学分析中的数据处理方法的研究吴新国，蔡汝秀，林智信，程介克（武汉大学化学系，武汉，４３００７２）关键词连串反应，速差动力学分析，比例方程法，肾上腺素，去甲肾上腺素动力学分析在分析化学中的作用和重要性已广为人知［１］，速差动力学分析是其...     

A spectrum stripping method for the computer-coupled activation analysis of unknown samples by γ-ray spectrometry

A spectrum stripping method for the computer-coupled activation analysis of unknown samples using γ-ray spectrometry is discussed. Before the unscrambling of the γ-ray is performed using standard spectra of the components, each spectrum is smoothed, statistically weighted and corrected for background. The photopeaks of the standard spectra are then aligned with the respective peaks of the sample spectrum, one at a time after correcting for gain drift if necessary, and the undesired components are stripped out. After successive subtraction, the characteristic spectrum of the desired element is compared with that of the standard to determine its weight. The results obtained using the present method are as good as those obtained from least-squares analysis in ideal cases, but appear to be better when assumptions inherent in the least-squares method are no longer valid.     

Multicomponent kinetic determinations using multivariate calibration techniques

Multivariate calibration techniques for use in multicomponent kinetic-based determinations are reviewed. Multivariate calibration is a chemometric tool that continues to grow in popularity among analytical chemists. Multicomponent kinetic methods depend on differences in rates of reactions or processes to distinguish among the components. Kinetic profiles or a combination of kinetic profiles and spectra are commonly used. Because of their ability to process large quantities of data, multivariate calibration techniques are well suited for kinetic-based determinations. The concepts and principles of multivariate calibration are discussed first. Classical least squares regression, principal component regression, partial least squares regression and artificial neural networks are the multivariate calibration techniques considered here in detail. Recent examples of the application of these techniques to multicomponent kinetic determinations are reviewed. Both single and multiwavelength kinetic data are considered.     

An incremental isoconversional method for kinetic analysis based on the orthogonal distance regression

The parameters obtained from a kinetic analysis of thermoanalytical data often exhibit a conversion‐dependent behavior. A novel incremental isoconversional method able to deal with this phenomenon is proposed. The kinetic model is directly fitted to the experimental data using nonlinear orthogonal least squares procedure. The data are processed without transformations, so their error distribution is preserved. As the objective function is based on a maximum likelihood approach, reliable uncertainties of the parameters can be estimated. In contrast to other methods, the activation energy and the pre‐exponential factor are treated as equally important kinetic parameters and are estimated simultaneously. Validity of the method is verified on simulated data, including a dataset with local nonlinearity in the temperature variation. A practical application on the nonisothermal cold crystallization of polyethylene terephthalate is presented. © 2014 Wiley Periodicals, Inc.     

A consensus successive projections algorithm – multiple linear regression method for analyzing near infrared spectra

The successive projections algorithm (SPA) is widely used to select variables for multiple linear regression (MLR) modeling. However, SPA used only once may not obtain all the useful information of the full spectra, because the number of selected variables cannot exceed the number of calibration samples in the SPA algorithm. Therefore, the SPA-MLR method risks the loss of useful information. To make a full use of the useful information in the spectra, a new method named “consensus SPA-MLR” (C-SPA-MLR) is proposed herein. This method is the combination of consensus strategy and SPA-MLR method. In the C-SPA-MLR method, SPA-MLR is used to construct member models with different subsets of variables, which are selected from the remaining variables iteratively. A consensus prediction is obtained by combining the predictions of the member models. The proposed method is evaluated by analyzing the near infrared (NIR) spectra of corn and diesel. The results of C-SPA-MLR method showed a better prediction performance compared with the SPA-MLR and full-spectra PLS methods. Moreover, these results could serve as a reference for combination the consensus strategy and other variable selection methods when analyzing NIR spectra and other spectroscopic techniques.     

A novel baseline-correction method for standard addition based derivative spectra and its application to quantitative analysis of benzo(a)pyrene in vegetable oil samples

In the present work, a baseline-correction method based on peak-to-derivative baseline measurement was proposed for the elimination of complex matrix interference that was mainly caused by unknown components and/or background in the analysis of derivative spectra. This novel method was applicable particularly when the matrix interfering components showed a broad spectral band, which was common in practical analysis. The derivative baseline was established by connecting two crossing points of the spectral curves obtained with a standard addition method (SAM). The applicability and reliability of the proposed method was demonstrated through both theoretical simulation and practical application. Firstly, Gaussian bands were used to simulate 'interfering' and 'analyte' bands to investigate the effect of different parameters of interfering band on the derivative baseline. This simulation analysis verified that the accuracy of the proposed method was remarkably better than other conventional methods such as peak-to-zero, tangent, and peak-to-peak measurements. Then the above proposed baseline-correction method was applied to the determination of benzo(a)pyrene (BaP) in vegetable oil samples by second-derivative synchronous fluorescence spectroscopy. The satisfactory results were obtained by using this new method to analyze a certified reference material (coconut oil, BCR(?)-458) with a relative error of -3.2% from the certified BaP concentration. Potentially, the proposed method can be applied to various types of derivative spectra in different fields such as UV-visible absorption spectroscopy, fluorescence spectroscopy and infrared spectroscopy.     

Numerical Simulation of Chemical Equilibria and Photostationary States Using Spectrophotometric and Spectrofluorometric Data

A mathematical model describing series of experimental absorption and fluorescence spectra of multicomponent systems via equilibrium and photostationary concentrations of components of the systems was constructed. With photostationary concentrations, it is possible to take into account changes in the fluorescence spectra resulting from photochemical reactions. Ther unknown equilibrium and kinetic parameters of the model and also the spectra of pure components are found from experimental data by the nonlinear least-squares method. A software for the model was developed, and its applicability to the determination of the composition of multicomponent systems, resolution of the spectra of pure components, and determination of equilibrium and kinetic constants was demonstrated.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 3, 2005, pp. 386–394.Original Russian Text Copyright © 2005 by Rusalov.     

A new approach to near-infrared spectral data analysis using independent component analysis

This paper presents a new approach to near-infrared spectral (NIR) data analysis that is based on independent component analysis (ICA). The main advantage of the new method is that it is able to separate the spectra of the constituent components from the spectra of their mixtures. The separation is a blind operation, since the constituent components of mixtures can be unknown. The ICA based method is therefore particularly useful in identifying the unknown components in a mixture as well as in estimating their concentrations. The approach is introduced by reference to case studies and compared to other techniques for NIR analysis including principal component regression (PCR), multiple linear regression (MLR), and partial least squares (PLS) as well as Fourier and wavelet transforms.     

Simulations for evaluation of kinetic methods in differential scanning calorimetry. Part 1. Application to single-peak methods: Freeman-Carroll, Ellerstein, Achar-Brindley-Sharp and multiple linear regression methods

In order to simplify the choice between different kinetic methods used in differential scanning calorimetry, an interesting way for testing kinetic treatments is proposed, using simulated thermoanalytical curves computed from given kinetic parameters. Applied to the study of a polymerization, we tested the Freeman-Carroll, Ellerstein, multiple linear regression (reaction-order model) and Achar-Brindley-Sharp methods. The test of the validity of the methods is performed using the LSM parameter that represents the fit between the mathematical treatment used in the kinetic model and known data. The study reveals the importance of the number of points used, i.e. the resolution, in the thermoanalytical curve recording, especially for the Freeman-Carroll and Ellerstein methods, there being an increase in the relative error on all the kinetic parameters when the number of points is decreased. Maximum relative errors are reported for the pre-exponential factor calculations. Evaluation of the enthalpy error on the determination of the kinetic parameters has been performed. Simulations obtained with various enthalpies indicate the necessity in such cases of computing a relative dimensionless LSM parameter (relative to the amplitude of the phenomena) in order to compare different thermal effects.