A Computational Algorithm for the Polynomial Approximation Method of Sensitivity Analysis in Chemical Kinetics

This paper describes the logic for a program developed by the author to implement the polynomial approximation method (PAM) of sensitivity analysis for general kinetic purposes. The relevant equations and numerical details of the algorithm are outlined, a flow chart is provided, and some programming considerations are discussed in detail. A listing of the PAM code is given in the appendix. The paper also gives a few suggestions for possible improvements and extensions of the present algorithm.     

Electrochemical methods for speciation of trace elements in marine waters. Dynamic aspects

The contribution of electrochemical methods to the knowledge of dynamic speciation of toxic trace elements in marine waters is critically reviewed. Due to the importance of dynamic considerations in the interpretation of the electrochemical signal, the principles and recent developments of kinetic features in the interconversion of metal complex species will be presented. As dynamic electrochemical methods, only stripping techniques (anodic stripping voltammetry and stripping chronopotentiometry) will be used because they are the most important for the determination of trace elements. Competitive ligand exchange-adsorptive cathodic stripping voltammetry, which should be considered an equilibrium technique rather than a dynamic method, will be also discussed because the complexing parameters may be affected by some kinetic limitations if equilibrium before analysis is not attained and/or the flux of the adsorbed complex is influenced by the lability of the natural complexes in the water sample. For a correct data interpretation and system characterization the comparison of results obtained from different techniques seems essential in the articulation of a serious discussion of their meaning.     

Finding complex balanced and detailed balanced realizations of chemical reaction networks

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not “encoded” in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.     

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.     

Linear compartmental systems. I. kinetic analysis and derivation of their optimized symbolic equations

The study of many biological systems requires the application of a compartmental analysis, together with the use of isotopic tracers, parameter identification and methods to evaluate the mean parameters. For all this, the kinetic equations of the compartmental system as a function of its parameters are needed. In this paper, we present some considerations on the diagrams of connectivity of linear compartmental systems and obtain new properties from the matrix corresponding to the ordinary first-order linear differential equation systems which describe their kinetic behaviour. Using these properties, symbolic equations are obtained in a simplified form. These equations provide the instantaneous amount of substance in any compartment of the system when zero input is injected into one or more of the system compartments, solely as a function of those parameters of compartmental systems which really have an influence on the sought expression. This is unlike what happens in the other symbolic equations obtained in a previous contribution that included all the fractional transfer coefficients involved in the compartmental system, regardless of whether or not they had an influence on the instantaneous amount of substance.     

[Mn(AZT)_2(H_2O)_4](HTNR)_2·4H_2O的合成、晶体结构、热行为及感度性质(英文)

通过酸性2,4,6-三硝基间苯二酚(HTNR)的锰盐与3-叠氮-1,2,4-三唑(AZT)在水溶液中反应,制备得到一种新颖的锰配合物[Mn(AZT)2(H2O)4](HTNR)2·4H2O.通过元素分析和红外光谱对配合物进行了表征,用X射线单晶衍射分析确定其晶体结构.该配合物为三斜晶系,空间群为P1,中心锰(Ⅱ)离子为六配位的畸变的八面体结构,分子内和分子间强烈的氢键作用构成了有序的三维(3D)网状结构.采用差示扫描量热(DSC)和热重-微分热重(TG-DTG)分析技术研究了配合物的热分解特性,并预测了它的热分解反应机理.利用Kissinger方法和Ozawa-Doyle方法研究了其第一放热分解峰的分解动力学过程.其分解过程包括一个吸热峰和三个放热峰,在600℃的分解产物为MnO和MnO2的混合物.同时.对这个配合物进行了感度(撞击感度、火焰感度、摩擦感度)性能分析,结果表明,它对外界刺激具有很强的响应性和选择性.     

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.     

Adsorption kinetics at the solid/solution interface: statistical rate theory at initial times of adsorption and close to equilibrium

The kinetics of solute adsorption at the solid/solution interface has been studied by statistical rate theory (SRT) at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. A new kinetic equation has been derived for initial times of adsorption on the basis of SRT. For the first time a theoretical interpretation based on SRT has been provided for the modified pseudo-first-order (MPFO) kinetic equation which was proposed empirically by Yang and Al-Duri. It has been shown that the MPFO kinetic equation can be derived from the SRT equation when the system is close to equilibrium. On the basis of numerically generated points ( t, q) by the SRT equation, it has been shown that we can apply the new equation for initial times of adsorption in a larger time range in comparison to the previous q vs radical t linear equation. Also by numerical analysis of the generated kinetic data points, it is shown that application of the MPFO equation for modeling of whole kinetic data causes a large error for the data at initial times of adsorption. The results of numerical analysis are in perfect agreement with our theoretical derivation of the MPFO kinetic equation from the SRT equation. Finally, the results of the present theoretical study were confirmed by analysis of an experimental system.     

Mechanistic investigations and spectrokinetic parameter determination during thermoreversible photochromism with degradation: example of application to the triphenylimidazolyl dimer (TPID) system

A numerical method is proposed for the kinetic analysis of the experimental absorbance vs. time curves obtained during continuous irradiation and thermal equilibration of a thermoreversible photochromic system with degradation. The quantum yield amd molar absorption coefficients of the unstable coloured species can be determined simultaneously using a kinetic model which encompasses all details of the reaction mechanism including the degradation process. The efficacy and accuracy of this method are illustrated by an analysis of the triphenylimidazolyl dimer (TPID) system in toluene solution.     

Reactivity of monoenic and conjugated diene systems present in unsaturated olefin terpolymers—II. Reactions with methyl radicals

The experimental rate constants for the reactions of methyl radicals with model compounds simulating ethylidene-norbornene (ENB), methylene-norbornene (MNB) and isopropylidene-dicyclopentadiene (IPDCP) units in EPDM and EPTM elastomers are reported. These constants, as well as others reported in a previous paper or derived from the literature, have been used to perform a kinetic analysis of the grafting of styrene onto EPM, EP-ENB or EP-IPDCP in inert solvent. The systems of kinetic differential equations have been solved by numerical integration without steady state approximation. Valuable information has been obtained on the role of the nature of radical initiators and the sensitivity of the results to change with constants in the various steps.     

A composite methodology for multistage degradation of polymers

Five different analytical schemes for examining isothermal and nonisothermal degradation of polymers were reviewed and found inadequate for describing multistage decomposition. The different schemes were experimentally tested using thermogravimetric analysis data for an ethylene-vinyl acetate (EVA) copolymer, which exhibited a well-behaved two-step decomposition process in a nitrogen environment. Based on these experimental and analytical findings, a generalized methodology was developed capable of describing the exhibited complex decomposition behavior of polymers by combining two or more kinetic mechanisms in a series or parallel arrangement. This composite of combinational methodology thus extends established analytical schemes for describing complex decomposition of polymers in a rational manner, incorporating both experimental and theoretical considerations.     

Sensitivity analysis of complex kinetic systems. Tools and applications

Sensitivity analysis investigates the effect of parameter change on the solution of mathematical models. In chemical kinetics, models are usually based on differential equations and the results are concentration-time curves, reaction rates, and various kinetic features of the reaction. This review discusses in detail the concentration sensitivity, rate sensitivity, and feature sensitivity analysis of spatially homogeneous constant-parameter reaction systems. Sensitivity analyses of distributed parameter systems and of stochastic systems are also briefly described. Special attention is paid to the interpretation of sensitivity coefficients which can provide information about the importance and interconnection of parameters and variables. Applications of sensitivity analysis to uncertainty analysis, parameric scaling, parameter estimation, experimental design, stability analysis, repro-modeling, and investigation and reduction of complex reaction mechanisms are discussed profoundly.     

扩散不稳定相中的化学稳定性和时-空有序结构的形成

利用热力学和动力学的分析方法, 研究了化学稳定性和扩散稳定性的依赖关系。发现, 在远离平衡和强烈非理想的体系中, 不管体系是否扩散稳定, 化学反应可以是稳定的, 也可以是不稳定的。通过对Schlögl模型的分析, 表明扩散不稳定性和化学稳定性之间的竞争可以导致一类时空有序结构的形成。这一结果可以看作是耗散结构理论的推广和延伸。     

Comparison of photometry and conductometry for the determination of total carbonate by gas permeation flow injection analysis

The experimental system involves the permeative preconcentration of CO(2) from an acidified sample through a tubular silicone rubber membrane into a suitable receptor. Procedures for measuring the CO(2) collected in the receptor by the absorbance change of an acid-base indicator incorporated in the receptor or by the conductance change of the receptor are compared. Previous theoretical considerations of the photometric system are augmented for numerical modeling and the theoretical behavior of the conductometric system is considered in detail. Experimental data generally conform to theoretical expectations. Based on either reproducibility or sensitivity, the conductometric measurement method using a solution of 1-10mM tris(hydroxymethylamino)methane as receptor is recommended. The interference from sulfite or sulfide can be eliminated by adding acidic permanganate to the sample; considerably more involved arrangements are necessary to eliminate interferences from cyanide.     

Analyzing the uniqueness of the rate constants calculated from complex kinetic systems: A study of the hydrolysis of ciclohexanecarbonitriles

In this article, a novel methodology for the study of complex reaction mechanisms is explored, and applied to the kinetic analysis of the hydrolysis reactions of ciclohexanecarbonitriles. The kinetic data were first analyzed with the help of classic linear techniques. Subsequently, the determination of the rate constants by a non‐linear, least‐squares (LS) fitting method, followed by a novel eigenvalue‐eigenvector analysis of the sensitivity coefficients, permitted us to obtain the maximum possible information from the kinetic data. The non‐linear, LS‐fitting method, carried out by means of a new version of OPKINE program, allowed the calculation of all the rate constants of the mechanism; in addition, the sensitivity analysis permitted us to establish the uniqueness and reliability of calculated rate coefficients. Finally, the results of the sensitivity analysis were tested by means of a simulation procedure, and the results compared to those obtained from classic linear methods. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 611–626, 1999.     

EPDM accelerated sulfur vulcanization: a kinetic model based on a genetic algorithm

A simple closed form equation for the prediction of crosslinking of EPDM during accelerated sulfur vulcanization is presented. Such a closed form solution is derived from a second order non homogeneous differential equation, deduced from a kinetic model. The kinetic model is based on the assumption that, during vulcanization, a number of partial reactions occurs, both in series and in parallel, which determine the formation of intermediate compounds, including activated and matured polymer. Once written standard first order differential equations for each partial reaction, the differential equation system so obtained is rearranged and, after few considerations, a single second order non homogeneous differential equation with constant coefficients is derived, for which a solution may be found in closed form, provided that the non-homogeneous term is approximated with an exponential function. To estimate numerically the degree of crosslinking, kinetic model constants are evaluated through a simple data fitting, performed on experimental rheometer cure curves. The fitting procedure is a new one, and is achieved using an ad-hoc genetic algorithm, provided that a few points, strictly necessary to estimate model unknown constants with sufficient accuracy, are selected from the whole experimental cure curve. To assess the results obtained with the model proposed, a number of different compounds are analyzed, for which experimental or numerical data are available from the literature. The important cases of moderate and strong reversions are also considered, experiencing a convincing convergence of the analytical model proposed. For the single cases analyzed, partial reaction kinetic constants are also provided.     

On the Validity of the Steady-state Approximation in Non-isothermal Kinetics. Part III

The authors continue their considerations concerning the validity of the steady-state approximation in non-isothermal kinetics. A sequence of two first-order consecutive reactions with an active intermediate was subjected to kinetic analysis by numerical solution of the corresponding differential kinetic equations for a number of particular cases. The results demonstrated that the rate of change of concentration of the active intermediate is negligibly small if the assumption made in the isothermal case is also accepted for the non-isothermal case, i.e. k ₂(T(t))>> k ₁(T(t)). This revised version was published online in July 2006 with corrections to the Cover Date.     

Multistage reactions,equilibrium, and detailed balancing: A linear algebra approach

Methods of linear algebra are applied to (a) the problem of determining whether detailed balancing for some or all stages of a chemical process is implicit from the existence of steady state for some or all of the chemical species involved, and (b) the formulation of general concentration-type equilibrium relationships solely from kinetic considerations and the assumption of full detailed balancing.