STUDIES ON THERMOKINETICS.(Ⅰ)THEORY AND METHODS OP THERMOKINETICS

A chemical reaction taking place in a calorimeter is called a thermokinetic system.The recording curve of its temperature during the reaction is called a thermogram.It is very interesting to study the reaction kinetics from.its thermogram but the theory and methods of thermokinetics have not been developed into perfection yet.In this article,the thermokinetic equations of a reacting system are derived in the light of nonequilibrium thermodynamics.And the analytical expression of a thermogram can be derived from the thermokinetic equations.On this theoretical basis,a new research method in thermokinetics has been suggested     

用协同学方法研究化学反应速率和机理问题

用非平衡统计理论中的协同学方法分析了化学动力学中的反应速率和机理问题．对于任何给定的机理，通过引入一种非奇异变换，将相应的反应速率方程组直接地转换成Ｈａｋｅｎ形式，从而得到反应体系序参量以及其它变量的演化解析表达式．讨论了有机分子热分解的Ｒｉｃｅ－Ｈｅｒｚｆｅｌｄ机理．对醚的热分解链反应得到了一级动力学方程，理论结果与实验结果相符合．利用这种方法能解析地求解复杂反应的反应速率方程组，而不必引用在化学动力学中的“稳态近似”假设     

A computational algorithm for the Green's function method of sensitivity analysis in chemical kinetics

The recent interest in numerical modeling of chemical kinetics has generated the need for proper analysis of the system sensitivities in such models. This paper describes the logic for a program developed by the authors to implement the Green's function method of sensitivity analysis in complex kinetic schemes. The relevant equations and numerical details of the algorithm are outlined, two flow charts are provided, and some special programming considerations are discussed in some detail. Computer storage and computational time considerations are also treated. Finally, applications of sensitivity information to understanding complex kinetic system behavior and analyzing experimental results are suggested.     

Extrapolating H-atom transfer rate constants via thermochemical kinetics: The effect of tunneling

One of the important applications of chemical kinetics is the attempt to understand complex processes through kinetic modeling. This process frequently requires that rate constants be obtained by extrapolation of data either to higher or lower temperatures than the experimental, or by estimation or correlation with such data. Thermochemical kinetics combined with conventional transition state theory forms a framework from which this may be done. However, rate data for H transfer reactions may have a significant contribution from tunneling. In this work, a one dimensional approach to tunneling, consistent with conventional transition state theory, is taken to show how tunneling affects the extrapolation and correlation of rate constants in thermochemical kinetics. It is concluded that extrapolation and correlation are both quite good even when tunneling comprises 80% of the reaction. However, this is not without limitations, which are discussed. © 1993 John Wiley & Sons, Inc.     

Chemical instabilities during oxidation of 1,4-naphthalenediol in a homogeneous medium: II. Thermodynamic analysis and mathematical modeling

A possible mechanism of 1,4-naphthalenediol oxidation in the oscillatory regime has been considered, and a mathematical model describing the kinetics has been developed. Based on a thermodynamic Lyapunov function, it has been shown that the source of chemical instabilities is in the existence of autocatalytic steps and dynamic feedbacks. Qualitative analysis and numerical solution of the set of differential equations that model the reaction kinetics have been performed. The character of the stationary state and the possibility of bifurcations have been determined. The mathematical model satisfactorily describes the processes occurring in the system.     

Mathematical basis of the integral formalism of chemical kinetics. Compact representation of the general solution of the first-order linear differential equation

The standard approach in chemical and photochemical kinetics is to proceed from the kinetic scheme to the corresponding system of first-order differential equations, and then to integrate it, analytically or numerically. An equivalent integral formulation circumventing such system was recently developed on the basis of physical arguments. The mathematical basis of this ansatz is discussed here. A compact representation of the general solution of the linear first-order differential equation is also obtained.     

A Method to Determine the Dimension of Long-Time Dynamics in Multi-Scale Systems

Modeling reaction kinetics in a homogeneous medium usually leads to stiff systems of ordinary differential equations the dimension of which can be large. The problem of determination of the minimal number of phase variables needed to describe the characteristic behavior of large scale systems is extensively addressed in current chemical kinetics literature from different point of views. Only for a few of these approaches there exists a mathematical justification. In this paper we describe and justify a procedure allowing to determine directly how many and which state variables are essential in a neighborhood of a given point of the extended phase space. This method exploits the wide range of characteristic time-scales in a chemical system and its mathematical justification is based on the theory of invariant manifolds. The procedure helps to get chemical insight into the intrinsic dynamics of a complex chemical process.     

Études thermocinétiques de reactions lentes par microcalorimétrie à conduction

Calorimetry is a technique for studying kinetics, which can overcome the deficiencies of the methods commonly used, particularly when the reactions are carried out in non-aqueous solvents. Expression of the thermograms obtained by conduction microcalorimetry as equations and direct treatment of the experimental data with the aid of a non-linear regression programme makes it possible, in the case of slow reactions, to solve both simple and complex problems of kinetics of different orders. The saponification of ethyl acetate by potassium hydroxide in azeotropic ethanol served to test the validity of the proposed method.     

The method of quasi-stationary sensitivity analysis

A new sensitivity analysis technique is developed by utilizing Tihonov's singular perturbation theory. The described sensitivity analysis method deals with algebraic equations instead of solving the system of differential equations, which is the case in conventional sensitivity analysis. In the held of chemical kinetics, the proposed technique can supply information on the importance ofelemcntarv steps in complex reaction mechanisms. As examples, high-temperature propane pyrolysis and the chemistry of the unpolluted troposphere are studied.     

A new productivity function and stability criterion in chemical vapor transport processes

The crystal growth rate in a chemical vapor transport process using a closed system is analyzed on the basis of a one-dimensional configuration. A simplified model of vapor transport enables one to obtain a set of equations yielding the rates of reaction without a complete evaluation of the partial pressure gradients. This linear set comprises as many equations as independent chemical reactions. The effect of finite interface kinetics is formally taken into account. The efficiency of a one-reaction process is given by a function involving the mole fractions of the gaseous species and the stoichiometric coefficients in the formula equation. The features of such a productivity function are discussed. Maximum growth rate is achieved if the gaseous components are present in stoichiometric quantities. The concept of the productivity function is illustrated by chemical vapor transport systems involving binary and ternary gaseous phases. Proceeding from a two-phase source material, stability criteria that define stable one-phase and stable two-phase crystal growth are given. The kind of deposit may be changed by altering the amount of transporting agent. It is shown that limited interface kinetics favors a two-phase deposit.     

Sensitivity analysis and parameter estimation in dynamic modeling of chemical kinetics

A new approach to the dynamic modeling of chemical kinetics is presented. The technique is based on systematic planning of computer experiments, which allows an empirical model for the computed responses to be developed in the space of parameters. The empirical equations which are obtained provide complete information on the sensitivities with respect to various rate constants, disclosing their interrelationships. Utilization of these equations instead of numerical integration of the differential equations associated with the chemical reactions makes parameter estimation a trivial task. As a consequence the adequacy of the mechanism can be tested. The technique is applied to the thermal decomposition of propane.     

Stability of solutions to a reaction diffusion system based upon chemical reaction kinetics

In this paper, we deal with the stability problem to some mathematical models that describe chemical reaction kinetics. One is a set of ordinary differential equations induced by one reversible chemical reaction mechanism containing three chemical species. The other is a set of reaction diffusion equations based on the same chemical reaction. We show that all solutions of the model are asymptotically stable by applying the Liapunov method. We thus find that the concentration of each species has certain limits as time proceeds.      

从多重定态到化学振荡

通过对化学反应体系动力学模型的分析, 论证了通过在多重定态体系中引入适当慢反馈步骤设计化学振荡体系的可能性, 提出了这类体系的动力学方程具有振荡解的判据以及在参数平面内划分振荡区域的方法。采用这种途径具体分析了一氧化碳在铂催化剂上氧化产生振荡现象的机理。     

基于Arrhenius定理的化学动力学数值计算法

基于Arrhenius定理建立了一种新的化学动力学数值模拟方法.将其与化学动力学过程契合,能较好地体现化学动力学过程.将该方法对简单一级反应、平行反应和复杂的综合反应进行模拟计算,模拟结果与准确解相对误差小于0.5%.     

Modeling of nonlinear boundary value problems in enzyme-catalyzed reaction diffusion processes

A mathematical model of steady state mono-layer potentiometric biosensor is developed. The model is based on non stationary diffusion equations containing a non linear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents a complex numerical method (He’s variational iteration method) to solve the non-linear differential equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Approximate analytical expressions for substrate concentration and corresponding current response have been derived for all values of saturation parameter α and reaction diffusion parameter K using variational iteration method. These results are compared with available limiting case results and are found to be in good agreement. The obtained results are valid for the whole solution domain.     

Numerical modeling of titanium carbide synthesis in thermal plasma reactors

Titanium carbide powders synthesized in thermal plasma reactors are virtually always contaminated by soot. Equilibrium modeling predicts a viable process window without soot formation; however, this has not been achieved in practice. A numerical model incorporating chemical kinetics, nucleation and growth, and soot formation mechanisms has been developed to investigate this process. The chemical kinetic scheme teas based on ethylene pyrolysis and methane combustion with additional reactions to account for titanium-based molecules and the free carbon species found at plasma temperatures. Nucleation and .soot formation were based on simple kinetic models. The governing equations were integrated through time using typical temperature-time histories found by computational fluid dynamic (CFD) modeling of a radio frequency plasma torch. The results indicate that the synthesis is governed by interactions between several parallel processes and that there is a delicate balance between reactant stoichiometry, system pressure, cooling rate, product formation, and soot formation. This balance may be a limiting feature of ceramic carbide production in thermal plasma reactors.     

速差动力学分析法同时测量钆-镝混合物中的单一稀土

本文研究了稀土与新稀土显色剂DBC偶氮胂络合反应的动力学行为。稀土与试剂反应速率常数随着原子序数的增加而减小,发现了稀土动力学特性中的"钆断"现象。推导了钆、镝的动力学方程,提出了同时测量钆、镝二元混合物的速差动力学分析方法。测量了钆、镝相对浓度比为1:10-10:1的混合物试样,最低可测浓度为10^-7M,最大测量误差为13.5%。     

按独立组元计算复杂化学平衡的方法

本文通过分析独立组元的本质,提出了一个按独立组元来计算复杂化学平衡的方法。这个方法中的未知数和方程数比现有的自由能最小化法、质量作用方程组的方法和反应进度的方法中的未知数和方程数显著减少,因而计算过程大为简化。例如,对于计算一个由3个元素10个组元组成的复杂化学平衡体系来说,若采用其它方法须用电子计算机,而采用独立组元法仅须使用袖珍可编程序计算器即可完成。本文叙述了独立组元法的基本原理和具体方法,并根据理论分析和计算实践,将独立组元法与其它方法的优劣作了对比。     

Locally implicit solution of a reaction-diffusion system with stiff kinetics

The Tyson-Fife reaction-diffusion equations are solved numerically using a locally implicit approach. Since the variables evolve at very different time scales, the resulting system of equations is stiff. The reaction term is responsible for the stiffness and the time step is increased by using an implicit method. The diffusion operator is evaluated explicitly and the system of implicit nonlinear equations is decoupled. The method is particularly useful for parameter values in which the equations are very stiff, such as the values obtained directly from the experimental reaction rate constants. Previous efforts modified the parameters on the equations to avoid stiffness. The equations then become a simplified model of excitable media and, for those cases, the locally implicit method gives a faster although less accurate solution. Nevertheless, since the modified equations no longer represent a particular chemical system an accurate solution is not as important. The algorithm is applied to observe the transition from simple motion to compound motion of a spiral tip.