利用模式搜索法求取新的温度积分近似式

利用模式搜索法求取了一个新的温度积分近似式,给出了相应的估算动力学参数的方程。新的温度积分近似式根据数值计算结果得到,可靠性高。讨论了新的近似式计算值与温度积分数值积分结果的偏差。与其它近似式相比,新的温度积分近似式的表达式简单,精确度更高,非常适合非等温过程的动力学参数的计算。     

New approximate formula for the generalized temperature integral

A new procedure to approximate the generalized temperature integral $ \int_{0}^{T} {T^{m} {\text{e}}^{ - E/RT} } {\text{d}}T, $ which frequently occurs in non-isothermal thermal analysis, has been developed. The approximate formula has been proposed for calculation of the integral by using the procedure. New equation for the evaluation of non-isothermal kinetic parameters has been obtained, which can be put in the form: $$ \ln \left[ {{\frac{g(\alpha )}{{T^{(m + 2)0.94733} }}}} \right] = \left[ {\ln {\frac{{A_{0} E}}{\beta R}} - (m + 2)0.18887 - (m + 2)0.94733\ln {\frac{E}{R}}} \right] - (1.00145 + 0.00069m){\frac{E}{RT}} $$ The validity of the new approximation has been tested with the true value of the integral from numerical calculation. Compared with several published approximation, the new one is simple in calculation and retains high accuracy, which indicates it is a good approximation for the evaluation of kinetic parameters from non-isothermal kinetic analysis.     

DSC Analysis of the Induction Period in the Vulcanisation of Rubber Compounds

Vulcanisation of rubber compounds was studied by DSC under isothermal and non-isothermal conditions. The parameters of an Arrhenius-like equation describing the temperature dependence of induction period have been obtained both from isothermal and non-isothermal measurements. A new method for obtaining the kinetic parameters from non-isothermal measurements, based on the dependence of onset temperature of vulcanisation peak on heating rate, is presented. Also, a procedure for the evaluation of temperature difference between the furnace and sample is proposed. It has been shown that the treatment of non-isothermal DSC measurements gives the kinetic parameters free of systematic errors. The new method can also be used for studying other reactions exhibiting the induction period. This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistical and Mathematical Investigations for Determining the Binding Constants of Micelle with Reactants Molecules from Kinetic Data

Binding constants between reactants molecules with micelles are considered to be important parameters particularly in micellar catalysis area. Recently, we developed a statistical method based on multiple linear regression for determining those parameters from kinetic data (Phys. Chem. Liq. 2008, 46, 34–46). In the present work, we derived further two statistical equations from the same original equation using also multiple linear regression method. A substantial difference has been found between the results of those equations and with that of the recently published one. This strongly indicates that the statistical procedures are not valid for such a purpose, that is, the available statistical and graphical methods in the literature are also not suitable for such treatment. A mathematical procedure using iterative method for evaluating the binding constants is introduced. An equation for such treatment has also been derived from the same original equation, and a computer program for this purpose has been written. Application of the developed method to the kinetic data has been found to be quite successful. It has been concluded that the presented mathematical method is simple, reliable, and accurate.     

New linear integral kinetic parameters assessment method based on an accurate approximate formula of temperature integral

This work concerns a proposition of a new assessment method to obtain kinetic parameters from nonisothermal solid-state kinetics, based on a new and accurate approximate formula of temperature integral. The new formula was derived numerically by a two-step linearly fitting process without using any further approximating series. The relative error involved in the activation energy has been estimated and found to be less than 0.001% in the practical range of 15 < x < 60. A comparison of the suggested approximations to published approximates has shown significant improvements in terms of accuracy at high and low x values. The validity of the new method has been confirmed by computing activation energy from experimental data. Moreover, two approaches have been proposed to determine the kinetic reaction model and preexponential factor based on the new approximate formula. The comparison of the obtained results arising from the application of the present method to others obtained by the most widely reported methods in the literature shows a remarkable preeminence of the new method.     

Dependence of the frequency factor on the temperature: a new integral method of nonisothermal kinetic analysis

A new integral method of nonisothermal kinetic analysis has been developed with the dependence of the frequency factor on the temperature (A = A ₀ T ^m ). The new integral method is obtained from the newly proposed approximation for the general temperature integral, which is more accurate than the other existed approximations. For applications, nonisothermal thermoanalytical data obtained by theoretical simulation have been processed. The results have shown that the newly proposed integral method is an ideal solution for the evaluation of kinetic parameters from nonisothermal thermoanalytical data with the frequency factor dependent the temperature.     

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.     

DSC Study of Oxidation Induction Periods

A theory of the evaluation of kinetic parameters of induction periods for non-isothermal processes is outlined and a method to obtain the parameters from non-isothermal differential scanning calorimetry measurements, based on the dependence of onset temperature of oxidation peak on heating rate, is presented. The applicability of the method is demonstrated on the study of oxidation induction periods of edible oils and polyolefines. In all cases, the parameters of an Arrhenius-like equation describing the temperature dependence of induction period have been obtained. It is shown that the method gives the parameters not affected by oxygen diffusion which are transferable to be used in modelling the non-isothermal induction periods where the effects of diffusion, heat transfer and evolution of reaction heat are explicitly involved. A method of estimating the residual stability after a thermooxidative stress of the material is suggested. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetic Analysis of Thermogravimetric Data XXXI. Derivation of a non-linear kinetic compensation law

The kinetic compensation effect observed in heterogeneous non-isothermal kinetics is only an apparent effect. In general, the correlation derived between the kinetic parameters E and log A from TG curves can be described by means of a non-linear compensation law, expressed by Eq. (14). This equation may become approximately linear in certain particular cases, i.e. it may change into an isokinetic relation. The validity of the non-linear compensation law has been tested by using over 1000 sets of kinetic parameters reported earlier. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetics of hydroformylation of 1-decene using carbon-supported ossified HRh(CO)(TPPTS)3 catalyst

The kinetics of hydroformylation of 1-decene has been investigated using a carbon-supported ossified HRh(CO)(TPPTS)₃/Ba catalyst in a temperature range of 343–363 K. The effect of concentration of 1-decene, catalyst loading, partial pressure of H₂ and CO, and stirring speed on the reaction rate has been investigated. A first-order dependence was observed for catalyst concentration and hydrogen partial pressure. The rate showed a typical case of substrate inhibition for high 1-decene concentration. The rate varied with a linear dependence on P_CO up to a CO partial pressure of 5–6 MPa in contrast to the general trends; for most of the rhodium-phosphine catalyzed hydroformylation reactions, severe inhibition of rate is observed with an increase in CO pressure. A rate equation has been proposed, which was found to be in good agreement with the observed rate data within the limit of experimental errors. The kinetic parameters and activation energy values have been reported.     

On the Apparent Compensation Effect Found for Two Consecutive Reactions

A critical analysis of the use of an overall single rate reaction equation instead of the true rate equation corresponding to a complex process consisting in two consecutive reactions is presented. In accordance with this approximation, often used in the kinetic analysis of the system in which several reactions take place, the overall process is described by the apparent activation parameters (the apparent activation energy, E _ap, and the apparent pre-exponential factor, A _ap) and the apparent conversion function. The theoretical isotherms (α=α(t), where a is the conversion degree and t is the time) have been simulated for a system in which two consecutive reactions occur. In this case, the apparent activation parameters depends on: (a) the considered range of the temperature; (b) the temperature, for a given conversion degree. It is shown that the apparent activation parameters are corrrelated by the compensation effect relationship: lnA _ap=α*+β*E _ap where α* and β* are the parameters of the linear regression. The possibility of using the apparent kinetic parameters to predict the isotherms α=α(t) for temperatures lower than those for which these parameters were evaluated, is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-isothermal kinetic study on the decomposition of Zn acetate-based sol-gel precursor

The paper presents a non-isothermal kinetic study of the decomposition of Zn acetate-based gel precursors for ZnO thin films, based on the thermogravimetric (TG) data. The evaluation of the dependence of the activation energy (E) on the mass loss (Δm) using the isoconversional methods (Friedman (FR), Flynn-Wall-Ozawa (FWO) and Kissinger-Akahira-Sunose (KAS)) has been presented in a previous paper. It was obtained that the sample dried at 125°C for 8 h exhibits the activation energy independent on the heating rate for the second decomposition step. In this paper the invariant kinetic parameter (IKP) method is used for evaluating the invariant activation parameters, which were used for numerically evaluation of the function of conversion. The value of the invariant activation energy is in a good agreement with those determined by isoconversional methods. In order to determine the kinetic model, IKP method was associated with the criterion of coincidence of the kinetic parameters for all heating rates. Finally, the following kinetic triplet was obtained: E=91.7 (±0.1) kJ mol⁻¹, lnA(s⁻¹)=16.174 (±0.020) and F1 kinetic model.     

Linear sweep voltammetry at the tubular graphite electrode: Part II. Totally irreversible processes

The theory of linear sweep voltammetry at the tubular graphite electrode has been developed for irreversible processes. The convective diffusion differential equations have been transformed into an integral equation which is solved numerically. The current-potential curves have been calculated theoretically and verified experimentally. The dependence of the current-potential curves on velocity has been studied. A procedure for the determination of kinetic parameters, i.e. standard rate constant and transfer coefficient, is presented.     

Crystallization of a melt spun Fe-Ni based metallic glass

The crystallization kinetics of a melt spun Fe-Ni based alloy has been investigated, with both isothermal and continuous heating experiments, by means of differential scanning calorimetry. The alloy presents two separated crystallization processes. In order to perform the kinetic analysis of a melt spun metallic glass and to decide which kinetic model agrees better with the experimental crystallization data as the crystallized fraction x. We compare the experimental dependence of ln(k0f(x)) vs. (1-x) and that predicted, assuming different model equations for f(x). Both crystallization processes follow the JMAE equation and the master curve is the same for isothermal and non-isothermal data. This revised version was published online in July 2006 with corrections to the Cover Date.     

The ORAC Assay: Mathematical Analysis of the Rate Equations and Some Practical Considerations

ORAC (oxygen radical absorbance capacity), a method widely used for measuring the total antioxidant capacity of biological samples, can also be used for the determination of the relative reactivity of an antioxidant compound (XH) by examining the dependence of the rate of consumption of the probe (PH) on the concentration of XH; initial conditions are chosen in such a way that the rate of consumption of the starting reactants may be assumed to follow a drastically simplified kinetic scheme, and the steady‐state approximation for the concentration of the azo compound peroxyl (ROO^•) radical is invoked to simplify the analysis. Here we first attempted to find an analytical solution to the coupled first‐order ordinary differential equations (ODEs) of the minimal ORAC kinetic system, applying Lie symmetry group theory without any precondition. However, the Lie symmetry transformations applied to the Chini equation, which appeared after mathematical transformations, showed that the form of the coefficients of the Chini equation precluded the analytical solution of the minimal ORAC kinetic system through symmetry reduction. Consequently, an approximate analytical solution was sought, valid for the case when the bimolecular rate constant of XH with ROO^• (i.e., k_x ) was much larger than that of PH with ROO^• (i.e., k_p ). Using numerical solutions of the original set of ODEs of the ORAC kinetic system, the quality of the approximate solution was inspected under conditions that correspond to those employed in several ORAC methods together with a low initial concentration of the azo compound radical initiator. The simulations allowed us to conclude that the approximate analytical solution of the ODEs of the minimal ORAC kinetic system was not entirely devoid of academic interest, but its applicability was restricted to conditions where both k_x ≫ k_p and the initial concentration of XH was higher than that of PH.     

New trends in the kinetics of hydroformylation of vinyl acetate using Rh complex catalysts

The kinetics of hydroformylation of vinyl acetate using [Rh(CO)₂Cl]₂ complex catalyst has been investigated at 80 °C. The trends are quite different from those observed for the HRh(CO)(PPh₃)₃-catalyzed systems. The dependence of the rate on P(H₂) and P(CO) was found to be linear, whereas the dependence of rate on vinyl acetate concentration was found to be first order, followed by substrate-inhibited kinetics at higher olefin concentrations. The rate dependence on the catalyst concentration was found to be fractional order. A rate equation has been proposed and kinetic parameters evaluated.     

Improved Iterative Version of the Coats-Redfern Method to Evaluate Non-Isothermal Kinetic Parameters

An improved version of the Coats-Redfern method of evaluating non-isothermal kinetic parameters is presented. The Coats-Redfern approximation of the temperature integral is replaced by a third-degree rational approximation, which is much more accurate. The kinetic parameters are evaluated iteratively by linear regression and, besides the correlation coefficient, the F test is suggested as a supplementary statistical criterion for selecting the most probable mechanism function. For applications, both non-isothermal data obtained by theoretical simulation and experimental data taken from the literature for the non-isothermal dehydration of Mg(OH)₂ have been processed.This revised version was published online in November 2005 with corrections to the Cover Date.     

Sorption characteristics of an economical sorbent material used for removal radioisotopes of cesium and europium

Application study for the evaluation of sorption characteristics of sawdust as an economical sorbent material used for decontamination of radioisotopes cesium and europium from aqueous solution has been carried out in the present work. In this respect, sawdust (untreated and treated by HNO₃) has been prepared from the commercial processing of wood for furniture production. Pore properties of the activated carbon such as BET surface area, pore volume, pore size distribution, and pore diameter were characterized by N₂ adsorption and DFT software. Radiotracer method onto sawdust from aqueous solutions was studied in a batch technique with respect to pH, contact time, temperature. The kinetics of adsorption of Eu³⁺ and Cs⁺ have been discussed using five kinetic models namely, pseudo-first-order model, pseudo-second-order model, Elovich equation, intraparticle diffusion model, and modified Freundlich equation that have been tested in order to analysis the experimental data. Kinetic parameters and correlation coefficients were determined. It was shown that the second-order kinetic equation could describe the sorption kinetics for two metal ions. The metal uptake process was found to be controlled by intraparticle diffusion. Thermodynamic parameters, such as ΔH, ΔG and ΔS, have been calculated by using the thermodynamic equilibrium coefficient obtained at different temperatures. The obtained results indicated that endothermic nature of sorption process for both ^152+154Eu and ¹³⁴Cs onto sawdust.     

Kinetic analysis of thermogravimetric data obtained under linear temperature programming—a method based on calculations of the temperature integral by interpolation

A new technique, called interpolation method, with general application in the kinetic analysis of processes studied by thermogravimetry (TG) under linear temperature programming is developed. It is based on the linear relationship, with slope 1, between log g() and log I(γ, θ) for the appropriate kinetic function, where I(γ, θ) is the normalized temperature integral, θ the normalized temperature (θ=T/T₀) and γ a dimensionless activation energy (γ=E/RT₀). Values of log I(γ, θ) are calculated by linear interpolations in a pre-built table. This method can easily be programmed and implemented in a personal computer, where the results (kinetic parameters and quality of regressions for the kinetic functions considered) are typically obtained in a very short time. The method is validated by analyzing different simulated thermogravimetric curves and comparing the results with those determined with some classic methods taken from the literature. In addition, the results are compared with the values obtained by a similar method, also developed and explained in this paper, which involves the evaluation of all the values of the temperature integral by numerical integration, therefore, demanding a much larger calculation time. The interpolation method is found to be more accurate than other published methods, particularly in the case of thermogravimetric curves corresponding to processes with low activation energies. The results obtained are always similar to those determined by the integration method, which is taken as reference. Application of the technique to experimental data for various types of reactions shows that the results are in agreement with the published parameters and kinetic laws.     

Approximate equations for the determination of complexing parameters: Applicability criteria

Quantitative critera for the applicability of several approximate equations for finding complexing parameters are analyzed using a computer simulation technique. The Benesi-Hildebrand equation has been found most suitable for this purpose. The conclusions obtained are compared with the applicability criteria already known for approximate equations. By analyzing literature data it has been shown that it is possible to determine the correctness of published values for equilibrium constants of complexing and the extinction coefficient of a complex.