DTA curves and non-isothermal reaction rates

Differential thermal analysis (DTA) is an effective means for studying chemical reactions, but its application to reaction kinetics is handicapped by the involvement of temperature feedback from the reaction heat and by the solvent dependence of the thermal conductivity.General, empirical relationships are derived from digital computer application which allow to transform half width and shape index of a DTA curve of any first-order process in a uniformly temperated sample to the values of the corresponding rate curve at linearly increased temperature.The expressions are complemented by some new relationships for an n-order reaction and are useful for the kinetic study of complex processes.     

Mechanistic Analysis of Solution Reactions by Non-Isothermal Calorimetry

For the rapid kinetic and energetic analysis of reactions in solution (τ_20°C > 10^-4s) by differential thermal analysis (DTA), the following thermogram parameters are defined as characterizing the start of the reaction: 1. initial temperature, 2. activation energy of the initiation reaction. In conjunction with the shape index (asymmetry of the DTA curve) and the half width of the DTA curve referred to standard physical conditions (cell constant, heating rate, and temperature difference), these quantities allow a simple distinction between one-step reactions of first and second order and composite reactions. It is possible to recognize whether a process involves parallel, successive, or equilibrium reactions, or combinations of these. The reaction mechanism can be clarified in many cases by measurements at various concentrations and heating rates and by discussion of the enthalpy values. The shortened method described in this report for the evaluation of the thermograms was derived with the aid of an analog computer and checked experimentally.     

Constant rate thermal analysis for thermal stability studies of polymers

This paper explores the relationship between the shapes of temperature-time curves obtained from experimental data recorded by means of constant rate thermal analysis (CRTA) and the kinetic model followed by the thermal degradation reaction. A detailed shape analysis of CRTA curves has been performed as a function of the most common kinetic models. The analysis has been validated with simulated data, and with experimental data recorded from the thermal degradation of polytetrafluoroethylene (PTFE), poly(1,4-butylene terephthalate) (PBT), polyethylene (PE) and poly(vinyl chloride) (PVC). The resulting temperature-time profiles indicate that the studied polymers decompose through phase boundary, random scission, diffusion and nucleation mechanisms respectively. The results here presented demonstrate that the strong dependence of the temperature-time profile on the reaction mechanism would allow the real kinetic model obeyed by a reaction to be discerned from a single CRTA curve.     

Limiting cases of DTA curves of one-step reactions and their application to the study of complex processes

Useful relationships are discussed for DTA studies of reactions in solution which are based on two proved concepts:1.For missing thermal feedback, i. e. linear increase of the reaction temperature, the influence of the kinetic cell constant, c, appears exclusively as a product with the specific time of the reaction, u.2.Interference of temperature feedback by the reaction heat is considered by the ratio of the maximum temperature difference (DTA peak height) over the specific temperature difference of the reaction. This can be understood from the Semenov Theory of Thermal Ignition of Gases under Adiabatic Conditions.     

Determination of kinetic parameters from TG curves by non-linear optimization

The results obtained so far by kinetic analysis of non-isothermal experiments indicate that the kinetic parameters found by the conventional methods, in general, do not describe the experimental curve in an optimum manner. This is due to the fact that the initial differential equation is transformed into the logarithmic and, consequently, linear form and that the initial and final weights of the conversion curve cannot be determined exactly, which may falsify the slope of the curve.Investigations have shown that the determination of the kinetic parameters by non-linear optimization (simplex method) results in a better fit of the theoretical conversion curve to the experimental one. But this procedure gives optimum results only when the initial and final weights of the reaction can be determined exactly. If this is impossible, exact parameters can be obtained only by the use of the non-standardized TG curve.Examples are cited to prove that it is possible to evaluate overlapping reactions by the formation of intervals. However, the evaluation of conversion curves merely by the use of mathematical methods can easily result in an erroneous interpretation of the reaction course investigated. Therefore, it is necessary to check the mathematical results as to their physical and chemical meaning.     

Mixing efficiency and instrumental delay effect on recorded kinetic curves

The effect of reactant addition time and instrumental response time on recorded kinetic curves was considered. The mixing-time. effect was considered for first- and second-order reactions in the case that a simple function of the concentration is measured, and for first-order reactions in the more complex case of non-adiabatic enthal-pimetric measurements. For any ratio of addition time to half-transformation time the proposed equations allow calculation of the correct rate constant and the error in the calculated initial concentration extrapolated from the experimental curve and show which portion of the experimental curve must be disregarded owing to the misleading effect of the addition time. The distortion due to the response-time of a thermistor used as concentration transducer has been calculated from a simplified model. The experimental kinetic measurements performed by quasi- and non-adiabatic enthalpimetry agree very satisfactorily with the theoretical data.     

Influence of the particle size distribution on the CRTA curves for the solid-state reactions of interface shrinkage type

The kinetic curves at infinite temperature for the solid-state reactions of the interface shrinkage type were drawn theoretically by taking account the particle size distribution in the sample mixture. The CRTA curves for the reactions with the particle size distribution can be drawn by utilizing the universal kinetic curves at infinite temperature. The proper kinetic treatment for the CRTA curves with the particle size distribution is discussed in connection with the property of the kinetic equation with respect to the particle size distribution. The present kinetic consideration is taken as a simulation for the reactions with a certain distribution in among the reactant particles, produced preferably by the mass and heat transfer phenomena during the thermoanalytical measurements. The merit of the rate jump method by a single cyclic CRTA curve is also discussed on the basis of the present results.     

On the method of bae for the determination of kinetic parameters from DTA curves

The mathematical error in the method proposed by Bae for the determination of kinetic parameters from DTA curves has been corrected. The proposed equation does not contain thermal constants of the apparatus, and can be applied to DTA curves by an iterative method. The results obtained by the application of this equation to experimental DTA curves for the decomposition of sodium bicarbonate compared well with those from isothermal measurements, even when the DTA sample holder assembly was of the isolated cup-type instead of the block-type assembly recommended by Bae.     

Simulation of titration curves indicated with two indicator electrodes (biamperometry)

A rigorous method to simulate titration curves with indication using two indicator electrodes (biamperometry) is presented. Computer simulations can be carried out for reversible as well as for irreversible systems. The different parameters like the area of the individual electrodes, applied potential difference, heterogeneous rate constant, and the kinetic parameter were varied and investigated as to their influence upon the shape of the titration curves. The theoretically derived effects match with the effects obtained by experiment. Considering the effects described here, it is possible to tailor the shape of the titration curve by the experimental conditions for specific applications in order to get an optimum shape at the end point of the titration.     

The influence of grain size on the overall kinetics of surface-induced glass crystallization

A simple kinetic model of surface-induced glass crystallization is proposed. The grain size of glass powders, a constant density of surface nuclei and a steadily increasing temperature throughout the reaction are taken into account. The crystal growth rate and the density of surface nuclei can be estimated easily from overall kinetic curves (e.g. DTA curves) of powder of different grain size.The usefulness of the model is demonstrated in the case of the primary surface-induced crystallization of cordierite glass powders.     

The Removal of Time–Concentration Data Points from Progress Curves Improves the Determination of Km: The Example of Paraoxonase 1

Several approaches for determining an enzyme’s kinetic parameter K_m (Michaelis constant) from progress curves have been developed in recent decades. In the present article, we compare different approaches on a set of experimental measurements of lactonase activity of paraoxonase 1 (PON1): (1) a differential-equation-based Michaelis–Menten (MM) reaction model in the program Dynafit; (2) an integrated MM rate equation, based on an approximation of the Lambert W function, in the program GraphPad Prism; (3) various techniques based on initial rates; and (4) the novel program “iFIT”, based on a method that removes data points outside the area of maximum curvature from the progress curve, before analysis with the integrated MM rate equation. We concluded that the integrated MM rate equation alone does not determine kinetic parameters precisely enough; however, when coupled with a method that removes data points (e.g., iFIT), it is highly precise. The results of iFIT are comparable to the results of Dynafit and outperform those of the approach with initial rates or with fitting the entire progress curve in GraphPad Prism; however, iFIT is simpler to use and does not require inputting a reaction mechanism. Removing unnecessary points from progress curves and focusing on the area around the maximum curvature is highly advised for all researchers determining K_m values from progress curves.     

Analysis of DTA curves and calculation of kinetic data using computer technique

Principles of two computer programs useful for the evaluation of heterogeneous kinetics are described.The first program ALANTA allows to obtain the non-isothermal kinetic curve from the shape of general DTA peak using the DTA-equation derived elsewhere¹.The second program SQUEST determines the kinetic mechanism which is the most appropriate to a given non-isothermal kinetic curve and evaluates the corresponding kinetic parameters. The program decides between 19 kinetic models and uses both integral and differential methods of evaluation.     

Kinetic analysis of derivative curves in thermal analysis

Two methods of obtaining kinetic parameters from derivative thermoanalytical curves are proposed. The methods are based on the general form of kinetic formulae and are applicable to general types of reactions governed by a single activation energy. One method utilizes the linear relation between peak temperature and heating rate in order to estimate the activation energy, and only the information of the rate of conversion versus the temperature is necessary. The other method needs the information of both the conversion and the rate of conversion versus the temperature, and the Arrhenius plot is made for an assumed kinetic mechanism.

     

On the autoaccelerated character of the branched oxidation of polyolefins

Photochemical or thermal (at moderate temperatures) oxidation of hydrocarbon polymers is characterised by the existence of a pseudo-induction period, during which oxidation is autoaccelerated, and a steady state. This latter corresponds to the equilibrium between hydroperoxide (POOH) decomposition and formation processes. All the kinetic schemes of thermal ageing, based on the assumption that POOH decomposition is the only source of radicals (whatever its order), have a common feature : the steady-state rate is independent of the rate constant of POOH decomposition, as experimentally observed in samples containing variable concentrations of catalytic residues. Experimental data indicate that the duration of the pseudo induction period is proportional to the reciprocal of the POOH decomposition rate constant and independent of any other rate constant. This is an exclusive property of kinetic schemes in which POOH decomposition is unimolecular (whereas termination is bimolecular). The corresponding set of differential equations has been first resolved from the hypothesis of existence of a stationary state for radical concentration. Although this hypothesis is questionable, the corresponding analytical expression appears as a good approximative solution for the general case (no hypothesis of stationary regime). This expression displays interesting predictive properties. Some eventual kinetic implications of spatial heterogeneity of oxidation are examined. Certain variables, for instance the second derivative of the kinetic curve of carbonyl growth (or oxygen absorption), or simply the kinetic curve of mass variation, vary in a non-monotonous way with exposure time. Consideration of timescale associated to these variations can lead to a quantitative approach of the homogeneity. Schematically, if the characteristic time of non-monotonous variations is of the order of magnitude of the reciprocal of the rate constant of POOH decomposition or lower, the oxidation can be considered almost homogeneous. In the example under study : experimental data on thermal oxidation of poly(propylene) indicate that these systems are not too far from homogeneous ones.     

Reaction kinetics in thermal analysis. Part 1. The sensitivity of kinetic equations to experimental errors. A mathematical analysis

The frequent publication of contradicting or meaningless kinetic parameters and the resulting criticism of the “ill-conditioned nature” of non-isothermal reaction kinetics led the authors to an examination of the sensitivity of kinetic parameters to experimental errors. Using simple mathematical deductions, conditions were given at which about 10% precision of the kinetic parameters can easily be achieved. To obtain a graphic picture about the information content of a thermoanalytical curve and the effect of the systematic measurement errors, mathematical relationships were deduced to show the dependence of the kinetic parameters on the formal (geometric) characteristics of the thermoanalytical curves.     

A Method for Esterification Reaction Rate Prediction of Aliphatic Monocarboxylic Acids with Primary Alcohols in 1,4‐Dioxane Based on Two Parametrical Taft Equation

Esterification reaction rates of aliphatic monocarboxylic acids with primary alcohols in 1,4‐dioxane as inert solvent were investigated. Acids were esterified with 1‐propanol and alcohols with acetic acid as model reactants at a constant temperature of 60°C, at a fixed ionic strength and pH in a batch reactor with a constant volume. For evaluation of reaction rates, an exact kinetic equation for the equilibrium reaction was applied. Under these conditions and for low reactants, concentrations reaction rate depends only on the structure of reactants and, therefore, can be predicted by a correlation equation with two Taft coefficients (inductive and steric effects). From these equations, it is possible to estimate the esterification reaction rate constant for other acid‐alcohol pairs. This methodology may also be suitable for other kinetic systems measured under comparable experimental conditions.     

Proben-Abhängigkeit (PA) curves and simple anhydrous carbonate minerals

Marked modifications to carbonate DTA curves are caused by variations in the partial pressure of CO₂ gas in the furnace atmosphere. Calcite is used to illustrate the curve configurational changes which may occur. Attention is drawn to the effects of variations in: thermal conductivity of the gases used as furnace atmospheres, the furnace access to the ambient atmosphere, the volume of the furnace “tube“ and the size of the sample (and therefore the amount of self generated CO₂). These effects emphasise the care with which the constancy of DTA determination conditions must be maintained for content evaluation methods such as “Proben-Abhängigkeit“ curves.     

The problem of “inverse reaction kinetics” under the aspect of calorimetric measurements

It is shown that the DTA method performed in a twin stirring-type apparatus has a good chance to successfully meet with the problems of “Inverse Reaction Kinetics”, i.e. to find out an appropriate reaction mechanism including the prevailing activation data of the particular steps for a reacting system studied. Although experimental signal curves can be reproduced using a suitable model and integrating the system of differential equations involved, other ways have to be used for a less tedious approach to the best mechanism.In order to develop adequate diagnostic criteria, the informative potential of different parameters obtained by a simple first/second order evaluation program is studied. For complex processes in solution, the dependencies of such parameters on the initial reactant concentration or on the heating rate often reveal periods of constancy which indicate the rate-determining steps of the mechanism. Based on concentration series of DTA experiments applied to twenty different systems, the following order of increasing kinetic utility of the parameters was found by comparing the number of these occurring periods of constancy:Peak temperature < Overall enthalpy < Initial activation energy < Overall activation energy < Final temperature < Initial A-factor < Relative signal height < Overall A-factor ? Initial temperature < Initial reaction type index < Shape index < Overall reaction type index. By these results, my earlier theoretically founded assumption has been confirmed that the “mechanistic indices” are the best quantities to reveal the reaction mechanism of any reacting system studied.     

A Computer Program for the Evaluation of Non-isothermal Kinetic Parameters

A program for the evaluation of non-isothermal kinetic parameters is presented. The program allows evaluation of the kinetic parameters under constant heating rate or constant reaction rate conditions. The simulation of temperature vs. conversion curves is also possible. A regression method is included, which allows a discrimination between various conversion functions and also evaluation of the activation parameters. The program was tested with various simulated decomposition curves and the non-isothermal decomposition curves of calcium oxalate. The program is written in Visual BASIC 4.0 and can be run under Windows 95 ©.     

Open-circuit reduction of oxygen coverage on Pt by organic substances: II. Particular cases depending on the coverage degrees

Two particular cases of the open-circuit reduction of the oxygen coverage on Pt by organic substances are examined—at high and at low coverage degrees. Suitable expansion in series of the general equations of part I and some simplifications lead to linearized equations which can easily be verified experimentally. It is shown that the form of the initial section of the experimental curves (at high coverage degrees) can be explained either accepting a chemical reaction of the coverage with the organic substance or assuming that no chemical interaction proceeds and the form of the curve is determined by the double laye charing. The difference in the concentration dependences makes however these two mechanisms distinguishable. At low coverage degrees the experimental curves can be described accepting an electrochemical mechanism of reduction of the oxygen coverage with the adsorption of the organic substance as the rate determining step. The linearized equations derived allow the determination of the kinetic parameters of the process.