Erhard Koch

DTA curves and non-isothermal reaction rates

Abstract 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.

Reaction kinetics at linearly increased temperature. I. Comparative characterization of reactions in solution and solid phase in a unique “mechanistic diagram”

Abstract A complex reaction can be characterized kinetically in a special “Mechanistic Diagram”. From a time/rate plot recorded at constant heating, the shape index S and the reaction type index M may be calculated. The latter represents a sort of standardized, reciprocal half-width since it has to be referred to the activation parameters of a reference reaction. In practice, it is useful to take those apparent activation parameters which result from a first-order (or second-order) evaluation of either the initial or the total part of the signal. In a plane S versus M , all basic sorts of reaction may be recognized since they yield points (first- or second-order elementary processes), lines (e.g. order kinetics. 0 n n -order line. The diagnostic potential of this diagram is strongly increased if parametric curves due to experimental series, based on systematic changes of conditions (initial concentration of reactant, heating rate, pressure etc.) are considered. Constancy of S and M then will signal a temporary dominance of a part of the prevailing reaction mechanism.

Study of bimolecular reactions in solution by non-isothermal methods☆

Abstract The undistorted progress of bimolecular processes in solution can be studied by DTA experiments followed by the estimation of shape index and half-width and the reference of these quantities to the corresponding rate curves. Empirical relationships are presented which we derived by digital computer application and which allow calculation of the above corrected values for reactions with or without equimolecular ratio of the reactants. The application is illustrated by the evaluation of DTA curves of some reduction, oxidation and Diels-Adler reactions. Additional computer-generated DTA curves based on the evaluated activation data and reaction enthalpies confirm the results. The significance of the order in non-isothermal reaction kinetics, referred to time, is discussed.

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

Abstract 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

Reaction kinetics at linearly increased temperature. IV. Relationships between dta curves, rate curves and adiabatic calorimetry

Abstract A general concept is presented for the kinetic interpretation of DTA curves. This is based on the limiting conditions of a DTA measurement: either the kinetic cell constant is zero (adiabatic conditions), or infinite (rate curve). On the other hand, the self-heating effect (thermal feedback), based on the product of the reaction enthalpy with the reactant feed, may be absent (“ideal” kinetic DTA curve) or infinite (impulse reaction). Our recent formulae for the correction of the kinetic classification parameters, shape index and reaction type index, as well as other relationships and their utility, are successfully tested by application to ca. 2000 experimental DTA curves obtained in stirred solutions. The expressions reveal the influence of the activation parameters, heating rate, maximum signal height and cell constant and, therefore, allow a general discussion of the kinetics, independent of the experimental conditions.

NON-ISOTHERMAL REACTION ANALYSIS AND ARTIFICIAL INTELLIGENCE-A PROMISING COMBINATION FOR KINETIC STUDIES USING THERMOANALYTICAL METHODS *

Abstract Applications of the computer to various problems in the evaluation of TA records, obtained by DTA or UV reaction spectroscopy, are discussed with a view to model searches. preferentially in homogeneous kinetics, and are compared with chess computer strategies. For all TA methods based on proportionality between the temporary kinetic flux and signal amplitude, mechanistic codes can be calculated which allow comparison with elaborated theoretical codes of basic reaction mechanisms. All sources needed for a model-search program, and the complete set of such concentration codes for two-step models are presented. with a view to the differences between the codes of elementary reactions. A self-learning expert system, inducing both creation and study of new basic material, should be more effective than the tedious reproduction of the signals of individual experiments by fitting the respective activation and signal parameters, using various arbitrarily assumed models.

Thiocarbonyl azide s-oxide—II: The decomposition of thiobenzoylazide s-oxide

Abstract The reaction between thiobenzoyl chloride S oxide 4 , (R = C 6 H 5 ) and the azide ion at -80° leads to the labile thiobenzoyl azide S -oxide 5 , (R = C 6 H 5 ) Raising the temperature to -40° initiates decomposition of the latter to benzomtrile, nitrogen, sulfur and sulfur dioxide The thermally induced process was monitored by differential thermal analysis (DTA) which yielded a maximum heat effect at -11° The derived reaction enthalpy is ΔH=−45.6 kcal mole −1 and the activation parameters are ΔH ≠ = 20.2 kcal mol −1 ΔS ≠ = 6.3 eu (at −11°). The DTA shape index (S) and the reaction type index (M) are found to be in excellent agreement with a rate controlling first order reaction. Apart from the main peak at -11°, lack of a temperature difference signal throughout the range of measurement rules out an enthalpy-significant azide isomenzation and further suggests that decomposition takes place from a single isomer. Semi-empirical energy barrier calculations provide a rationale for the single conformer interpretation. The data are consistent either with a reaction in which N 2 and SO are expelled simultaneously or with the formation of a short-lived intermediate arising from N2 loss which rapidly eliminates sulfur monoxide. Intermediate formation of thiatriazole S -oxide cannot, however, be ruled out unambiguously. Since thioazides cyclize readily to thiatriazoles, whereas thioazide S oxides are not observed to cyclize, MO calculations have been carried out for the ring closures 2→3 and 5→6 (R= H) Orbital correlation diagrams for each potential energy surface show that ring formation is “allowed” in both cases. It is suggested that the variable chemical behavior of thioazides and their S -oxides is due to disruption of aromatic character in the hypothetical thiatriazole S -oxide product.

Reaction kinetics at linearly increased temperature. II. DTA study of uncatalyzed bromate oscillators

Abstract Uncatalyzed bromate oscillators, composed of sodium bromate and some phenol and aniline derivatives in dilute sulphuric acid, are studied by means of DTA. Up to five non-oscillatory DTA peaks are obtained, apart from oscillatory structures observed under certain conditions. Systematic changes of the initial concentrations of bromate, bromide or the aromatic compounds reveal different onset temperatures and heights of the peaks. It is concluded that 1,2-diquinones, brominated aromatic compounds, their dimers and/or di- or tribrominated aromatic molecules are formed as transients which carry information regarding the kinetic prehistory of the reaction from one peak to the next one which appears at higher temperature.

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

Abstract 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.

Reaction kinetics at linearly increased temperature. III. Initial temperatures and heights of peaks in concentration series

Abstract For reactions in solution, the readily available initial temperatures and heights of the DTA peaks of experimental concentration series give a first insight into the prevailing reaction mechanism. The results for ten various systems studied show dramatic differences in the correlation of maximum signal height, referred to the concentration of varied reactants vs. initial temperature. The different types of such a correlation are discussed both for isolated and overlapping peaks, under inclusion of consecutive faster processes.