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Reaction Kinetics in Differential Thermal Analysis

In differential thermal analysis, the temperature at which the maximum deflection is observed varies with heating rate for certain types of reactions. An expression can be derived relating this variation with the kinetics of the reaction. By making a number of differential thermal patterns at different heating rates, the kinetic constants can be obtained directly from the differential thermal data. Measurements of the variation of peak temperature with heating rate have been made for several minerals of the kaolin group, the values of the kinetic constants determined, and these values compared with corresponding values obtained for both the same samples and similar material by conventional isothermal techniques. Some factors affecting the results are discussed. The method of differential thermal analysis (DTA) has been universally accepted by mineralogical laboratories as a rapid and convenient means for recording the thermal effects that occur as a sample is heated. Changes in heat content of the active sample are indicated by deflections shown by a line representing the differential temperature. It is conventional to represent an endothermic effect by a negative deflection and an exothermic effect by a positive deflection. The deflections, whether positive or negative, are called peaks.

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Variation of Peak Temperature With Heating Rate in Differential Thermal Analysis

Clay minerals are of non uniform composition and particle size. Also their identification and nomenclature have given much confusion. Examples are given. Quantitative analysis of clay minerals from deposits and soils, by X-ray, thermo- and infrared analysis is treated. Examples are given of the large variability in the results; even for X-ray and electron microscope pure- and 85 to 90% chemical pure samples of kaolinite a well defined clay mineral. They are caused mainly by varying conditions of crystal growth from which result differences in isomorphous replacements, structure, ordering and strain. An amorphous weathering substance coating the mineral particles (Beilby layer) upsets in particular quantitative analyses of the finer kinds of clay minerals. Clay minerals from soils have, as compared to those from pure deposits, in particular formed by hydrothermal action, only poor characteristics of small intensity. Examples are given. Quantitative analyses are further hindered by specific characteristics for a certain mineral being masked by those of other minerals which usually occur in the same sample. Examples are given.

Quantitative analysis of clay minerals and their admixtures

Summary Thermoanalytical techniques offer attractive ways of determining kinetic parameters. There are obvious convenience and economy in making a single set of measurements in a few hours and performing extensive computations while the equipment is generating data on another material. This apparent gain in efficiency has led to considerable effort in planning computations which lead to easy extraction of the activation energy, the apparent kinetic order, the rate constant from a single curve. To enable these computations, simplifying assumptions had to be made. The following statements provide a set of cautions based on past work. Nearly all solid decompositions are topo-chemical in nature. Many reactions have some reversible step which leads to effects due to changing atmospheres or pressures. The variation of k with τ does not provide an accurate measure of the activation energy except under very reproducible conditions. The derivative dlnk/d(1/τ) is a partial, not a full, derivative and there is gener...

Kinetic Investigations by Techniques of Thermal Analysis

Kinetics of thermal decomposition of the solid state

AKt;TRACT From their isothermal experiments, Murray and White drew the conclusion that the dehydration reaOions of clays are first-order with a rate factor of Arrhenius form. The object of this paper is to discuss whether differential thermal analysis can be used to confirm or refute this hypothesis. The problem, previously considered by Murray and White, of a sample heated at a constant rate throughout is recalled. Particular attention is drawn to the effect of heating rate on the temperature at which the maximum rate of reaction occurs. To apply to differential thermal analysis, the treatment must be extended to take account of thermal gradients; as the mathematics involved is cumbersome, only results are considered. The most important result concerns the effects of sample size and dilution on the position of the turning-point. A disagreement with the results of experiments on kaolinite is pointed out; it is argued that only a small part of this disagreement is due to simplifications made in developing the theory, and it is concluded that the hypothesis that the clay reactions are first-order, with a rate factor of Arrhenius form, is only approximate.

E. C. Sewell

Papers

The Consequences for Differential Thermal Analysis of Assuming a Reaction to be First-Order