Kinetic Investigations by Techniques of Thermal Analysis

139

The "kinetic compensation effect" arises from deficiencies in the Arrhenius equation. Determination of the pre-exponential factor generally comprises only the reconciliation of the expression of the temperature dependence of the rate (the exponential term) with the observed rate. The applicability of the Arrhenius equation to a particular reaction could be tested by finding constancy or a predictable variation in the "frequency factor" with changes in experimental conditions or sample treatment or history.The Arrhenius equation is widely used in heterogeneous kinetics for two reasons. First, the relationship is well established in homogeneous kinetics; second, the form of the equation assures the user that numbers for the constants in the equation can be calculated. It is only necessary to adjust the form of f(&~/dt) or, for non-isothermal reactions, f(&~/dt) until, subjectively, a straight-line relationship is found when the logarithm of that function is plotted against 1/T.When this plot has been prepared and the "best straight line" drawn, the slope is ascribed to an activation energy, divided, of course, by R In 10. The difference is ascribed to a frequency factor according to the equationThe value of this "frequency factor" can vary by several orders of magnitude for a given reaction by different observers and sometimes by the same observer with small changes in conditions. The variation suggests immediately that the equation k r = Ae -etRr

mentioning

confidence: 95%

An examination of the kinetic compensation effect

Garn

1975

139

“…These authors are aware of the fact -often disregarded -that the starting vacuum of 10 -8 torr cannot be maintained when the reaction begins. As Garn [15] points out: "it is popularly supposed that if one withdraws gases from a chamber by continuous pumping, the pressure is everywhere equal to the indicated pressure... If there is a source of gases, the supposition is invalid".…”

Section: Methodsmentioning

confidence: 97%

Thermolysis under vacuum: Essential influence of the residual pressure on thermoanalytical curves and the reaction products

Rouquérol¹,

Ganteaume²

1977

This paper examines the influence of residual pressures in the range from 10-~to 5 torr on the course of thermal analysis. With the help of examples concerning in particular the thermolysis of gibbsite, AI(OH)3 , it is shown that a) the control of residual pressure is of virtually no use unless the rate of decomposition is also controlled (otherwise, the TG curves represent a composite phenomenon, which is practically unintelligible); b) the influence of residual pressure may be unexpectedly high both on the shape of the TG curves (and therefore on the apparent kinetic parameters) and on the nature (porosity, structure) of the products.The influence of the gas atmosphere on a thermal decomposition of the type solid A ~ solid B + gas is widely accepted. In 1951, Rowland and Lewis [1] in this way explained the usual DTA trace for calcite thermolysis, where the onset of decomposition may be observed as soon as 650 ~ (low partial pressure of CO~) and where "the reaction progressively becomes more vigourous until a peak is reached at about 925 ~ the temperature at which the reaction would begin if the furnace had been filled with COz at one atmosphere pressure. In 1960, Garn suggested simplification of the situation by operating under self-generated atmospheres [2], and several devices were proposed and used in order to control the overall pressure, e.g. the "cold sink", especially convenient in the case of water evolution [3], or the discontinuous and automatic gas extractor [4]. Nevertheless, "vacuum" was often considered as one pressure at which it may be worthwhile to carry out one experiment in order to complement a set of data obtained under higher pressures. Indeed, various authors, such as Eyraud et al. at the time of the first vacuum TG experiments, pointed out the "simplifying" part played by vacuum-operation, which was supposed to eliminate disturbing phenomena such as adsorption or diffusion processes [5] or secondary reactions [6] and to give rise to the simplest mechanism with higher decomposition rate [7]. Now pressures lower than I torr, which are usually referred to as "vacuum", actually cover a wide experimental range, down to 10 -~ torr, whereas the range of medium and *

“…The condition of virtually any of the materials under consideration will differ depending upon the path by which it reached that point in time -or even level of decomposition. In any real case, the conditions of the sample at, say, 50 % decomposition will depend upon the geometry and/or atmosphere as well as the heating rate [6]. The reaction is by no means homogeneous.…”

mentioning

confidence: 99%

“…The arguments of homogeneous kinetics do not apply. For inorganic systems it is well known to solid state kineticists that a single description will not fit the whole course of reaction [6]. Hulbert [7] and Young [8] have shown that at least five distinct regions can be identified in some isothermal decompositions.…”

mentioning

confidence: 99%

Non-isothermal kinetics

Garn

1974

Self Cite

The flurry of controversy over MacCallum and Tanner's [1] suggestion that only isothermal methods can be used to evaluate the order of reaction, the preexponential factor and the activation energy has brought out several deficiencies in our view of both isothermal and non-isothermal kinetics as applied to decompositions of solids.Hill [2], in his criticism of MacCallum and Tanner's conclusion, appeals to authority (Kissinger [3]) which has been under criticism from several quarters. The statement that "The only effect of an instantaneous change of temperature is in the velocity of thermal motion of the particles", is too specific. Assuming we could perform that instantaneous change, we know only that we have changed the total energy. Whether or not the increment in energy leads to instability and change in direction and/or velocity will depend upon the temperature and, in some cases, other variables.In citing the authority, Hill failed to note that the expressionwas already shown to be incomplete by Kissinger's own data. Both the dilution and the radius of the sample holder influence the rate, so the rate is a function of at least three variables. Other work [4] suggests that Primo, rather than r, is the appropriate variable. Kissinger's DTA curve also displays a clear lag in temperature during the decomposition of kaolinite, so dT/dt is varying quite markedly during the event. But dT/dt, rather than T, is used in his calculations of the activation energy. The actual value used, apparently, was the nominal heating rate. By measuring outside the sample, this very real gradient could be shoved under the carpet, but this concealment would not change its reality.The analogy suggested by Hill is indeed infirm; referring to an arrow in flight he states (Zeno's hypothesis) "although the arrow is in motion, at any moment it is at rest". More accurately, for some purposes it may be considered at rest. MacCallum 's [5] reply is pertinent; if the arrow were aflame, its condition would depend upon the instant of time chosen. But there are other variables. A particular 16"