Programmed temperature kinetics

Kinetic studies at several temperatures followed by application of the Arrhenius equation as described constitutes the usual procedure for the measurement of activation parameters, but other methods have been described. Bunce et al. eliminate the rate constant between the Arrhenius equation and the integrated rate equation, obtaining an equation relating concentration to time and temperature. This is analyzed by nonlinear regression to extract the activation energy. Another approach is to program temperature as a function of time and to analyze the concentration-time data for the activation energy. This nonisothermal method is attractive because it is efficient, but its use is not widespread. ... 

The techniques referred to above (Sects. 1—3) may be operated for a sample heated in a constant temperature environment or under conditions of programmed temperature change. Very similar equipment can often be used differences normally reside in the temperature control of the reactant cell. Non-isothermal measurements of mass loss are termed thermogravimetry (TG), absorption or evolution of heat is differential scanning calorimetry (DSC), and measurement of the temperature difference between the sample and an inert reference substance is termed differential thermal analysis (DTA). These techniques can be used singly [33,76,174] or in combination and may include provision for EGA. Applications of non-isothermal measurements have ranged from the rapid qualitative estimation of reaction temperature to the quantitative determination of kinetic parameters [175—177]. The evaluation of kinetic parameters from non-isothermal data is dealt with in detail in Chap. 3.6. 

A thermochemical method that simultaneously measures differences in heat flow into a test substance and a reference substance (whose thermochemical properties are already well characterized) as both are subjected to programmed temperature ramping of the otherwise thermally isolated sample holder. The advantage of differential scanning calorimetry is a kinetic technique that allows one to record differences in heat absorption directly rather than measuring the total heat evolved/... 

Edel, ., and Baltzer, M. O. (1980), Nonisothermal kinetics with programmed temperature steps, I. Pharm. Sci., 69,287-290. 

Ortiz Uribe, M. I., Romero Salvador, A., and Irabien Gulias, A. (1985), Kinetic analysis for Uquid-phase reactions from programmed temperature data. I. Simple analysis of potential kinetic laws, Thermochem. Acta, 94, 323-331. 

Conventional kinetic studies are carried out under isothermal conditions, but the kinetic analyses based on experiments during which the reactant is subjected to a programmed temperature variation have provided additional interesting possibilities. 

The kinetics of a first-order reaction are very similar to those represented by the contracting volume equation [70], except in the final stages of reaction when a approaches 1.00. In measurements of reactivity, or in comparisons of properties of similar substances, the first-order expression can sometimes be used as a convenient empirical measurement of rate. The assumption of first-order behaviour is often made in the kinetic analyses of programmed temperature experiments (see Chapter 5). The software supplied with many commercial instruments often provides only order-based equations for kinetic analysis of data, whereas other equations more obviously applicable to solids, such as those given here, are not tested. 

Thus data for isothermal kinetic analyses consist of sets of measured values of a, t (da/d/), t (da/d/), a, etc., that may be interconverted. The temperature (and accuracy limits of all data) for each experiment are also recorded. For programmed temperature (non-isothermal) experiments similar data are recorded, together with the important additional temperature-time relationship, so that (if required) values of a, t and T can be calculated for each measurement. 

The kinetics of dehydroxylation of Mg(OH)2 are sensitive to the prevailing pressure of water vapour, a factor which lead Sharp [6] to conclude that the value of should only be determined imder conditions of controlled atmosphere. From consideration of the ranges of values of which have been reported, 67 to 400 and 80 to 125 kJ mol fi om dynamie and from isothermal methods, respectively, it is concluded that more sophisticated analyses of the programmed temperature data are required. The most reliable value of Z , is identified [6] as 84 kJ mol, comparable with, or slightly greater than, the reaetion enthalpy. 

Kinetic data measured for the decomposition of calcium carbonate under isothermal and under programmed-temperature conditions [11] and varied reaction environments influencing the ease of removal of the CO2 product, show that the apparent values of the kinetic parameters k, A and may be influenced by sample heating rate, reactant self-cooling, sample mass, geometry and particle size, which determine the rate because of the reversible nature of the decomposition [12]. These effects can lead to compensation behaviour [13]. 

Dieckmann V., Schenck H.J., Horsfield B., Welte D.H. (1998) Kinetics of petroleum generation and cracking by programmed-temperature closed-system pyrolysis of Toarcian shales. Fuel 77, 23-31. 

Figure 40. Twelve different patterns of temperature programs used to study the effect of temperature programs on kinetic parameters estimated by nonisothemal prediction. (Reproduced from Ref. 334 with permission.)...

Schenk H. J., Di Primio R. and Horsfield B. (1997) The conversion of oil into gas in petroleum reservoirs. Part 1 comparative kinetic investigation of gas generation from crude oils of lacustrine, marine and fluviodeltaic origin by programmed-temperature closed-system pyrolysis. Org. Geochem. 26, 467-481. 

The techniques of thermal analysis stimulated an interest in the estimation of reaction kinetic parameters from programmed temperature experiments. Some of this background was covered by Brown and Galwey in Chapter 3 of Volume 1 [Vol.l, Ch.3]. A major advance was... 

Resistively heated-filament pyrolyzers offer the most versatility of the available units. They allow a wide range of programmed temperature and time profiles including stepped pyrolysis. This allows the elucidation of the thermal stability profile of the sample it provides data to allow the kinetic analysis of polymer degradation and may facilitate the identification of unknown samples. 

The results presented in Figures 6.11.17-6.11.21 were calculated with the commercial program Presto-Kinetics (solver for differential equations, www.cit-wulkow. de). The maximum temperature of the ARGE catalyst is about 260 °C as the Fe catalyst then starts to deactivate by sintering, which substantially lowers the internal surface area (Kuntze, 1991). Hence, to be on the safe side, 250 °C was chosen as the maximum allowable temperature. 

If the parameters of the kinetics and heat transfer are known, the PA synthesis can be simulated by modern computers and programs to solve differential equations. Here this was carried out by the commercial program Presto-Kinetics (www.cit-wulkow.de), which is frequently used in this book. The results are given in Figure 6.13.1 by the axial profiles of temperature (tube axis), o-xylene conversion, and selectivity to phthalic anhydride for a tube length of 3 m. 

The microkinetics analysis, as a useful and powerful tool to interpret, harmonize and consolidate the study of catal3dic phenomena, can describe various results obtained at wide experimental conditions. For ammonia synthesis reaction discussed in this section, the microkinetic models are evaluated from the experimental data such as the sticking coefficient of dissociated nitrogen adsorption, the spectrum of programmed-temperature desorption of adsorbed nitrogen as well as the kinetics of ammonia synthesis at industrial conditions and at laboratory conditions are far from equilibrium. 

Thermogravimetiy can be used either under programmed temperatures to identify the various transformations undergone by a system during a rise in temperature or under isothermal condition for kinetic measurements. 

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