Kinetic data, from isothermal measurements

In order to find points of equal degrees of conversion (or equal Q-values) in Figure 2.18, van Geel [115] developed the method to evaluate kinetic data from the so-called isoconversion lines. A heat generating substance that follows Equation (2-11), when stored under isothermal conditions at different temperatures has generated an equal amount of heat (Q) when the product of t exp(-Ea/RT) has the same value. Thus, for two heat generation/time curves measured at Ti and T2, the same amount of heat (Q) has been generated, and thus the conversion is equal when ... 

Table 4.11.5 Comparison of kinetic data obtained from isothermal measurements in atubular fixed bed reactor with that from TG/DTG experiments (Jung, 2005).

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. 

Measurement of the extent to which the adsorbent removes the adsorbate from a liquid or gaseous phase. The data is used to construct adsorption isotherms and is often fitted to a model to provide information about binding constants, adsorption maxima and other parameters, and also speciation of surface complexes. Kinetic data may also be obtained. 

The parameters in Eq. (2.59) are usually determined from the condition that some function mean-square deviations between the experimental and calculated curves (the error function). The search for the minimum of the function Nelder-Mead algorithm.103 As an example, Table 2.2 contains results of the calculation of the constants in a self-accelerating kinetic equation used to describe experimental data from anionic-activated e-caprolactam polymerization for different catalyst concentrations. There is good correlation between the results obtained by different methods,as can be seen from Table 2.2. In order to increase the value of the experimental results, measurements have been made at different non-isothermal regimes, in which both the initial temperature and the temperature changes with time were varied. 

The induction time is the time involved between the instant where the sample reaches its initial temperature and the instant where the reaction rate reaches its maximum. In practice, two types of induction times must be considered the isothermal and the adiabatic. The isothermal induction time is the time a reaction takes to reach its maximum rate under isothermal conditions. It can typically be measured by DSC or DTA. This assumes that the heat release rate can be removed by an appropriate heat exchange system. Since the induction time is the result of a reaction producing the catalyst, the isothermal induction time is an exponential function of temperature. Thus, a plot of its natural logarithm, as a function of the inverse absolute temperature, delivers a straight line. The adiabatic induction time corresponds to the time to maximum rate under adiabatic conditions (TMRJ). It can be measured by adiabatic calorimetry or calculated from kinetic data. This time is valid if the temperature is left increasing at the instantaneous heat release rate. In general, adiabatic induction time is shorter than isothermal induction time. 

Abstract. One more method of study of the short-range order kinetics of H-atoms over tetrahedral interstices in lutetium (Lu) is proposed. It can be realized by the using of available data of measurements of heat capacity for h.c.p.-Lu-H interstitial solid solutions during the isothermal annealing. Comparison of estimated-parameters data from heat capacity and residual electrical-resistivity measurements is performed. It is shown that kinetics of heat capacity and residual resistivity at low temperatures is caused by the unique nature (short-range order relaxation) and can be described by two relaxation times at least. 

Several different mathematical procedures have been suggested for extracting kinetic information from sets of a,T data obtained at different heating rates, p. Friedman s method [54] is to plot ln(do5 d/)i against 1/7, measured at the same value of from a,T curves at different heating rates Pi (or different isothermal reaction temperatures, T). The parallel lines obtained have slopes = -E /R and different intercepts = ln[ f( )J. A value for A is obtained by extrapolation of a plot of the intercept against to a = 0. 

Zsako and Lungu [71] found compensation behaviour in kinetic data obtained from non-isothermal TG measurements for 134 decomposition reactions of bis(dioximato)cobalt(lII) compounds. The slopes of the compensation trends are influenced by both the organic ligand and the constituent anion which enters the coordination shell during reaction. 

Kinetic parameters measured by rising temperature techniques are considered by some workers to be less reliable than those calculated from isothermal data because of the additional assumptions required by the theory. Use of different applicable equations can give different values of A, and g(nr) [25,54,55]. Ingier-Stocka [55]... 

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