Thermokinetic parameter

Thermal methods in kinetic modelling. Methods for the estimation of thermokinetic parameters based on experiments in a reaction calorimeter will be discussed below. As mentioned in section 5.4.4.3, instantaneous heat evolved due to a single reaction is directly proportional to the reaction rate. Assume that the reaction is of first order. Then for isothermal operation ... 

This test can be used to give early detection of the initial exothermicity. It is possible to estimate thermokinetic parameters (e.g., the activation energy and the adiabatic self-heat rate) and to estimate how the initial temperature for self-sustaining reactions will vary with the quantity of material present. 

Martinez, M. R., Estimation of Gas-Phase Thermokinetic Parameters Thermochemical Group Additivity Computer Program (TGAP). NTIS AD-762-614 and AD-769-631, 1973. 

FIGURE 13.5 Calorimetric and volumetric data obtained from adsorption calorimetry measurements Raw pressure and heat flow data obtained for each dose of probe molecule and Thermokinetic parameter (a), Volumetric isotherms (b), Calorimetric isotherms (c), Integral heats (d), Differential heats (e), Site Energy Distribution Spectrum (f). (From Damjanovic, Lj. and Auroux, A., Handbook of Thermal Analysis and Calorimetry, Further Advances, Techniques and Applications, Elsevier, Amsterdam, 387-438, 2007. With permission.)... 

Plot of the variation of the thermokinetic parameter as a fnnction of the adsorbed amount of probe. 

Measurement of the thermokinetic parameter can be used to provide a more detailed characterization of the acid properties of solid acid catalysts, for example, differentiate reversible and irreversible adsorption processes. For example, Auroux et al. [162] used volumetric, calorimetric, and thermokinetic data of ammonia adsorption to obtain a better definition of the acidity of decationated and boron-modified ZSM5 zeolites (Figure 13.7). 

FIGURE 13.7 Variation of the thermokinetic parameter (in minutes) versus the ammonia uptake for a H-ZSM5 sample and boron-modified H-ZSM5. (From Auroux, A., Sayed, M. B., and Vedrine, J. C., Thermochim. Acta, 93, 557-60, 1985. With permission.)... 

When the thermokinetic parameter was plotted versus the amount of NH3 adsorbed for samples of H-ZSM5 (Si/Al = 10.3) pretreated at 400 and 800°C it was found that the maximum time constant is higher for the sample pretreated at 800°C than for that pretreated at 400°C [103]. In fact, the increase of the pretreatment temperature caused dealumination extra-framework aluminum species were created that restricted the access to the channels and created diffusional limitations. 

Snee, T.)., Bassani, C. and Ligthart, ).A.M. (1993) Determination of the thermokinetic parameters of an exothermic reaction using isothermal adiabatic and temperature programed calorimetry in conjunction with spectrophotometry. Journal of Loss Prevention in the Process Industries, 6 (2), 87. 

Finally, the systematic determination of the time constants (or thermokinetic parameters) of the calorimetric signal peaks gives information on the diffusion... 

The thermokinetic parameter was calculated as a function of coverage to separate the different processes involved in the adsorption mechanism. Furthermore, for the runs involving only reversible adsorption (the second adsorption run for each sample), accurate evaluation of the initial heat was possible by extrapolating the curves to zero coverage on a semilogarithmic... 

The thermokinetic parameter as defined above provides semiquantitative information on the kinetics of the processes occurring in a calorimeter. The rigorous mathematical modeling of the thermokinetics for heat-flow calorimeters (2,34,42,130-132) and isoperibol calorimeters (133) has been recently discussed. Using these methods it is possible to obtain quantitatively the energetic as well as the kinetic parameters describing a number of important processes such as adsorption, desorption, consecutive processes involving the formation of adsorption intermediates, and chemical reactions. 

Various applications of adsorption calorimetry in the study of heterogeneous catalysis have been presented in this review. It has been seen that this technique can provide valuable information about the thermodynamic and kinetic properties of the catalyst surface sites. In cases where the adsorbed species reach thermodynamic equilibrium with the catalyst, the differential heat of adsorption versus coverage is a measure of the number and strength of the various surface sites, whereas the corresponding entropy of adsorption is a probe of the mobility of the adsorbed species on these surface sites. The thermokinetic parameter provides information about the rates of surface processes. This information is particularly useful in those processes for which the above enthalpic and entropic measurements have been made. 

Table 11.10. The Precision of the Thermokinetic Parameters for di- -butyl Peroxidt Evaluated from 16 Runs (168)...

This kind of experimental evaluation automatically yields very reliable estimates on the thermokinetic parameter E/R, because, simply said, the value obtained describes quite differing individual experiments with equal quality. Quite consciously the input value for the simulation has not been mentioned thus far. 

Suspension polymerization of styrene, thermokinetic parameters for scale-up 432... 

The surface acidity of three commercial mordenite (MOR) zeolites with Si/Al ratios of 10, 60, and 80 has been evaluated by adsorption micro calorimetry at 423 K, using pyridine as a probe molecule [210]. As could be expected from the Si/Al ratios, the total pyridine uptakes varied in the order MOR-10 >MOR-60 >MOR-80. The initial differential heats of adsorption were in the range 215-220 kJ mol After a sudden drop, Qdiff changed slightly and stepwise over a relatively wide range of pyridine uptake (at least for MOR-10) and then steeply decreased. The site-energy distributions and the thermokinetic parameters versus coverage were also determined [210]. 

Another sign of development is that a growing number of thermokinetic parameters are accompanied by estimations of their accuracy. In the best cases, these uncertainty estimates are based not on the error analysis of a single experiment but reflect the comparison of several independent experimental or theoretical studies and therefore incorporate systematic errors of the various methods. In the past, such evaluations were performed by human experts, but as the dataset grows, perhaps a new paradigm for this process is required. Data collaboration approaches have been suggested which could place this task in the hands of wide communities (and computer software), rather than small groups of experts. 

Fig. 3.7 Thermokinetic parameter as a function of pyridine uptake on mordenite samples (from [16])...

The kinetics of heat release during adsorption can be monitored by the change in thermokinetic parameter t [14], The calorimetric signal decreases exponentially with the time of adsorption after the maximum of each adsorption peak. This can be expressed in the form D = where D and Dm are the deviation at time... 

As it can be seen in Fig. 12.8, the kinetic of CO adsorption on Pt based catalysts did not change when the adsorption and the pre-treatment were performed at higher temperature. As expected, the thermokinetic parameter firstly increases to reach a maximum and then slowly decreases showing that CO is almost completely irreversibly adsorbed on the surface of Pt-based catalyst. The amount held by the strong chemisorption sites at a certain adsorption temperature gives valuable information about the catalysts behaviour towards poisoning. Indeed, as deduced from volumetric data, 93 and 85 % of the total amount of CO was irreversibly adsorbed on Pt/C Tanaka catalyst for the powder pre-treated at 25 °C and CO adsorbed at 30 °C, and for the same sample pre-treated at 100 °C and CO adsorbed at 80 °C, respectively. Similar... 

Fig. 12.8 Variation of the thermokinetic parameter, T, versus CO uptake for Pt/C sample (Tanaka, lot 103-1341R)...

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