Isothermal kinetic measurements

The time course of the emission intensity is proportional to the concentration of the HEI and, in the case of isolated HEIs, the rate constant for its decomposition is obtained from the CL emission curves. Isothermal kinetic measurements give rise to the activation parameters for the whole transformation and can be used for mechanistic discussion in the case of isolated HEI ° . Specific CL methods have also been used to determine... 

Maeder, M., Molloy, K.J., and Schumacher, M.M., Analysis of non-isothermal kinetic measurements, Anal. Chim. Acta, 1997, 337, 73-81. 

The dehydration of kaolinite has been the subject of several kinetic studies and Brett et al. [1] summarize the salient features of the mechanisms proposed for the sequence of reactions by which kaolinite is converted to mullite (920 to 1370 K). The first step, water loss, is most satisfactorily described by a two-dimensional diffusion equation. Brindley et al. [57] proposed this model from isothermal kinetic measurements (670 to 810 K) and reported a marked increase of in a maintained pressure of water vapour. Anthony and Gam [58] concluded that random nucleation is rate limiting at low pressures of water vapour and that this accounts for reports of first-order kinetic behaviour. Increase in the rate of nucleation, as the (HjO) is increased, is ascribed to a proton transfer mechanism, and acceleration of the growth process may result from contributions due to the onset of the reverse reaction. 

Springmaim, S., Friedrich, G Himmen, M Sommer, M. and Eigenberger, G. (2002) Isothermal kinetic measurements for hydrogen production from hydrocarbon fuels using a novel kinetic reactor concept Appl. Catal. A, 235, 101-111. 

Isothermal kinetic measurements fall into two categories method 1, in which the rate and extent of reaction at constant temperature are continuously monitored in the DSC and method 2, in which a partially cured sample is heated in the DSC to measure the residual heat of reaction. An advantage of method 1 is the simultaneous measurement of conversion and rate of conversion, which are necessary for some kinetic analyses. It should be noted that vitrification will occur during method 1 measurements if Tcure is less than Tg,. Method 2 has the advantage of simultaneous measurement of and conversion, from which the Tg-conversion relationship can be established. Both thermal and UV cure reactions can be measured by these methods. 

Traditional Isothermal Kinetics Measurements of conversion-rate of conversion-time data by isothermal method 1 and conversion-time data by isothermal method 2 were described earlier in this section. Isothermal method 1 measurements have the advantage of simultaneously measuring conversion (a) and rate of conversion (daJdt), which allows use of derivative forms of the rate equation such as Eqs. (2.82) and (2.86). Both conversion and rate of conversion data are necessary to model autocatalytic kinetics [e.g., using Eq. (2.86)]. Isothermal method 2 yields both Tg and conversion at a series of times and temperatures (see Rg. 2.70 as an example). However, the measurements are time-consuming, and since the reaction rate is not measured, it must be calculated mathematically, or integrated forms of the rate equation such as Eqs. (2.83)-(2.85) must be used. To perform these analyses generally requires use of a spreadsheet. 

The very fact that both the width of the energy spectrum and the characteristic desorption energy vary with time, makes nonisothermal kinetic data less reliable than isothermal data. This difficulty may be overcome by determining portions of the complete isothermal desorption kinetics at different temperatures. This reduces the original problem, of determining the energy spectrum from nonisothermal desorption kinetics, to a set of equivalent problems, each of which associated with the extraction of the desorption energy distribution from isothermal kinetics measured at different temperatures. 

Thermal analyses of the sodium salts of several sulphuroxyacids, including some non-isothermal kinetic data, have been reported [813], Evidence for the formation of SOi radicals during such reactions has been obtained [348] by electron spin resonance measurements. 

References to a number of other kinetic studies of the decomposition of Ni(HC02)2 have been given [375]. Erofe evet al. [1026] observed that doping altered the rate of reaction of this solid and, from conductivity data, concluded that the initial step involves electron transfer (HCOO- - HCOO +e-). Fox et al. [118], using particles of homogeneous size, showed that both the reaction rate and the shape of a time curves were sensitive to the mean particle diameter. However, since the reported measurements refer to reactions at different temperatures, it is at least possible that some part of the effects described could be temperature effects. Decomposition of nickel formate in oxygen [60] yielded NiO and C02 only the shapes of the a—time curves were comparable in some respects with those for reaction in vacuum and E = 160 15 kJ mole-1. Criado et al. [1031] used the Prout—Tompkins equation [eqn. (9)] in a non-isothermal kinetic analysis of nickel formate decomposition and obtained E = 100 4 kJ mole-1. 

Comparative studies [1127] of the kinetics of decomposition of similar salts containing related pyridine ligands have been used to investigate the strength of M—N bonds in coordination compounds. Non-isothermal DSC measurements were used to determine values of E for the reactions... 

In dynamic systems we may have the situation where a series of runs have been conducted and we wish to estimate the parameters using all the data simultaneously. For example in a study of isothermal decomposition kinetics, measurements are often taken over time for each run which is carried out at a fixed temperature. 

Future work in this area will involve the extension of these techniques to other temperatures in an effort to better characterize the overall reaction kinetics of these two processes. In addition, degree of cure obtained through isothermal DSC measurements will be compared with the fraction of acetylene consumed as measured by isothermal FTIR experiments for the same temperature and time. Also, the effect of the incorporation of metal fillers on the isomerization and crosslinking reactions will be addressed. 

Using a "home made" aneroid calorimeter, we have measured rates of production of heat and thence rates of oxidation of Athabasca bitumen under nearly isothermal conditions in the temperature range 155-320°C. Results of these kinetic measurements, supported by chemical analyses, mass balances, and fuel-energy relationships, indicate that there are two principal classes of oxidation reactions in the specified temperature region. At temperatures much lc er than 285°C, the principal reactions of oxygen with Athabasca bitumen lead to deposition of "fuel" or coke. At temperatures much higher than 285°C, the principal oxidation reactions lead to formation of carbon oxides and water. We have fitted an overall mathematical model (related to the factorial design of the experiments) to the kinetic results, and have also developed a "two reaction chemical model". 

Therefore a particular method was chosen (4). We worked on a statistical population of crystals in order to minimize the dispersion and on simultaneous measurement of all faces in order to compare their growth rate under the same conditions of supersaturation and temperature. Therefore classical (R,o ) isotherms were obtained. Experimentally we grew at the same time and in the same solution a single crystal and twin. Whereas growth rate measurements of the forms hOL are relatively simple (thanks to the fact that the b axis is a binary axis) (Figure lb), the kinetic measurements of the p 110 and p llO forms are more difficult. 

Two different isothermal reactors designed, not for kinetic measurements, but for the observation of equilibria by means of simultaneous spectroscopic and conductivity measurements were devised by two groups (Holdcroft and Plesch, 1985 Pask and Nuyken, 1983). The purpose of both was to observe how a binary ionogenic equilibrium of the type... 

Schoenemann, E., Hahn, H., and Bracht, A. (1991), Determination of kinetic parameters from non-isothermal conductivity measurements by an integral method, Thermochim. Acta, 185(1), 171-176. 

It is useful to examine the consequences of a closed ion source on kinetics measurements. We approach this with a simple mathematical model from which it is possible to make quantitative estimates of the distortion of concentration-time curves due to the ion source residence time. The ion source pressure is normally low enough that flow through it is in the Knudsen regime where all collisions are with the walls, backmixing is complete, and the source can be treated as a continuous stirred tank reactor (CSTR). The isothermal mole balance with a first-order reaction occurring in the source can be written as... 

To obtain a more realistic estimation of the behavior of an autocatalytic reaction under adiabatic conditions, it is possible to identify the kinetic parameters of the Benito-Perez model from a set of isothermal DSC measurements. In the example shown in Figure 12.11, the effect of neglecting the induction time assumes a zero-order reaction leading to a factor of over 15 during the time to explosion. Since this factor strongly depends on the initial conversion or concentration of catalyst initially present in the reaction mass, this method must be applied with extreme care. The sample must be truly representative of the substance used at industrial scale. For this reason, the method should be only be applied by specialists. 

Comparison of the Values of the Adsorption Coefficients Found from Kinetic Measurements and from Adsorption Isotherms... 

Continuously operated, fixed bed reactors are frequently used for kinetic measurements. Here the reactor is usually a cylindrical tube filled with catalyst particles. Feed of a known composition passes though the catalyst bed at a measured, constant flow rate. The temperature of the reactor wall is usually kept constant to facilitate an isothermal reactor operation. The main advantage of this reactor type is the wealth of experience with their operation and description. If heat and mass transfer resistances cannot be eliminated, they can usually be evaluated more accurately for packed bed reactors than for other reactor types. The reactor may be operated either at very low conversions as a differential reactor or at higher conversions as an integral reactor. 

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