Isothermal reduction curves

When the samples were etched mildly, the anomalous increase upon annealing was not observed. In an isothermal annealing experiment performed at 423 K for As—H complexes, the exponential decay given by Eq. (3) was verified for a 50 times reduction in concentration. In Fig. 11 the results of a series of 30 min isochronal anneals are shown for each of the donor-H complexes. The curves are given by Eq. (3) with an assumed attempt frequency of 1013 s-1 and binding energies of 1.32 eV for P—H and 1.43 eV for As—H and Sb—H. 

Fig. 11.10 The reduction of the initial reactant concentration as a function of the Da number, showing the unifying ability of the use of characteristic time ratios. The curves are solutions to the kinetic expressions for batch and LCFR with half-, first-, and second-order kinetics. [Reprinted by permission from D. H. Sebastian, Non-Isothermal Effects in Polymer Reaction Engineering, in Temperature Control Principles for Process Engineers, E. P. Dougherty, Ed., Hanser, Munich, 1993.]...

The average pore size for sample SG 5.T in Table 2 was determined by the MP method. The average pore diameters for the heat-treated samples were taken from the maxima in the PSD curves drawn using the BJH method from the desorption branches of the corresponding isotherms presented in Fig. 3. It may be noted that the most significant change in pore diameter was caused by heat-treatment at 500°C. This shift along with the severe reduction in the Sbet to only c. 50 m g was mainly due to the transformation into rutile. 

Fig. 11 shows an example of the calculated reduction rate after burnout assuming plug flow in the burnout zone (isothermal PFR at 1300 C, 2 s mean residence time). The two curves in the figure represent two different reburn models, once PFR only and once PSR plus PFR in series. The figure shows that the maximum reduction predicted varies between 82 % and 95 %, depending on the model for the reburn zone. However, the calculated reduction rates or higher than the measured. 

Figure 14.3.14 Simulated cyclic voltammograms for initial reduction where reactant is strongly adsorbed, = 10. (a) Nemstian reaction, Langmuir isotherm, (b) Nemstian system, Frumkin isotherm, IgTo JRT = -1.5. (c) Irreversible reaction, k%ffl(7rDQvFIRT) = 1, a = 0.5, Frumkin case, 2gToJRT = 0.6. Additional curves in the figure show variation of Fq/Fq,s as a function of E during scan. [Reprinted from S. W. Feldberg in Computers in Chemistry and Instrumentation, Vol. 2, Electrochemistry, J. S. Mattson, H. B. Mark, Jr., and H. C. MacDonald, Jr., Eds., Marcel Dekker, New York, 1972, Chap. 7, by courtesy of Marcel Dekker, Inc.]...

Crossley et al. (40) used a computer reduction technique for the DSC isothermal curve which was developed to replace the use of a planimeter. The data reduction was divided into two phases (1) mechanism-independent solutions for the reactant fraction, a, and various functions of a (where a is the reactant fraction remaining at time f) and (2) solutions for mechanism-dependent rate constants. For the first phase, the DATAR program was developed, which consisted of the following Ordinal points referred to a coarse data, and evenly spaced in time over the time span of the DSC curve, are read directly into the computer. Up to 1000 points may be read, but 40-50 are usually sufficient for acceptable accuracy. The resultant fraction remaining at time t is calculated by the equation I... 

Fig. 6.3. Numerical modeling of the thermal regime in the lithosphere of the Oued el-Mya Basin, Takhoukht region. Solid line ist the base of the lithosphere as determined by intersection of the current geotherm with solidus curve for peridotite (shown in Fig. 6.4). Long dashed lines are isotherms Moho = base of the crust comp, transition = location of pyroxene peridotite-garnet peridotite compositional transition in the mantle. The considerable rise of isotherms is related to periods of thermal activation in the lithosphere in the Permian-Tfiassic and Cretaceous, Reduction of the crust thickness occurred during basement stretching (in the Ordovician-Devonian and Cretaceous) and during Permian erosion...

The reliability of peak detection based on the first and second derivatives depends on the slope of the curve, i.e. on the number of points/peak. In isothermal chromatograms the broadening of the peak with retention time must be taken into consideration by means of hardware or software manipulations. With sample-point reduction during the run, broad peaks with a small slope will be transferred to narrow peaks with more distinct first and second derivatives. This may be achieved by varying the sampling rate in steps controlled by retention time stored in the computer or by condensing several samples into one medium point. 

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