F curves

As will be demonstrated in Chapter 4, however, the presence of micropores distorts the Type II isotherm in a sense which is reflected in a much increased value of the constant c. In such cases the value of c is no guide at all to the course of the isotherm on the external surface. Consequently the appropriate criterion for choosing the correct f-curve for a particular system is the similarity in chemical properties and not in c-values l>etween the solid under test and the reference solid. 

The f-curve and its associated t-plot were originally devised as a means of allowing for the thickness of the adsorbed layer on the walls of the pores when calculating pore size distribution from the (Type IV) isotherm (Chapter 3). For the purpose of testing for conformity to the standard isotherm, however, a knowledge of the numerical thickness is irrelevant since the object is merely to compare the shape of the isotherm under test with that of the standard isotherm, it is not necessary to involve the number of molecular layers n/fi or even the monolayer capacity itself. 

FIG. 17-73 Normal (perpendicular) rapping efficiency for various precipitated dust layers having about 0.03 g diist/cm (0.2 g diist/in ) as a function of maximum acceleration in multiples of g, Curve 1, fly ash, 200 or 300°F, power off. Curve 2, fly ash, 70°F, power off also 200 or 300°F, power on. Curve 3, fly ash, 70°F, power on. Curve 4, cement-ldln feed, 300°F, power off. Curve 5, cement dust, 300°F, power off. Curve 6, same as 5, except power on. Curve 7, cement-ldln feed, 300°F, power on. Curve 8, cement dust, 200°F, power off. Curve 9, same as 8, except power on. Curve 10, cement-ldln feed, 200°F, power off. Curve 11, same as 10, except at 70°F. Curve 12, cement-ldln feed, 200°F, power on. Curve L3, cement-ldln feed, 70°F, power on. °C = (°F — 32) x %. [Spioull, Air Polliit. Control Assoc. J., i.5, 50 (1965).]... 

Figure 8-14. E-curve, F-curve, and A-curve for a typicai system with dead space.

Fig. 1.23 E-f curves for the corrosion of zinc (see Fig. 1.22) showing the relationship between and i) for the cathodic and anodic half reactions...

Tenets (i) and (ii). These are applicable only where the reactant undergoes no melting and no systematic change of composition (e.g. by the diffusive removal of a constituent) and any residual solid product phase offers no significant barrier to contact between reactants or the escape of volatile products [33,34]. When all these conditions are obeyed, the shape of the fraction decomposed (a) against time (f) curve for an isothermal reaction can, in principle, be related to the geometry of formation and advance of the reaction interface. The general solution of this problem involves intractable mathematical difficulties but simplifications have been made for many specific applications [1,28—31,35]. 

The few remaining discrepancies are probably due to error in the assumed relative reflecting powers. To test this, we made use of an F-curve for OF obtained by linear extrapolation from Na+ and Cf, and one for Tii+ from CF and K+. These F-curves (which are not reproduced here because of uncertainty in their derivation) lead to structure factors which are, for the same final parameter values, also in good but not complete agreement with the observed intensities. Possibly somewhat different F-curves (corresponding to non-linear extrapolation) would give better agreement, but because of the arbitrariness of this procedure no attempt was made to utilize it. 

On account of the lack of definite knowledge of the F-curves no attempt was made to account for the intensities of Laue spots. 

The theoretically obtained electron densities of ions may be used for the calculation of the so-called F curves, which give the effective reflecting power of the ion as a function of the angle of reflection and the wave-length of X-rays, and which are of use in the determination of crystal structures. It may be mentioned that the high maximum value of the electron density at the nucleus given by our calculations provides considerable justification for the method of determining crystal structures with the aid of the relative intensities of Laue spots produced by crystal planes with complicated indices. 

These F-values are not so reliable as those calculated by Hartree s method. On the other hand, they are obtained with much less labor, Hartree s calculations having so far been carried out for only a small number of atoms. In figure 10 F-curves are shown for Li+, Na+, K+, and Rb+ as obtained by the method described in this paper, by Hartree s method and by the Thomas-Fermi method. It is seen that for all... 

The correct potential for a preparative electrolysis is normally chosen by inspection of a steady state current-potential (i-F) curve. Figure 1 shows a typical i-E curve for the reduction of anthracene at a mercury cathode in dimethylformamide (Peover et al., 1963) the curve shows two reduction waves. In the potential range where the current rises with variation of the potential, the rate of an electron transfer process is increasing while in the plateau regions the rate of the electron transfer... 

Figure 3.21. F-curve response to a step change in tracer concentration.

Here 0 = t/T and Co is the tracer inlet feed concentration. The corresponding relationships for the F-curve response are ... 

This means that the F-curve can be obtained from the E-curve as its slope. Referring to Fig. 3.21... 

Setting k = 0, simulate the tracer response (F-curves) for 3 perfectly-stirred tanks in series. 

For a step change in the feed tracer from 0 to Cao and giving an F-curve response. 

This program is designed to simulate tracer experiments for residence time distributions based on a cascade of 1 to 8 tanks-in-series. An nth-order reaction can be run, and the steady-state conversion can be obtained. The important parameters to change are as follows for the tracer experiments k, CAINIT, and CAO ( = 0 for E curve, = 1 for F curve). For reaction studies, the parameters to change are n, k, CAO, and CAINIT. 

Note if K = 0, the program generates an F-curve for the non-ideal reactor. 

Where the F, curve is near vertical values cannot be read accurately, and this will introduce a considerable uncertainty into the design. 

The shaded area under the E(tr) curve and the difference between the ordinates on the F-curve at tr = 1.2 and tr = 1.5, 0.83 - 0.7 = 0.12, represent the fraction of the tracer that had residence times between these two times. 

Performance enhancement, in heat exchangers, 13 276-278 Performance-failure (P-F) curve, 15 462 Performance orientated packaging (POP), 18 2... 

Figure 8.2 Theoretically calculated f and f" curves In the neighbourhood of the L edges of europium (solid line) and gold (dashed line) are shown. Wavelengths that were chosen for measurement of peak, Inflection point and remote data in each case are marked by arrows and labelled.

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