Fractional filling

Thus the mobility picture for water fully loaded into NaX zeolite fits together at least semiquantitatively. Further tests of the model based on newer NMR techniques have been proposed (9) and are in progress. Diffusion and other NMR data (45, 45) indicate on the one hand that the water mobility is greater at lower than maximum loadings, but on the other hand that the picture is not that simple. A theory based on fractionally filled cages in equilibrium with filled cages seems to be required. 

Note that the denominator of Equation 5.21 contains the internal portion of the particle partition function and the ideal gas contribution, so that the division indicated accounts for the nonideal gas effect. When Equation 5.21 is put into Equation 5.17, Qjj, the fractional filling of cavity i by a type J molecule, is obtained ... 

With values for the fractional filling of each cavity type, hydrate density may be determined based upon a unit crystal. Additional required input data are the dimensions of a unit crystal, the number of water molecules per crystal and the number of small and large cavities per unit crystal, as specified in Table 2.2. Based upon a single unit cavity, the hydrate density (p) may be calculated by the formula ... 

From the computer program included with this book, at 277 K the hydrate is predicted to be sll with a dissociation pressure of 12.9 atm. The length of one side of sll is 17.3 A, with 136 water molecules, as well as 16 small (512) and 8 large (51264) cavities per unit cell. The fractional filling of each cavity (9, ) is given in the below table ... 

However, it should be remembered that the fractional filling is a function of the product Cjjfj, rather than either factor in the product. Finally, in the original van der Waals and Platteeuw approach the Langmuir constants for both adsorption and enclathration were only functions of temperature for each molecule type retained at the individual site or cavity. In the modified approach below, the Langmuir constants are also a function of cage size, or the unit cell volume, which is a function of the hydrate guests, temperature, and pressure. 

Determine the fractional filling rate Qflu/Q that will fill an isothermal, constant-density, stirred tank reactor while simultaneously achieving the steady-state conversion corresponding to flow rate Q. Assume a second-order reaction with ai kt = 1 and t = 5 h at the intended steady state. 

In 1947 Dubinin and Radushkevich put forward an equation for the characteristic curve in terms of the fractional filling, W/W0, of the micropore volume, W0. This relation is usually expressed in the form... 

The two-constant versions of Equation (11.2) and other virial expansions can be applied to the low fractional filling section of isotherms on the faujasite zeolites, provided that the temperature is not too low. In this manner it is then possible to obtain the Henry s law constant, kH. 

The moduli for a dry ceramic powder in this regime of very small deformation are given by the moduli for the particles and the volume fraction, filled by the ceramic powder as follows ... 

Figure 1 Depth profile of radon loss fraction. Filled circles and error bars represent the mean and standard error of the radon loss fraction from all samples from the indicated depth for which the Cs/ Ra ratio is less than 0.05. The boxes represent 1 a deviation and the whiskers the extreme values of each population. The number of samples is given in the column on the right. The curve corresponds to Equation (1) with an emanating power of 0.28 and...

Here W is the amount of adsorption at P/Po, Wo the micropore volume, Eq the characteristic energy, and the affinity coefficient., 3Eo can be associated with the isosteric heat of adsorption, qst,. =i/e, at the fractional filling of 1/e using the heat of vapourization, AH , at the boiling point ... 

Fig. 5 shows the low pressure adsorption isotherms of n-nonane by the micropore entrance modified ACF and the pristine ACF. These adsorption isotherms were determined under the almost equilibrium conditions. A remarkable enhancement of n-nonane adsorption with the micropore entrance modification is observed in the low P/Po region, although the adsorption amounts at high P/Pq region almost coincide with each other. The fractional filling of n-nonane at saturation is almost constant irrespective of the surface modification with TTS the ratios of the saturation n-nonane adsorption Wo(nonane) to the saturation Nj adsorption Wo(N2) for the modified ACF and ACF were 0.72 and 0.70, respectively. Thus, the low pressure uptake depends sensitively on the chemical state of the external surface, while the fractional filling at saturation does not change. Consequently, the slight uptake of the pristine ACF should be caused by the limitation of micropore diffusion. The diffusion limitation can be removed by application of n-nonane pressure of P/Pq >0.1 according to the result shown in Fig. 5. Accordingly, a marked enhancement of low pressure adsorption by the micropore-entrance modification is associated with enrichment of n-nonane molecules at the entrance of the micropore due to favourable interaction of n-nonane with hydrocarbon chains of TTS. The amount of the n-nonane enrichment can be estimated from the comparison of both adsorption isotherms in Fig. 5. With the adsorption amount indicated by the horizontal broken line, the equal amount of adsorption for both samples is obtained at different relative pressures of 0.065 (for ACF) and 0.02 (for TTS-modified ACF). That is, application of P/Pq = 0.065 is necessary for the prescribed adsorption in the case of ACF, whereas the TTS-modified ACF does not need such a high P/Pq. Application of P/Po = 0.02 is sufficient for the adsorption by the TTS-modified ACF. Thus, the TTS-modification increases the concentration...

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