Pore diameter, and

The limiting cases of greatest interest correspond to conditions in which the mean free path lengths are large and small, respectively, compared with the pore diameters. Recall from the discussion in Chapter 3 that the effective Knudsen diffusion coefficients are proportional to pore diameter and independent of pressure, while the effective bulk diffusion coefficients are independent of pore diameter and inversely proportional to pressure. 

Let us now assemble the complete set of dimensionless parameters for the problem. These are set out in Table 11.1, where the last column indicates the nature of their dependence on the external pressure p, the mean pore diameter and the pellet radius a. Symbols ft and 0... 

Pore diameter and distribution are important factors. Small pores limit the accessibihty of internal surface because of increased resistance to diffusion of reactants inwards. Diffusion of products outwards also is slowed, and degradation of those produces may result. 

Figure 1. Influence of T1O2 content of LT-aerogels on relative proportion of Si-O-Ti connectivities R = [Si-0-Ti]/(Si-0-Si], mean pore diameter, and initial rate (to) of a-iso-phorone ep>oxidation with t-butyl hydroperoxide at 60 C. Data taken from ref. [18].

In the presence of polyethylene oxide MW 300,000 at a concentration of 0.025 g liter , variations in pH and ionic strength have no effect on elution volumes and a single calibration curve is obtained as shown in Figure 4 and Table II. This behavior presumably also results from modification of the glass surface by the polyethylene oxide surfactant, but in this case charge effects appear to be completely suppressed and the effective pore diameter and volume reduced. Such an interpretation is also in accord with the fact that the elution voliomes are lower with polyethylene oxide than with Tergitol, since Tergitol is a much smaller molecule than the polyethylene oxide. 

Ordinary or bulk diffusion is primarily responsible for molecular transport when the mean free path of a molecule is small compared with the diameter of the pore. At 1 atm the mean free path of typical gaseous species is of the order of 10 5 cm or 103 A. In pores larger than 1CT4 cm the mean free path is much smaller than the pore dimension, and collisions with other gas phase molecules will occur much more often than collisions with the pore walls. Under these circumstances the effective diffusivity will be independent of the pore diameter and, within a given catalyst pore, ordinary bulk diffusion coefficients may be used in Fick s first law to evaluate the rate of mass transfer and the concentration profile in the pore. In industrial practice there are three general classes of reaction conditions for which the bulk value of the diffusion coefficient is appropriate. For all catalysts these include liquid phase reactions... 

Whether Knudsen or bulk diffusion dominates the mass transport process depends on the relative magnitudes of the two terms in the denominator of equation 12.2.6. The ratio of the two diffusivity parameters is obviously important in establishing these magnitudes. In this regard, it is worth noting that DK is proportional to the pore diameter and independent of pressure whereas DAB is independent of pore size and inversely proportional to the pressure. Consequently, the higher the pressure and the larger the pore, the more likely it is that ordinary bulk diffusion will dominate. 

The mean pore diameter and the pore volume decrease respectively from 67 A and 0.46 cm7g for calcined SBA-15 to 56 A and 0.32 cm3/g for GFP/SBA-15. A decrease of SSA was also observed from 648 m2/g for SBA-15 to 456 m2/g for the hybrid material. These values suggest that GFP molecules can be embedded within the SBA-15 pores/channels and not simply adsorbed on the external surface of the mesoporous silica. 

Figure 1 shows that the catalysts maintain their mesoporous structure with type IV isotherm. It can be observed a reduction in surface area, pore volume and pore diameter and slight increase in textural porosity as the concentration of aluminum increases (Table 1), due to the increase in the wall thickness in the mesoporous material as we have found previously [3],... 

Pore diameter and interpore spacing are determined by two large groups of factors those that affect carrier density on the surface of a pore bottom and those that affect only the distribution... 

Figure 11. SEM photograph showing smaller pore diameter and larger pore density near the surface than in the bulk in 5% HF at 6 V.24...

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