Radius, mean pore

This is very important as several other properties are dependent upon it. If the porosity is too high, the article will be weak and will not retain liquid. The pore structure should also be taken into account. When a ceramic material is hred, although the internal surface area decreases as the material approaches zero porosity, the mean radius of the pores increases. Thus, when the internal surface area is 3 mVg the mean pore radius may be of the order of 10 m, while when the internal surface has dropped to 0-5 mVg the mean pore radius may be about 4-5 x 10 m. The mean pore radius may reach a value as high as 9 x 10 m as the ware approaches zero porosity during firing. It is thus obvious that at some point the pores must start to close up. This closing of the pores with the approach of vitrification is borne out by results of permeability measurements. 

A platinum on silica gel catalyst was prepared by impregnation of silica gel (BDH, for chromatographic adsorption) by a solution containing 0.5% (wt.) of sodium hydroxide and 0.5% (wt.) of chloroplatinic acid (both of analytical grade). The dried catalyst contained 1% (wt.) of platinum and a corresponding amount of the alkaline component. The BET surface area of the catalyst was 40 m2/g, the mean pore radius 150 A. The catalyst was always reduced directly in the reactor in a stream of hydrogen at 200°C for 2 hr. 

Table 3.6 gives data on the mean pore radius and surface area of some commercial supports and catalysts. The BET surface areas of most commercial catalysts range from several up to about 1000 m /g. 

Figure 9 Molecular restriction factor as a function of the ratio of molecular radius to pore radius for paracellular permeants in Caco-2 cell monolayers. Mean pore radius is 1.2 nm.

When the hydrogen pressure is 1 atm, and the temperature is 77 °K, the experimentally observed (apparent) rate constant is 0.159 cm3/ sec-g catalyst. Determine the mean pore radius, the effective diffusivity of hydrogen, and the catalyst effectiveness factor. 

Having obtained a measure of surface area, a mean pore size may be calculated by simplifying the pore system into np cylindrical pores per unit mass of adsorbent, of mean length Lp and mean pore radius rp. 

Of these three mechanisms, i.e. molecular diffusion, laminar flow and Knudsen diffusion, only two are important in pressure-driven separations. These are laminar flow and Knudsen diffusion. These can be qualitatively understood as follows. If the molecules "see each other much more than they see the pore wall (which means the mean free path of the molecules is much smaller than the mean pore radius), laminar ow a molecular diffusion are important. The laminar flow is much larger, howcver, nd thelhdlecular flow can be neglected (Present and de Bethune 1949). If the molecules see the pore wall much more than they see each other, only Knudsen diffusion will occur. Thus, the molecular diffusion can be neglected in all circumstances. From now on it will be assumed, that only laminar flow and Knudsen diffusion occur. 

There are few studies in literature reporting pure gas permeabilities as well as separation factors of mixtures. Vuren et al. (1987) reported Knudsen diffusion behavior of pure gases for y-alumina membranes with a mean pore radius of 1.2 nm. Separation experiments with a 1 1 H2/N2 mixture showed, that the theoretical Knudsen separation factor [of 3.7, Equation 6.4)j for this mixture could be obtained (Keizer et al. 1988 see also Figure 6.2). In Figure 6.2, the effect of process parameters is also demonstrated. The separation factor is a function of the pressure ratio over the membrane, which is the ratio of the pressure on the permeate-side to that on the feed-side. For pressure ratios approaching unity, which means the pressure on both sides of the... 

R is the effective mean radius of macromolecules dissolved in the eluent d is the effective mean pore radius... 

Osada et al. [52] have also grafted PMAA to a porous substrate in order to achieve an environmentally sensitive membrane. This sensitivity was termed a chemical valve function because mechanochemical forces caused the pores to enlarge and contract. PMAA was grafted onto poly(vinyl alcohol) (PVA) films which had a mean pore radius of 4 pm. The water permeation of the membrane was strongly affected by the conformational state of the PMAA grafts. At low pH the chains were contracted and the water permeability was... 

Catalyst Surface area (m2/g) Pore volume (cm3/g) Mean pore radius (A)... 

A commercially available 5% Pt/Al203 catalyst (Engelhard Industries 4759) was used in this study. The catalyst sample had a mean particle size of 55 pm as measured by light scattering, a BET surface area of 140 m2/g, a mean pore radius of 50 A and a density of 5.0 g/ml. The platinum loading was 4.65%, and the platinum dispersion was 0.28 as measured by static CO titration (ref. 11). 

Mean Particle Size (jim) Pt % Dispersion Surface Area (m2/g) Real Density (g/ml) Apparent Density (g/ml) Pore Volume (ml/g) Mean Pore Radius (A)... 

K. Striking is the broad distribution of jump times of water in cell walls coextending from times of liquid water to ice. We can compare water in cell walls with supercooled water with a broad scale of mobilities. The reduction of the apparent T may be induced by the interaction water/mucopolysaccharid groups. Water in charcoal with mean pore radius of 13 A shows a broader distribution of t but with a... 

Three mesoporous silica gels, with variable mean pore radius and specific surface area, have been studied. The substrates are named according to their approximated mean pore diameter. Measured values appeared to differ somewhat from the product names.30 The Kieselgels 40, 60 and 100 have a mean pore diameter of 4.2, 7.0 and 12.0 nm, respectively. Specific surface area increases with decreasing pore radius. Measured values, using the BET method, are given in table 9.3. 

The porosity of AKP-30 (AKP-15) tubes, made with optimum [APMA] was 42.5% (43.2%) after firing at 500°C, measured with the Archimedes method by immersion in mercury. The sintered compacts had a porosity of 34.8% (34.5%). Their pore-size distributions, measured by mercury porosimetry are given in Figure 3. The mean pore radius was found to be 60 (92) nm. 

The commercial catalyst used in this work contains 12 wt% Ni and 83 wt% a-Al203. It has a BET total surface area of 3.4m /g and a unimodal pore size distribution with volume 0.155 cc/g, mean pore radius 1600 A and void fraction 0.362. Its activation required a reduction which was carried out under atmospheric pressure in situ, for 72 hrs at 850°C by means of a pure dried hydrogen flow of lOO Nl/hr. These severe reduction conditions were required because 20 wt% of the Ni was present as NiAl204-spinel phase, which could only be reduced above 770°C. It led to a very active catalyst, with a specific Ni-surface area of 0.68 m Ni/g.cat. 

The above kinetics is valid for small particles when the process rate is controlled by the chemical reaction at the surface. Diffusion effects should be accounted for large-size particles. Table 5.8 presents the calculation of the effectiveness factor [24] for spherical particles of 6 mm diameter and a mixture 1 3 phenol/hydrogen at 2 bar and 423 K. Other data are BET internal surface S = 40m2/g, mean pore radius 150 A, catalyst density pp = 1000kg/m3, particle void fraction = 0.3,... 

If the pores have a well-defined shape there is a simple relationship between rh and the mean pore radius, rp. Thus, in the case of nonintersecting cylindrical capillaries... 

TOTAL SURFACE AREA, ACTIVE SURFACE AREA, POROSITY, AND MEAN PORE RADIUS OF A CATALYST... 

The important properties of the catalyst for characterization purposes are the total surface area, dispersion of metallic nickel, pore volume, and mean pore radius. Determine each of these, using the experimental data given in the respective calculation steps. 

Calculate the porosity and the mean pore radius. The particle porosity may be readily determined by a helium pycnometer and a mercury porosimeter. In the pycnometer, the solid skeletal volume Vs is obtained. The skeletal density ps is found from the sample weight Ws ... 

For example, if the mesopore structure consists of a set of open-ended, non-intersecting cylinders, the mean pore radius, fp, is given by... 

To examine the dependence of the mean reaction rate on the porous structure we should describe the relationships between all parameters of Equation 8.1 and the structural parameters mean pore radius, void fraction and surface area per unit particle volume 5. 

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