Voids average pore diameter

In 1971, Hiatt et al. found that polyethylene oxide (PEO) of molecular weight about 100000 prevented the adsorption of rabies virus to porous glass with an average pore diameter of 1250 A. The support was modified by passage of one void volume of 0.4% solution of the polymer in water, followed by 5 or more volumes of distilled water or buffered salt solution. The virus was effectively purified from the admixtures of brain tissue fluid by means of size-exclusion chromatography on the modified glass column [28]. 

We will next consider the case of a lew silica content co-gel. A 5% silica-content silica-alumina was prepared by precipitation of aluminum isdsutoxide and tetraethoxv-silane as described for the silica-free gel. After gelation water was added just sufficient to fill the pore voids of the gel. The added water led to formation of a boehmite-rich hase during recrystallization. After drying at 120 and calcination at 500 0 for 16 hours, a transitional alumina hase is formed with a surface area of 410 m /g and a pore volume of 1.9 oc/g. This silica-alumina had an average pore diameter of 18 nm, similar to the silica-free material discussed previously. Steam treatment of this 18 nm pore diameter silica-alumina at 870°C (1600 ) in 90% H20-10% N2 for 16 hours resulted in a material with surface area of 196 m /g. This surface area is much hi er than expected for an amori ous gel and is consistent with silica enrichment of the outer surface during the recrystallization step vhere water was added to the pores of the amoridious gel. Silica stabilization of bodunite alumina by formation of a surface Aiase complex has been reported in recent work (9). ESCA analysis also indicates silica surface enrichment vhen compared to the amori ous gel. 

If ten times the amount of water is added to the undried 5% Si02 content gel than required to fill the pore voids a much more dense silica-alumina jAiase is formed than in the previous example. After drying at 120 and calcination at 500 a material of 283 m2/g surface area and a pore volume of 0.9 oc/g is formed. The average pore diameter of this material is 8 nm. There is an unmistakable parallel in the recrystallization of the silica-free gel to the 5% silica-content silica described here. Addition of limited water to the amorphous gel produces large pores and a hi pore volume. Addition of water so that a slurry is formed with the amorphous gel results in smaller pores and a relatively dense phase i n recrystallization. 

Rather than using an inert solvent to precipitate the copolymer and form the pores, the polymerization may be carried out in the presence of an inert solid agent such as finely divided calcium carbonate to create the voids within the bead. Later, the solid is also extracted from the copolymer. Both of these polymerization processes create large (although probably different) inner pores. The average pore diameter can be varied within the range of 20 A to 500 A. 

We need to examine a particular model for physical adsorption that has been extremely useful over the years in the characterization of the porous materials that are often employed as catalyst support structures or as catalysts in their own right. The basic question is how to measure the internal (pore) surface area of a material that is perhaps 50% void and has an average pore diameter on the order of 5 nm (see... 

In a first approximation the average size of pore diameter has no effect on porosity, even though a superficial view leads to other conclusions. A mental experiment may be of assistance imagine a pore and its outside wall, decrease both to identical scale, then the ratio of void to outside volume remains constant. Of course the re-... 

There is a tendency for an increase in the difference between the and Ys values with increasing size of primary particles. For instance, it is minimal (and A"< 1) for amorphous S A23 (average particle diameter =6.9 nm, deviation of the pore shape from the random voids between spherical particles... 

A fundamental characteristic of a porous medium is its specific surface area E (expressed in m per kilogram of material). Qualitatively, we have E = ps d), where ps is the density of the compacted solid devoid of pores (typically, ps I g/cm ), and d is the diameter of the capillary. For a pore diameter d = 10 jim, E is of the order of 100 m /kg. Another important parameter of the porous medium is its void fractional volume Therefore, its average density is ps l — ). The surface area Ev per unit volume is... 

A commercial cumene cracking catalyst is in the form of pellets with a diameter of 0.35 cm which have a surface area. Am, of 420 m g and a void volume, Vm, of 0.42cm g. The pellet density is 1.14g cm. The measured l -order rate constant for this reaction at 685K was 1.49cm s g . Assume that Knudsen diffusion dominates and the path length is determined by the pore diameter, dp. An average pore radius can be estimated from the relationship fp = 2Vm/Am if the pores are modeled as noninterconnected cylinders (see equation 4.94). Assuming isothermal operation, calculate the Thiele modulus and determine the effectiveness factor, tti, vmder these conditions. 

However, the solute velocity vi is different than V2 for two reasons. First, the solute will not fit into the entire pore diameter but only into a smaller equivalent pore of diameter (d-2R). This imphes that the void fraction for the solute will be smaller than that for the solvent. Second, because the solute is forced to be more towards the center of the pore, it will encounter average velocities somewhat higher than those averaged over the entire diameter of the pore. One theory typical of efforts on this subject gives for the solute velocity... 

This equation is particularly useful for mixtures of particles of various sizes for which only average diameter and voids are available, and if it is desired to determine the ultimate degree to which material is a cke But the treatment of pore-space developed by Smith et at is capable fri further extension. Assume that the three types of pores shown in Figure 27 are composed of spheres separated by a distance ft. The area contained iu each pore is then... 

When considering a packed bed the interparticle or interstitial porosity amounts to approximately 40%. The average diameter of these interstitial voids calculates for a fairly regular packing to 0.4 times of the particle diameter, e.g. a regularly packed bed with 15 p,m particle creates interstitial pores of 6 pm. A bimodal particle size distribution of silicas employed for preparative columns can often be found, e.g. a major distribution around 15 pm and a minor peak at 4 pm. These small particles are thought to occupy the interstices between the 15 pm diameter particles and thus to stabilize the bed. 

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