Pore surface area distribution

The pore surface distribution (r) is the surface area per unit pore radius. By chain differentials one can write 

The last column in Table 11.1 gives values of D r) calculated from equation (11.22) and also plotted in Fig. 11.8. 

The total area under the volume and area distribution curves is proportional to the total pore volume and pore area, respectively. By taking the ratio of the graphical area in any interval to the total graph area A, the pore volume or surface area in any interval can be calculated 

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Figure 11.12 (a) Pore surface area distribution versus pressure plot, (b) Pore surface area distribution versus radius plot. Intrusion curve (->) extrusion curve ( ). 

Fig. 3.29. Pore volume and pore surface-area distribution for PAM formed from 3BS paste. Pore radius of 0.1 pm is assumed to be the limit between micro- and macro- (transport) pores [36],...

Pore. size and surface area distribution. Pore sizes and pore volume distributions may be calculated from the relative pressures at which pores are filled (in the adsorption mode) or emptied (in the desorption mode). Fig. 3.45 shows the pore size distribution of a commercial y-alumina. The distribution is very broad both meso- and macropores are present. In practice this is usually a desired situation a texture consisting of a network of large pores (main roads) and small pores (side roads) is ideal. 

Porosimetry data can be graphed in a variety of ways and can be tailored to the purpose of the study. Plotting volume versus pore size will easily display the pore sizes observed in the sample. Pore size distributions can be calculated from the raw data and plotted to give the pore volume per unit radius interval. Other parameters can be calculated from porosimetry data, including average pore radius [40,48], surface area [7,39,40], pore surface area [6], particle size [40], and density [6,49]. 

Most of the adsorbents used in the adsorption process are also useful to catalysis, because they can act as solid catalysts or their supports. The basic function of catalyst supports, usually porous adsorbents, is to keep the catalytically active phase in a highly dispersed state. It is obvious that the methods of preparation and characterization of adsorbents and catalysts are very similar or identical. The physical structure of catalysts is investigated by means of both adsorption methods and various instrumental techniques derived for estimating their porosity and surface area. Factors such as surface area, distribution of pore volumes, pore sizes, stability, and mechanical properties of materials used are also very important in both processes—adsorption and catalysis. Activated carbons, silica, and alumina species as well as natural amorphous aluminosilicates and zeolites are widely used as either catalyst supports or heterogeneous catalysts. From the above, the following conclusions can be easily drawn (Dabrowski, 2001) ... 

Although an increase in meso pore surface area and activity will result in an increase in conversion and resid conversion, Table IV also shows that there is no simple correlation between the observed catalyst properties and these results. Apparently other aspects such as pore size distribution and pore chemistry also play an important role. 

The particle size and surface area distributions of pharmaceutical powders can be obtained by microcomputerized mercury porosimetry. Mercury porosimetry gives the volume of the pores of a powder, which is penetrated by mercury at each successive pressure the pore volume is converted into a pore size distribution. Two other methods, adsorption and air permeability, are also available that permit direct calculation of surface area. In the adsorption method, the amount of a gas or liquid solute that is adsorbed onto the sample of powder to form a monolayer is a direct function of the surface area of the sample. The air permeability method depends on the fact that the rate at which a gas or liquid permeates a bed of powder is related, among other factors, to the surface area exposed to the permeant. The determination of surface area is well described by the BET (Brunauer, Emmett, and Teller) equation. 

The method provides an estimate of surface area almost independent of the B.E.T. value, and the two values have been compared for a large number of materials including aluminas, silica-aluminas, silicas, and clays. It is shown that the surface area distribution should generally be derived from the adsorption branch of the isotherm and that the above comparison then provides a measure of the validity of the physical assumptions, and hence gives an indication of the character of the pores. 

The pore volume and surface area distribution vs. pore radius for PAM formed from pastes with various phase compositions and densities are given in Fig. 10.20 [23]. The curves for chemically prepared Pb02 are also provided for comparison. When the PAM is obtained by formation of basic lead sulfate pastes, the pore volume grows gradually within a wide range of radii (0.05 to 1.2 pm). For chemically prepared Pb02, the total pore volume attains its maximum value within a very narrow range of radii. A steep rise in the surface area curve for... 

For a given pore volume distribution and a surface area distribution as given in the above equations, we calculate the cumulative specific pore volume and the cumulative specific surface area as shown below ... 

The most fundamental characteristics of any industrial catalyst is its chemical composition. The other factors such as surface area, distribution of pore volumes, pore sizes, stability and mechanical properties are also very important. Such catalysts as metals or oxides of various kinds (pure or mixed) are not thermally stable in the high surface area form in which they have to be applied. So, they are prepared as small particles bonded to the support material, usually oxides, such as alumina and silica gels. 

Roberts BF. A procedure for estimating pore volume and surface area distributions from sorption isotherms. J Coll Interf Sci 1967 23(2) 266-273. 

Table II. Pore Size and Surface Area Distribution for Pillared Clays and Zeolites...

The specific surface area distribution as a function of the pore radius, the... 

The method to be described determines the pore size distribution in a porous material or compacted powder surface areas may be inferred from the results. 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

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