Surface area distribution

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. 

Fig. 2. Platinum crystallite size distribution for 0.12 ng cm-1 ultrathin platinum film (Fig. 1). Full line, number distribution broken line, surface area distribution. 

Fig. 4. Platinum crystallite size distribution for 2.5% (w/w) platinum/silica catalyst (Fig. 3). Full line, number distribution broken line, surface area distribution. After T. A. Dorling, and R. L. Moss, J. Catal. 7, 378 (1967) and R. L. Moss, Platinum Metals Rev. 11 (4), 1 (1967).

Surface Area Distribution s(D), the percentage of particles with a certain surface area plotted against the equivalent diameter. 

Future improvements in the application of laboratory dissolution data to natural systems will come not (only) from additional work on laboratory kinetics, but will also depend heavily on much more comprehensive studies of surface area distribution, evolution, and accessibility to attack by fluids in natural systems, and by improved understanding of thermodynamic properties of natural fluids. Only in this way will laboratory kinetic data contribute to solving environmental problems such as nuclear waste disposal and evaluating the impact of acid deposition. 

However, nitrogen adsorption reveals considerable differences, as shown in Fig. 5.14, in terms of surface area distribution of a 28-day hydrated C3S specimen [20], or of specific surface area as a function of hydration time... 

Fig. 5.14 Surface area distribution of a 28-day hydrated Ca3Si05 sample measured by nitrogen adsorption (Skalny).

Figure 12.28 shows the particle surface area size distribution before the Mount Pinatubo eruption (Fig. 12.28a), inside the main aerosol layer several months after the eruption (Fig. 12.28b), and almost two years after the eruption (Fig. 12.28c). (See Chapter 9.A.2 for a description of how particle size distributions are normally characterized.) Prior to the eruption, the surface area distribution is unimodal, with typical radii of 0.05-0.09 /xrn and a number concentration of l-20 particles cm 1. In the main stratospheric aerosol layer formed after the eruption, the distribution is bimodal...

FIGURE 12.28 Particle surface area distributions in the stratosphere (a) before Mount Pinatubo eruption, (b) August 20, 1991, over California, and (c) May 7, 1993, over California (adapted from Russell et al. (1996) and Goodman et al. (1994)). 

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

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) ... 

The 9-parameter is also subject to uncertainty. It is likely that Whitby s (1978) estimates of 9 (Table 10.1) do not reflect the true surface area distribution, since they were based on the average size spectrum of aerosols and assumed spherical particles. Adsorption/desorption kinetics (Kamens et al., 1995 Rounds and Pankow, 1990,1993) and relative humidity (Goss and Eisenreich, 1997 Lee and Tsai, 1994 Pankow et al., 1993 Storey et al., 1995 Thibodeaux et al., 1991) influence the adsorption of POPs onto aerosols, and the Junge-Pankow model does not take these factors into account. 

Since atmospheric aerosols comprise particles with a wide range of sizes, it is often convenient to use mathematical models to describe the atmospheric aerosol distribution (Seinfeld and Pandis, 1998). A series of mathematical models have been proposed, of which the lognormal distribution has been the most used in atmospheric applications (Seinfeld and Pandis, 1998 Horvath, 2000). Useful discussions of the various aerosol size distribution models are provided by Seinfeld and Pandis (1998) and Jaenicke (1998). In general, atmospheric aerosols size distributions are shown graphically in terms of the volume (or mass) distributions, surface area distributions, or number distributions as a function of particle size (Jaenicke, 1998). 

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. 

Fig. 1 Graphs showing (a) fractogram and copper concentration in eluent, (b) corresponding size distribution, (c) copper concentration distribution and element ratio distribution of copper in soil sample, and (d) copper per unit surface area distribution.

Lipfert, F. W. Daum, M. L. Cohen, S. "Methods for Estimating Surface Area Distributions of Common Building Materials" Brookhaven National Laboratory, Upton, NY 11973, 1985. 

Figure 3. An example of the log-normal distribution function in normalized linear form for CMD = 1.0 and Og = 2.0, showing the mode, median and mean of the size distribution, the surface area distribution median and mean diameters, the mass distribution median and mean diameters, and the diameter of average mass. Reproduced with permission from Raabe OG (1970). Generation and characterization of aerosols. In Inhalation Carcinogenesis (MG Hanna, P Nettersheim and JR Gilbert, eds), pp. 123-172. Proceedings of a Biology Division, Oak Ridge National Laboratory Conference. Oak Ridge, TN, USA US Atomic Energy Commission...

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