Macropore size distribution

The computer-reconstructed catalyst is represented by a discrete volume phase function in the form of 3D matrix containing information about the phase in each volume element. Another 3D matrix defines the distribution of active catalytic sites. Macroporosity, sizes of supporting articles and the correlation function describing the macropore size distribution are evaluated from the SEM images of porous catalyst (Koci et al., 2006 Kosek et al., 2005). Spatially 3D reaction-diffusion system with low concentrations of reactants and products can be described by mass balances in the form of the following partial differential equations (Koci et al., 2006, 2007a). For gaseous components ... 

New applications of zeolite adsorption developed recently for separation and purification processes are reviewed. Major commercial processes are discussed in areas of hydrocarbon separation, drying gases and liquids, separation and purification of industrial streams, pollution control, and nonregenerative applications. Special emphasis is placed on important commercial processes and potentially important applications. Important properties of zeolite adsorbents for these applications are adsorption capacity and selectivity, adsorption and desorption rate, physical strength and attrition resistance, low catalytic activity, thermal-hydrothermal and chemical stabilityy and particle size and shape. Apparent bulk density is important because it is related to adsorptive capacity per unit volume and to the rate of adsorption-desorption. However, more important factors controlling the raJtes are crystal size and macropore size distribution. 

The rate of n-paraffin desorption generally controls the overall production rate (18, 19). The diffusion of n-paraffins in commercial 5A molecular sieves is reported to be controlled by either micropore diffusion or macropore diffusion, or both, depending on the molecular sieve crytal size and macropore size distribution of the adsorbent (20). A 5A molecular sieve adsorbent with smaller crystal size and optimum macropore size distribution would have a faster adsorption-desorption rate and, therefore, a higher effective capacity. 

Figures la-d shows typical cross-sections of isotropic PE foams and longitudinal and transverse sections of PLA foams. In the first case, image analysis characterization was used to determine the macropore size distribution. In the second case, a complete morphological description requires the determination of the density, size distribution, orientation and dispersion of the ultramacropores as well as the orientation and the size distribution of the macropores. The preliminary steps of the image quantification, i.e., gray level image transformations and binary image processing are detailed elsewhere [15].

The macropore size distributions of C8-C18 obtained from mercury porosimetry data had two peaks however, the peak observed at very high pressures of mercury is not considered because of the possible collapse of the structure at high pressures. The macropore diameter decreases in going from C8 to C16, with exception of C12 whose pore diameter is higher than that of C8. The pore diameter of C18 is also found to be higher than that all other samples except C12. 

L.C., Drake, H.L., Ritter. 1945. Macropore-Size Distributions in Some Typical and the Calculation of Permeability Therefrom, Ind. and Eng. Chem. Analytical Edition, vol. 17, 787 pages. 

Ritter, H.L. Drake, L.C. Macropore-size distributions in some typical porous substances. Ind. Eng. Chem. 1945, 17 (12), 787-791. 

Gross AF, Nowak AP (2010) Hierarchical carbon foams with independently tunable mesopore and macropore size distributions. Langmuir 26(13) 11378-11383... 

FIGURE 1.14. Macropore size distribution determined from mercury penetration measurements for (i3) carbon molecular sieve (b) Linde 5A (extrudales), and (c) H-Zeolon (H-mordenite). 

Reduces residual oxygen content Reduces surface area of carbon aerogels and xerogels Reduces pore volumes of carbon aerogels and xerogels Increases macropore size distribution... 

Ritter HL, Drake LC. Pressure porosimetry and determination of complete macropore size distribution. Ind Eng Chem Analyt Ed 1945 17 782-786. 

In the last decades, templating schemes toward materials with a uniform meso-or macropore size distribution and an ordered pore arrangement of the pores... 

Ritter H. L. and L. C. Drake (1945). Pressure porosimeter and determination of complete macropore-size distributions . Industrial Engineering Chemistry 17 782-786. 

The simplest way of introducing Che pore size distribution into the model is to permit just two possible sizes--Tnlcropores and macropotes--and this simple pore size distribution is not wholly unrealistic, since pelleted materials are prepared by compressing powder particles which are themselves porous on a much smaller scale. The small pores within the powder grains are then the micropores, while the interstices between adjacent grains form the macropores. An early and well known model due to Wakao and Smith [32] represents such a material by the Idealized structure shown in Figure 8,2,... 

Case (c). The pore size distribution is strictly bimodal, with macropores... 

Whereas at the lower end of its range mercury porosimetry overlaps with the gas adsorption method, at its upper end it overlaps with photomicrography. An instructive example is provided by the work of Dullien and his associates on samples of sandstone. By stereological measurements they were able to arrive at a curve of pore size distribution, which was extremely broad and extended to very coarse macropores the size distribution from mercury porosimetry on the other hand was quite narrow and showed a sharp peak at a much lower figure, 10nm (Fig. 3.31). The apparent contradiction is readily explained in terms of wide cavities which are revealed by photomicrography, and are entered through narrower constrictions which are shown up by mercury porosimetry. 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Activated carbons for use in Hquid-phase appHcations differ from gas-phase carbons primarily in pore size distribution. Liquid-phase carbons have significantly more pore volume in the macropore range, which permits Hquids to diffuse more rapidly into the mesopores and micropores (69). The larger pores also promote greater adsorption of large molecules, either impurities or products, in many Hquid-phase appHcations. Specific-grade choice is based on the isotherm (70,71) and, in some cases, bench or pilot scale evaluations of candidate carbons. 

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

When the catalyst is expensive, the inaccessible internal surface is a liabihty, and in every case it makes for a larger reactor size. A more or less uniform pore diameter is desirable, but this is practically reahz-able only with molecular sieves. Those pellets that are extrudates of compacted masses of smaller particles have bimodal pore size distributions, between the particles and inside them. Micropores have diameters of 10 to 100 A, macropores of 1,000 to 10,000 A. The macropores provide rapid mass transfer into the interstices that lead to the micropores where the reaction takes place. 

The effects of the concentration of divinylbenzene on pore-size distribution and surface areas of micropores, mesopores, and macropores in monosized PS-DVB beads prepared in the presence of linear polymeric porogens have been studied (65). While the total surface area is clearly determined by the content of divinylbenzene, the sum of pore volumes for mesoforms and macropores, as well as their pore-size distribution, do not change within a broad range of DVB concentrations. However, the more cross-linked the beads, the better the mechanical and hydrodynamic properties. 

The advantages of monosized chromatographic supports are as follows a uniform column packing, uniform flow velocity profile, low back pressure, high resolution, and high-speed separation compared with the materials of broad size distribution. Optical micrographs of 20-p,m monosized macroporous particles and a commercial chromatography resin of size 12-28 p,m are shown in Fig. 1.4. There is a clear difference in the size distribution between the monodispersed particles and the traditional column material (87). 

FIGURE 1.3 15- m macroporous packing material, (a) Narrow particle-size distribution, (b) Close-... 

Surface area is one of the most important factors in determining throughput (amount of reactant converted per unit time per unit mass of catalyst). Many modem inorganic supports have surface areas of 100 to >1000 m g The vast majority of this area is due to the presence of internal pores these pores may be of very narrow size distribution to allow specific molecular sized species to enter or leave, or of a much broader size distribution. Materials with an average pore size of less than 1.5-2 nm are termed microporous whilst those with pore sizes above this are called mesoporous materials. Materials with very large pore sizes (>50 nm) are said to be macroporous, (see Box 4.1 for methods of determining surface area and pore size). 

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. 

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