Macropores and transition pores

In (8) and (9), I is the intensity scattered by one electron, and Sr are the specific surfaces, or surface areas per unit mass of coal, of the macropores and transition pores, respectively the constant C. is proportional to the weak but constant scattering from the micropores b is a constant characterizing the micropore dimensions M and A are respectively the mass of the sample and its cross-section area perpendicular to the incident beam T is the x-ray transmission and a is a constant inversely proportional to the average dimensions of the transition pores. The factor 1/T is included in (9) to take account of the absorption of x-ray in the samples, since (3) was developed under the assumption that the samples were non-absorbing. The transmission T can be expressed—... 

After we had determined I A and calculated I for the coal samples, we evaluated the specific surfaces S° and S for the macropores and transition pores in the 15 coals. These specific surfaces are listed in Table 1. We estimate that the uncertainty in the specific surfaces is about 40%. 

The effect of mineral matter is so small that it is completely negligible compared to the combined specific surface of the macropores and transition pores in coals with scattering curves which have a shoulder. 

In Table 1 we list the sum of the specific surfaces of the macropores and transition pores and also the specific surfaces obtained by low temperature nitrogen adsorption and by adsorption of carbon dioxide at room temperatures. The nitrogen and carbon dioxide specific surfaces are taken from the PSOC data bank, except for coal PSOC 105. Since the specific surfaces in the data bank for this coal appeared questionable, they were remeasured by R. G. Jenkins at Pennsylvania State University. 

At the time we wrote the manuscript for Reference (7), we were unable to relate the high fraction of transitional pores found in many of the coals to any other property of the coals. We have now concluded (11) that there are inflections in the scattering curves only for coals with fixed carbon contents in the interval from about 72% through 83% per cent (dry, mineral-matter free) and that for these coals, the specific surface of the transitional pores is appreciably larger than the specific surface of the macropores. As would be expected from our interpretation of the inflection (11), the specific surfaces of the transitional pores in all of the subbltumlnous coals in Table 1 except PSOC 138 are much larger than the specific surfaces of the macropores, and there is a tendency for the total x-ray specific surfaces [i. e., the sum of the specific surfaces of the macropores and transitional pores, as calculated by... 

Carbons may have closed and open pores with a large variety of dimensions from a few Angstroms to several microns. In terms of structure, the pores in active carbons are divided into three basic classes [66, 69] macropores, transitional pores, and micropores. Pores are formed during the production of carbon (pyrolysis of its precursors), or can be formed by other means such as oxidation by 02, air, C02, or H20 [66]. According to Dubinin s... 

Porosity refers to the volume of pores in a solid. It contributes to the internal surface area of the sample and can influence the kinetics of adsorption. Diffusion into and out of pores is often considered responsible for slow adsorption and desorption processes. Pores vary in size and shape. They have been classified according to their average widths as micropores which are of the order of molecular dimensions (<2 nm), meso- or transitional pores which are between 2-50 nm and macropores which are larger than 50 nm (Sing et al., 1985). The sum of all the pores is called the pore volume (porosity). 

It is convenient to categorize pores into several size ranges. The largest pore radii amenable to analysis by the Kelvin equation are about 1000 A which corresponds to relative pressures near 0.99. Pores with radii greater than this are termed macropores . Dubinin calls pores in the Kelvin range, from about 15 to 1000 A, transitional and pores with radii less than about 15 A micropores . The failure of V-t plots to pass through the origin has led to the postulation of submicropores with radii less than about 7 A. 

The experimental data obtained are given in graphs as functions of the relative elongation of the pellets (A l/l) on the adsorption value (ml/ gram) or on degree of filling of the micropores (0), where 0=1 represents the adsorption of water at a relative equilibrium pressure p/p = 0.4—i.e., when the micropores are completely filled and when the capillary condensation in the transitional pores and macropores of the secondary porous structure of the pellets has not yet begun. 

For porous sorbents, most of the surface area is not on the outside of the particle but on the inside pores of the sorbent (Figure 2.20) in complex, interconnected networks of micropores (diameters smaller than 2 nm), mesopores (2 to 50 nm), also known as transitional pores, and macropores (greater than 50 nm) [57], Most of the surface area is derived from the small-diameter micropores and the medium-diameter transitional pores [56], Porous sorbents vary in pore size, shape, and tortuosity [58] and are characterized by properties such as particle diameter, pore diameter, pore volume, surface areas, and particle-size distribution. 

The term proportional to S° in (8) describes the scattering from the macropores and was obtained by rewriting (3), while the middle term was selected to give a reasonable and convenient approximation to the contribution from the transition pores. An intensity with this form is expected— from pores randomly distributed in a material with uniform electron density. This expression has the desired properties of approving a constant value for small h and of being proportional to h for large h. 

There are pronounced shoulders on the scattering curves for PSOC Coals 105, 022, and 188, while there are no shoulders on the curves for Coals 197 and 138. The shoulders in the scattering curves from Coals 185 and 181 are less evident, and a shoulder can be seen for Coal 212 only after careful inspection. These results suggest that there will be well-defined shoulders in the scattering curves only when the specific surface of the transition pores is at least ten times as great as that of the macropores. 

We therefore suggest that the x-ray scattering method can be useful in studies of the pore structure of coals. In particular, the scattering curves from medium-rank and low-rank coals can provide an estimate of the specific surfaces associated with the macropores and the transition pores. This information is difficult to obtain by other techniques. 

Pore structure can markedly affect char reactivity. Coals in general are highly porous with a polymodal pore size distribution. Pores normally are classified into macropores (>500 A in diameter), transitional pores (20-500 A in diameter), and micropores (<20 A in diameter). Upon pyrolysis, the pores in the coal open up, but the, char still contains microporosity. Coal chars in general, and lignitic chars in particular, retain coal s polymodal pore distribution. Surface areas of coal chars are in the range 100-800 m2/g. Most of this surface area and, therefore, most of the active surface reside inside the pores, so accessibility of reactive gases to active sites is very important. 

For coarse coal particles with high ash content, diffusion of oxygen through the ash layer often determines the overall combustion rate. The inner pores in the ash layer can be divided into micropores of 0.004-0.0012 /im, transition pores of 0.0012-0.03 fim and macropores of 0.03-1 fim diameter. Experiments showed that the macropores constitute the main channels for mass transfer. 

As our earlier investigations of coal suggested that the scattering was due to pores in the coal (7), we analyzed our scattering data under the assumption that the scattering was produced by three classes (15) of pores—macropores, with dimensions of 1 micron or more transitional pores, which have dimensions of a few hundred A, and micropores, which were not larger than about 20 or 30 A. 

The total x-ray specific surfaces of Beulah lignite determined at the University of North Dakota and the University of Missouri agree within the estimated uncertainty. For the specific surfaces of the macropores and the transitional pores, the agreement, though still within the estimate uncertainty, is not so close. This greater difference may be a result of the fact that the scattering curves from the Universities of North Dakota and Missouri were determined by fits of Equation (3) with n = 2 and n = 1,... 

The transitional-pore specific surfaces listed in Table 1 for all of the subbltumlnous coals except PSOC 138 are about 3 to 8 times as large as the corresponding macropore specific surfaces. The ratio of the area associated with the transitional pores to that for the macropores is large enough in these subbltumlnous coals that at least a trace of an Inflection can be seen on careful examination of the scattering curves. On the other hand, for the subbltumlnous Coal 138 and for the lignites, the specific surfaces of the macropores and the transitional pores are more nearly equal, and no inflection is evident in the scattering curves. 

The ability to distinguish between the specific surfaces associated with the macropores and the transitional pores is, we feel, a very useful property of small-angle x-ray scattering especially since few other techniques can identify the contributions of these two pore classes to the specific surface. 

In the preceding section, we calculated the specific surfaces of the macropores and the transitional pores from the scattering curves We now would like to suggest a method which we feel may be useful for obtaining at least a rough estimate of the distribution of pore dimensions in low-rank coals ... 

If our suggestion that Equation (4) approximates the pore-dimension distribution in lignites is correct, there is no unique way to classify the pores as macropores, transitional pores, and micropores, at least for pores smaller than about 3000 A. Instead, there is a continuous distribution of the pore dimensions from about 4 A to at least 3,000 A. However, the fact that the pore classes may not be uniquely defined does not invalidate the alternative and essentially equivalent analysis of the data in which we employed Equation (3) to determine the x-ray specific surface. 

Zeolites, as previously described, are crystalline microporous solids with well-defined structures made up of interlocking microporous Si04 and A104. Microporous means that the pores have dimensions of less than 20 A, on the order of the size of many petroleum-related molecules, and their crystalline nature means that they have a narrow pore distribution (mesoporous materials have pore sizes between 20 A and 500 A, macroporous materials have pores larger than 500 A). This combination of features not only restricts the size of molecules that can enter the pores, but also the dimensions of the transition state and of the molecules that can successfully leave. For these reasons, zeolites have been termed shape selective. ... 

Ordered macroporous materials with pore sizes of more than 50 nm appeared in the late 1990s with the development of a method using colloidal crystals of monodisperse spheres as a new template.The walls of macroporous materials are larger than those of mesoporous materials, and a number of well-ordered macroporous crystalline transition metal oxides have been prepared.The preparation method... 

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