Pore size distribution porous

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). 

The relation between the dusty gas model and the physical structure of a real porous medium is rather obscure. Since the dusty gas model does not even contain any explicit representation of the void fraction, it certainly cannot be adjusted to reflect features of the pore size distributions of different porous media. For example, porous catalysts often show a strongly bimodal pore size distribution, and their flux relations might be expected to reflect this, but the dusty gas model can respond only to changes in the... 

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,... 

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

A Type II isotherm indicates that the solid is non-porous, whilst the Type IV isotherm is characteristic of a mesoporous solid. From both types of isotherm it is possible, provided certain complications are absent, to calculate the specific surface of the solid, as is explained in Chapter 2. Indeed, the method most widely used at the present time for the determination of the surface area of finely divided solids is based on the adsorption of nitrogen at its boiling point. From the Type IV isotherm the pore size distribution may also be evaluated, using procedures outlined in Chapter 3. 

Isotherms of Type 111 and Type V, which are the subject of Chapter 5, seem to be characteristic of systems where the adsorbent-adsorbate interaction is unusually weak, and are much less common than those of the other three types. Type III isotherms are indicative of a non-porous solid, and some halting steps have been taken towards their use for the estimation of specific surface but Type V isotherms, which betoken the presence of porosity, offer little if any scope at present for the evaluation of either surface area or pore size distribution. 

Type IV isotherms are often found with inorganic oxide xerogels and other porous solids. With certain qualifications, which will be discussed in this chapter, it is possible to analyse Type IV isotherms (notably those of nitrogen at 77 K) so as to obtain a reasonable estimate of the specific surface and an approximate assessment of the pore size distribution. 

The principal aim of the second edition of this book remains the same as that of the first edition to give a critical exposition of the use of the adsorption methods for the assessment of the surface area and pore size distribution of finely divided and porous solids. 

In writing the present book our aim has been to give a critical exposition of the use of adsorption data for the evaluation of the surface area and the pore size distribution of finely divided and porous solids. The major part of the book is devoted to the Brunauer-Emmett-Teller (BET) method for the determination of specific surface, and the use of the Kelvin equation for the calculation of pore size distribution but due attention has also been given to other well known methods for the estimation of surface area from adsorption measurements, viz. those based on adsorption from solution, on heat of immersion, on chemisorption, and on the application of the Gibbs adsorption equation to gaseous adsorption. 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

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. 

Supports. The principal component of a typical catalyst is the porous support (49,50). Most supports are robust soHds that can be made with wide ranges of surface areas and pore size distributions. The most widely appHed supports are metal oxides others are carbon, kieselguhr, organic polymers, and zeoHtes. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

The third line of development was to increase the selectivity in order to achieve the highest possible resolution to address difficult separations. This may be achieved by a very narrow pore size distribution of the media, e.g., such as achieved by porous silica microspheres (PSM) or by modifying the porous phase by a composite material, e.g., as for Superdex. In practice, this material shows a maximum selectivity over the separation range (e.g., see Fig. 2.2). 

A narrow pore size distribution is essential to HOPC. To separate polymer samples with various average molecular weights, users need to prepare columns packed with porous materials of a uniform but different pore size, e.g., 10, 13, 18, and 24 nm. In contrast, a broader pore size distribution is common in a SEC column. A need to analyze a wide range of molecular weights (over many decades) by a single set of columns has spread the use of these columns. 

The porous materials that offer the narrowest possible pore size distribution are those that have cylindrical pores of uniform diameter penetrating the entire medium without branching. Branching gives polymer molecules in the junctions extra conformational entropy. An agglomerate of tiny pieces of these porous materials, interlaced with larger voids (much larger than the pore size), should also be chosen. 

This paper will be limited to a discussion of our packed column studies in which we have addressed attention to questions regarding, (a) the role of ionic strength and surfactant effects on both HDC and porous packed column behavior, (b) the effects of pore size and pore size distribution on resolution, and (c) the effects of the light scattering characteristics of polystyrene on signal resolution and particle size distribution determination. 

Porous packed systems represent in addition to the hydrodynamic effect, the possibility for separation due to size-related exclusion of particles from the pores, essentially LEG. In this section a brief overview of some of o ir more recent results pertaining to the question of pore size distribution effects will be given, fore detailed discussions are presented elsewhere (23>2U). 

Fig. 3.23 shows pore volume distributions of some commercially important porous materials. Note that zeolites and activated carbon consist predominantly of micropores, whereas alumina and silica have pores mainly in the me.sopore range. Zeolites and active carbons have a sharp peak in pore size distribution, but in the case of the activated carbon also larger pores are present. The wide-pore silica is prepared specially to facilitate internal mass-transfer. 

D.W. Aksnes, K. Forland, L. Kimtys 2001, (Pore size distribution in meso-porous materials as studied by H NMR), Phys. Chem. Chem. Phys. 3, 3203. 

In addition, mercury intrusion porosimetry results are shown together with the pore size distribution in Figure 3.7.3(B). The overlay of the two sets of data provides a direct comparison of the two aspects of the pore geometry that are vital to fluid flow in porous media. In short, conventional mercury porosimetry measures the distribution of pore throat sizes. On the other hand, DDIF measures both the pore body and pore throat. The overlay of the two data sets immediately identify which part of the pore space is the pore body and which is the throat, thus obtaining a model of the pore space. In the case of Berea sandstone, it is clear from Figure 3.7.3(B) that the pore space consists of a large cavity of about 85 pm and they are connected via 15-pm channels or throats. 

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