Porous solids pore size distribution

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). 

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... 

Although a number of methods are available to characterize the interstitial voids of a solid, the most useful of these is mercury intrusion porosimetry [52], This method is widely used to determine the pore-size distribution of a porous material, and the void size of tablets and compacts. The method is based on the capillary rise phenomenon, in which excess pressure is required to force a nonwetting liquid into a narrow volume. 

Vinten et al. (1983) demonstrated that the vertical retention of contaminated suspended particles in soils is controlled by the soil porosity and the pore size distribution. Figure 5.8 illustrates the fate of a colloidal suspension in contaminated water during transport through soil. Three distinct steps in which contaminant mass transfer may occur can be defined (1) contaminant adsorption on the porous matrix as the contaminant suspension passes through subsurface zones, (2) contaminant desorption from suspended solid phases, and (3) deposition of contaminated particles as the suspension passes through the soil. 

ISEC, which was introduced by Halasz and Martin in 1978 [119], represents a simple and fast method for the determination of the pore volnme, the pore size distribution profile, and the spe-cihc snrface area of porous solids. Generally, ISEC is based on the principle of SEC. SEC, also referred to as gel permeation or gel filtration chromatography, is a noninteractive chromatographic method that separates analytes according to their size by employing a stationary phase that exhibits a well-dehned pore distribution. 

The pore-size distribution is the distribution of pore volume with respect to pore size (Figure 3.66). It is an important factor controlling the diffusion of reactants and products in the porous solid and thus an essential property for its characterization. The computation of pore size distribution involves a number of assumptions, and therefore reporting of the data should always be accompanied by an indication of the method used for its determination. 

KJS method to calculate pore size distributions for hydrophobic porous solids... 

To achieve a significant adsorptive capacity an adsorbent must have a high specific area, which implies a highly porous structure with very small micropores. Such microporous solids can be produced in several different ways. Adsorbents such as silica gel and activated alumina are made by precipitation of colloidal particles, followed by dehydration. Carbon adsorbents are prepared by controlled burn-out of carbonaceous materials such as coal, lignite, and coconut shells. The crystalline adsorbents (zeolite and zeolite analogues are different in that the dimensions of the micropores are determined by the crystal structure and there is therefore virtually no distribution of micropore size. Although structurally very different from the crystalline adsorbents, carbon molecular sieves also have a very narrow distribution of pore size. The adsorptive properties depend on the pore size and the pore size distribution as well as on the nature of the solid surface. 

Condensation can, therefore, take place in narrow capillaries at pressures which are lower than the normal saturation vapour pressure. Zsigmondy (1911) suggested that this phenomenon might also apply to porous solids. Capillary rise in the pores of a solid will usually be so large that the pores will tend to be either completely full of capillary condensed liquid or completely empty. Ideally, at a certain pressure below the normal condensation pressure all the pores of a certain size and below will be filled with liquid and the rest will be empty. It is probably more realistic to assume that an adsorbed monomolecular film exists on the pore walls before capillary condensation takes place. By a corresponding modification of the pore diameter, an estimate of pore size distribution (which will only be of statistical significance because of the complex shape of the pores) can be obtained from the adsorption isotherm. 

Porous carbon materials mostly consist of carbon and exhibit appreciable apparent surface area and micropore volume (MPV) [1-3], They are solids with a wide variety of pore size distributions (PSDs), which can be prepared in different forms, such as powders, granules, pellets, fibers, cloths,... 

In Chapters 4 and 6, several methods of characterization of solids that are normally used for catalyst testing were described. In particular, the parameters which characterize the surface morphology of a porous catalyst are the same that characterize a porous adsorbent, that is, the specific surface area, S [m2/g], the micropore volume, W1 [cm3/g], the sum of the micropore andmesopore volumes, that is, the pore volume, W [cm3/g], and the pore size distribution (PSD), AVp/ADp (see Chapter 6). 

Unsteady state diffusion in monodisperse porous solids using a Wicke-Kallenbach cell have shown that non-equimolal diffusion fluxes can induce total pressure gradients which require a non-isobaric model to interpret the data. The values obtained from this analysis are then suitable for use in predicting effectiveness factors. There is evidence that adsorption of the non-tracer component can have a considerable influence on the diffusional flux of the tracer and hence on the estimation of the effective diffusion coefficient. For the simple porous structures used in these tests, it is shown that a consistent definition of the effective diffusion coefficient can be obtained which applies to both the steady and unsteady state and so can be used as a basis of examining the more complex bimodal pore size distributions found in many catalysts. 

Many catalysts are porous solids of high surface area and with such materials it is often useful to distinquish between the external and internal surface. The external surface is usually regarded as the envelope surrounding discrete particles or agglomerates, but is difficult to define precisely because solid surfaces are rarely smooth on an atomic scale. It can be taken to include all the prominences plus the surface of those cracks, pores and cavities which are wider than they are deep. The internal surface comprises the walls of the rest of the pores, cavities and cracks. In practice, the demarcation is likely to depend on the methods of assessment and the nature of the pore size distribution. The total surface area (As) equals the sum of the external and internal surface areas. The roughness of a solid surface may be characterized by a roughness factor, i.e. the ration of the external surface to the chosen geometric surface. 

D. W. Aksnes and L. Kimtys, H and 2H NMR studies of benzene confined in porous solids melting point depression and pore size distribution. Solid State NMR, 2004, 25,146-152. 

The boundary condition of zero accumulation on the interface between macropores and solid phase is imposed. The effective diffusivity of the porous sample G1 with bimodal pore size distribution is summarized in Fig. 16, where the sample macro-porosity macro is varied on the horizontal axis. This effective diffusivity is compared with a situation where the diffusion transport in nanopores is omitted. The contribution of the transport through the nano-porous solid phase to the total diffusion flux is significant. The calculated effective... 

The macro-porosity emacro and the correlation function corresponding to the macro-pore size distribution of the washcoat were evaluated from the SEM images of a typical three-way catalytic monolith, cf. Fig. 25. The reconstructed medium is represented by a 3D matrix and exhibits the same porosity and correlation function (distribution of macro-pores) as the original porous catalyst. It contains the information about the phase at each discretization point— either gas (macro-pore) or solid (meso-porous Pt/y-Al203 particle). In the first approximation, no difference is made between y-Al203 and Ce02 support, and the catalytic sites of only one type (Pt) are considered with uniform distribution. 

Early studies involving NMR include the work by Hanus and Gill is [6] in which spin-lattice relaxation decay constants were studied as a function of available surface area of colloidal silica suspended in water. Senturia and Robinson [7] and Loren and Robinson [8] used NMR to qualitatively correlate mean pore sizes and observed spin-lattice relaxation times. Schmidt, et. al. [9] have qualitatively measured pore size distributions in sandstones by assuming the value of the surface relaxation time. Brown, et. al. [10] obtained pore size distributions for silica, alumina, and sandstone samples by shifting the T, distribution until the best match was obtained between distributions obtained from porosimetry and NMR. More recently, low field (20 MHz) NMR spin-lattice relaxation measurements were successfully demonstrated by Gallegos and coworkers [11] as a method for quantitatively determining pore size distributions using porous media for which the "actual" pore size distribution is known apriori. Davis and co-workers have modified this approach to rapidly determine specific surface areas [12] of powders and porous solids. 

Because the shape of the pores is not exactly cylindrical, as assumed in the derivation of Equation 3.12, the calculated pore size and pore size distribution can deviate appreciably from the actual values shown by electron microscopy. If a pore has a triangular, rectangular or more complicated cross-section, as found in porous materials composed of small particles, not all the cross-sectional area is filled with mercury due to surface tension mercury does not fill the comers or narrow parts of the cross-section. A cross-section of the solid, composed of a collection of nonporous uniform spheres during filling the void space with mercury is shown in Figure 3.3. Mayer and Stowe [15] have developed the mathematical relationships that describe the penetration of mercury (or other fluids) into the void spaces of such spheres. 

In the last decade, a variety of microporous and mesoporous materials have been developed for applications in catalysis, chromatography and adsorption. Great attention has been paid to the control of (i) pore surface chemistry and (ii) textural properties such as pore size distribution, pore size and shape. Recently, a new field of applications for these materials has been highlighted [1-3] by forcing a non-wetting liquid to invade a porous solid by means of an external pressure, mechanical energy can be converted to interfacial energy. The capillary pressure, Pc p, required for pore intrusion can be written from the Laplace-Washbum relation,... 

Porous solids generally have a pores size distribution and in many cases this results in a complicated transport mechanism which is a combination of the different mechanisms described above. This is also the case when the pores size are ranged near the boundaries between these different mechanisms. 

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