Pore area size distribution

As a result, stage I directs the overall porosity of xerogel emin < e < emax), stage II determines the pore volume - size distribution, and stage III includes the decrease of surface area (the main factors here are pH, temperature and remaining liquid content). 

Size can refer to volume, area, or length, and therefore pore-size distribution may be defined in terms of any one of these properties. In practice, the definition of size adopted is highly dependent upon the method of measurement. For example, the area size distribution of pores is often measured by image analysis of soil thin sections, while water retention data are usually interpreted in terms of the distribution of pore diameters (Bullock Thomasson, 1979). For consistency with the definition of the Peclet number, we have chosen to define size in terms of length, L. Dullien (1991) has proposed the following interrelationships between the different definitions of size L = VIS in three-dimensions or L=AJP in two-dimensions, where V is volume, S is surface area, A is cross-sectional area and P is perimeter. These relations can be used to compare pore-size distributions measured using different methods. 

After treatment at 800° or 1000°C the areas calculated from the porosimetry curves were higher than those from gas adsorption. This was due to the porosimetry curve being a measurement of the pore neck size distribution rather than the pore body distribution, which can lead to an under estimation of the volume associated with the wider pores and an overestimation of that associated with the narrower pores in materials with complex pore geometries in which a fraction of the wider pores may not be directly accessible, with a subsequent overestimation of the calculated area. 

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). 

Physical properties affecting catalyst perfoniiance include tlie surface area, pore volume and pore size distribution (section B1.26). These properties regulate tlie tradeoff between tlie rate of tlie catalytic reaction on tlie internal surface and tlie rate of transport (e.g., by diffusion) of tlie reactant molecules into tlie pores and tlie product molecules out of tlie pores tlie higher tlie internal area of tlie catalytic material per unit volume, tlie higher the rate of tlie reaction... 

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. 

Type 1 isotherms, as will be demonstrated in Chapter 4, are characteristic of microporous adsorbents. The detailed interpretation of such isotherms is controversial, but the majority of workers would probably agree that the very concept of the surface area of a microporous solid is of doubtful validity, and that whilst it is possible to obtain an estimate of the total micropore volume from a Type I isotherm, only the crudest guesses can be made as to the pore size distribution. 

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. 

Various methods have been devised for incorporating the bv correction into calculations of pore size distribution. Some of them involve the length of the pores and the area of their walls others the area of the walls only and yet others avoid the direct involvement of either the length or the area. Up to the present, virtually all the procedures have been restricted to nitrogen as the adsorptive. 

The evaluation of pore size distribution by application of the Kelvin equation to Type IV isotherms has hitherto been almost entirely restricted to nitrogen as adsorptive. This is largely a reflection of the widespread use of nitrogen for surface area determination, which has meant that both the pore size distribution and the specific surface can be derived from the same isotherm. 

Cumulative surface area from pore size distribution... 

Each of the procedures described in Section 3.6 for the calculation of pore size distribution involves a value of the pore area y4f for each successive group of pores. In the Roberts procedure 6A, can be immediately obtained from the corresponding pore volume and pore radius as (for... 

The Use of Gas Adsorption for the Determination of Surface Area and 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... 

We therefore felt it timely to attempt a critical exposition and assessment of the common methods for the evaluation of the surface area and pore size distribution of solids from adsorption measurements. Our main concern has therefore been with the use of adsorption data for these purposes rather than with adsorption per se and it is for this reason that our treatment of theoretical matters, whilst sufficiently detailed to bring out the nature of the assumptions underlying the various methods, is not exhaustive we have not set out to write a text-book or a treatise on adsorption, and our choice of material from the literature has been dictated solely by its seeming suitability for the explanation or illustration of the topic under discussion. 

It is less well known, but certainly no less important, that even with carbon dioxide as a drying agent, the supercritical drying conditions can also affect the properties of a product. Eor example, in the preparation of titania aerogels, temperature, pressure, the use of either Hquid or supercritical CO2, and the drying duration have all been shown to affect the surface area, pore volume, and pore size distributions of both the as-dried and calcined materials (34,35). The specific effect of using either Hquid or supercritical CO2 is shown in Eigure 3 as an iHustration (36). 

Catalyst performance depends on composition, the method of preparation, support, and calcination conditions. Other key properties include, in addition to chemical performance requkements, surface area, porosity, density, pore size distribution, hardness, strength, and resistance to mechanical attrition. 

Activated carbons are made by first preparing a carbonaceous char with low surface area followed by controlled oxidation in air, carbon dioxide, or steam. The pore-size distributions of the resulting products are highly dependent on both the raw materials and the conditions used in their manufacture, as maybe seen in Figure 7 (42). 

The large majority of activated alumina products are derived from activation of aluminum hydroxide, rehydrated alumina, or pseudoboehmite gel. Other commerical methods to produce specialty activated aluminas are roasting of aluminum chloride [7446-70-0], AIQ calcination of precursors such as ammonium alum [7784-25-0], AlH2NOgS2. Processing is tailored to optimize one or more of the product properties such as surface area, purity, pore size distribution, particle size, shape, or strength. 

Rehydration Bonded Alumina. Rehydration bonded aluminas are agglomerates of activated alumina, which derive their strength from the rehydration bonding mechanism. Because more processing steps are involved in the manufacture, they are generally more expensive than activated aluminum hydroxides. On the other hand, rehydration bonded aluminas can be produced in a wider range of particle shape, surface area, and pore size distribution. 

Characterization. When siHca gel is used as an adsorbent, the pore stmcture determines the gel adsorption capacity. Pores are characterized by specific surface area, specific pore volume (total volume of pores per gram of solid), average pore diameter, pore size distribution, and the degree to which entrance to larger pores is restricted by smaller pores. These parameters are derived from measuring vapor adsorption isotherms, mercury intmsion, low angle x-ray scattering, electron microscopy, gas permeabiHty, ion or molecule exclusion, or the volume of imbibed Hquid (1). 

In addition to surface area, pore size distribution, and surface chemistry, other important properties of commercial activated carbon products include pore volume, particle size distribution, apparent or bulk density, particle density, abrasion resistance, hardness, and ash content. The range of these and other properties is illustrated in Table 1 together with specific values for selected commercial grades of powdered, granular, and shaped activated carbon products used in Hquid- or gas-phase appHcations (19). 

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. 

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. 

Transition aluminas are good catalyst supports because they are inexpensive and have good physical properties. They are mechanically stable, stable at relatively high temperatures even under hydrothermal conditions, ie, in the presence of steam, and easily formed in processes such as extmsion into shapes that have good physical strength such as cylinders. Transition aluminas can be prepared with a wide range of surface areas, pore volumes, and pore size distributions. 

Porosity and pore-size distribution usually are measured by mercury porosimetry, which also can provide a good estimate of the surface area (17). In this technique, the sample is placed under vacuum and mercury is forced into the pore stmcture by the appHcation of external pressure. By recording the extent of mercury intmsion as a function of the pressure appHed, it is possible to calculate the total pore volume and obtain the population of the various pore sizes in the range 2 nm to 10 nm. 

Characterization. Ceramic bodies are characterized by density, mass, and physical dimensions. Other common techniques employed in characterizing include x-ray diffraction (XRD) and electron or petrographic microscopy to determine crystal species, stmcture, and size (100). Microscopy (qv) can be used to determine chemical constitution, crystal morphology, and pore size and morphology as well. Mercury porosknetry and gas adsorption are used to characterize pore size, pore size distribution, and surface area (100). A variety of techniques can be employed to characterize bulk chemical composition and the physical characteristics of a powder (100,101). 

Characterization. The proper characterization of coUoids depends on the purposes for which the information is sought because the total description would be an enormous task (27). The foUowiag physical traits are among those to be considered size, shape, and morphology of the primary particles surface area number and size distribution of pores degree of crystallinity and polycrystaUinity defect concentration nature of internal and surface stresses and state of agglomeration (27). Chemical and phase composition are needed for complete characterization, including data on the purity of the bulk phase and the nature and quaHty of adsorbed surface films or impurities. 

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