Pore size distribution method

Calculation of pore size distribution (Method of Pierce, also of Orr and DallaValle )... 

BS 1902-3.16 1990. Methods of testing refractory materials, general and textural properties Determination of pore size distribution (method 1902-316). 

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. 

Brunauer and co-workers [211, 212] proposed a modelless method for obtaining pore size distributions no specific capillary shape is assumed. Use is made of the general thermodynamic relationship due to Kiselev [213]... 

Horvath G and Kawazoe K 1983 Method for oaloulation of effeotive pore size distribution in moleoular sieve oarbon J. Chem. Eng. Japan 16 470-5... 

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. 

Foster s neglect of the role of the adsorbed film was unavoidable in the then absence of any reliable information as to the thickness of the film. It is now known that in fact the effect of the film on the calculated result is far from negligible, as will be demonstrated shortly. Since, however, all the methods of calculating pore size distributions involve a decision as to the upper limit of the range to be studied, this question needs to be discussed first. In effect one has to choose a point corresponding to point G in Fig. 3.1, where the mesopores are deemed to be full up. If the isotherm takes the course GH there are no further cores to be considered in any case but if it swings upwards as at GH, the isotherm is usually so steep that the Kelvin-type approach becomes too inaccurate (cf. p. 114) to be useful. 

In the pioneer work of Foster the correction due to film thinning had to be neglected, but with the coming of the BET and related methods for the evaluation of specific surface, it became possible to estimate the thickness of the adsorbed film on the walls. A number of procedures have been devised for the calculation of pore size distribution, in which the adsorption contribution is allowed for. All of them are necessarily somewhat tedious and require close attention to detail, and at some stage or another involve the assumption of a pore model. The model-less method of Brunauer and his colleagues represents an attempt to postpone the introduction of a model to a late stage in the calculations. 

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. 

Fig. 3.18 Pore size distributions of a silica geP GSSO, calculated from the desorption branch of the isotherm at 77 K by dilTerent methods. (A) x,...

Calculation of pore size distribution (Roberts Method"). Worked example from desorption branch of nitrogen isotherm on... 

Fig. 3.20 Pore size distributions (calculated by the Roberts method) for silica powder compacted at (A) Ibtonin" (B) 64tonin (C) 130 ton in". The distributions in (a) were calculated from the desorption brunch of the isotherms of nitrogen, and in (h) from the adsorption branch.

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. 

These procedures proposed by Dubinin and by Stoeckli arc, as yet, in the pioneer stage. Before they can be regarded as established as a means of evaluating pore size distribution, a wide-ranging study is needed, involving model micropore systems contained in a variety of chemical substances. The relationship between the structural constant B and the actual dimensions of the micropores, together with their distribution, would have to be demonstrated. The micropore volume would need to be evaluated independently from the known structure of the solid, or by the nonane pre-adsorption method, or with the aid of a range of molecular probes. 

The computation of mesopore size distribution is valid only if the isotherm is of Type IV. In view of the uncertainties inherent in the application of the Kelvin equation and the complexity of most pore systems, little is to be gained by recourse to an elaborate method of computation, and for most practical purposes the Roberts method (or an analogous procedure) is adequate—particularly in comparative studies. The decision as to which branch of the hysteresis loop to use in the calculation remains largely arbitrary. If the desorption branch is adopted (as appears to be favoured by most workers), it needs to be recognized that neither a Type B nor a Type E hysteresis loop is likely to yield a reliable estimate of pore size distribution, even for comparative purposes. 

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. 

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. 

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. 

The models of Matranga, Myers and Glandt [22] and Tan and Gubbins [23] for supercritical methane adsorption on carbon using a slit shaped pore have shown the importance of pore width on adsorbate density. An estimate of the pore width distribution has been recognized as a valuable tool in evaluating adsorbents. Several methods have been reported for obtaining pore size distributions, (PSDs), some of which are discussed below. 

Describe the method for estimating pore size distribution. 

Porosity and surface area are routinely measured by nitrogen absorption-desorption, mercury intrusion, and low-angle X ray. The electron microscope (EM) provides direct visual evidence of pore size and pore-size distribution. Thus, a combination of EM and conventional methods of pore-size measurement should provide reliable information on the pore structure of polymers. 

The broad pore size distribution of Sepharose makes it well apt for the analysis of broad molecular mass distributions of large molecules. One example is given by the method for determination of MWD of clinical dextran suggested in the Nordic Pharmacopea (Nilsson and Nilsson, 1974). Because Superose 6 has the same type of pore size distributions as Sepharose 6, many analytical applications performed earlier on Sepharose have been transformed to Superose in order to decrease analysis time. However, Sepharose is suitable as a first try out when no information about the composition of the sample, in terms of size, is available. 

The physical characterisation of membrane structure is important if the correct membrane is to be selected for a given application. The pore structure of microfiltration membranes is relatively easy to characterise, SEM and AFM being the most convenient method and allowing three-dimensional structure of the membrane to be determined. Other techniques such as the bubble point, mercury intrusion or permeability methods use measurements of the permeability of membranes to fluids. Both the maximum pore size and the pore size distribution may be determined.1315 A parameter often quoted in manufacturer s literature is the nominal... 

The effects of various pore-size distributions, including Gaussian, rectangular distributions, and continuous power-law, coupled with an assumption of cylindrical pores and mass transfer resistance on chromatographic behavior, have been developed by Goto and McCoy [139]. This study utilized the method of moments to determine the effects of the various distributions on mean retention and band spreading in size exclusion chromatography. 

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