Porous distribution

The use of adsorption isotherms is subject to both theoretical and experimental limitations. There is effectively a minimum relative pressure value specific to each adsorbate (e.g. P/Pq = 0.42 for nitrogen, 0,2 for CCI4) which corresponds to the minimum value of the surface tension for the phase to remain in liquid form. Below this critical value, the liquid adsorbate is unstable and vaporises spontaneously, an effect represented on the desorption curves by a sharp drop in the adsorbed volume. Depending on the significance of this variation, the porous distribution calculated from the desorption data may show an artefact in the pore size domain corresponding to this process (3-4 nm in diameter). For a porous solid where this phenomenon occurs, it is advisable to study the adsorption curve. 

Figure 1.7 shows the physisorption isotherm, obtained using the non continuous volumetric technique, of a mesoporous alumina (type IV isotherm) and the results of analysis procedures (BET transform, /-curve, BJH porous distribution). This solid presents a specific surface area of approximately 200 m /g with the narrow pore size distribution at around 10 nm. The shape of the /-curve shows that it does not contain any micropores. 

Figure 1.7 Isotherm of a alumina (A), BET transform (B), BJH porous distribution (C) and r-curve (D).

Figure 1.9 Isotherms (A) and porous distributions (B) during an operation and regeneration cycle.

Figure 1.11 Porous distribution obtained from the curve in Figure 1.10,...

The power of electrochemical impedance spectroscopy (EIS) is well acknowledged and widely used in various systems [130, 131]. The history of impedance of porous, distributed electrodes in liquid electrolytes goes back to the early 1960s (see Refs. 132, 133), and some later works [134, 135]. In the context of accumulators, interpretation of electrode impedance was already long ago considered as a promising way to acquire information on the current state of the electrodes [136]. The same refers to the study of corrosion [137, 138]. Nowadays,... 

Transmission microscopy is realized using a Philips CM30 apparatus at 300 KV. DRX spectra were realized on a diffractometer Philips 1700 by scanning between 5 to 70° at l°/mn. Porous distribution is determined by mercury intrusion after elimination of gas over night at 200°C in an oven (Autopore II 9220 V3.01). Acidobasic properties characteristics of solids were estimated by studying the reactivity of 2-methyl 3-butyn-2-ol (MBOH) (ref. 3). 

The textural and the structural characterisation performed on the Pd/AbOs catalyst prepared by sol-gel method, shows a BET surface area of 270 m /g, a mesoporous texture and a uniform porous distribution with an average pore diameter of 3.3 nm. The metallic dispersion obtained by hydrogen chemisorption is 45 %. This later result is confirmed by the palladium particles diameter varying between 1 and 10 nm with an average of 3 nm obtained form the MET analysis. The palladium content determined by inductively coupled plasma is closely to 1.9 %. No significant BET surface area decrease nor a metallic dispersion loss were observed when the catalyst is aged under catalytic conditions up to the steady state. Since the thermal stability of the catalyst is needed to minimize the modification of the palladium particles structure, the later result justifies the choice of the sol-gel synthesis method and the calcinations temperature (700°C) selection. 

Porous silicon (pSi) at atomic scale is a crystalline material however, it presents a random porous distribution with branches of different morphologies and sizes, as discussed along this book. The description of this disordered porous structure is one of the main theoretical challenges. Due to the fabrication process, pSi presents different surface saturations and internal stmctural strains, both should be adequately simulated. In addition, the inhomogeneity of pSi produces broadening of the photoluminescence response that could be caused by a spread of local bandgaps if there is only a partial interconnection between the nanostructures (Calcott 1977). 

The acidic natural chnoptilolite, AZH-1, was prepared by acid treatmerrt of Na-exchanged (AZ) natural clinoptilolite (NZ) [11R2]. The nitrogen adsorption indicated that the acid sarrtple has a homogeneoirs porous distribution and a considerable increase in the rrricropore voltrme with respect to NZ and AZ zeolites. 

Physically, in the catalyst layer both carbon and electrolyte phases are porous structures. However, in modelling, porous carbon and electrolyte clusters are usually replaced by the two interpenetrating continuum media (phases). The idea of representing a porous distribution of potentials by continuous functions of space is usually referred to as a rnacrohomogeneous approach. 

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). 

Below the critical temperature of the adsorbate, adsorption is generally multilayer in type, and the presence of pores may have the effect not only of limiting the possible number of layers of adsorbate (see Eq. XVII-65) but also of introducing capillary condensation phenomena. A wide range of porous adsorbents is now involved and usually having a broad distribution of pore sizes and shapes, unlike the zeolites. The most general characteristic of such adsorption systems is that of hysteresis as illustrated in Fig. XVII-27 and, more gener-... 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

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,... 

Now suppose e(a) denotes the total void volume associated with pores of radii < a, per unit volume of the porous medium. This includes the contributions of any dead-end pores. Chough these are not taken into account in the distribution function f(a,ri). Then we shall write... 

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. 

If a Type I isotherm exhibits a nearly constant adsorption at high relative pressure, the micropore volume is given by the amount adsorbed (converted to a liquid volume) in the plateau region, since the mesopore volume and the external surface are both relatively small. In the more usual case where the Type I isotherm has a finite slope at high relative pressures, both the external area and the micropore volume can be evaluated by the a,-method provided that a standard isotherm on a suitable non-porous reference solid is available. Alternatively, the nonane pre-adsorption method may be used in appropriate cases to separate the processes of micropore filling and surface coverage. At present, however, there is no reliable procedure for the computation of micropore size distribution from a single isotherm but if the size extends down to micropores of molecular dimensions, adsorptive molecules of selected size can be employed as molecular probes. 

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. 

If the solute is uniformly distributed through the soHd phase the material near the surface dissolves first to leave a porous stmcture in the soHd residue. In order to reach further solute the solvent has to penetrate this outer porous region the process becomes progressively more difficult and the rate of extraction decreases. If the solute forms a large proportion of the volume of the original particle, its removal can destroy the stmcture of the particle which may cmmble away, and further solute maybe easily accessed by solvent. In such cases the extraction rate does not fall as rapidly. 

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