Mesopore size distribution

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. 

A vast amount of research has been undertaken on adsorption phenomena and the nature of solid surfaces over the fifteen years since the first edition was published, but for the most part this work has resulted in the refinement of existing theoretical principles and experimental procedures rather than in the formulation of entirely new concepts. In spite of the acknowledged weakness of its theoretical foundations, the Brunauer-Emmett-Teller (BET) method still remains the most widely used procedure for the determination of surface area similarly, methods based on the Kelvin equation are still generally applied for the computation of mesopore size distribution from gas adsorption data. However, the more recent studies, especially those carried out on well defined surfaces, have led to a clearer understanding of the scope and limitations of these methods furthermore, the growing awareness of the importance of molecular sieve carbons and zeolites has generated considerable interest in the properties of microporous solids and the mechanism of micropore filling. 

Sample 5 is close to an H2-type hysteresis, whereas 6 and 7 can be tentatively assigned to H3- and Hi-type hystereses, respectively [27]. The hystereses are caused by capillary condensation in interparticle pores and the shape is an indication of a particular particle morphology. Sample 7 has a more regular narrow mesopore size distribution, whereas sample 5 is more complex with pores of... 

Thus, either type I or type IV isotherms are obtained in sorption experiments on microporous or mesoporous materials. Of course, a material may contain both types of pores. In this case, a convolution of a type I and type IV isotherm is observed. From the amount of gas that is adsorbed in the micropores of a material, the micropore volume is directly accessible (e.g., from t plot of as plot [1]). The low-pressure part of the isotherm also contains information on the pore size distribution of a given material. Several methods have been proposed for this purpose (e.g., Horvath-Kawazoe method) but most of them give only rough estimates of the real pore sizes. Recently, nonlocal density functional theory (NLDFT) was employed to calculate model isotherms for specific materials with defined pore geometries. From such model isotherms, the calculation of more realistic pore size distributions seems to be feasible provided that appropriate model isotherms are available. The mesopore volume of a mesoporous material is also rather easy accessible. Barrett, Joyner, and Halenda (BJH) developed a method based on the Kelvin equation which allows the calculation of the mesopore size distribution and respective pore volume. Unfortunately, the BJH algorithm underestimates pore diameters, especially at... 

Figure 4.42 Calculated mesopore size distribution for the steamed Y-zeolite based on the BET adsorption. The ammonium exchanged Y-zeolite has no mesopores.

The calculation method for the mesopore size distribution generally follows that described by Barret, Joyner and Halenda [79, 85]. With the so-called BJH method, the pore sizes using a certain pore geometry are calculated along the isotherm. This involves an imaginary emptying of condensed adsorptive in the pores in a... 

In the past it was very common to derive the mesopore size distribution from the desorption branch of the isotherm. The above considerations make it clear that this practice is questionable especially for Type H2 hysteresis loops, and can lead to misinterpretations [90]. Indeed a significant downward turn in the desorption branch of a N2 isotherm at p/po 0.4 leads to an apparent sharp maximum in the pore size distribution curve at 2 nm which is totally artefactual. Although no general guidelines exist on whether the adsorption or desorption branch should be used for computation, it should be understood that with Type H2 and H3 hysteresis loops, reliable results are much more Hkely to be obtained if the adsorption branch is used [21]. 

Mesopore size distribution analysis showed a very narrow distribution with a peak pore diameter of about 27 A for the calcined samples. It can be seen that the pore wall thickness of the calcined samples was in the 18-19 A and did not change much by adding additional cations. The increased hydrothermal stability observed was, therefore, not due to any increase in pore wall thickness. For the water-treated samples, the adsorption isotherms and pore size distribution curves showed that after hydrothermal treatment the pore size distribution was... 

Further characterization of the synthesized materials included the calculation of the mesopore size distributions according to the procedure recently published by Kruk et al. [34]. As can be seen in Fig. 4 the distribution of primary mesopores for CeMCM-41 is narrower than that for the corresponding MCM-41 sample. 

The N2 adsorption-desorption isotherm at -196°C and the micro- and mesopore size distributions are presented in figure 2. In the partial pressure range -0.02-0.3 the upward deviation indicates the presence of supermicropores (15-20A) or small mesopores (20-25A). From the De Boer t-plot the presence of an important microporosity can be deduced, so a unique combined micro- and mesoporosity is present for this type of material. Indeed, this combined pore system is confirmed when considering the micropore (Horvath-Kawazoe) and mesopore (Barrett-Joyner-Halenda) size distributions with maxima at respectively 6A and 17.5 A pore diameter (figure 5). An overview of the surface area, micro- and mesoporosity data of the unmodified PCH can be found in table 1. 

Recently, the Horvath-Kawazoe (HK) method for slit-like pores [40] and its later modifications for cylindrical pores, such as the Saito-Foley (SF) method [41] have been applied in calculations of the mesopore size distributions. These methods are based on the condensation approximation (CA), that is on the assumption that as pressure is increased, the pores of a given size are completely empty until the condensation pressure corresponding to their size is reached and they become completely filled with the adsorbate. This is a poor approximation even in the micropore range [42], and is even worse for mesoporous solids, since it attributes adsorption on the pore surface to the presence of non-existent pores smaller than those actually present (see Fig. 2a) [43]. It is easy to verify that the area under the HK PSD peak corresponding to actually existing pores does not provide their correct volume, so the HK-based PSD is not only excessively broad, but also provides underestimated volume of the actual pores. This is a fundamental problem with the HK-based methods. An additional problem is that the HK method for slit-like pores provides better estimates of the pore size of MCM-41 with cylindrical pores than the SF method for cylindrical pores. This shows the lack of consistency [32,43]. Since the HK-based methods use CA, one can replace the HK or SF relations between the pore size and pore filling pressure by the properly calibrated ones, which would lead to dramatic improvement of accuracy of the pore size determination [43] (see Fig. 2a). However, this will not eliminate the problem of artificial tailing of PSDs, since the latter results from the very nature of HK-based methods. 

Equation 5 is analogous to Eq. 2 discussed above. As illustrated in Figure 4b, the mesopore size distributions determined from nitrogen and argon adsorption data were essentially the same, when calculations were carried out for adsorption branches of isotherms using the corresponding KJS-calibrated relations (Eqs. 2 and 5) [18]. 

For many of activated microporous carbons,80"84 the isotherms exhibit prominent adsorption at low relative pressures and then level off, i.e., the isotherms exhibit Type I behavior. Type I isotherms may be also observed in the mesoporous materials with pore sizes close to the micropore range. In particular, in the case of gas adsorption on highly uniform cylindrical pores, the adsorption isotherms exhibit discernible steps at relative pressures down to 0.1 or perhaps even lower.85"87 Such Type I behavior can be indicative of some degree of broadening of the mesopore size distribution. 

C. Nguyen and D. D. Do, Effects of probing vapors and temperature on the characterization of micro- and mesopore size distribution of carbonaceous materials, Langmuir 16(18), 7218-7222 (2000). 

In calculations of the mesopore size distribution from physisorption isotherms it is generally assumed (often tacitly) (a) that the pores are rigid and of a regular shape (e.g. cylindrical capillaries or parallel-sided slits), (b) that micropores are absent, and (c) that the size distribution does not extend continuously from the mesopore into the macropore range. Furthermore, to obtain the pore size distribution, which is usually expressed in the graphical form AV /Arp vs. rp, allowance must be made for the effect of multilayer adsorption in progressively reducing the dimensions of the free pore space available for capillary condensation. 

It is evident from the above considerations that the use of the physisorption method for the determination of mesopore size distribution is subject to a number of uncertainties arising from the assumptions made and the complexities of most real pore structures. It should be recognized that derived pore size distribution curves may often give a misleading picture of the pore structure. On the other hand, there are certain features of physisorption isotherms (and hence of the derived pore distribution curves) which are highly characteristic of particular types of pore structures and are therefore especially useful in the study of industrial adsorbents and catalysts. Physisorption is one of the few nondestructive methods available for investigating meso-porosity, and it is to be hoped that future work will lead to refinements in the application of the method -especially through the study of model pore systems and the application of modem computer techniques. 

There are several reasons why nitrogen (at 77 K) is generally accepted as the most suitable adsorptive for mesopore size analysis. First, the thickness of the N2 multilayer is largely insensitive to differences in adsorbent particle size or surface structure (Carrott and Sing, 1989). Second, the same isotherm can be used for the evaluation of both the surface area and the mesopore size distribution (Sing et al. 1985). However, in spite of these considerations, there is an emerging view that ideally more than one adsorptive should be used for the characterization of meso-porous solids (e.g. see Machin and Murdey 1997 Llewellyn et al., 1997). 

The plateau of a Type IV isotherm is normally taken as the starting point for the computation of the mesopore size distribution. If all the pores are full, the first step in the notional desorption process (e.g. frompjp° of 0.95 to 0.90) involves only the removal of capillary condensate. Each subsequent step involves both the removal of condensate from die cores of a group of pores and the thinning of the multilayer in the larger pores (i.e. those pores already emptied of condensate). In the following treatment the symbol uK is used to represent the inner core volume and, as before, vp is the pore volume. The corresponding radii are rK and rp. 

Important trends of double-mesopore structural development resulting from the water-treatment are revealed in Figure 2 by the N2 adsorption-desorption isotherms and the corresponding BJH pore size distribution based on the desorption branch for the representative samples mentioned above. The isotherm of the normally synthesized DMS simple shows a typical irreversible type IV adsorption isotherm with two separate, well-expressed HI hysteresis loops as defined by lUPAC at relative pressures p/po of 0.2-0.45 and that of 0.8-1.0, respectively. The first condensation step on the isotherm at p/pQ=0.2-0.45 is similar to that for usual MCM-41 materials, however, obviously, this inflection at higher relative pressures differs completely from that of previously-synthesized mesoporous materials in the aspect of their effects on the mesoporous frameworks of the product, namely, this material is of a clear double mesopore size distribution. After 1 day of postsynthesis hydrothermal treatment, the properties of the samples changed dramatically. Compared with the normally synthesized DMS sample, the water-treated sample at 373K shows more steep adsorption steps at 0.25-0.4p/po and 0.8-1.0p/po, respectively, suggesting that double-... 

Nitrogen adsorption-desorption isotherms were used to determine the BET surface areas of the samples using a sorption analyzer AUTOSORB-1 (manufacturer American Quantachrome Corporation). The total pore volume of the materials and mesopore size distribution were also determined. 

In the field of N2 adsorption, the development of model mesoporous materials like MCM-41 and SBA-15, showing a uniform mesopore size distribution in the range of 2 - 20 nm, has led to numerous studies to determine the PSD accurately. Since it is widely known that the BJH model underestimates the mesopore size, these studies resulted in adaptation of existing models and development of new... 

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