Pore size distributions adsorption isotherms

A novel approach is reported for the accurate evaluation of pore size distributions for mesoporous and microporous silicas from nitrogen adsorption data. The model used is a hybrid combination of statistical mechanical calculations and experimental observations for macroporous silicas and for MCM-41 ordered mesoporous silicas, which are regarded as the best model mesoporous solids currently available. Thus, an accurate reference isotherm has been developed from extensive experimental observations and surface heterogeneity analysis by density functional theory the critical pore filling pressures have been determined as a function of the pore size from adsorption isotherms on MCM-41 materials well characterized by independent X-ray techniques and finally, the important variation of the pore fluid density with pressure and pore size has been accounted for by density functional theory calculations. The pore size distribution for an unknown sample is extracted from its experimental nitrogen isotherm by inversion of the integral equation of adsorption using the hybrid models as the kernel matrix. The approach reported in the current study opens new opportunities in characterization of mesoporous and microporous-mesoporous materials. 

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. 

Everett concludes that in systems where pore blocking can occur, pore size distribution curves derived from the desorption branch of the isotherm are likely to give a misleading picture of the pore structure in particular the size distribution will appear to be much narrower than it actually is. Thus the adsorption branch is to be preferred unless network effects are known to be absent. 

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.

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. 

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... 

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). 

Activated carbons for use in Hquid-phase appHcations differ from gas-phase carbons primarily in pore size distribution. Liquid-phase carbons have significantly more pore volume in the macropore range, which permits Hquids to diffuse more rapidly into the mesopores and micropores (69). The larger pores also promote greater adsorption of large molecules, either impurities or products, in many Hquid-phase appHcations. Specific-grade choice is based on the isotherm (70,71) and, in some cases, bench or pilot scale evaluations of candidate carbons. 

Another property of importance is the pore volume. It can be measured indirectly from the adsorption and/or desorption isotherms of equilibrium quantities of gas absorbed or desorbed over a range of relative pressures. Pore volume can also be measured by mercury intrusion techniques, whereby a hydrostatic pressure is used to force mercury into the pores to generate a plot of penetration volume versus pres- sure. Since the size of the pore openings is related to the pressure, mercury intrusion techniques provide information on the pore size distribution and the total pore volume. 

Table 2. Characteristics of the silica templates and the corresponding carbon materials a unit cell parameter Sbet- specific surface area Vp total pore volume (at P/Po=0.95) Pore size determined according to the BJH method - Maximum value of the BJH pore size distribution peak calculated from the adsorption branch of the N2 isotherm.

Figure 1. N2 adsorption (filled) and desorption (open symbols) isotherms for a) pure and Fe-modified SBA-15 and their N-doped carbon replicas b) pure and Fe-modified MLV-0.75 and their N-doped replicas (for clarity, the relevant isotherms are shifted up by 200 or 600 cm3g 1). Pore size distributions calculated from the desorption isotherms with the modified BJH method for c) pure and Fe-modified SBA-15 and CMK-3 carbons d) pure and Fe-modified MLV-0.75 and OCM carbons.

The nitrogen adsorption isotherms for the onion-like Fe-modified MLV-0.75 materials are of type IV, although their hysteresis loops are of complex types, HI, H2, and H3. The H2-type hysteresis loop indicates the presence of bottle-shaped pores. The pore sizes obtained with the BJH method can be assigned to entry windows of mesopores. For pure MLV-0.75 and Fe-modified MLV-0.75 (x = 1.25), the pore size distributions exhibit two peaks (Fig. Id). The first peak appears at 9.0 and ca. 6 nm for MLV-0.75 and Fe-MLV-0.75, respectively. The shift of the broad peak maximum of the distribution curve... 

The structure of the catalysts was characterized by X-ray diffraction, IR-spectroscopy and transmission electron microscopy, their thermal stability was followed by thermal analytical method. The specific surface area and pore size distribution of the samples were determined by nitrogen adsorption isotherms. 

The N2 adsorption isotherms of the two Beta samples are depicted in Figure 1(b). The material prepared from silanized seeds exhibits a significant higher N2 adsorption compared to the Beta (0) sample, suggesting the presence of a secondary porosity. This is confirmed by the pore-size distributions derived from the Ar isotherms applying the... 

Figure 1. (a) XRD patterns (b) N2 adsorption isotherms at 77 K (c) Pore size distributions. 

Chemical composition was determined by elemental analysis, by means of a Varian Liberty 200 ICP spectrometer. X-ray powder diffraction (XRD) patterns were collected on a Philips PW 1820 powder diffractometer, using the Ni-filtered C Ka radiation (A, = 1.5406 A). BET surface area and pore size distribution were determined from N2 adsorption isotherms at 77 K (Thermofinnigan Sorptomatic 1990 apparatus, sample out gassing at 573 K for 24 h). Surface acidity was analysed by microcalorimetry at 353 K, using NH3 as probe molecule. Calorimetric runs were performed in a Tian-Calvet heat flow calorimeter (Setaram). Main physico-chemical properties and the total acidity of the catalysts are reported in Table 1. 

Many adsorbents, particularly the amorphous adsorbents, are characterized by their pore size distribution. The distribution of small pores is usually determined by analysis, using one of several available methods, of a cryogenic nitrogen adsorption isotherm, although other probe molecules are also used. The distribution of large pores is usually determined by mercury porisimetry [Gregg and Sing, gen. refs.]. 

Pore size distribution data obtained from adsorption isotherms and from mercury porosimetric measurements show that in addition to the micropores characteristic of the parent zeolite, the DAY zeolites contain secondary pores with radii of 1.5nm (supermicropores) and lOnm (mesopores) (36,47). The secondary pores in USY-B have a radius of 5nm. It was also shown that the micropore volume of DAY amounts to about 75 percent of that of NaY (36). Due to dealumination and the formation of secondary pores, the total pore volume of DAY is considerably larger than that of NaY zeolite (0.56 vs. 0.29 cc/g). 

A number of models have been developed for the analysis of the adsorption data, including the most common Langmuir [49] and BET (Brunauer, Emmet, and Teller) [50] equations, and others such as t-plot [51], H-K (Horvath-Kawazoe) [52], and BJH (Barrett, Joyner, and Halenda) [53] methods. The BET model is often the method of choice, and is usually used for the measurement of total surface areas. In contrast, t-plots and the BJH method are best employed to calculate total micropore and mesopore volume, respectively [46], A combination of isothermal adsorption measurements can provide a fairly complete picture of the pore size distribution in sohd catalysts. Mary surface area analyzers and software based on this methodology are commercially available nowadays. 

Figure 1.6 Top Low-temperature nitrogen adsorption ( ) and desorption (x) isotherms measured on a calcined SBA-15 mesoporous silica solid prepared using an EO20PO70EO20 block copolymer [54]. Bottom Pore size distribution derived from the adsorption isotherm reported at the top [54]. A high surface area (850 m2/g), a uniform distribution of cylindrical nanopores (diameter —90 A), and a large pore volume (1.17 cm3/g) were all estimated from these data. These properties make this material suitable for use as support in the preparation of high-surface-area solid catalysts. (Reproduced with permission from The American Chemical Society.)...

Figure 5.5 shows the variation of the pore size distribution as a function of cycles of surface-modification-based N2 adsorption isotherms. The pore size decreases with the modification cycle number. The reduction of the mesopore size for each cycle should be about twice the single-layer thickness. Accordingly, the effective singlelayer thickness is about 6 to 7 A based on the above BET measurements. This value is close to those estimated from the frequency changes of a quartz crystal balance for ultrathin fihns prepared by the surface sol-gel process on 2-D substrates." " ... 

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]. 

Characterization measurements. Surface areas and pore size distributions were obtained from adsorption isotherms, using BET and BJH methods. The pore size distribution was computed from the... 

The shape of the hysteresis loop in the adsorption/desorption isotherms provides information about the nature of the pores. The loops have been classified according to shape as A, B and E (De Boer, 1958) or as HI - H4 by lUPAC (Sing et al, 1985). Ideally, the different loop shapes correspond to cylindrical, slit shaped and ink-bottle pores the loops in the isotherm IV and V of Figure 5.3 correspond to cylindrical pores. Wide loops indicate a broad pore size distribution (for an example see Fig. 14.9). The absence of such a loop may mean that the sample is either nonporous or microporous. These generalizations provide some initial assistance in assessing the porosity of a sample. In fact the adsorption/desorption isotherms are often more complicated than those shown in Figure 5.3 owing to a mixture of pore types and/or to a wide pore size distribution. 

Nitrogen adsorption and desorption isotherms were performed at 77 K on a Micromeritics ASAP 2400 volumetric adsorption system. The pore size distribution and surface area were deduced from the adsorption isotherms using the BJH method and the BET equation. 

---