Pore size determination

The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. 

A factor militating against the use of other adsorptives for pore size determination at the present time is the lack of reliable r-curves. The number of published isotherms of vapours such as benzene, carbon tetrachloride or the lower alkanes, or even such simple inorganic substances as carbon dioxide, on a reasonable number of well-defined non-porous adsorbents, is very small. 

Membrane Cliaraeterization MF membranes are rated bvtliix and pore size. Microfiltration membranes are imiqiielv testable bv direct examination, but since the number of pores that rnav be obsen ed directlv bv microscope is so small, microscopic pore size determination is rnainlv useful for membrane research and verification of other pore-size-determining methods. Furthermore, the most critical dimension rnav not be obseiA able from the surface. Few MF membranes have neat, cvlindrical pores. Indirect means of measurement are generallv superior. Accurate characterization of MF membranes is a continuing research topic for which interested parties should consult the current literature. 

In selecting cloths made from synthetic materials, one must account for the fact that staple cloths provide a good retentivity of solid particles due to the short hairs on their surface. However, cake removal is often difficult from these cloths - more than from cloths of polyfilament and, especially, monofilament fibers. The type of fiber weave and pore size determine the degree of retentivity and permeability. The objective of the process, and the properties of particles, suspension and cake should be accounted for. The cloth selected in this maimer should be confirmed or corrected by laboratory tests. Such tests can be performed on a single filter. These tests, however, provide no information on progressive pore plugging and cloth wear. However, they do provide indications of expected filtrate pureness, capacity and final cake wetness. 

The pore size is the most important parameter that specifies the column used in HOPC. The pore size determines the boundary of MW in the segregation... 

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.

Cellophane is frequently used for dialysis and it has a pore size of approximately 4—8 gm, which makes it impermeable to molecules with a relative molecular mass in excess of about 10 000. The development of a variety of membrane materials in which the pore size is much more rigorously controlled, has led to wider applications of ultrafiltration (Table 3.11). Various cellulose and polycarbonate membranes are available with pore sizes down to 5 nm which are capable of excluding molecules with a relative molecular mass of about 50. The internal structure of such membranes, as well as the pore size, determines their exclusion range and as a result precise specifications of membranes vary from one manufacturer to another. 

Allen, T. Particle Size Measurement, Volume 1, Powder Sampling and Particle Size Measurement Volume 2, Surface Area and Pore Size Determination, 5th edn. (Chapman and Hall, London, 1997)... 

The classical Kelvin equation assumes that the surface tension can be defined and that the gas phase is ideal. This is accurate for mesopores, but fails if appUed to pores of narrow width. Stronger sohd-fluid attractive forces enhance adsorption in narrow pores. Simulation studies [86] suggest that the lower limit of pore sizes determined from classical thermodynamic analysis methods hes at about 15 nm. Correction of the Kelvin equation does lower this border to about 2 run, but finally also the texture of the fluid becomes so pronounced, that the concept of a smooth hquid-vapor interface cannot accurately be applied. Therefore, analysis based on the Kelvin equation is not applicable for micropores and different theories have to be applied for the different ranges of pore sizes. 

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. 

The pore size distributions of Ti-MCM-41 synthesized in this work are shown in Fig. 2. All of the samples showed a sharp distribution without addition of TMB and the use of methanol solvent resulted in the expansion of pore channel size. The average pore sizes determined by N, adsorption were 4.0nm and 2.8nm when the added solvents were methanol and ethanol, respectively. In this case, the used surfactant was C22TMAC1. In addition, the expansion of BJH pore size of Ti-MCM-41 was observed by the addition of TMB. A broad pore size distribution was investigated by using TMB as an auxiliary chemical. The mean pore size was ca. 7.5nm in methanol solvent. 

The pore size distribution determination is illustrated in Figure 10. Again, the pore size distribution determination method does not result in the actual membrane pore size and pore size determination. It does, however, give a means of comparing different fdter media. A narrow pore size distribution is required for effective filtration and filtration validation. 

Desalting or buffer exchanges are often required between purification steps. At the laboratory scale, the protein solution is placed in a tube of a semipermeable polymer membrane immersed in the desired buffer. The membrane pore size determines the minimum molar mass of the compounds that are retained. Small molecules with a molar mass below the membrane cut-off will flow freely across the membrane until the osmotic pressure equilibrium is reached. Complete buffer exchange requires several changes of the dialysis liquid. The process should be carried out at a temperature around 4°C, to avoid loss of activity. 

Obviously the pore size determines which molecules can access the acidic sites inside the zeolite framework (molecular sieving effect) and is responsible for the shape selectivity observed with these materials (see later). The catalytic activity is also influenced by the acid strength of these sites which is determined by the Si/Al ratio (see above). The latter can be increased by post-synthesis removal of A1 atoms. Dealumination can be achieved by treatment with a... 

An ideal matrix for gel filtration should consist of partides of a hydrophilic polymer, that is as inert as possible, as rigid as possible, uncharged, and of uniform size (Patel 1993). Suitable materials are naturally occurring polymers, such as agarose or dextran, which have been stabilised by chemical cross linking, and also synthetic polymers such as polyacrylamide. These materials are available as spherical partides of different diameter (10-500 pm) and pore sizes the pore size determines the range of optimal molecular weight separation (Table 4-1). 

Incorporation of the measured contact angle in mercury intrusion porosimetry data is essential for an accurate determination of the pore size distribution. Both the advancing and static angle methods are suitable to carry out this measurement, leading to very similar results. For most oxidic materials and supported oxides, the contact angle is 140° and incorporation of the actual contact angle is less critical in the pore size determination. However, important deviations are observed in carbon and cement-like materials, with contact angles of > 150° and < 130°, respectively. This has been shown by comparison of the pore size distribution obtained from mercury porosimetry and N2 adsorption measurements. 

Microscopic methods. While microscopic methods provide direct visual information on membrane morphology as discussed earlier, determination of pore size, especially meaningful pore size distribution, by this type of methods is tedious and difficult. Advances have been made on the electron microscopy techniques to visualize membrane surface pores. For example, Merin and Cheryan [1980] have developed a replica-TEM technique to observe membrane surface pores. Nevertheless, microscopic methods have remained primarily as a surface morphology characterization tool and not as a pore size determination scheme. 

Depth filtration fundamentally differs from the use of media in which pore size determines the size of particle retained. Such filters may be said to be absolute at a particle diameter closely related to the size of the pore, so that there is a relatively sharp division between particles which pass the filter and those that are retained. An analogy with sieving may be drawn for this mechanism. The life of such filters depends on the number of pores available for the passage of fluid. 

Textural properties are important in the field of catalyst design for heterogeneous catalysis Surface area and pore size determine the accessibility to active sites and this is often related to catalytic activity and selectivity in catalysed reactions Therefore textural properties are often a target of catalyst design. 

Pore size determined according to the BJH method - Maximum value of the BJH pore size distribution peak calculatedfrom the adsorption branch of the N2 isotherm. 

It must be concluded that the quantitative determination of micropore size is still an ambiguous problem new theories, models, mechanisms and simulations are still under study [56-58]. Therefore isotherm interpretations must be used carefully and can be considered as useful mainly for qualitative studies. No reliable method has been developed for the determination of the micropore size distribution. At present the most promising approach appears to be that of pre-adsorption linked with the use of various probe molecules of known size and shape [59-61]. For example, this approach has been applied successfully for silica compacts characterisation in [61] using spherical symmetrical inert molecules, such as neopentane and trimethylsiloxysilane [(CH3)3SiO]4Si with diameters of 6.5 and 11.5 A respectively. In general the limited availability of volatile probe molecules with diameters extending above 10 A puts a restriction on the applicability of this method. Furthermore effective pore sizes determined by this technique depend on the kinetic and thermodynamic properties of the... 

Fig. 4.18. Maximum and mean flow pore size determinations by bubble pressure point test [3].

P. Uchytil, Z. Wagner, J. Rocek and Z. Broz, Possibility of pore size determination in separation layer of ceramic membrane using permeation method. /. Membr. Sci., 103... 

Criteria for immobilized liquid membrane (ILM) support selection can be divided into two categories structural properties and chemical properties. Structural properties include geometry, support thickness, porosity, pore size distribution and tortuosity. Chemical criteria consist of support surface properties and reactivity of the polymer support toward fluids in contact with it. The support thickness and tortuosity determine the diffusional path length, which should be minimized. Porosity determines the volume of the liquid membrane and therefore the quantity of carrier required. The mean pore size determines the maximum pressure difference the liquid membrane can support. The support must be chemically inert toward all components in the feed phase, membrane phase, and sweep or receiving phase. 

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