Porosimetry

1 Porosity, Porosimetry, Structure. - The increase in experimental sensitivity by hyperpolarized xenon, is remarkable. A number of recent developments in Xe NMR spectroscopy were reviewed with direct applications to the study of mesopore space in solids (37 references). Experiments illustrated include the rapid characterization of the void space in porous solids, including the in situ study of processes such as diffusion and hydration, and imaging with chemical shift resolution. 

If the contact angle between liquid and solid is greater than 90 , then at equilibrium the pressure on the convex side of the meniscus must be greater than on the concave side. Thus if a porous solid is immersed in a nonwetting liquid such as mercury there will be no penetration of the pores until the 

Pnr =2-n rtf CosQ FIGURE 2.14. Force balance for mercury penetrometer. 

TABLE 2.15. Pore Radius fiNT Mercury Penetration as Function of Pressure 

Some values of P and for mercury (6 t 40°, a 480 dyne/cm) are summarized in Table 2.15. It is evident that penetration of the smaller pores characteristic of microporous adsorbents is achieved only at very high pressures. 

The mercury porosimeter is simply an instrument designed to apply a controlled mercury pre.ssure to the adsorbent and record the volume of mercury penetrating the pore structure. Because of practical limitations on the maximum pressure, the minimum pore radius which can be measured by this 

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Interestingly, a general thermodynamic relationship allows the surface area of a porous system (without ink bottles) to be calculated from porosimetry data, note Section XVII-16B. The equation is [45]... 

It is these kinds of uncertainties that have led to the development of mercury porosimetry, in which, since the meniscus is convex, the mercury has to be forced into the pores under pressure. Mercury porosimetry is the subject of Section 3.9. 

Mercury porosimetry is a technique which was originally developed to enable pore sizes to be determined in the macropore range where, as pointed out in... 

The technique of mercury porosimetry consists essentially in measuring the extent of mercury penetration into an evacuated solid as a function of the applied hydrostatic pressure. The full scope of the method first became apparent in 1945 when Ritter and Drake developed a technique for ... 

Pore size distribution—comparison of results by mercury porosimetry and by adsorption of nitrogen... 

Since in practice the lower limit of mercury porosimetry is around 35 A, and the upper limit of the gas adsorption method is in the region 100-200 A (cf. p. 133) the two methods need to be used in conjunction if the complete curve of total pore volume against pore radius is to be obtained. 

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. 

Fig. 3J1 Comparison of pore volume size distributions for Clear Creek sandstone" (courtesy Dullien.) Curve (A), from mercury porosimetry curve (B), from photomicrography (sphere model).

The pressures involved in porosimetry are so high (e.g. 1000 atm = 6-6 ton in" ) that the question as to whether the pore structure is damaged by mercury intrusion naturally arises. This possibility was recognized by Drake, but as a result of several intrusion-extrusion runs at pressures up to 4000 atm on a number of porous catalysts Drake concluded that any deformation caused by compression was elastic and therefore not permanent. 

Values of pore volume of samples of porous silica, determined by ethanol titration (v (EtOH)) and by mercury porosimetry (v (Hg, i) and v (Hg, ii)) ... 

In their original work Drake and Ritter found that the curves of volume against pressure for the penetration and withdrawal did not coincide. Numerous investigations since then have confirmed that hysteresis is a general feature of mercury porosimetry. 

Perhaps the best known explanation of reproducible hysteresis in mercury porosimetry is based on the ink bottle model already discussed in connection with capillary condensation (p. 128). The pressure required to force mercury with a pore having a narrow (cylindrical) neck of radius r, will be... 

Comparison of surface areas determined by mercury porosimetry and by nitrogen adsorption ... 

Fig. 3.35 Mercury porosimetry intrusion-extrusion plots of alumina gels prepared from solutions of aluminium monohydrate in A, propan-2-ol (2-5w/v%) B, propan-2-ol (4-9w/v%) C, 2-methylpropan-2-ol (4-9 w/v%) D, 2-methylpropan-2-ol (9-5 w/v%) E,butan-2-ol (9-5 w/v%). -------, ascending, intrusion curve -----, descending, extrusion curve.

Values of specific surface of alumina gels determined by nitrogen adsorption and by mercury porosimetry ... 

Mercury porosimetry is generally regarded as the best method available for the routine determination of pore size in the macropore and upper mesopore range. The apparatus is relatively simple in principle (though not inexpensive) and the experimental procedure is less demanding than gas adsorption measurements, in either time or skill. Perhaps on account of the simplicity of the method there is some temptation to overlook the assumptions, often tacit, that are involved, and also the potential sources of error. 

In a pore system composed of isolated pores of ink-bottle shape, the intrusion curve leads to the size distribution of the necks and the extrusion curve to the size distribution of the bodies of the pores. In the majority of solids, however, the pores are present as a network, and the interpretation of the mercury porosimetry results is complicated by pore blocking effects. 

The incorporation of the new material without any increase in the overall length of the book has been achieved in part by extensive re-writing, with the compression of earlier material, and in part by restricting the scope to the physical adsorption of gases (apart from a section on mercury porosimetry). The topics of chemisorption and adsorption from solution, both of which were dealt with in some detail in the first edition, have been omitted chemisorption processes are obviously dependent on the chemical nature of the surface and therefore cannot be relied upon for the determination of the total surface area and methods based on adsorption from solution have not been developed, as was once hoped, into routine procedures for surface area determination. Likewise omitted, on grounds of... 

Porosity and pore-size distribution usually are measured by mercury porosimetry, which also can provide a good estimate of the surface area (17). In this technique, the sample is placed under vacuum and mercury is forced into the pore stmcture by the appHcation of external pressure. By recording the extent of mercury intmsion as a function of the pressure appHed, it is possible to calculate the total pore volume and obtain the population of the various pore sizes in the range 2 nm to 10 nm. 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Table 2 illustrates this point where, by using mercury porosimetry, carbon densities at 0.1 MPa and 404 MPa have been used to calculate the Ifactional volumes of macro/meso, micropore and skeletal carbon for some carbons based on the following ... 

With these facts in mind, it seems reasonable to calculate the pore volume from the calibration curve that is accessible for a certain molar mass interval of the calibration polymer. A diagram of these differences in elution volume for constant M or AM intervals looks like a pore size distribution, but it is not [see the excellent review of Hagel et al. (5)]. Absolute measurements of pore volume (e.g., by mercury porosimetry) show that there is a difference on principle. Contrary to the absolute pore size distribution, the distribution calcu-... 

Much of the difficulty in demonstrating the mechanism of breakaway in a particular case arises from the thinness of the reaction zone and its location at the metal-oxide interface. Workers must consider (a) whether the oxide is cracked or merely recrystallised (b) whether the oxide now results from direct molecular reaction, or whether a barrier layer remains (c) whether the inception of a side reaction (e.g. 2CO - COj + C)" caused failure or (d) whether a new transport process, chemical transport or volatilisation, has become possible. In developing these mechanisms both arguments and experimental technique require considerable sophistication. As a few examples one may cite the use of density and specific surface-area measurements as routine of porosimetry by a variety of methods of optical microscopy, electron microscopy and X-ray diffraction at reaction temperature of tracer, electric field and stress measurements. Excellent metallographic sectioning is taken for granted in this field of research. 

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