Porosimetry, mercury

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 

Eveluetion of specific surface from Type IV isotherms of nitrogen, from the aree under the curve of log(pVp) against n 

Adsorbent Adsorp. Branch y4V(m g Desorp. Branch Adsorp. Branch Desorp. Branch y47(m g ) Average (NiVfm g- ) 

Section 3.7, the gas adsorption method breaks down for practical reasons. Since the angle of contact of mercury with solids is 140° (see later), and therefore more than 90°, an excess pressure Ap is required to force liquid mercury into the pores of a soh d. The idea of using mercury intrusion to measure pore size appears to have been first suggested by Washburn who put forward the basic equation 

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  

Mercury porosimetry is the most suitable method for the characterization of the pore size distribution of porous materials in the macropore range that can as well be applied in the mesopore range [147-155], To obtain the theoretical foundation of mercury porosimetry, Washburn [147] applied the Young-Laplace equation 

AP is the pressure difference in a sector, across the interface between two neighboring phases y is the surface tension 

The Physical Chemistry of Materials Energy and Environmental Applications 

FIGURE 4.66 Mercury making contact with a cylindrical pore. 

The pressure difference across the interface between two contiguous phases is given by 

In this method, mercury (which is a non-wetting liquid) is forced into the pores of a dry sample. For each applied pressure, the volume of mercury entering the sample porous structure is determined very accurately (e.g. by measuring the variation of capacity induced by the reduction in height of the Hg column connected to the measuring cell). The relationship between pressure P and pore radius rp is given by the modified Laplace equation (Washburn equation) 

With thin supported ceramic membranes, the pore volume due to the membrane is relatively small and better results are obtained if a major part of the support is scraped off. Specific preparation of samples (e.g. support embedded in a resin) can change the results [39]. If the membrane weight is known and if its pore size can be well differentiated from that of the support the method can be used to determine the porosity of a supported layer. 

In parallel with mercury porosimetry in which a non wetting liquid is used, we can mention the suction porosimetry in which a wetting liquid like water (0 0 Jc/2) is held within the porous solid [5]. In this case the Laplace equation predicts that it will experience a reduced hydrostatic pressure, inversely proportional to the radius of pores in which menisci are formed. The lower limit of pore size accessible to this technique is around a few tens of microns. 

This technique is one of the most important and extensively used methods in the characterisation (porous volume, specific surface area and pore size distribution) of porous inorganic materials [40,41]. Nevertheless, real solid/gas interfaces are complex, leading to uncertainties in the assumptions made, and different mechanisms may contribute to physisorption (e.g. monolayer-multilayer ad- 

The adsorption and desorption isotherms of an inert gas (classically N2 at 77 K) on an outgassed sample are determined as a function of the relative pressure (Prei = p/Po/ the ratio between the applied pressure and the saturation pressure. The adsorption isotherm is determined by measuring the quantity of gas adsorbed for each value of p/po by a gravimetric or a volumetric method (less accurate but simpler). A surface acoustic wave device can also be used as a mass sensor or microbalance in order to determine the adsorption isotherms of small thin films samples (only 0.2 cm of sample are required in the cell) [42,43]. 

Whereas from nitrogen sorption data a size distribution can only be extracted for mesopores (with pore diameter 2 nm dp 50 nm), standard mercury porosimetry is used to obtain complete pore size distributions in the pore diameter range from 7.5 nm to 150 [im. During the characterization experiment, the sample is first surrounded and then progressively intruded by mercury, as the pressure is increased. Experimental results are commonly plotted as invaded pore volume versus applied pressure (see Fig. 5.9a). The Washburn equation describes at which (capillary) pressure a cylindrical pore of diameter dp is invaded 

9 (a) Mercury porosimetry data for dried copper hydroxide precipitate, pure intrusion case, pore volume distribution by Eq. 5.4 (taken from Job et al. (2006a)). 

Weighing of the sample before and after the porosimetry experiment can quantify the mercury which has intruded pores and is subsequently entrapped within the sample. In the case of pure intrusion, the full detected mercury volume remains within the sample, as revealed by the depressurization branch in Fig. 5.9a. If no mercury is found in the porous solid after porosimetry, the volume change of the sample may be measured (by mercury pycnometry as explained below) to confirm the assumed extent of irreversible shrinkage. 

For gels, the mechanisms involved during mercury porosimetry tests depend strongly on the microstructure, which is related to the synthesis (Leonard et ah, 2008) and drying conditions (Job et ah, 2005) therefore, one must carefully examine the measurement results to be sure of the mechanisms involved. If data corresponding to densification are analyzed using software based on the Washburn equation (usually provided with porosimeters) this yields an unphysical pore size distribution. 

For macroporous samples (pore size greater than 50 nm), the absence of any capillary condensation phenomenon means that only the specific surface area can be obtained from the adsorption isotherm using the BET equation. Mercury porosimetry (Paragr. 1.2) will then be necessary to obtain the pore size distribution. 

Finally, the study of micropores (size 2 nm) and ultramicropores (size 0.7 nm) will be essentially qualitative and is still currently subject to numerous studies of a fundamental nature (cf. Paragr. 1.1.3.2). 

Various models have been put forward (Table 1.1) to describe these experimental adsorption isotherms. These models differ from each other in terms of hypotheses on the nature of the sites, or on the influence of the adsorbed quantity (coverage) on the heat of adsorption. Depending on the type of materials studied and the probe molecule used, it will be necessary to use one or other of the following expressions to describe the adsorption isotherm. 

Of the equations proposed to express the adsorbed volume as a function of the equilibrium pressure, the BET model is the most often used to describe physical adsorption. It is based on the following hypotheses  

Prior to measuring the quantities adsorbed, a degassing (or pre-treatment) stage is carried out. The purpose of this is to eliminate the compounds adsorbed on the surface of the sample (H2O, CO2, etc.). This stage, which is essential to the quality of the results, has been the subject of numerous methodological studies in the literature, which have contributed to an in-depth understanding of the parameters that need to be checked (temperature, rate of temperature increase, atmosphere, partial pressure of H2O, etc.). 

Controlled pore glass (CPG) has application as media for size exclusion and afQnity chromatographic media, commonly used to separate proteins. Nominally, the pore diameter should be 10 times the protein diameter. Most proteins [51] have a diameter below 3 nm. CPGs are required to have sharp, unimodal pore distributions, that is a high volume of pores of similar size. Clearly, a means of investigating pore size, pore 

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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. 

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).

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-... 

Menchutkin reaction 53 Mercury porosimetry (MP) 149 Merocyanine dye 57, 58 Methacrylic acid 162... 

The catalyst consists of 3-mm pellets that pack to a bulk density of 1350 kg/m and = 0.5. Mercury porosimetry has found 7 ore = 5nm. The feed mixture to a differential reactor consisted of 5mol% SO2 and 95mol% air. The following initial rate data were obtained at atmospheric pressure ... 

In order to describe the geometrical and structural properties of several anode electrodes of the molten carbonate fuel cell (MCFC), a fractal analysis has been applied. Four kinds of the anode electrodes, such as Ni, Ni-Cr (lOwt.%), Ni-NiaAl (7wt.%), Ni-Cr (5wt.%)-NijAl(5wt.%) were prepared [1,2] and their fractal dimensions were evaluated by nitrogen adsorption (fractal FHH equation) and mercury porosimetry. These methods of fractal analysis and the resulting values are discussed and compared with other characteristic methods and the performances as anode of MCFC. 

The wetting ability of the anode electrode was evaluated as the contact angle measured by the capillary rise method. The value of fractal dimension of anode electrode of MCFC was calculated by use of the nitrogen adsorption (fractal FHH equation) and the mercury porosimetry. 

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