Mercury porosimetry theory

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). 

This short overview illustrates the large complexity of the SEC processes and explains the absence of a quantitative theory, which would a priori express dependence between pore size distribution of the column packing—determined for example by mercury porosimetry—and distribution constant K in Equation 16.4. Therefore SEC is not an absolute method. The SEC columns must be either calibrated or the molar mass of polymer species in the column effluent continuously monitored (Section 16.9.1). 

We are not going to deal with all these examples of application of percolation theory to catalysis in this paper. Although the physics of these problems are different the basic numerical and mathematical techniques are very similar. For the deactivation problem discussed here, for example, one starts with a three-dimensional network representation of the catalyst porous structure. Systematic procedures of how to map any disordered porous medium onto an equivalent random network of pore bodies and throats have been developed and detailed accounts can be found in a number of publications ( 8). For the purposes of this discussion it suffices to say that the success of the mapping techniques strongly depends on the availability of quality structural data, such as mercury porosimetry, BET and direct microscopic observations. Of equal importance, however, is the correct interpretation of this data. It serves no purpose to perform careful mercury porosimetry and BET experiments and then use the wrong model (like the bundle of pores) for data analysis and interpretation. 

We now consider application of percolation theory to describing mercury intrusion into porous solids. First we briefly recall the main physical principles of mercury porosimetry (in particular, the Washburn equation). These principles are treated in detail in many textbooks [e.g., Lowell and Shields 49)]. The following discussions (Sections IV,B and IV,C) introduce general equations describing mercury penetration and demonstrate the effect of various factors characterizing the pore structure on this process. Mercury extrusion from porous solids is briefly discussed in Section IV,D. 

A) Pressure-controlled mercury porosimetry procedure. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+i-Pi >dP>0 where Pj+i, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters of porous medium such as total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson applied percolation theory to calculate permeability from mercury-injection data. 

Hg specific pore volume measured by mercury porosimetry Kc m<75 m diameter between 2 and 7.5 nm determined by Broekhoff-de-Boer theory V volume obtained by addition of tag, Tc m<7 5mii and Sbet specific surface si02 silica particle diameter measured by TEM. 

The basical theories, equipments, measurement practices, analysis procedures and many results obtained by gas adsorption have been reviewed in different publications. For macropores, mercury porosimetry has been frequently applied. Identification of intrinsic pores, the interlayer space between hexagonal carbon layers in the case of carbon materials, can be carried out by X-ray dififaction (XRD). Recently, direct observation of extrinsic pores on the surface of carbon materials has been reported using microscopy techniques coupled with image processing techniques, namely scarming tunneling microscopy (STM) and atomic force microscopy (AFM) and transmission electron microscopy (TEM) for micropores and mesopores, and scanning electron microscopy (SEM) and optical microscopy for macropores [1-3],... 

On initial inspection the results obtained from serial sectioning of LMPA intruded samples appear at odds with the principle theory behind intrusion and retraction as predicted by the Washburn equation. But further inspection shows it is not the Washburn equation, but mercury porosimetry that is at fault. Pore network models have often been used to characterise the behaviour of pore structure in relation to mercury porosimetry. But the model is only as good as the assumptions and the data that it is based iqron. Without artificially shielding the network, the model caimot propa ly detomine the correct psd and cannot derive a more spatially accurate structure that could be used for diffusion and reaction modelling. In order to characterise the pore structure more accurately, we need to introduce some of the elements usually revealed by LMPA intrusion tests. 

Mercury porosimetry (or intrusion) Measurement of the specific porous volume and of the pore size distribution function by applying a continuous increasing pressure oti liquid mercury such that an immersed or submerged porous solid is penetrated by mercury. If the porous body can withstand the pressure without fracture the Washburn equation, relating capillary pressure to capiUaiy diameter allows converting the pressure penetration curves into a size distribution curve. If a sample is contracted without mercury intrusion, a specific mechanical model based on the buckling theory must be used... 

We review a recently developed molecular-based approach for modeling mercury porosimetry. This approach is built on the use of a lattice model of the porous material microstructure and the use of mean-field density fiuictional theory (MF-DFT) calculations and Monte Carlo simulations to calculate the three-dimensional density distribution in the system. The lattice model exhibits a symmetry between the adsorption/desorption of a wetting fluids and intnision/extrusion of a nonwetting fiuid. In consequence, macroscopic approaches used previously to transform mercury porosimetry curves into gas adsorption iso erms are essentially exact in the context of the model. We illustrate the approach with some sample results for intrusion and extrusion in Vycor and controlled pore glass (CPG). 

Lowell S. and J. E. Shields (1984). Theory of mercury porosimetry hysteresis . Powder Technology 38 121-124. 

The commercial sample, spherical bead activated carbon, was supplied by Kureha Chemical Industry. This activated carbon is referred to as Kureha carbon, which has a total micropore volume of 0.56 cm g" and a BET surface area of 1300 m g . The detailed textural properties of Kureha carbon are reported elsewhere [9]. The pore size distribution was evaluated in terms of the simulation of the density hmctional theory (DFT) using the isotherm data of nitrogen adsorption at 77 K and relative pressures up to 0.2. Only micropores contribute to the total pore volume and surface area. This was further confirmed by mercury intrusion porosimetry, no significantly additional porosity was observed in the pore size range from 2 nm to 100 pm. So, the investigated adsorbent is a purely microporous material and its pore size distribution covers the range from 0.4 to 1.9 nm [9]. 

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