Characterization of Porous Solids
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mesoporous (2 nm < pore diameter < 50 nm), or macroporous (50 nm < pore diameter).1"2 These size limits are somewhat artificial since they arise from nominal limits associated with characterization techniques, but are now accepted in most applications. Full description of a porous solid may require many parameters such as porosity, density, surface area, pore volume, pore size (mean, hydraulic radius/diameter, pore size distribution), pore connectivity, pore shape, pore surface roughness, and others. Unfortunately, these parameters are commonly used without precise definition. Porosity is the volume fraction of a solid that is porous. Several questions arise given this definition. Depending on the measurement technique, either open porosity or total porosity is obtained. Also, the measure of the open-pore volume varies with the probe used. Therefore, when porosity values are reported, they should also be accompanied by a description of the measurement. The problem is particularly acute for powders where intergranular voids may or may not be included as "porosity." "Density" can also be ambiguous. Skeletal density is the density of the solid matrix only. Density as measured by helium (or other fluid) displacement may be lower than the true density if closed porosity is present. Bulk density is the mass of the porous solid per total sample volume (solid phase + closed porosity + open porosity). However, for porous powders, bulk density may refer to the bulk density of either individual particles or the powder bed.3 "Surface area" can vary dramatically depending on both technique and data analysis method. The surface area of both open and closed pores is measured via scattering, but only the accessible porosity is detected with adsorption or mercury porosimetry. Depending on the tempera-
ture and adsorbate size, the measured surface area can vary. Pore size distributions (PSDs) are presented in either cumulative (volume versus radius/diameter) or differential form (dV/dr versus r). Here V is volume and r pore radius. For very broad PSDs, the logdifferential distribution is also presented as dV/dlogio(r) as a function of pore size. To further confuse the situation, cumulative or differential PSDs are also sometimes normalized by the total pore volume. Gas/Vapor Adsorption One of the oldest methods for quantifying pore structure is traced to Langmuir's work relating the volume of gas adsorbed (V) to relative pressure P/Po, where Po is the saturation pressure.4 The Langmuir model assumes monolayer adsorption and is thus limited to chemisorption and microporous solids. Brunauer, Emmett, and Teller (BET) modified Langmuir theory to account for multiple layers. BET is now the standard approach for analyzing nitrogen adsorption data at 77 K to determine the specific surface area. For BET analysis, the adsorption data (V vs. P/Po) is plotted in the linear form of the BET equation:1 l/(V(Po/P-l))=l/(V m C) + (C-l)/(V m QP/P 0 . (1) In the relative pressure range of 0.05 to 0.3, Equation 1 is usually linear and the desired
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