Pore wall roughness

Another factor which can lead to BET areas slightly higher than those from porosimetry is pore wall roughness. Slight surface roughness will not alter the porosimetry surface area since it is calculated from the pore volume while the same roughness will be measured by gas adsorption. 

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

Pore wall is rough at atomic scale for all pores. ... 

We emphasize that the exclusion of partitioning objects from pore space occurs because the overlap of the objects with the pore walls is forbidden. It is rather natural to relate this phenomenon to the wall area subject to overlap, specifically area s per unit pore volume. (We add that the wall area due to surface roughness with a scale much smaller than that of the partitioning object should not be counted.)... 

Constriction if the pore radius rp is not much larger than the radius of the diffusing solute molecule rm, the molecule frequently collides with the pore wall whereby its diffusion is impeded, the more so for rm/rv closer to unity. It is difficult to predict the magnitude of this effect. It can be roughly estimated by the semiempirical Renkin equation, which applies to diffusion of reasonably spherical molecules (or particles) in a straight cylindrical capillary ... 

The surface area of n cylindrical pores open at the ends would be rm 2r)L if the pore walls were smooth and there were no pore intersections. However, with a moderately high internal void fraction (e = 0.3A).6) and randomly oriented pores, intersections are frequent, and the wall area of a pore is reduced where two pores intersect. Since any slice through a solid with a random pore structure will have e open fraction, the surface of the cylindrical pores is assumed to be reduced by the same fraction, and the surface is proportional to (1 — e). Allowing for an irregular surface of the pore walls, which increases the area by a roughness factor, r.f., the total surface per gram is... 

If our pore is a very long one (L large) then at some value of x, say Xm, all reactant diffusing through the pore will have had so many collisions with the pore wall that it will have reacted to product, and beyond this point Ca will be substantially zero. Xm is thus defined as the maximum depth that the reaction can penetrate into a pore. We can find a rough value of x as follows. If we consider only diffusive flow of reactant into the pore then the flow through the pore mouth is ... 

The roughness factor for the catalyst pore walls. This is the actual microscopic area divided by the area which would be obtained if siu ace roughness on a molecular scale were smoothed out. 

FIG. 18 Average energies for krypton adsorbed at 120 K in a rough-walled cylindrical pore. The dependence of the Kr-Kr (gg) and the Kr-pore wall fgsj energies on the number of atoms adsorbed. are shown separately, together with their sum. The Kr monolayer capacity under these conditions is about 130 atoms. (From Ref. 125.)... 

Thus, the study of the structural characteristics of ordered mesoporous silicas using improved procedure (CONTIN/MEM-j) or a complex model of cylindrical pores and voids between spherical particles suggests that the use of alcohol in the reaction solution and additional aging of the reaction product causes increased roughness of the pore walls. However, the textural porosity of MCM-41 samples synthesized with the presence of ethanol is lower than that of MCM-48 and SBA-15 synthesized without alcohol. The roughness of the pore walls and residual organics provide the appearance of WAW adsorbed in a mixture with an organic solvent. 

Notes The specific surface area (in mVg) and the pore volumes (in cmVg) of nanopores (Sna o and at radius for the model of cylindrical pores for LiChrolut EN (or half-width for carbon adsorbents) R<1 nm, mesopores (S eso and V eso) at 1 < / < 25 nm and macropores (5 acro and V acro) at / > 25 nm were determined by integration of the fs(R) and/v(/ ) functions, respectively. The fractal dimension Djj2 and D 2o values were determined from the nitrogen and water adsorption isotherms. The Aw value determines the average error of the model of pores due to roughness of the pore walls. 

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