Obtaining Pore Radius from the Two Slopes

The following then is the information that one would hope to extract from these plots. Assuming one can relate the slopes of L and H to areas either by comparison to non-porous standard or through the theoretical x treatment, one has the areas corresponding to the L slope and corresponding to the H slope, (x treatment would use the analytical expressions of Eqs. (4) and (5).) These are related to the physical quantities of the total 

The total pore volume, Vp, should be well approximated by the intercept mentioned. At this point a geometry must be assumed to analyze further. If cylindrical pores are assumed then there will be an average length per pore, (/). Basing the following upon a fixed amount of adsorbent, conventionally exactly 1 g, one can construct the following equations  

(17) is capable of yielding a range of values for the pore radius using the slopes and intercepts of the standard plots for both micropores and 

In the case of the analysis of mesopores (Fig. 14) a separate determination of Vp may be obtained using Eqs. (10) and (11). The pressure used in Eq. (10) is that at which a sudden increase is observed or the average value in the step, n is for the purpose of calculating t extracted from the L portion of the standard plot or its extrapolation. Both of these assumptions are approximations. In general there is also a distribution of either pore sizes or of adsorption energies, which complicates this simplistic analysis. These complications can be overcome and are addressed in Chapter 6. The simple treatment however follows along these lines. 

Thus for an isotherm indicating mesoporosity one should be able to obtain all of the physical quantities unambiguously. This analysis requires very good data to yield results. Notice that in step 3, that Ap and A should be much larger than A. If this is not the case then there is a high uncertainty in A and obtaining a nonsense answer is possible. 

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