Network and Pore Connectivity Effects

As discussed above, hysteresis loops can appear in sorption isotherms as result of different adsorption and desorption mechanisms arising in single pores. A porous material is usually built up of interconnected pores of irregular size and geometry. Even if the adsorption mechanism is reversible, hysteresis can still occur because of network effects which are now widely accepted as being a percolation problem [21, 81] associated with specific pore connectivities. Percolation theory for the description of connectivity-related phenomena was first introduced by Broad-bent et al. [88]. Following this approach, Seaton [89] has proposed a method for the determination of connectivity parameters from nitrogen sorption measurements. 

A typical network effect is illustrated in Fig. 1.15 in the case of three pores of different size. During adsorption the smallest pores are filled first and the largest pores last, resulting in the filling sequence A, B and C. The vapor needed to fill remote pores can be transported either through the liquid or vapor phase. During the desorption process, the order in which the liquid nitrogen would become unstable is C, B and A, i.e. the reverse. 

However, desorption follows the meniscus receding mechanism, and vaporization occurs only in pores connected to the vapor phase. As a result, pore C remains fiUed until pore B is emptied, and the sequence of evaporation is in fact B and C together followed by A. This mechanism can lead to very steep Type H2 hysteresis loops. Indeed, a common diagnostic feature of many hysteresis loops is that the steep region leading to the lower closure point occurs at nearly the same relative pressure. It is almost independent of the porous adsorbent, but mainly dependent on the adsorptive. In case of nitrogen this happens at a relative pressure p/po 0.4 [21]. 

In the past it was very common to derive the mesopore size distribution from the desorption branch of the isotherm. The above considerations make it clear that this practice is questionable especially for Type H2 hysteresis loops, and can lead to misinterpretations [90]. Indeed a significant downward turn in the desorption branch of a N2 isotherm at p/po 0.4 leads to an apparent sharp maximum in the pore size distribution curve at 2 nm which is totally artefactual. Although no general guidelines exist on whether the adsorption or desorption branch should be used for computation, it should be understood that with Type H2 and H3 hysteresis loops, reliable results are much more Hkely to be obtained if the adsorption branch is used [21]. 

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