Qualitative description of gas permeation

As discussed in Section 9.4.1, the contribution of Knudsen diffusion to the total flux decreases with decreasing pore radius of the membrane material. Initially the selectivity of binary mixtures of gases is constant and equal to the Knudsen value. 

Lin et al. [67] reported in the region between pore diameters of 3.0-2.0 nm small negative deviations for He/N2 mixtures, but with pore diameters 2.0 nm a strong increase occurs to values above the Knudsen value. This is a t5ipical phenomenon for microporous systems together with the onset of activated gas permeation. 

As will be shown, it is useful to distinguish microporous membranes in systems with relatively large, intermediate and small pores. This is discussed by de Lange and Burggraaf et al. [59,63] and is schematically shown in Fig. 9.20. Note that here the location of the minima and the shape of the potential as a function of z is given schematically and is not exact. 

Simulation results yielding pictures as given for region C2 are reported by Petropoulos and Petrou [83]. For mesopores the minimum in the potential curves is equal to the (isosteric) adsorption heat at free surfaces with respect 

With decreasing pore size the desorption energy from the wall to the gas phase within the pores (the maximum in the curves in Fig. 9.20) becomes smaller but remains positive. This implies that the molecules in the central part of the pore behave in a Knudsen-like marmer (i.e. no intermolecular collision) and can pass each other (region Cj, upper part of Fig. 9.20) but nevertheless are not free and follow curved trajectories (see Ref. [83] and Sections 9.4.3.1-2). In this region c we can speak of a surface flow enhanced micropore diffusion (SEMP). Because in surface diffusion the activation energy is a fraction of the adsorption heat (see 

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