The force field in very fine pores

Calculations of the interaction energy in very fine pores are based on one or other of the standard expressions for the pair-wise interaction between atoms, already dealt with in Chapter 1. Anderson and Horlock, for example, used the Kirkwood-Miiller formulation in their calculations for argon adsorbed in slit-shaped pores of active magnesium oxide. They found that maximum enhancement of potential occurred in a pore of width 4-4 A, where its numerical value was 3-2kcalmol , as compared with 1-12, 1-0 and 1-07 kcal mol for positions over a cation, an anion and the centre of a lattice ceil, respectively, on a freely exposed (100) surface of magnesium oxide. 

A more detailed treatment has been given by Gurfein and his associates who chose as their pore model a cylinder with walls only one molecule thick. A few years later, Everett and Fowl extended the range of models to include not only a slit-shaped pore with walls one molecule thick, but also a cylinder tunnelled from an infinite slab of solid and a slit formed from parallel slabs of solid. 

The ratio 0/0 is thus a measure of the enhancement of the energy of adsorption in a micropore as compared with that on an open surface. In curve (i) of Fig. 4.9 this ratio is plotted as a function of d/r and, as is seen, the enhancement is still appreciable when d = l-Sr, but has almost disappeared when d = 2r , i.e. when the slit is only two molecular diameters wide. Even when d/r = 1, which corresponds to a single molecule tightly packed into the width of the slit, the enhancement is only 1-6-fold. The effect 

As would be expected, the enhancement of potential in cylindrical pores turns out to be considerably greater than in dits, as curve (ii) of Fig. 4.9 clearly demonstrates. At R/r = 2 the enhancement is more than 50 per cent, and it is still appreciable when R/r = 3 (R = radius of cylinder). The calculations show that at radii in excess of R = 1086ro, the single minimum (comparable with Fig. 4.8(c)) develops into a ring minimum (i.e. two minima are present in any axial plane, cf. Fig. 4.8(a)). 

These calculations lend theoretical support to the view arrived at earlier on phenomenological grounds, that adsorption in pores of molecular dimensions is sufficiently different from that in coarser pores to justify their assignment to a separate category as micropores. The calculations further indicate that the upper limit of size at which a pore begins to function as a micropore depends on the diameter a of the adsorbate molecule for slit-like pores this limit will lie at a width around I-So, but for pores which approximate to the cylindrical model it lies at a pore diameter around 2 5(t. The exact value of the limit will of course depend on the actual shape of the pore, and may well be raised by cooperative effects. 

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