HK Model for Slit-Shaped Pores

Consider a slit pore with the nuclei of the sorbent molecules in the lattice planes forming the pore-waU spaced at a distance L apart. If the diameter of the sorbent molecules is denoted as ds and that of the adsorbate molecules as dA, then the number of molecule layers M that can be accommodated laterally as the pore gets filled up can be estimated as  

Note that the intemuclear distance at zero interaction energy for an adsorbate-sorbent system is now denoted as as to differentiate it from a a, which is the zero interaction energy distance for an adsorbate-adsorbate system. The expressions for as and a a are as follows  

The second type of molecules (marked B in the figure), comprising n — 2) number of layers, will interact effectively only with two parallel planes of gas 

The average interaction energy for M 2 can be calculated by weighing the energy potentials of the molecules by the actual number of layers of molecules possessing the corresponding energy  

On applying the correction for isotherm non-linearity given by Cheng and Yang (1994), the modified HK-CY equation is obtained as  

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Figure 4.6. Pore size distribution of faujasite zeolite as predicted by original HK models and the corrected HK models for slit-shaped pores (Rege and Yang, 2000, with permission).

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