Theoretical investigation of relationships between characteristic energy and pore size for adsorption in micropores

Starting from the relationship between the mean field (Φ̄) and the characteristic adsorption energy (E), relationships are derived for the dependence of the characteristic energy on pore size. Specifically, relationships between the characteristic adsorption energy E in the Dubinin-Radushkevich (D-R) and Dubinin-Astakhov (D-A) equations and the pore dimension of the slit-shaped pores are derived and discussed for three adsorption regions: the Henry's law region, the moderate coverage region, and the high coverage region. The results show that the characteristic energy E is a complicated function of many factors including pore size and coverage (θ), as well as temperature (T). There is no simple correlation between characteristic energy E and pore size L for the whole range of θ. Nevertheless, in the moderate coverage region, θ ≈ 0.2-0.8, the simple inverse proportionality may apply although it is only a crude approximation. The characteristic energy depends on the pore size more strongly in the high coverage region and less strongly in the Henry's law region. Moreover, the results reveal that, when the pore size is in the range of 1-2 times the diameter of the adsorbate molecule, different potential average schemes yield very close values for the mean field, indicating that the average scheme is not important in this case.