Micromeritics ASAP 2020 Confirm Operator's Manual page 416

Appendix F
Figure F-1 shows the density profile for argon at a carbon surface as calculated by density
functional theory for a temperature of 87.3 K and a relative pressure of about 0.5.
Figure F-1. Density Profile for Argon on Carbon at 87.3 K and a Relative Pressure of 0.5
This figure represents a cross-section of the region near the surface. Note the layerwise dis-
tribution of adsorbate; the first monolayer is sharply defined and a third layer can be
distinguished. The area under the profile curve represents the amount adsorbed per unit area
at this pressure. The positions of the maxima are separated by a distance determined by the
size of the adsorptive atom.
Given the density profile, the amount adsorbed at the stated pressure can be easily calculated
as the integral over the profile. Repeating this calculation over a range of pressures yields the
adsorption isotherm for the model. If the value of H is very large, the isotherm obtained cor-
responds to that of an external, or free, surface. If H is smaller, a range of pressures is reached
where two minima exist for the grand potential, showing the presence of two metastable
phases having different density distributions but the same chemical potential. The phase with
the lower GPE is the stable one. As the pressure is increased, a point is reached where the
other phase becomes the stable one. This phase transition reflects condensation of adsorbate
in the pore; the pressure at which it occurs is called the critical pore-filling pressure. This
pressure is analogous to the condensation pressure predicted by the Kelvin equation in the
classical model of pore filling.
Figure F-2 shows how the profiles change with pressure for a model pore with H = 40 ang-
stroms. The insets show the density profiles for the corresponding points of the isotherm.
F-4
ASAP 2020 Confirm
202-42811-01 - Mar 2011