Micromeritics ASAP 2460 Operator's Manual page 384

Appendix F
Figure D-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 distribution 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 iso-
therm for the model. If the value of H is very large, the isotherm obtained corresponds 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 distribu-
tions 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 equa-
tion in the classical model of pore filling.
Figure D-2 shows how the profiles change with pressure for a model pore with H = 40 Å. The insets
show the density profiles for the corresponding points of the isotherm.
F-4
ASAP 2460 Operator's Manual
246-42800-01 - Aug 2013