Micromeritics GEMINI VII Operator's Manual page 220

B DFT Models
As noted previously, at equilibrium, the whole system has a minimum (Helmholtz) free energy,
known thermodynamically as the grand potential energy (GPE). Density functional theory
describes the thermodynamic grand potential as a functional of the single-particle density
distribution; therefore, calculating the density profile that minimizes the GPE yields the equilibrium
density profile. The calculation method requires the solution of a system of complex integral
equations that are implicit functions of the density vector. Since analytic solutions are not possible,
the problem must be solved using iterative numerical methods. Although calculations using these
methods still require supercomputing speed, the calculation of many isotherm pressure points for
a wide range of pore sizes is a feasible task. The complete details of the theory and the
mathematics can be found in the papers listed under
The following graphs and accompanying text illustrate the results of using density functional
theory to predict the behavior of a model system.
Figure 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.
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.
B - 4
DFT Model References on page B -
Figure 1. Density Profile for Argon on
Carbon at 87.3 K and a Relative
Pressure of 0.5
Gemini VII Operator Manual
239-42828-01 (Rev H ) — May 2021
17.