BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 86

Further investigations based on comparison of the density profile provided by the
LDFT and that determined with GCMC simulations showed that in the case of
inhomogeneous fluid more rigorous analysis requires accounting for the density
distribution in the region of a few collision diameters in the proximity of a given
point. For this reason, it is now customary to apply non-local density functional
theory (NLDFT), which involves the incorporation of short-range smoothing
functions. In this manner, it has been possible to obtain good agreement with the
density profiles determined by Monte Carlo molecular simulations. The non-local
density functional theory (NLDFT) is well established and widely presented in
the literature. The distribution of density in a confined pore can be obtained for an
open system in which a pore is allowed to exchange mass with the surroundings.
From the thermodynamic principle, the density distribution is obtained by mini-
mization of the following grand potential written below for the one-dimensional
case:

( ) ( ) ( ) ( )

∫

W r z = r z f z +Φ −m r dz (50)

Here p( z ) is the local density of the adsorbed fluid at a distance z from one of
the walls of the pore, f( z ) is the intrinsic molecular Helmholtz free energy of the
adsorbate phase, is the chemical potential. The flee energy f( z ) comprises the
ideal, mean-field attractive terms, and the excess free energy (repulsive) term as
a function of smoothed weighted average. A new approach based on NLDFT to
determine pore size distribution (PSD) of active carbons and energetic hetero-
geneity of the pore wall was proposed by others. The energetic heterogeneity is
modeled with an energy distribution function (EDF), describing the distribution
of solid- fluid potential well depth (this distribution is a Dirac delta function for
an energetically homogeneous surface). The approach allows simultaneous de-
termining of PSD (assuming slit shape) and EDF (from nitrogen isotherms by
using a set of local isotherms calculated for a range of pore widths and solid fluid
potential well depths. It was found that the structure of the pore wall surface dif-
fers significantly from that of graphitized carbon black. This could be attributed to
defects in the crystalline structure of the surface, active oxide centers, finite size
of the pore walls (in either wall thickness or pore length), and so forth. Those fac-
tors depend on the precursors and the process of carbonization and activation and
hence provide a fingerprint for each adsorbent. Ustinov and Do approach gives
an accurate representation of the experimental adsorption isotherm. The pore size
distributions indicate quite significant differences in the porosity of the carbons
studied in the range of micropores and mesopores [1, 11, 36].

1.2.2.8 JARONIEC-CHOMA METHOD
The integral equation that mention before was solved for various continuous func-
tions representing the distribution F(B). For example, Wojsz and Rozwadowski
solved the integral equation for distribution functions F(B) other than the Gaussian