BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 145

1.3.3.5 SHN ALGORITHM
Shortcomings of conventional PSD estimation techniques, as mentioned earlier,
various procedures have been used conventionally to extract the pore size distribu-
tions of various adsorbents from available adsorption isotherms. In the so-called
“direct methods,” a prespecified isotherm was used along with some assumed
distribution (for f(r)) and then the corresponding values of (Pi) were computed
by algorithm. The proposed distribution was decided to be acceptable, if and only
if, the computed isotherm could reconstruct the experimental data. It was clear-
ly demonstrated in our recent article that for each local adsorption isotherm (or
kernel), infinite distributions (multiple solutions) can theoretically reproduce the
adsorption data, while only one of them provide proper distribution for the adsor-
bent. Many other suboptimal solutions (which can successfully filter-out the noise
and exactly recover the true underlying isotherm hidden in a set of noisy data) can
be entirely inappropriate and may lead to exceedingly misleading distributions.
This is not surprising, because all of these unrealistic distributions are actually the
optimal solutions of a minimization problem with no definite physical meaning.
Langmuir isotherm has been employed in both synthetic isotherm data generation
step and PSD recovery process. This algorithm demonstrates the optimal perfor-
mances of new proposed technique (SHN2) for recovery of a pre specified true
ramp function PSD from various noisy datasets using different orders of regular-
izations. Figure 1.9 illustrates similar performances for single, double and triple
peak Gaussians as true pore size distributions. All predictions were computed us-
ing the optimum levels of regularization (*), which were found via LOOCV meth-
od and verified manually. As it can be seen in Fig.1.9 he new proposed method
(SHN2) provides excellent prediction for pore size distributions when appropriate
order of regularization with optimum regularization level have been employed.
Figure 1.9 illustrates the selected performances of our newly proposed method for
various PSDs using first order regularization technique at optimum levels of regu-
larization. In all above predictions, the Halsey correlation was used for prediction
of adsorbed film thickness in both isotherm generation step and PSD recovery. In
all cases, Halsey correlation was used in generation steps while Harkins and Jura
(Hal-HaJu), Deboer (Hal-dB), Micromeritics (Hal-Micr), and Kruk and Jaroniec
(Hal-KJ) correlations were employed,respectively, in the PSD recovery opera-
tions. Evidently, the new proposed method performs adequately for all choices
of adsorbed film thickness correlations. In other words, the choice of correlation
used for estimation of adsorbed film thickness is not crucial.
1.3.4 COMPARISON BETWEEN RECENT STUDY WORKS ABOUT
SIMULATION AND MODELING METHODS FOR PSD CALCULATING IN
CARBONS MATERIALS
Kowalczyk et al. [15] description of benzene adsorption in slit-like pores with
IHK and DFT methods and by ASA algorithm and GCMC simulation. In mod-