BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 71

classical models, but it appears there is still a lack of studies on the modeling and
simulation methods of controlling pore structures in carbon based nano adsor-
bents, that focus on parameters such as range of applied temperatures in activation
state and applied special catalysts in activation condition that affect controlling
of pore structure of carbon materials. This field of research has a great room for
improvement in pore structure control modeling and simulation methods of car-
bon materials. There is no definite answer to this argument since each of these
adsorbents has its own advantages and disadvantages in their special applications.

1.2 MATHEMATICAL MODELING FOR PSD AND ADSORPTION
PARAMETERS CALCULATING IN CARBON NANO ADSORBENTS
Finding a reliable, accurate, and flexible method for the determination of PSD of
porous adsorbents still remains an important concern in the area of characteriza-
tion of porous materials. Although a large number of researches have been done
in this area, some constraints such as type of adsorbate, adsorbent characteristics,
adsorption temperature, applicable range of pore size, and range of relative pres-
sure limit the applicability of each model in all cases. The lack of such method
is tangible by rapid development of new porous materials and their wide appli-
cations in various fields. In the present study, the following three well-known
models were used in order to obtain PSD for two series of chemically activated
carbons and the results are compared. It is increasingly common to study adsorp-
tion processes, whether on free surfaces or in confined spaces such as pores by
modeling or simulation techniques. The reach aim of these studies is frequently
to develop an understanding that will better enable adsorption measurements to
be used to characterize various adsorbents in terms of their surface properties
or pore structure. Modeling and simulation methods include: Grand Canonical
Monte Carlo (GCMC), density functional theory (DFT), LJ potential, BJH, Novel
Olgorithms method such ASA, Verlet, SHN, HK and IHK method, DR method,
DS method (Stoeckeli method), etc. [121].
There is also a different approach based on a single adsorption isotherm. Here,
total adsorption amount, which is simply a summation of the adsorbed molecules
on various adsorption sites, is equal to an integral of the local adsorption on par-
ticular sites multiplied by a PSD function, integrated over all sizes:

∞
q = ∫

( ) ( ) ( )

P L P , f L dL

(1)

0

where θ(L, P) is the local adsorption isotherm (kernel) evaluated at bulk pressure
P and local pore size (L), and F(L) denotes the PSD of the heterogeneous solid
adsorbent. Solving for the PSD function is an ill-posed problem unless the form
of function is defined. Various models by assuming different kernels (Langmuir,
Freundlich, BET, DR, DA, Sips, Toth, Unilan, Jovanovich, Fowler and Harkins)
and mathematical functions (Gaussian, Gamma) for PSD have been presented.