Environmental Engineering Reference
In-Depth Information
PSDs is very surprising and can be caused by the low sensitivity and the simplifi-
cations of the mentioned above methods [145].
The advantage of these models is that they are experimentally convenient and
do not need complicated PSD calculations. In 1998, Bhatia successfully applied
the combination of finite element collocation technique with regularization meth-
od to extract various double peak PSDs from synthetic isotherm data points con-
taminated with 1% normally distributed random errors using DR isotherm. They
applied the constraint of non- negativity of solutions by simply using a Newton-
Raphson technique. Although they reported that the method is stable over a wide
range of values of the regularization parameter, the application of non- negativ-
ity constraint usually provides unrealistic solutions. Some researchers proposed a
new method based on the modification of DR equation by introducing adsorption
density and correlating between the pore filling pressure and critical pore size
for nitrogen adsorption at 77 K. The results are found comparable with other
popular PSD methods such as MP, JC, HK, and DFT. In addition to uncertainty
about the general performance of this model as a result of some assumptions in
the model derivation, it is relatively complicated and the procedure for obtaining
PSD is cumbersome. The average diameter of the mesopores is usually calculated
from the nitrogen adsorption data using Kelvin equation. Recently, Shahsavand
and Shahrak proposed two new algorithms (SHN1, SHN2) for reliable extrac-
tion of PSD from adsorption and condensation branch of isotherms. According
to their results, it seems that these two methods have also some limitation similar
to the other previous ones. The regularization technique that used for obtaining
optimum value of regularization parameter is challengeable in these models. In
addition, the basis of these methods is Kelvin equation, whichunlikely provides
reliable PSD for microporous solids. Although much has been done to address
the PSD of porous adsorbents, up to now, no general reliable theory is available
leading to the conclusion that for microporous carbons the extensive investiga-
tion should still continue. In the recent study works, have tried as a novel work
to extend the analysis on PSD of porous carbon nano adsorbents by investigating
the effects of different parameters on it. Some well-known models based on Du-
binin's method namely, Dubinin-Stoeckli (DS) and Stoeckli models and etc., were
used to investigate the effects of these parameters on the porosity of AC samples,
and the results were compared with the two widely used methods of Horvath-
Kawazoe (HK) and improved Horvath-Kawazoe (IHK) for the determination of
PSD of micro or mesoporous solids. These models were derived based on ben-
zene as a reference adsorbate, or N
2
or Ar, because this gases provides more ac-
curate estimations than other adsorbates. On this basis, adsorption isotherm data
of benzene at 30°Cor N
2
in 77k or Ar in 87 Kwere used to determine the PSD of
each carbon samples. Table 1.5 summarizes novel models for characterization of
pores and determines the PSD in carbon materials [1, 2, 133].
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