Environmental Engineering Reference
In-Depth Information
tions describing the equilibrium desorption transition is defined by the following
relation:
( )
q =q χ
h
(
D
,)(
h
D
)
dD
(74)
exp
loc
in
in
in
Ù(
D
)
Here,
t
-
,
tt
<
˜
˜
(
)
cr
q
Dh
,
=
t
š
cr
loc
in
œ
(75)
˜
˜
1,
elsewhere
represents the kernel of the theoretical isotherms generated from the DBD ap-
proach in pores of different diameters, , and is the normalized differential PSD
function. As mentioned above, the kernel of the integral equation (given by Eq.
(74)) was obtained assuming there is spinodal condensation in the spherical pores.
By applying (as proposed by us previously) the ASA algorithm along with the
stabilizing first-order Tihkonov's regularization term and regularization param-
eter was selected through a series of trials by an interactive judgment of the solu-
tion. During the regularization, some of the artificial shoulders and stairs were
smoothed out.
1.2.2.13 DRS AND DI MODEL (DUBBINI-IZOTOVA, DUBBINI-
RADUSKEVICH-STOEKLI)
The classical Dubinin-Radushkevich (DR) equation is commonly used in its lin-
ear form for analysis of active carbons and micropore size analysis that mention
before. The DR equation was applied to the nitrogen experimental isotherm at
77 K using values. From this data, the micropore width (L) and following equa-
tions were used with the assumption of a slit-shaped pore:
(
)
(
)
= +×
2
(76)
log log
W
log log
W
M
log (
PP
/
)
0
0
The micropore volume is calculated from the intercept of a log (W) vs plot, while
the slope, M, of the best fit line is related to the adsorption energy, , as follows:
M
=−
2.303
×
(
RT
/
E
)
2
(77)
where is the ideal gas constant and is the adsorption temperature in Kelvin. It has
also been shown that the parameter is related to the average micropore half-width
by the equation:
b
k
x
=
(78)
E
The similarity coefficient is a shifting factor, which at a given temperature de-
pends only on the adsorbate and is equal to , where is the adsorption energy of
a reference vapor (typically benzene). For nitrogen at 77 K, is equal to a value
 
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