Environmental Engineering Reference
In-Depth Information
1.2.1.2 THEORETICAL MODELS FOR ADSORPTION POTENTIAL
DISTRIBUTION CALCULATING
The amount adsorbed a (after conversion to the adsorbate volume V) measures the
pore volume accessible to adsorption. If V
t
is the maximum volume adsorbed, the
difference Vt- Vre presents the unoccupied pore volume associated with the ad-
sorption potentials smaller than A, and denotes the non-normalized integral distri-
bution function of the adsorption potential, X*(A). Its first derivative with respect
to A is the non-normalized differential distribution function X(A):
( )
(
)
( )
*
dV V
−
dX
A
dV
A
( )
n
t
XA
=
=
=
(12)
dA
dA
dA
In terms of the condensation approximation the adsorption potential distribution
(APD), X(A), gives essentially the same information as the distribution function
of the adsorption energy. Because for microporous carbons the amount adsorbed
plotted against the adsorption potential is a temperature independent function, the
use of Eq. (12) for calculation of APD is fully justified. The distribution function
X(A) can be calculated by numerical differentiation of the characteristic adsorp-
tion curve V(A), which is obtained by plotting the amount, adsorbed as a func-
tion of the adsorption potential. Previous experimental and theoretical studies of
nitrogen adsorption on active carbons indicate some opportunities for using APD
for characterization of these adsorbents. It was shown that the minimum or inflec-
tion point on the nitrogen APD curve located at about4 kJ mol
-1
before the peak
representing the monolayer formation), can be used to evaluate the monolayer
capacity. However, the other minimum, whichappears in the range of lower ad-
sorption potentials, determines the micropore volume. Thus, a typical APD curve
for nitrogen on a microporous carbon at 77 Kexhibits two distinct peaks, which
represent the monolayer formation (the peak located between 4 and 8 kJ mol-l)
-l
)
and the subsequent volume filling of micropores (the peak between 0.5 and 3 kJ
mol
-l
). The APD curves for nitrogen on the micro and mesoporous carbons at 77K
are decreasing functions of A and exhibit an inflection point in the range between
3 and 5kJ/mol, which reflects the completion of the monolayer formation. A sharp
increase of the APD curve with decreasing value of A from two to zero reflects the
capillary condensation in mesopores. A comparison of the total specific surface
area and those evaluated by the BET method and by the -plot method (shows that
the APDmethod gives much smaller values. The values of S
t,X(A)
seem to be more
realistic than those obtained by the BET method and -plot analysis, which are
based on the BET model, because in contrast to the BET model the APD method
allows for a more accurate estimation of the amount adsorbed in the monolayer.
The methods based on the BET model do not take into account the correction for
molecules adsorbed inside micropores and therefore, they overestimate the total
specific surface area of microporous solids, where is the relative adsorption and is
the thermal coefficient of the limiting adsorption taken with the minus sign. We
Search WWH ::
Custom Search