Biomedical Engineering Reference
In-Depth Information
geneous surfaces (Hasan et al., 2008; Unlu and Ersoz, 2006). It assumes an initial
surface adsorption followed by a condensation effect resulting from extremely strong
solute-solute interaction. The general form of Freundlich model is as follows:
= ()
/
1
n
QKC
e
(4)
F
e
where,
K
F
((L/mg)
1/n
) is Freundlich isotherm constant and
n
is the Freundlich isotherm
exponent constant.
K
F
is correlated to the maximum adsorption capacity and
n
gives
an indication of how favorable the adsorption process is (Hosseini et al., 2003). The
linear form of this model is expressed as in the following equation:
=
()
log
Q
log
K nC
1
log
(5)
e
F
e
The values of
K
F
and
n
can be obtained by plotting log
Q
e
versus log
C
e
.
The Redlich-Peterson equation only differs from the Langmuir-Freundlich equa-
tion by the absence of exponent on
C
e
at the numerator part of the equation (Ng et al,
2002). Meanwhile, the Dubinin-Radushkevitch (D-R) isotherm describes the adsorp-
tion on a single type of uniform pores and can be applied to distinguish between physi-
cal and chemical adsorption. This isotherm does not assume a homogeneous surface or
a constant adsorption potential (Unlu and Ersoz, 2006).
KiNetiC models (adsorPtioN KiNetiCs)
Three kinetic models, pseudo-first-order, pseudo-second-order, and intra-particle dif-
fusion model are used to fit the experimental data. The mathematical description of
these models is given below. The conformity between data predicted by any of these
models and the experimental data is indicated by the correlation coefficient R
2
. The
model of higher values of R
2
means that it successfully describes the adsorption kinet-
ics.
The differential form of the pseudo-first-order kinetic model could be expressed by
the following equation (Ho and McKay, 1998; Igwe and Abia, 2007)
dQ
dt
t
=−
kQ Q
1
(
)
(6)
e
t
where,
t
is the time (min) and
k
1
is the equilibrium rate constant of the pseudo first
order adsorption (min
-1
). Integrating equation (6) by applying the boundary conditions,
t
= 0 to
t
=
t
and
Q
t
= 0 to
Q
t
=
Q
e
, yields the following integral equation:
log/ (
QQQ
−=0 4342
1
)
.
k t
(7)
e
e
The value of the model parameters
k
1
can be determined by plotting log (
Q
e
- Q
t
) ver-
sus
t
to give a straight line of slope 0.4342
k
1
and intercept of log
Q
e
.
The differential form of the pseudo-second-order kinetic model is expressed by the
following equation (Ho and McKay, 1998):
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