Biomedical Engineering Reference
In-Depth Information
Au-O, Rh-B and Sa-O dyes. However, a large portion (>85%) of the equilibrium uptake was
accomplished within 12 or 20 min, indicating a rapid surface adsorption of cationic dyes did
occur on γ-PGA [27]. The kinetic data were modeled with the following pseudo first order
and pseudo second order equations [72-74] given by
q = q [1- exp(-k t)]
(3)
t
e
1
t
q=
(4)
t
1
t
+
q
2
kq
e
2e
where, q
t
and q
e
is the dye uptake (mg/g) at time t and equilibrium, respectively, k
1
(L/min)
and k
2
(g/mg min) are first order and second order rate constants, and k
2
q
e
2
(mg/g min)
represents initial adsorption rate (h). Fitted kinetic parameters obtained by non-linear
regression (Marquart-Levenberg algorithm) are summarized in Table 5 [27,70,71]. Based on
two error parameters, r
2
(coefficient of determination) and χ
2
(chi-square statistic), the pseudo
second order model gave a more precise fit, suggesting the rate of dye uptake may be largely
controlled by chemisorption mechanism involving valence forces through sharing or
exchange of electrons [74]. Following a rise in dye concentration from 100-200 mg/L, the
second order rate (g/mg min) of dye uptake dropped from 1.04 x 10
-2
- 4.75 x 10
-3
for Au-O,
6.95 x 10
-3
- 4.50 x 10
-3
for Rh-B and 2.18 x 10
-3
- 5.25 x 10
-4
for Sa-O. It is apparent that
once the readily available active sites on γ-PGA are occupied, the rate of dye uptake
decreases [27].
The adsorption kinetics of BB-Y dye (100 mg/L) conducted at three different
temperatures (301, 318 and 333 K) showed a rapid uptake with time (92-98% within 20 min),
but diminished on elevating the temperature [71]. The pseudo second order model fitted the
kinetic data best, with the derived q
e
values being declined by 59.58 mg/g for a temperature
raised from 301 to 333 K, accompanied by the rate climbing from 1.50 x 10
-3
- 6.25 x 10
-3
g/mg min, probably because of acceleration in the mobility of dye cations at higher
temperatures. In addition, the dominant surface adsorption through ion exchange and absence
of any particle diffusion may account for the reduced dye uptake at an elevated temperature,
as the particle diffusion is an endothermic process [74]. Furthermore, the higher the
temperature, the lower the ion exchange capacity and the larger the physical adsorption
capacity [75]. The activation energy (E
a
, kJ/mol) was determined using the Arrhenius
equation [71], which relates the rate constant (k) and temperature (T, Kelvin) according to the
expression,
E
a
⎛
⎞
-
⎜
⎟
k=Ae
RT
(5)
⎝
⎠
where A (g/mg min) is the temperature-independent pre-exponential factor. The E
a
value
obtained was 37.21 kJ/mol, which was greater than the range (<30.00 kJ/mol) reported for a
diffusion-controlled reaction [71], implying the adsorption of BB-Y dye by γ-PGA was only
reaction-controlled.
