Supplementary Data
Water Defluoridation by Alumina Modified Turkey Clinoptilolite:
Equilibrium, Kinetic Models and Experimental Design Approaches
Selim Selimoglua, Esra Bilgin Simsekb*, Ulker Bekerc
a
Yıldız Technical University, Chemical Engineering Department, 34210, Istanbul, Turkey
b
Yalova University, Chemical and Process Engineering Department, 77100, Yalova, Turkey
c
TÜBITAK Marmara Research Center, Institute of Chemical Technology, 41470, Gebze,
Turkey
S1. Adsorption Isotherms
Langmuir model
Langmuir isotherm is based on homogeneous adsorption in which each molecule has constant
enthalpies and sorption activation energy. All sites have the same affinity in magnitude for the
adsorbate (Langmuir 1916). The non-linear form is expressed as:
qe 
Q.b.Ce
1  b.Ce
(S1.1)
where Ce is equilibrium concentration of fluoride in solution (mg L-1), qe is the amount of
adsorbate adsorbed per g of adsorbent at equilibrium (mg g-1), Q is Langmuir monolayer
coverage capacity (mg g-1), b is adsorption equilibrium constant.
RL is the dimensionless separation factor constant which expresses the essential characteristics
of Langmuir isotherm, and it is defined as:
R L
1
1  b.Ci 
(S1.2)
where Ci is the initial adsorbate concentration (mg L-1). The value of RL indicates the shape of
isotherm to be either favorable (0<RL<1), RL>1 for unfavorable, RL=1 for linear and RL>0 for
irreversible.
1
Freundlich model
Freundlich isotherm assumes multilayer adsorption, with non-uniform distribution of
adsorption heat and affinities over the heterogeneous surface (Açıkyıldız et al. 2015). The nonlinear equation is shown as:
qe  K F .C e 1 / n
(S1.3)
where KF and n are the Freundlich constants related to adsorption capacity and adsorption
intensity, respectively.
Dubinin-Radushkevich model
Dubinin–Radushkevich (D-R) isotherm model does not assume a homogenous surface or
constant adsorption potential (Dubinin and Radushkevich, 1947). The model helps in
understanding the adsorption type if physical or chemical. The non-linearized form of D–R
equation is given as (Eq. (S1.4)):
qe  qm .e
   . 
2
(S1.4)

  R.T .ln 1 

1 

Ce 
(S1.5)
where qm is the theoretical adsorption capacity (mg g-1), β is isotherm constant (mol2 K-1J-2), ε
is Polanyi potential. The apparent energy of adsorption (E) was calculated using the following
relationship (Eq. (S1.6)):
 1 
E 
 2  


(S1.6)
The mean adsorption energy (E) is calculated to classify the process of adsorption into
chemical, physical and ion exchange. If the value of E is in between 8 and 16 kJ mol-1, the
adsorption process is said to be chemical adsorption, and the value below 8 kJ mol-1 indicates
the physical adsorption (Milmile et al. 2011).
2
S2. Adsorption Kinetics
The time dependence of adsorption on solid surfaces is known as adsorption kinetics. Kinetic
of adsorption gives idea about the process efficiency. Steps of sorption often involve chemical
reaction between functional groups on the adsorbent and target metal ion.
Lagergren's Pseudo First Order Model
In 1898, Lagergen offered the first order rate equation for the adsorption of liquid-solid
(Lagergren 1898). It was the first one explaining the adsorption of liquid-solid systems based
on solid capacity. The non-linear form of model is shown as (Eq. (S1.7)):
qt  qe ( 1  e k 1 .t )
(S1.7)
where qe and qt are the amounts of adsorbed fluoride at equilibrium (mg g-1) and at time t (min),
k1 (min-1) is the pseudo-first order rate constant. By taking the integral of both sides with
boundary conditions t=0 qt=0 and t=t qt=qt, the linear form of equation is (Eq. (S1.8)):
 k 
log  qe  qt   log  qe    1  t
 2.303 
(S1.8)
To find the rate constant, plot of 𝑙𝑜𝑔(𝑞𝑒 − 𝑞𝑡 ) vs t is drawn.
Pseudo Second Order Model
Ho and McKay described the pseudo second order model which assumes the rate limiting step
might be chemical adsorption with sharing or electron exchange (Ho and MckKay 1999). Ho’s
second-order rate equation has been called pseudo-second-order rate equation to distinguish
kinetic equations based on adsorption capacity from concentration of solution. The non-linear
equation model is:
dqt
2
 k2 .  qe  qt 
dt
(S1.9)
where k2 is the second order rate constant (g mg-1 min-1). The initial sorption rate (
h  k 2 .( qe ) 2 ) can be calculated by using the model parameters. Integrating Eq. (S1.9) with
the conditions qt = 0 at t = 0 and qt =qt at t = t yields;
3
1
1
  k2t
 qt  qe  qe
(S1.10)
If equation is linearized;
t
1
1

 t
2
qt k2 qe qe
(S1.11)
Intraparticle Diffusion
External mass transport and intraparticle diffusion are the main two steps of kinetic throughout
the adsorption. External mass transport is thought to be only rate controlling step for the initial
few minutes of adsorption. Then, initial rapid rate of uptake quickly slows down and
intraparticle diffusion starts becoming rate controlling step. The rate of particle transport
depending on this mechanism is slower than adsorption on the outside surface site of the
adsorbent.
In the model developed by Weber and Morris, the initial rate of intraparticular diffusion is found
by linearization of the curve below (Raji and Pakizeh 2014);
qt  kid .t 0.5
(S1.12)
where kid is the Weber Morris intraparticular diffusion rate constant (mg g-1 min-0.5). If 𝑡 0.5 is
plotted against 𝑞𝑡 , the slope of 𝑘𝑖𝑑 is obtained. When intraparticle diffusion is the rate limiting
step, there should be a straight line with slope 𝑘𝑖𝑑 . For Weber-Morris model, it is significant
for the 𝑞𝑡 − 𝑡 0.5 plot to go through the origin if the intraparticle diffusion is the only ratelimiting step. However, it does not always occur and film diffusion and intraparticle diffusion
may both control the adsorption. Thus, the slope is not equal to zero in such condition.
Intraparticle diffusion constant (D, m2 min-1) is found from the Fick’s law;
  2 D 2t 

 2 


r


F (t )  1  e o  




0.5
(S1.13)
Rearranging equation;
ln 1  F (t )2   
 2 D 2t
ro2
(S1.14)
And also;
4
 C  Ct 
F (t )   i

 Ci  Ce 
(S1.15)
𝑟0 : Particle diameter
Elovich model
Zeldowitsch offered a new kinetic equation for heterogeneous chemical adsorption of gases on
solid surfaces. The nonlinear form of model is (Eq.(S1.16)):
dqt
  .q
  e t 
dt
(S1.16)
where α is initial sorption rate (mg g-1 min-1) and β is the surface activation energy for chemical
sorption (g mg-1). The equation can be simplified by assuming αβt >> t and applying the
boundary conditions (qt = 0 at t = 0 and qt = qt at t = t):
qt 
1

ln  .  
1

ln  t 
(S1.17)
If a plot of qt versus ln(t) yields a linear relationship, the sorption process fits the Elovich
equation. Additionally, for an adsorption system, let t ref be the longest time in adsorption
process and q ref is the solid phase concentration at time t = t ref , equation (S1.17) can be written
as;
qref 
1

ln  .  
1

ln  tref

(S1.18)
Subtracting (S1.17) from (S1.18) and dividing both sides with q ref yields dimensionless
Elovich equation as below;
qt  1

qef  qref .
  t
 ln 
  tref

  1

 1
By defining RE  
 qref 

 t
qt
 RE ln 
 tref
qef


  1

(S1.19)

 as approaching equilibrium factor of Elovich equation,

(S1.20)
If (qt/qref) vs. (t/tref) are drawn, 𝑅𝐸 is found from slope. The curves may vary with 𝑅𝐸 value, as
either flat or steep. According to the curvature of the curves, which depends on 𝑅𝐸 values, four
5
zones are classified: when 𝑅𝐸 > 0.3 (zone I), the curve rises slowly; when 𝑅𝐸 between 0.1 and
0.3 (zone II), the curve rises mildly; when 𝑅𝐸 is between 0.02 and 0.1 (zone III), and the curve
rises rapidly; when the 𝑅𝐸 < 0.02 (zone IV), the curve instantly approaches equilibrium (Wu
et al. 2009).
6
Table S1. Isotherm model parameters by nonlinear method for fluoride adsorption
Dubinin-Radushkevich
Freundlich
Langmuir
Parameters
pH 3.0
pH 5.0
pH 7.0
pH 3.0
pH 3.0
25 °C
25 °C
25 °C
40 °C
55 °C
Unit
b
(L mg-1)
0.136 ± 0.11
0.00513 ± 0.08
0.0013 ± 0.18
0.001 ± 0.01
0.0118 ± 0.03
Q
(mg F- g-1)
7.885 ± 1.2
4.657 ± 0.8
2.494 ± 0.3
7.560 ± 1.5
8.429 ± 1.03
RL
-
0.423
0.951
0.987
0.990
0.894
R2
-
0.937
0.777
0.381
0.423
0.857
χ2
-
6.561
1.558
13.692
7.642
3.543
n
-
1.531 ± 0.18
1.022 ± 0.28
0.172 ± 0.02
0.440 ± 0.03
1.048 ± 0.15
KF
-
3.622 ± 0.4
0.424 ± 0.17
1.9E-05 ± 3E-05
0.161 ± 0.04
1.406 ± 0.36
R2
-
0.960
0.778
0.690
0.977
0.986
χ2
-
1.461
1.623
5.901
0.677
0.544
β
(mol2 kJ-2)
5.6E-09 ± 1.E-09
9.0E-09 ± 2.3E-09
5.9E-08 ± 1.6E-08
2.0E-08 ± 0.5E-08
7.5E-09 ± 3.2E-08
qm
(mol g-1)
0.0055 ± 0.002
0.0047 ± 0.005
0.00031 ± 0.0004
0.0432 ± 0.031
0.0159 ± 0.04
E
(kJ mol-1)
9.449
7.416
2.911
5.00
8.137
R2
-
0.948
0.765
0.689
0.977
0.961
χ2
-
1.928
1.894
5.784
0.642
0.707
7
Fig. S1. Nonlinear isotherm plots of fluoride adsorption onto Z-Al at different pHs
8
Table S2. Kinetic model parameters by linear method for the sorption of F- onto Z-Al
Elovich
Intra-Particular Diffusion
Pseudo Second Order
Order
Pseudo First
Parameter
Unit
25 °C
40 °C
55 °C
qe
mg g-1
0.755 ± 0.03
0.602 ± 0.06
0.289 ± 0.02
k2
min-1
0.0034 ± 0.001
0.0031 ± 0.002
0.0032 ± 0.004
R2
-
0.95
0.90
0.70
qe
mg g-1
1.004 ± 0.03
0.911 ± 0.06
0.7561 ± 0.09
k2
g mg-1 min-1
0.0143 ± 0.011
0.0220 ± 0.06
0.0639 ± 0.03
h
mg g-1 min-1
0.0144
0.0183
0.0365
R2
-
0.99
0.99
0.99
kid-1
mg g-1 min-
0.0410 ± 0.03
0.0404 ± 0.014
0.0228 ± 0.019
R2
0.5
-
0.95
0.98
0.73
kid-2
mg g-1 min-
0.0064 ± 0.004
0.0050 ± 0.001
0.0056 ± 0.003
-
0.92
0.94
0.61
D
nm2 min-1
0.276
0.2646
0.2714
β
g mg-1
7.001 ± 1.2
7.535 ± 1.6
14.399 ± 3.7
α
mg g-1 min-1
0.0748 ± 0.028
0.0825 ± 0.031
2.6536 ± 0.86
RE
-
0.147
0.148
0.093
R2
-
0.96
0.98
0.91
R2
0.5
9
Table S3. Kinetic model parameters by nonlinear method for the sorption of F- onto Z-Al
Elovich
Pseudo Second Order
Order
Pseudo First
Parameter
Unit
25 °C
40 °C
55 °C
qe
mg g-1
0.919 ± 0.04
0.862 ± 0.05
0.639 ± 0.03
k2
min-1
0.009 ± 0.002
0.008 ± 0.001
0.300 ± 0.08
R2
-
0.951
0.972
0.962
qe
mg g-1
0.962 ± 0.04
1.028 ± 0.07
0.661 ± 0.02
k2
g mg-1 min-1
0.019 ± 0.005
0.009 ± 0.003
0.549 ± 0.184
h
mg g-1 min-1
0.0175
0.009
0.239
R2
-
0.966
0.978
0.977
β
g mg-1
15.47 ± 0.94
9.757 ± 0.91
36.578 ± 3.5
α
mg g-1 min-1
8.038 ± 2.62
0.784 ± 0.29
27.75 ± 6.4
RE
-
0.066
0.113
0.041
R2
-
0.993
0.988
0.999
10
(a)
(b)
(c)
(d)
Fig. S2. Linear kinetic modeling of fluoride adsorption onto Z-Al (a) Pseudo-first order; (b)
Pseudo-second order (c) Elovich model (d) Weber-Morris particle diffusion (pH 5.0, T: 25oC)
11
Fig. S3. Nonlinear kinetic modeling of fluoride adsorption onto Z-Al (pH 5.0)
12
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