American Journal of Analytical Chemistry, 2013, 4, 404-419
10.4236/ajac.2013.48051 Published Online August 2013 (http://www.scirp.org/journal/ajac)
Application of Response Surface Methodology for
Optimization of Fluoride Removal Mechanism by Newely
Developed Biomaterial
Ria Bhaumik, Naba Kumar Mondal*, Soumya Chattoraj, Jayanta Kumar Datta
Department of Environmental Science, The University of Burdwan, Burdwan, India
Email: *nkmenvbu@gmail.com
Received May 17, 2013; revised June 17, 2013; accepted July 15, 2013
Copyright © 2013 Ria Bhaumik et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
The adsorption capacities of new biomaterials derived from lemon leaf (Citrus sp.) toward fluoride ions have been ex-
plored by varying different physicochemical parameters such as pH, initial concentration, adsorbent dose, contact time,
stirring rate and temperature. The entire study was done through batch process. Maximum fluoride adsorption of 96.9%
- 98.8% was achieved with an initial concentration of 10 mg/L. Langmuir isotherm model well expressed fluoride ad-
sorption onto LLD-1, LLD-2 and LLD-3. According to correlation coefficient, the fluoride adsorption onto these 3 ad-
sorbents was correlated well with pseudo-second-order kinetic model. From thermodynamic study, the spontaneous
nature and feasibility of the adsorption process with negative enthalpy (H0) value also supported the exothermic nature
were shown. The rate of fluoride adsorption was mathematically described as a function of experimental parameters and
was modeled through Box-Behnken (Response surface methodology). The results showed that the responses of fluoride
adsorption were significantly affected by the quadratic term of pH, initial concentration, contact time and temperature
and the statistical analysis was performed by ANOVA which indicated good correlation of experimental parameters.
Keywords: Lemon Leaf; Fluoride; Adsorption; Langmuir Isotherm; Pseudo-Second-Order Kinetic Model;
Thermodynamic Study; Response Surface Methodology
1. Introduction
Fluorine is one of the strong electronegative elements
and its gaseous form is tremendous powerful oxidizing
agent. It exists in underground water as fluoride ion (F).
However, natural abundance of fluorine ranges from
0.06% to 0.09% by weight in the earth crust [1].
Fluoride is mainly toxic to the human body when it
exceeds the threshold limit of 1.5 mg/L [2]. The excess
intake of fluoride may cause fluorosis (dental and skele-
tal), neurological damage [3] decreasing growth and in-
telligence [4]. There is a tremendous demand for for re-
moval of fluoride from drinking water. In recent years,
various plant materials like coconut shell [4], bone char,
[5] tamarind seed, neem and kikar leaves [6], Barmuda
grass [7] neem charcoal [8], Moringa oleifera seed [9]
have also been used as adsorbents for defluoridation.
There is a gap in knowledge about the carbonized and
chemically treated forms. But classical batch adsorption
technique is unable to provide fine optimization. To
overcome such a problem by taking the help of comput-
erize optimization process called Response Surface
Methodology (RSM), in this study lemon leaf was cho-
sen for fluoride adsorption as dried powder (LLD-1),
carbonized form (LLD-2) and chemically treated (LLD-3)
together to establish new adsorbents for defluoridation.
Due to carbonization high specific surface area occurred
in the adsorbent and due to chemical treatment, more
binding sites appear which are responsible for more fluo-
ride adsorption than naturally occurring materials.
It is well known that consumption of lemon leaf is one
of the most common fruit grown mainly in all tropical
countries, including India. In fresh samples, high levels
of calcium occur in the vacuoles and especially the inner
tangenital walls of epidermal and sub-epidermal cells
near the gap of the abscission zone. Calcium containing
crystals (calcium oxalate) is also abundant in vacuoles of
the cortex parenchyma and leaf blade sides [10]. In 2004,
Storey and Leig explained citrus leaves accumulate large
amounts of calcium in palisade, spongy mesophyll and
crystal containing idioblast cells.
*Corresponding author.
Copyright © 2013 SciRes. AJAC
R. BHAUMIK ET AL. 405
RSM (Response Surface Methodology), an empirical
modeling technique [11], is used to estimate the rela-
tionship between a set of controllable experimental fac-
tors and observed results. RSM consists of 3 major steps:
performing statistically designed experiments, estimating
the coefficients in a mathematical model and predicting
the response and checking the adequacy of the model.
RSM can avoid the limitations of conventional methods
and is commonly used in many fields [12]. In this study a
class of three level complete factorial designs (Box-
Behnken model) was used to determine the show and the
effects of major operating variables on fluoride adsorp-
tion and to find the combination of variables resulting in
maximum fluoride adsorption efficiency. This design was
applied using Design Expert Software 7.0 with six vari-
ables at 3 levels. Four different parameters such as initial
fluoride concentration, pH, contact time and temperature
were selected as the critical variables. A total of 17 ex-
periments have been employed in this work to estimate
the effects of the six main independent variables on fluo-
ride adsorption efficiency.
This present study searches new technology involving
the removal of fluoride from contaminated water due to
adsorption based on binding capacities of calcium (with
fluoride) presented in lemon leaf. The major advantages
of this study fluoride adsorption by lemon leaf powder,
activated carbon and chemically treated lemon leaf pow-
der also include low cost, high efficiency and minimize-
tion of fluoride contaminated water.
2. Adsorbents Development
The adsorbent material named as lemon leaves were ob-
tained from University farm and were washed with dou-
ble distilled water in the laboratory. Then the leaves were
dried at 50˚C for 24 h. One-third leaves were cut and
grinded well by using mortar and pestle and then sieved
to obtain the desired size fractions (250 µm) and used as
adsorbent LLD-1. Another 1/3 rd dried leaves are acti-
vated with 1% HCHO solution and then again dried in
oven maintained temperature range of 120˚C - 140˚C for
a period of 12 hrs. After that the ash material were
ground and sieved [6] and used as adsorbent LLD-2. And
the remaining part of leaves were treated with Ca+2 solu-
tion extracted from eggshell (LLD-3) [13] and used as
adsorbent.
3. Fluoride Adsorption Experiments
The defluoridation studies were conducted for the opti-
mization of various experimental conditions like pH,
initial concentration, adsorbent dose, contact time, stir-
ring rate and temperature through batch process. The
adsorption isotherm, kinetics and thermodynamic study
were also done in this study. All the experiments were
carried out at room temperature. Fluoride ion was meas-
ured with a specific ion-selective electrode (Orion ion
selective) by use of TISAB II solution to maintain pH 5 -
5.5.
The amount of fluoride adsorbed per unit adsorbent
(mg fluoride/g adsorbent) was calculated according to a
mass balance on the fluoride concentration using Equa-
tion (1):
ie
e
CCxV
qm
(1)
The percent removal (%) of fluoride was calculated
using the following equation

Removal(%) 100
ie
e
CC
x
C
(2)
4. Results and Discussions
4.1. Characterization of the Adsorbents
Physico-chemical characterizations of the adsorbents
were shown in Table 1 and these characterizations were
done by using standard methods.
From Table 1 comparing the important characteristics
of LLD-1, LLD-2 and LLD-3, the carbon content of
LLD-2 was higher than others due to increasing in the
ash content.
Table 1 shows that LLD-3 and LLD-2 have the higher
surface area and total pore volume than LLD-1 indicating
the roughness of pore walls and increasing of additional
active sites. Then more active sites are responsible for
adsorption of fluoride ions onto the surface of the LLD-3
and LLD-2 than LLD-1.
Scanning electron microscopy (SEM) (Figure 1) helps
to explain the surface structure of the powder consisting
of the fine particles of irregular shape and size on exter-
nal surface. Figure 1(c) shows SEM images of LLD-3
having particle size of 250 µm, where some deposits of
calcium were observed only in the sample by modifica-
tion of lemon leaf pure dust (LLD-1) (Figure 1).
Table 1. Physico-chemical Characteristics of LLD-1, LLD-2,
LLD-3.
Physical characteristicsLLD-1 LLD-2 LLD-3
pH 6.2 6.7 8.5
EC (mho/cm) 1.5 1.6 1.7
Bulk density (g/cm3) 0.86 0.62 0.84
Solubility in water (%)0.5 0.7 0.8
Solubility in acid (%) 0.6 0.75 0.89
Moisture content (%) 4.2 4.6 4.9
Ash content - 6.12 -
BET Surface area 285.6 824.3 804.5
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406
(a)
(b)
(c)
Figure 1. Scanning Electron Microscopy (SEM) images of
LLD-1 (a), LLD-2 (b), LLD-3 (c).
FTIR measurements (Figure 2) of LLD-1, LLD-2 and
LLD-3 showed the presence of peaks 589 - 607 cm1 are
due to P-O bending vibration, 882 - 1098 cm1 are due to
P-O stretching vibration. The inferred peaks at 2918 -
3628 cm1 are due to adsorption water. An adsorption
bands are shown at 691 - 696 cm1 and at 3571 - 3694
cm1 which are attributed to the OH groups.
Zero point charge (pHZPC) of 3 adsorbents (LLD-1,
LLD-2 and LLD-3) was measured by the solid addition
method [14]. Changes in final pH from initial pH indi-
cate the adsorptive process through dissociation of func-
tional groups as the active sites on the surface of adsorb-
ents. Figure 3 shows the point of zero charge of LLD-1,
LLD-2 and LLD-3 7.0, 6.5 and 6.2 respectively. At low
pH, the surface of the adsorbent is positive and reaction
predominates and at higher pH the surface of adsorbent is
negative. Here, the pH of the fluoride solution becomes
lower than point charge, the association of fluoride ions
with the adsorbent surface easily takes place and this
study the surface of LLD-3 is more effective than LLD-2
and LLD-1.
4.2. Effect of pH
The pH of the fluoride solution varied from 2 to 10 and
the pH was adjusted by adding 0.1 (N) NaOH and 0.1 (N)
HNO3 soultion. Figures 4(a) and (b) show that both ad-
sorption and fluoride uptake capacity are maximum at
pH 6.0. Here, it is also shown that fluoride ions are more
attached to the surface of LLD-3 due to chemically
treated with Ca+2 solution (extracted from eggshell) at pH
lower than pH zpc. pH played a vital role in fluoride ad-
sorption onto biosorbent [15]. However, many research-
ers [16,17] reported that biosorption of fluoride depends
on the functional groups on the adsorbent and their ionic
states. There are several studies concluded that biomass
based biosorbent have several functional groups (such as
amines, carbaryl, thiol, sulfhydryl, alcohol, phenol and
phosphate groups) [18,19]. Study results reveled that
highest fluoride adsorption occur at acidic pH (6.0) for
all adsorbents. These sorption characteristics could be
attributed to the ionic sorption with cationic (H+) ad-
sorbent surface [17]. Under acidic condition the surface
of the adsorbent transformed to a positively charged
which facilitated the sorption of fluoride ion through
anion exchange [18]. However, the percentage of fluo-
ride removal inhibited at higher pH, this might be attrib-
uted to the increase of hydroxyl ions leading to formation
of aqua complexes.
4.3. Effect of Initial Concentration and
Adsorption Isotherm Models
In the batch adsorption study after selection of pH the
initial concentration (1.5, 3.0, 5.0, 10.0, 15.0 mg/L) is
varied. Adsorption of fluoride (Figures 5(a) and (b))
increases up to initial concentration 10.0 mg/L (for all
the three adsorbents) whereas at higher concentration
adsorption is decreased. Lower concentration causes
more interaction of fluoride ions with the binding sites
and at higher concentration increase in the number of
ions are responsible for competition in availability of
binding sites in the adsorbent surface [20].
Moreover as the total available adsorption sites were
limited, they became saturated at a higher concentration
[14]. Similar trend has been reported for fluoride removal
by using neem charcoal and eggshell dust [21,22]. The
results of Figure 5 demonstrate that the amount of ad-
sorbed fluoride increased with the increase of initial
fluoride concentrations. The increase of fluoride
Copyright © 2013 SciRes. AJAC
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Copyright © 2013 SciRes. AJAC
407
(a)
(b)
(c)
Figure 2. FTIR sprectrum of a) LLD-1, b) LLD-2 and c) LLD-3 before fluoride adsorpiton.
R. BHAUMIK ET AL.
408
246810
-3
-2
-1
0
1
2
3
(p
H
i
-p
H
f
)
p
H
LLD-1
LLD-2
LLD-3
Figure 3. Zero point charge curve of LLD-1, LLD-2 and LLD-3.
2
4
6
8
10
0
20
40
60
80
100
B
C
D
LLD-1
LLD-2
LLD-3
% of fluoride adsorpiton
p
H
246810
60
62
64
66
68
70
72
74
76
78
80
82
Fluoride uptake capacity (mg/g)
p
H
LLD-1
LLD-2
LLD-3
(a) (b)
Figure 4. (a) Effect of pH on % of fluoride adsorption. (Initial fluoride concentration of 10 ppm; adsorbent dose 0.05 g/L of
solution; contact time of 60 min, stirring rate 550 rpm, temperature 303 K). (b) Effect of pH on fluoride uptake capacity. (Ini-
tial fluoride concentration of 10 ppm; adsorbent dose 0.05 g/L of solution; contact time of 60 min, stirring rate 550 rpm, tem-
perature 303 K).
concentration is the main driving force behind overcom-
ing all mass transfer resistance of the fluoride, between
the aqueous and solid phases [18]. This phenomena lead
to increase the equilibrium sorption, until whole adsorb-
ent saturation was achieved [14]. In fluoride adsorption
isotherm study the equilibrium data isotherm analysis
onto LLD-1, LLD-2 and LLD-3 at pH 6.0 and 303 K
temperature were analyzed using Langmuir, Freundlich,
D-R and Tempkin isotherms. The isotherm parameters
with their linear form are listed in Table 2. The maxi-
mum adsorption capacity of fluoride (qmax, from Lang-
muir model) onto LLD-3 surface is higher (38.46 mg/g)
than LLD-2 and LLD-1 which correspond to complete
monolayer coverage. The value of RL is also more in
LLD-3 than other indicating better adsorbent. According
o Freundlich isotherm the value of “n” is high in LLD-2 t
Copyright © 2013 SciRes. AJAC
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0
2
4
6
8
10
12
14
16
50
60
70
80
90
100
B
C
D
LLD-1
LLD-2
LLD-3
% of fluoride adsorption
Initial concentration (mg/L
)
0 2 4 6 810121416
0
20
40
60
80
100
120
140
160
Fluoride uptake capacity (mg/g)
Initial concentration (mg/g)
LLD-1
LLD-2
LLD-3
(a) (b)
Figure 5. (a) Effect of initial concentration on % of fluoride adsorption (pH 6.0; adsorbent dose 0.05 g/L of solution; contact
time of 60 min, stirring rate 550 rpm, temperature 303 K). (b) Effect of initial concentration on fluoride uptake capacity. (pH
6.0; adsorbent dose 0.05 g/L of solution; contact time of 60 min, stirring rate 550 rpm, temperature 303 K).
Table 2. Parameters of isotherm models of fluoride adsorption onto LLD-1, LLD-2 and LLD-3.
Isotherm models LLD-1 LLD-2 LLD-3
KL = 0.072 KL = 0.204 KL = 0.083
RL = 0.93 RL = 0.83 RL = 0.92
qm = 7.63 qm = 27.03 qm = 38.46
Langmuir
R2 = 0.84 R2 = 0.98 R2 = 0.99
Kf = 0.45 Kf = 0.035 Kf = 0.036
n = 1.72 n = 6.06 n = 6.53 Freundlich
R2 = 0.73 R2 = 0.96 R2 = 0.96
qmax = 42.5 qmax = 27.41 qmax = 27.03
KDR = 0.123 KDR = 0.01 KDR = 0.007
ES = 2.85 ES = 10 ES = 11.95
D-R
R2 = 0.94 R2 = 0.92 R2 = 0.92
B1 = 5.18 B1 = 5.44 B1 = 4.79
KT = 9.43 KT = 1.71 KT = 1.81 Tempkin
R2 = 0.76 R2 = 0.89 R2 = 0.89
and LLD-3, which also indicates both (6.06 and 6.53
respectively) adsorbents are more effective in fluoride
adsorption process than LLD-1. The maximum adsorpi-
ton capacity (qmax) obtained from D-R isotherm of LLD-1,
LLD-2 and LLD-3 are 4.25, 27.41, 27.03 respectively
lower than the value of adsorption capacity obtained
from Langmuir isotherm. D-R isotherm gives β constant,
and idea about the mean free energy (Es, kJ·mol1) of
adsorbate when it is transferred to the surface of the solid
from infinity in the solution. The Es value of LLD-1,
LLD-2 and LLD-3 are 2.85, 10 and 11.95 directing the
physical adsorption mechanism of fluoride onto these
adsorbents [22]. Tempkin isotherm constant are shown in
Table 2. From the isotherm analysis, it is clear that ad-
sorption nature of fluoride onto LLD-1, LLD-2 and
LLD-3 adsorbents best fitted to Langmuir and D-R iso-
Copyright © 2013 SciRes. AJAC
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410
therm model which suggests uniform binding energy on
the whole surface of the adsorbents. These results also
signify that fluoride ions were adsorbed by a monolayer
formation.
4.4. Effect of Adsorbent Dose
At lower adsorbent dose, Figure 6(a) shows in case of
LLD-1, LLd-2 and LLD-3 percentage of fluoride adsorp-
tion is low but fluoride uptake capacity is high (Figure
6(b)). The B-Sp line as flat suggesting the highest fluo-
ride adsorption occurs at 0.1 g/L and the followings re-
mains constant. This is probably due to the overlapping
of active sites at higher dosage and subsequently reduc-
ing the net surface area [23].
4.5. Effect of Contact Time
Figures 7(a) and (b) indicate the variations of fluoride
adsorption by LLD-1, LLd-2 and LLD-3 adsorbents with
respect to contact time. It has been revealed form this
study that percentage of fluoride adsorption and adsorp-
tion capacity both increased due to increasing of contact
time and the curve gets equilibrium after 120 minutes. The
removal efficiency of fluoride was increased which in-
creasing time is probably due to participation of specific
functional groups and active surface sites on adsorbents
surfaces [17,24]. Similar findings were also reported by
[24] for fluoride removal on biomass of Spirogyra sp.
However, removal decreased after 120 minutes indicat-
ing the possible monolayer of fluoride ions on the outer
surface, pores of both the adsorbents and pore diffusion
onto inner surface of adsorbent particles [14].
4.6. Effect of Stirring Rate
The stirring rate in adsorption study is an essential pa-
rameter which can enhance a certain turbulance insuring
a good contact between the adsorbate and adsorbent [24].
To determine the effect of stirring rate 250 rpm to 850
rpm speeds were chosen. Figures 8(a) and (b) show
fluoride adsorption occurred rapidly in the first stirring
rate from 250 rpm and at 550 rpm the fluoride adsorption
rate and uptake capacity both are highest. Then beyond
550 rpm both remain more or less constant in case of
these adsorbents due to higher speeds better contact be-
tween the fluoride ions and adsorbent surface is possible.
In this study at 550 rpm, LLD-3 shows better fluoride
adsorption rate (98.8%) and uptake capacity (41.4 mg/g)
than other.
4.7. Effect of Temperature and
Thermodynamic Study
The influence of temperature in adsorption process is
very important because increasing the temperature in-
duces a decrease in the adsorption capacity of fluoride on
the adsorbent surface. Figures 9(a) and (b) shows re-
ducing percentage of both fluoride adsorption and adsorp-
tion capacity due to increase of temperature beyond 313
K to 333 K. From Table 3 the values of ΔG0 (Gibbs free
energy of adsorption, kJ·mol1) at different temperatures,
indicates the feasibility of the process and the spontane-
ous nature of fluoride ions onto adsorbents [22]. In case
of tested adsorbents, during values of ΔG0 due to in-
creasing temperatures suggests the lower temperature
makes the adsorption easier [22]. The value of ΔH0
0.0
0.1
0.2
0.3
0.4
0.5 80
82
84
86
88
90
92
94
96
98
100
B
C
D
LLD-1
LLD-2
LLD-3
% of fluoride adsorption
Adsorbent dose (g/L)
0.0 0.1 0.2 0.3 0.4 0.5
0
50
100
150
200
250
300
350
400
% of fluoride adsorption
Adsorbent dose (g/L)
LLD-1
LLD-2
LLD-3
Figure 6. (a) Effect of adsorbent dose (g/L) on % of fluoride adsorption. (Initial fluoride concentration of 10 ppm; pH 6.0;
contact time of 60 min, stirring rate 550 rpm, temperature 303 K). (b) Effect of adsorbent dose (g/L) on fluoride uptake ca-
pacity. (Initial fluoride concentration of 10 ppm; pH 6.0; contact time of 60 min, stirring rate 550 rpm, temperature 303 K).
Copyright © 2013 SciRes. AJAC
R. BHAUMIK ET AL. 411
0
50
100
150
200
250
20
30
40
50
60
70
80
90
100
B
C
D
LLD-1
LLD-2
LLD-3
% of fluoride adsorption
C
ontact time (minute
)
050100 150 200 250
5
10
15
20
25
30
35
40
45
Fluoride uptake capacity (mg/g)
Contact time (minute)
LLD-1
LLD-2
LLD-3
Figure 7. (a) Effect of contact time (minute) on % of fluoride adsorption. (Initial fluoride concentration of 10 ppm; pH 6.0;
adsorbent dose 0.1 g/L; stirring rate 550 rpm, temperature 303 K). (b) Effect of contact time (minute) on fluoride uptake ca-
pacity. (Initial fluoride concentration of 10 ppm; pH 6.0; adsorbent dose 0.1 g/L; stirring rate 120 rpm, temperature 303 K).
200
300
400
500
600
700
800
900 40
50
60
70
80
90
100
B
C
D
LLD-1
LLD-2
LLD-3
%
of fluoride adsorpiton
Stirring rate (rpm
200 300 400 500600 700 800 900
15
20
25
30
35
40
Fluoride uptake capacity (mg/g)
Stirring rate (rpm)
LLD-1
LLD-2
LLD-3
Figure 8. (a) Effect of stirring rate (rpm) on % of fluoride adsorption (Initial fluoride concentration of 10 ppm; pH 6.0; ad-
sorbent dose 0.1 g/L; contact time 180 min; temperature 303 K). (b) Effect of stirring rate (rpm) on fluoride uptake capacity.
(Initial fluoride concentration of 10 ppm; pH 6.0; adsorbent dose 0.1 g/L; contact time 180 min; temperature 303 K).
(enthalpy change of adsorption, kJ·mol1) and ΔS0 (en-
tropy change of adsorption, kJ·mol1) are also shown in
Table 3, which indicate fluoride adsorption process onto
LLD-1, LLD-2 and LLD-3 are explained by the exo-
thermic in nature and the negative values of ΔS0 indicate
that during the fluoride adsorption the solid-solution in-
terface researches a more organized structure (decrease
of randomness).
4.8. Adsorption Kinetics Study
The experimental parameters (pH, initial concentration,
adsorbent dose, contact time, stirring rate and tempera-
ture) are responsible for their potential impact on per-
centage of fluoride adsorption and uptake capacity.
These parameters also greatly influence on the external
surface available for fluoride ion binding, diffusion
properties and concentration gradient. Table 4 shows the
values of pseudo-first, pseudo-second order kinetic con-
stants and intraparticle diffusion model. Comparing these
models, the fluoride adsorption is well fitted to the
pseudo-second order kinetic model and the adsorption
rate (h, mg·g1·min1) was calculated shown in Table 4.
Copyright © 2013 SciRes. AJAC
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412
310
315
320
325
330
335
340
345 20
30
40
50
60
70
80
90
100
B
C
D
LLD-1
LLD-2
LLD-3
% of fluoride adsroption
Temperature (K)
310 315 320 325 330 335 340 345
20
25
30
35
40
45
Fluoride uptake capacity (mg/g)
Temperature (K)
LLD-1
LLD-2
LLD-3
Figure 9. (a) Effect of temperature (K) on % of fluoride adsorption. (Initial fluoride concentration of 10 ppm; pH 6.0; ad-
sorbent dose 0.1 g/L; contact time 180 min; stirring rate 650 rpm). (b) Effect of temperature (K) on fluoride uptake capacity.
(Initial fluoride concentration of 10 ppm; pH 6.0; adsorbent dose 0.1 g/L; contact time 180 min; stirring rate 650 rpm).
Table 3. Thermodynamic parameters of fluoride adsorption onto LLD-1, LLD-2 and LLD-3.
Thermodynamic parameters Temperature (K) LLD-1 LLD-2 LLD-3
303 7.792 9.321 10.01
313 5.332 6.191 6.41
323 2.872 3.061 2.81
G0
333 0.412 0.069 0.79
H0 82.33 104.16 119.09
S0 0.246 0.313 0.36
The value of h is high in LLD-3, LLD-2 and LLD-1 re-
spectively which indicates all tested adsorbents are effec-
tive in fluoride adsorption.
4.9. Box-Behnken Statistical Analysis
In the present study, Box Behnken design was used to
predict the fluoride adsorption rate. The complete design
model was composed of 17 experimental runs with three
replicates at the center points. The significant of the
model was justified by the ANOVA. The ANOVA of
fluoride adsorption rate is given in Tables 5-7. The
model F-value is the ratio of mean square for the indi-
vidual term to the mean square for the residual. The Prob
> F value is the probability of F-statistics value and is
used to test the null hypothesis. The parameters having
an F-statistics probability value less than 0.05 are said to
be significant. The pH of the solution, adsorbent dose,
contact time, initial fluoride concentration, stirring rate
and temperature are very effective in fluoride adsorption.
Among these output variables, pH of the solution, initial
fluoride concentration, contact time and temperature had
a significant effect on fluoride adsorption. Once the op-
timization was ever the experimental and model pre-
dicted values of the response variables were compared.
The plot between experimental (actual) and predicted
values of fluoride adsorption rate is shown in Figures
10(a), (b) and (c). A good correlation between input and
output variables are also shown by the model.
4.10. Effects of Experimental Parameters on
Fluoride Adsorption
The effects of different experimental parameters such as
solution pH, initial fluoride concentration, contact time
and temperature on the fluoride adsorption is shown in
Figures 11 (a)-(i). The fluoride adsorption capacity was
increased with increase in initial fluoride concentration,
contact time and decreased in solution pH and tempera-
ture. The adsorption of fluoride adsorption favors com-
paratively at low pH and room temperature. Tables 5-7
how the model F-value of LLD-1, LLD-2 and s
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Table 4. Parameters of kinetic models of fluoride adsorption onto LLD-1, LLD-2 and LLD-3.
Kinetic models LLD-1 LLD-2 LLD-3
qe1 = 2.33 qe1 = 1.01 qe1 = 1.14
Kad1 = 0.009 Kad1 =0.01 Kad1 = 0.014 Pseudo-first-order
R2 = 0.25 R2 = 0.8 R2 = 0.41
qe2 = 47.62 qe2 = 45.45 qe2 = 48.91
Kad2 = 0.07 Kad2 = 0.001 Kad2 = 0.002 Pseudo-second-order
R2 = 0.99 R2 = 0.99 R2 = 0.99
Kit = 2.03 Kit = 1.13 Kit = 0.691
I = 4.07 I = 25.44 I = 31.92
Intra-particle diffusion
R2 = 0.97 R2 = 0.79 R2 = 0.72
Table 5. Analysis of variance for fluoride adsorption rate onto LLD-1. ANOVA for response surface Quadratic Model Analy-
sis of variance table [Partial sum of square s-Type III].
p-value source
prob > F Sum of Squares df Mean Square F
Value
P
Probability
Model
<0.0001 14578.51 9 1619.83 65.45 <0.0001
A-initial
concentration 2614.10 1 2614.10 105.62 <0.0001
0.0001 B-pH 3110.35 1 3110.35 125.67 <0.0001
C-contact time
0.0001 1404.50 1 1404.50 56.75 <0.0001
AB
0.0001 1482.25 1 1482.25 59.89 <0.0001
AC
0.0541 132.25 1 132.25 5.34 <0.0541
BC
0.0727 110.25 1 110.25 4.45 <0.0727
A2
0.0001 1615.50 1 1615.5 65.27
B2
0.0001 2556.64 1 2556.64 103.29
C2
0.0002 1259.03 1 1259.03 50.87
Residual 173.26 7 24.75
Lack of fit
0.1999 171.26 6 28.54 14.27 <0.1999
Pure error 2.00 1 2.00
Cor Total 14751.76 16
Std. Dev.
0.9883 4.98 R-Squared
Mean
0.9732 52.88 Adj R-Squared
C.V. %
0.9174 9.41 Pred R-Squared
Press 1219.09 Adeq Precision 21.296
Copyright © 2013 SciRes. AJAC
R. BHAUMIK ET AL.
414
Table 6. Analysis of variance for fluoride adsorption rate onto LLD-2.
p-value source prob > F Sum of Squares df Mean Square F Value P Probability
Model 6387.32 9 709.70 248.87 <0.0001
A-initial concentration
<0.0001 668.52 1 668.52 243.43 <0.0001
B-contact time
<0.0001 1891.13 1 1891.31 663.15 <0.0001
C-temp
<0.0001 1081.13 1 1081.13 379.11 <0.0001
AB 2.25 1 2.25 0.79 0.4039
AC 56.25 1 56.25 19.72 0.0030
BC 441.00 1 441.00 154.64 <0.0001
A2 30.81 1 30.81 10.80 0.0134
C2 242.37 1 242.37 84.99 <0.0001
Residual 19.96 7 2.85
Lack of fit 0.1999 71.20 4 4.30 4.67 0.1182
Pure error 2.76 3 4.30
Cor Total 6407.28 16
Std. Dev. 0.9969 4.98 R-Squared
Mean 0.9929 57.46 Adj R-Squared
C.V. % 0.9641 2.94 Pred R-Squared
Press 230.16 Adeq Precision 46.152
Table 7. Analysis of variance for fluoride adsorption rate onto LLD-3.
p-value source prob > F Sum of Squares df Mean Square F Value P Probability
Model
<0.0001 2784.73 14 198.91 209.93 <0.0001
A-initial concentration
<0.0001 802.32 1 802.32 846.76 <0.0001
B-pH
<0.0001 111.93 1 111.93 118.13 <0.0001
C-temp
<0.0001
D-contact time
<0.0001
247.45
101.12
1
1
247.45
101.12
261.16
106.72
<0.0001
<0.0001
AB 0.0002 25.00 1 25.00 26.38
AC 0.0591 4 1 4 4.22 0.0591
AD
0.0051
BC
0.1637
BD
<0.0001
CD
0.3217
10.42
2.05
210.25
1.00
1
1
1
1
10.42
2.05
210.25
1.00
10.99
2.16
221.9
1.06
0.0051
0.1637
<0.0001
0.3217
A2
<0.0001
B2
<0.0001
167.86
443.06
1
1
167.86
443.06
177.16
464.00
<0.0001
<0.0001
C2
<0.0001
D2
<0.0001
42.77
49.50
1
1
42.77
49.50
45.14
52.24
< 0.0001
< 0.0001
Residual 13.27 14 0.95
Lack of fit 0.0412 12.52 10 1.25 6.67 0.0412
Pure error 0.75 4 0.19
Cor Total 2798.00 28
Std. Dev. 0.9953 0.97 R-Squared 0.9953
Mean 0.9905 75.00 Adj R-Squared 0.9905
C.V. % 0.9695 1.30 Pred R-Squared 0.9695
Press 85.23 Adeq Precision 50.456
Copyright © 2013 SciRes. AJAC
R. BHAUMIK ET AL. 415
Design-Expert® Software
removal
C olor point s by value of
removal:
92
13
A
ctual
Predicted
Predicted vs. Actual
94.00
73.25
52.50
31.75
11.00
11.76 32.08 52.39 72.71 93.02
(a)
Design-Expert® Software
Removal
Color points by value of
Removal:
92
56
2
3
Predicted vs. Actual
93.00
83.75
Predicte
d
74.50
65.25
56.00
56.00 65.0474.07 83.11 92.14
Actua
l
(b)
Copyright © 2013 SciRes. AJAC
R. BHAUMIK ET AL.
Copyright © 2013 SciRes. AJAC
416
Design-Expert® Software
Removal
Color points by value of
Removal:
92
56
2
3
Predicted vs. Actual
93.00
83.75
Predicte
d
74.50
65.25
56.00
56.0065.04 74.07 83.11 92.14
Actua
l
(c)
Figure 10. The plot of predicted versus actual values for fluoride adsorption rate onto (a) LLD-1, (b) LLD-2, (c) LLD-3.
LLd-3 are 65.45, 248.87 and 209.93 respectively which
imply the model is significant. There is only 0.01% of
chance that a “model F value” this large could occur due
to noise. The values of “prob > F” less than 0.05 indicate
model terms are significant, where values greater than
0.1 direct the model terms are not significant.
4.11. Optimization of Process Variables
The numerical optimization was applied to optimize the
fluoride adsorption process and the optimum values of
various parameters are provided in Table 8. A desirabil-
ity value of 1.0 was obtained after optimizing the process
parameters.
5. Conclusion
This work investigated the adsorption of fluoride onto
LLD-1, LLD-2 and LLD-3. Experiments were made as a
function of different adsorption parameters (pH, initial
fluoride concentration, adsorbent dose, contact time and
stirring rate and temperature). Response surface method-
ology by the Box-Behnken model was used to examine
the role of three process factors on fluoride removal. It
was shown that a second-order polynomial regression
model could properly interpret the experimental data
with coefficient of determination (R2) value of 0.9969
and an F value of 248.87. The simultaneous optimization
of the multiresponse system by desirability function in-
dicated that 92.74%, 92.52%, 92.24% adsorption of fluo-
ride can be possible by using the optimal conditions of
pH, initial fluoride concentration, contact time and tem-
perature. The Langmuir, Freundlich, D-R and Tempkin
isotherm models were used for the description of fluoride
adsorption phenomenon. The data were good agreement
with both Langmuir and D-R isotherms. The kinetics of
fluoride adsorption was controlled by pseudo-second
order kinetic model for all the tested adsorbents. How-
ever, LLD-1 also showed the agreement with in-
tra-particle diffusion model. The adsorptions of fluoride
onto LLD-1, LLD-2 and LLD-3 were found to be exo-
thermic in nature. This study shows that the Box-
Behnken model is suitable to optimize the experiments
for fluoride removal through adsorption.
6. Acknowledgements
Authors express their sincere thanks to Professor J K
R. BHAUMIK ET AL. 417
Copyright © 2013 SciRes. AJAC
LLD-1 LLD-2 LLD-3
Design-Expert® Sof tware
removal
Des ign Points
92
13
X1 = A: init ial conc ent ration
X2 = B: p H
Ac t ual F act or
C: c ont ac t t im e = 125. 00
0.26 2.02 3.77 5.53 7.29
2.00
4.00
6.00
8.00
10.00
removal
A
: initial concentration
B: pH
28.6203 28. 6203
42.0374
42.0374
55.4546
68.8718
82.2889
22
(a)
Des ign-Ex pert ® Software
removal
Des ign Points
85
24
X1 = A: ini t ial c o n
X2 = B: contact time
Act ual Fac t or
C: temp = 328.00
0.26 2.02 3.77 5.53 7.29
10.00
67.50
125.00
182.50
240.00
removal
A: initial con
B: contact tim
e
34.5681 43.7767
52.9852
62.1937
62.1937
71.4022
4444
(d)
Des ign -Ex pert ® Soft ware
Removal
Des i gn Point s
92
56
X1 = A: init ial c onc ent ra ti on
X2 = B: PH
Act ual Fac t or s
C: temp = 328.00
D: c ont ac t t im e = 125. 00
0.26 2.02 3.77 5.53 7.29
2.00
4.00
6.00
8.00
10.00
Removal
A
: initial concentration
B: PH
61.5576
66.2938
66.2938
71.0301
75.7663
80.5025
4444
(g)
Des ign-Ex pert ® Soft ware
remov al
Des ign Points
92
13
X1 = A: initial c oncent ration
X2 = C: contact time
Act ual Fac tor
B: pH = 6. 00
0.26 2.023.77 5.537.29
10.00
67.50
125.00
182.50
240.00 removal
A: initial concentration
C: contact tim
e
32.9334
44.3746 55.81 58
67.2571
78.6983
(b)
Des ign-Expert® Software
remov al
Design Points
85
24
X1 = A: initial c on
X2 = C: temp
Actual Factor
B: c ontac t t ime = 125.00
0.26 2.02 3.775.53 7.29
313.00
320.50
328.00
335.50
343.00
removal
A: initial con
C: tem
p
51.3637
58.1178
64.8719
71.626
78.3801
4444
(e)
Des ign-Expert ® S oftware
Remov al
Des ign Point s
92
56
X1 = A: init ial c oncent ration
X2 = C: temp
Act ual Fact ors
B: PH = 6.00
D: cont act tim e = 125. 00
0.26 2.02 3.77 5.53 7.29
313.00
320.50
328.00
335.50
343.00
Removal
A
: initial concentration
C: tem
p
62.5822
67.2605
71.9387 76.617
81.2952
4444
(h)
Des ign-Expert ® Soft ware
remov al
Design Point s
92
13
X1 = B : pH
X2 = C: contact time
Act ual F ac t or
A: init ial conc ent ration = 3. 77
2.00 4.00 6.008.00 10.00
10.00
67.50
125.00
182.50
240.00
removal
B: pH
C: contact ti m
e
24.8296
37.8949
50.9602
50.9602
64.0255
77.0908
22
(c)
Design-Expert® Soft ware
removal
De s ign Points
85
24
X1 = B: contact time
X2 = C: temp
Actu al F ac t or
A: init ial c on = 3. 77
10.00 67.50 125.00 182.50 240.00
313.00
320.50
328.00
335.50
343.00
removal
B: contact time
C: t em
p
36.5553
45.9826
45.9826
55.4098
64.8371
74.2644
4444
(f)
Design-Expert® Software
Removal
Des i gn Point s
92
56
X1 = A: init ial c onc ent rat ion
X2 = D: c ont ac t t im e
Actual Factors
B: PH = 6. 00
C: t em p = 328. 00
0.26 2.02 3.77 5.53 7.29
10.00
67.50
125.00
182.50
240.00
Removal
A
: initial concentration
D: contact ti m
e
70.7102 74.996979.2836
83.5703
87.857
22
4444
(i)
Figure 11. The effects of (a) and (g) solution pH and initial fluoride concentration, (b) and (d) and (i) contact time and initial
fluoride concentration, (c) contact time and pH, (e) and (h)temperature and initial fluoride concentration, (f) temperature
and contact time.
Table 8. The optimum values of the experimental parameters.
Parameters LLD-1 LLD-2 LLD-3
pH 6.15 - 7.34
Contact time (min) 143.73 45.97 203.47
Initial concentration (mg/L) 6.03 2.94 6.66
Temperature (K) - 328.09 336.10
Adsorption 92.74 92.52 92.24
R. BHAUMIK ET AL.
418
Datta for his encouragement and active support of doing
such laborious work. Authors also like to express their
gratitude.
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