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1. Synthesis of nickel sulfide nanoparticles loaded on activated carbon as
a novel adsorbent for the competitive removal of Methylene blue and
Safranin-O
M. Ghaedi a,⇑
, M. Pakniat b
, Z. Mahmoudi b
, S. Hajati c,⇑
, R. Sahraei d
, A. Daneshfar d
a
Chemistry Department, Yasouj University, Yasouj 75918-74831, Iran
b
Chemistry Department, Faculty of Science, Persian Gulf University, Bushehr, Iran
c
Department of Physics, Yasouj University, Yasouj 75918-74831, Iran
d
Chemistry Department, Ilam University, Ilam, Iran
h i g h l i g h t s
Synthesis of NiS nanoparticle-loaded
activated carbon as a novel adsorbent.
Synthesis of the adsorbent with high
surface area of 1018 m2
/g according
BET.
Efficient and rapid removal of dyes in
binary solutions within 5 min.
Response optimization by using
response surface methodology.
g r a p h i c a l a b s t r a c t
a r t i c l e i n f o
Article history:
Received 31 October 2013
Received in revised form 3 December 2013
Accepted 11 December 2013
Available online 21 December 2013
Keywords:
Adsorption
Binary mixture
Methylene blue
NiS nanoparticle loaded activated carbon
Safranin-O
a b s t r a c t
Nickel sulfide nanoparticle-loaded activated carbon (NiS-NP-AC) were synthesized as a novel adsorbent
for simultaneous and rapid adsorption of Methylene blue (MB) and Safranin-O (SO), as most together
compounds in wastewater. NiS-NP-AC was characterized using different techniques such as UV–visible,
Fourier transform infrared spectroscopy (FTIR), energy-dispersive X-ray spectroscopy (EDX), X-ray dif-
fraction (XRD), field emission scanning electron microscopy (FESEM) and Brunauer–Emmett–Teller
(BET). The surface area of the adsorbent was found to be very high (1018 m2
/g according BET). By using
central composite design (CCD), the effects of variables such as pH, adsorbent dosage, MB concentration,
SO concentration and contact time on binary dyes removal were examined and optimized values were
found to be 8.1, 0.022 g, 17.8 mg/L, and 5 mg/L and 5.46 min, respectively. The very short time required
for the dyes removal makes this novel adsorbent as a promising tool for wastewater treatment applica-
tions.
Different models were applied to analyze experimental isotherm data. Modified-extended Langmuir
model showed good fit to equilibrium data with maximum adsorption capacity at 0.022 g of adsorbent.
An empirical extension of competitive modified-extended Langmuir model was proposed to predict the
simultaneous adsorption behavior of MB and SO. Kinetic models were applied to fit the experimental data
at various adsorbent dosages and initial dyes concentrations. It was seen that pseudo-second-order equa-
tion is suitable to fit the experimental data. Individual removal of each dye was also studied.
Ó 2013 Elsevier B.V. All rights reserved.
1386-1425/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.saa.2013.12.083
⇑ Corresponding authors. Tel./fax: +98 7412223048 (M. Ghaedi).
E-mail addresses: m_ghaedi@mail.yu.ac.ir (M. Ghaedi), Hajati@mail.yu.ac.ir
(S. Hajati).
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 123 (2014) 402–409
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and
Biomolecular Spectroscopy
journal homepage: www.elsevier.com/locate/saa

2. Introduction
Dyes contaminations present in aqueous media generate serious
environmental hazards. Dyes enter to the versatile ecosystem from
industrial effluents of the paper, cosmetics, plastics, rubber, print-
ing, pharmaceutical, leather, and textile industries [1,2]. The dyes
generally have complex aromatic structure and thus most of them
are highly resistant to breakdown by chemical, physical, and bio-
logical treatments [3,4]. The dyes are well-known water pollutants
that very small amount of those is toxic to aquatic life. The entrance
of large amount of dyes, organics, bleaches or salts to ecosystem
greatly influences the physicochemical properties of freshwater
[3–5]. Among these techniques, the adsorption process is good can-
didate for the removal of organic compounds and dyes from waste-
water [5–7]. Particularly, among various dyes classification, the
highest toxicity is associated with the cationic dyes such as Methy-
lene blue (MB) and Safranin-O (known as Basic Red 2). Many
researchers have utilized adsorption technique for the removal of
toxic dyes from wastewater by using various adsorbents like ami-
no-functionalized acrylamide–maleic acid hydrogels [8], bottom
ash, deoiled-soya [9], Fe-zeolitic tuff [10], Brazil nut shells [11],
cross-linked chitosan [12], banana pith [13,14] coir pith [15,16], ba-
gasse pith [17], corn cob [18], sawdust [19] and apple pomace [20].
Nanomaterials, which benefit from unique advantages, indicate
special physical and chemical properties. The size, surface struc-
ture and interparticle interaction of nanomaterials (Thoroughly
different from bulk value) have positive correlation with their dis-
tinguished properties and their potential applications. Nanoparti-
cle-based materials were used to increase the surface area and
the number of reactive atoms of the adsorbent for large-scale
and high dye removal percentage in short time via adsorption.
Metal sulfides are known with interesting electronic properties
and several technological applications [21]. Among metal sulfides
family, nickel sulfide has attracted much attention as a transforma-
tion-toughening agent for materials used in semiconductor appli-
cations [22], catalysts [23], and cathode materials for
rechargeable lithium batteries [24]. Composition of nickel-based
nanoparticles depends on conditions such as pH, concentration of
reagent, temperature and reaction time. General procedures for
the preparation of nickel sulfide are classified as high-temperature
solid-state reaction and vapor phase reaction [25,26], hydrother-
mal [27], and solvothermal [28].
Great challenge remains to develop a facile and green method
for creating NiS nanoparticles from simple precursor. A major
interest now is the development of organometallic or inorganic
compounds for the preparation of nanoparticles. In this research,
NiS nanoparticles were prepared at the best conditions and then
the properties of this nanomaterial were characterized using dif-
ferent techniques.
Multivariate approaches are frequently used to optimize the
variables by significant reduction in the number of required exper-
iments. This procedure permits to obtain optimum conditions and
to consume less reagent at least laboratory work. These procedures
are faster and cheaper than traditional univariate approaches.
These methods permit simultaneous investigation on the effect of
factors. The development of mathematical models allows investiga-
tion on the relevance and statistical significance of factors as well as
evaluation of their interaction. Multivariate designs are based on
factors and responses (qualitative or quantitative). Optimum oper-
ation conditions are obtained by using complex experimental de-
signs such as Doehlert matrix (DM), Central Composite design
(CCD) or Box–Behnken design (BBD) [29–31]. CCD is one of the most
accepted designs under response surface methodology (RSM). In
this work, CCD was used to study the individual and synergetic ef-
fect of factors such as contact time (min), adsorbent dosage (g), pH,
MB concentration (mg/L) and SO concentration (mg/L) on the
removal percentages of Methylene blue (MB) and Safranin-O as
responses. The dyes structures were presented in Fig. S1.
Nickel sulfide nanoparticle-loaded activated carbon (NiS-
NP-AC) was prepared and used as a novel adsorbent for rapid indi-
vidual and simultaneous removal of MB and SO. The performance
of NiS-NP-AC for MB and SO removal was investigated and opti-
mized. Different kinetic and equilibrium models were used to
assess the experimental data.
Experimental
Instruments and reagents
All chemicals including NaOH, HCl and KCl with the highest
purity available were purchased from Merck (Darmstadt,
Germany). Dyes solutions were prepared by dissolving their appro-
priate amounts in double distilled water. The test solutions were
prepared by diluting stock solution to the desired concentrations.
The pH was adjusted and measured using pH/Ion meter model-
270. Absorbance spectra of MB and SO were taken in a wide range
of wavelength (k) from 200 to 800 nm, using Analytik Jena UV–
Visible spectrophotometer model Specord 250 with a fixed slit
width of 2 nm and scan speed of 1000 nm/min.
Preparation of dyes solutions
The stock solutions of MB and SO dyes were prepared with 1.0–
20 g/L concentration. The experimental solutions were prepared by
diluting the stock solution with distilled water when necessary.
The test solutions containing desired combinations of MB and SO
were prepared by diluting solutions of MB and SO and mixing them
in the test medium. The initial pH of single and binary solution was
adjusted to the required value by using concentrated HCL or NaOH
solutions before mixing with the adsorbent.
Preparation of NiS-NP-AC
Nickel sulfide nanoparticles (NiS-NP) were synthesized in aque-
ous solution at room temperature and were loaded on the surface
of activated carbon (AC) as follows. Firstly, 0.568 g of Ni(CH3COO)2-
2H2O and 0.548 g of thioacetamide were dissolved in 100 mL of
distilled water and then 10 ml of 2 mol/L of aqueous ammonia
solution was slowly added to which under strong stirring for
20 min. Next, Initial white precipitate of NiS was mixed thoroughly
with 5 g of the activated carbon in an ultrasonic bath. Finally, the
pH was adjusted to 12 and the mixture was maintained at room
temperature for 10 h thus leading to direct growth of the NiS-
NP-AC in the solution.
Model validation
In order to evaluate the fit quality of the experimental data, the
following statistical indices are employed for the multi-component
systems [2,30,31].
A normalized standard deviation (SD) was used to quantita-
tively compare the applicability of isotherm and kinetic models
to multi-component systems:
SD ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P ðqe;expqe;calÞ
qe;exp
h i2
m 1
v
u
u
t
ð1Þ
where qe,exp and qe,cal are the equilibrium experimental and calcu-
lated dyes amounts adsorbed per unit adsorbent mass, respectively,
and m is the number of data points (see Table S1).
M. Ghaedi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 123 (2014) 402–409 403

3. Non-linear chi-square statistical test (v2
) [32], (the best-fit iso-
therm) is given as (see Table S1):
v2
¼
X ðqe;exp qe;calÞ2
qe;cal
ð2Þ
where qe,exp and qe,cal are experimental and calculated adsorption
capacities, respectively. The better the agreement between each
model and the experimental data, the larger v2
would be obtained
(Tables S2 and S3).
Measurement of dyes adsorption
All experiments for single and binary solution of MB and SO
were carried out using 0.005–0.025 g of NiS-NP-AC in 50 ml beak-
ers on an IKA magnetic stirrer operating at 750 rpm to obtain the
optimum conditions. Working temperature was chosen to be the
room temperature. The MB and SO adsorption capacities of the
adsorbent in single and binary dye solutions were determined at
time interval of 2–34 min. The effect of pH on the adsorption
was studied by adjusting pH of 10 mg/L sample solution in the
range of 1–11 in single dye solution. For single dye solutions, the
concentrations were determined by measuring maximum absor-
bance for MB and SO, occurring at 665 and 519 nm, respectively.
The amount of each dye was determined by using its calibration
curve at the mentioned wavelength. In binary solutions, the absor-
bance spectra were used to find the optimal wavelength for each
dye at which minimum impact of other component was observed.
The amount of MB or SO adsorbed at equilibrium, qe (mg/g) was
calculated as follows:
qe ¼ VðC0 CeÞ=M ð3Þ
where C0 is the initial dye concentration (mg/L) in the solution; Ce is
the residual dye concentration (mg/L) at equilibrium; V is the vol-
ume (L) of the solution; and M is the weight (g) of the adsorbent
used.
Results and discussion
Characterization of the adsorbent
Optical properties of the NiS-NPs have strong correlation with
their size and nature. A reflective UV Vis absorption spectrum of
the NiS-NPs has strong dependence on initial reagent concentra-
tion, rate of their mixing, pH, time and temperature (Fig. S2a). By
using the absorbance spectra, band gap of NiS-NPs was determined
from plot of (ahm)2
versus hm. It was found that the band gap of NiS-
NPs has negative correlation with its size due to quantum size ef-
fect. The evaluated band gap (2.86 eV) of NiS-NPs is larger than its
direct band gap (2.65 eV) [33]. Fig. S2b shows PL spectrum of the
as-synthesized NiS-NPs (excitation at 340 nm) at room tempera-
ture. The PL spectrum of the NiS-NPs shows a peak centered at
555.04 nm. This Photoluminescence (PL) spectrum may be due to
different NiS-NPs morphologies, though the detailed reasons are
unclear at present.
The intense and sharp diffraction peaks, shown in Fig. S3, sug-
gest that the obtained product is well crystallized. All the diffrac-
tion peaks can be ascribed to the pure NiS phase (according to
JCPDS Card No. 12-0041). The broadened diffraction peaks, confirm
that the obtained samples are nanoscale. No remarkable diffrac-
tions corresponding to impurities such as Ni and NiOx in the
XRD pattern were observed, indicating that a pure NiS phase has
been formed.
FTIR spectrum of the as-synthesized NiS-NPs shows a peak at
3429 cm-1
which can be ascribed to the absorption of H2O on the
sample. Two weak peaks at 2920 and 2885 cm-1
are due to C–H
stretching modes. The local elemental composition of the as-
formed nanoparticles was studied by EDX as shown in Fig. 1. It
confirms that the nanoparticles are composed of Ni and S. A little
amount of oxygen was determined in this analysis, which may
be due to the oxidation of a low amount of the product in air.
FESEM images of AC and NiS-NP-AC are shown in Fig. 2a and b,
respectively. These images reveal that the morphology of the prod-
uct is quasi-spherical. BET analysis and some properties of the NiS-
NPs are shown in Table S4. As seen, high surface area of the sample
makes it possible to adsorb large amount of dyes in short time
using small amount of the adsorbent [34].
Fig. 1. Energy dispersive X-ray spectrum of NiS nanoparticles.
404 M. Ghaedi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 123 (2014) 402–409

4. Central Composite Design (CCD)
Central composite design (CCD) was used to study the individ-
ual and joint effects of the factors on the responses. The CCD helps
to avoid doing unnecessary experiments and it helps to investigate
the synergies amongst the factors. Half-fractional CCD with totally
32 experimental runs for five factors of pH, adsorbent dosage, con-
tact time, MB concentration and SO concentration was designed.
The total 32 experimental runs were divided to 16 cube points, 6
center points in the cube and 10 axial points. MB and SO removal
percentages were considered as responses. Values of the Factors
and responses are listed in Table S5.
The model given as
%R ¼ b0 þ
X
5
i¼1
bixi þ
X
5
i¼1
biix2
i þ
X
4
i¼1
X
5
j¼iþ1
bijxixj ð4Þ
was used to optimize and predict each response (%R) against the
factors, where xi, xj are the values of the factors and b0, bi, bii and
bij are the constant, linear, quadratic and interaction coefficients,
respectively, corresponding to significant factors. Significant and
insignificant terms were determined and then predictive model
was obtained by implementing Eq. (4) in terms of the significant
factors. The results of ANOVA are presented in Table 1 and
Table S6. The facts that P-values for some terms in these tables
are less than the confidence level (0.05) and the P-value for lack
of fit is higher than 0.05 indicate the adequacy and significance of
the model. The terms x1; x3; x4; x2
1; x2
3; x2
4 and x1x3 were found to be
significant for the MB removal, which means that the time, adsor-
bent dosage and MB concentration affect the MB removal linearly
and quadratically. The interaction of the time and adsorbent dosage
also affect the response. For the removal of SO, the terms
x1; x3; x4; x2
1; x2
3 and x2
4 were found to be significant, which means
that the time, adsorbent dosage, concentration of MB affect the re-
sponse linearly and quadratically.
The optimized values for the factors pH, adsorbent dosage, MB
concentration, SO concentration and contact time were found to
be 8.1, 0.022 g, 17.8 mg/L, 5 mg/L and 5.46 min, respectively. At
this condition, the removal percentage for each dye was predicted
to be 99.9% with desirability 0.999 (see Fig. 3). To make a test on
the reliability of this prediction, an experiment was run at the ob-
tained optimal condition and the removal percentage of each dye
Fig. 2. FESEM images of (a) the activated carbon and (b) the NiS nanoparticles loaded on activated carbon.
Table 1
Analysis of variance for the removal of MB (%R).
Source DF Seq SS Adj SS Adj MS F P
Regression 20 13866.3 13866.3 693. 31 11.65 0.000
Linear 5 10678.5 2238.3 447.65 7.52 0.003
Time (x1) 1 2246.1 651.0 650.98 10.94 0.007
pH (x2) 1 142.7 20.7 20.65 0.35 0.568
Adsorbent (x3) 1 7502.2 1825.8 1825.77 30.68 0.000
MB (x4) 1 372.3 297.4 297.43 5.00 0.047
SO (x5) 1 415.3 141.5 141.52 2.38 0.151
Square 5 2278.1 2278.1 455.61 7.65 0.003
Time time (x2
1) 1 316.9 534.8 534.81 8.99 0.012
pH pH(x2
2) 1 1.3 43.2 43.24 0.73 0.412
Adsorbent Adsorbent (x2
3) 1 1190.6 1389.9 1389.3 23.35 0.001
MB MB (x2
4) 1 576.0 628.7 628.74 10.56 0.008
SO SO (x2
5) 1 193.2 193.2 193.21 3.25 0.099
Interaction 10 909.7 909.7 90.97 1.53 0.248
Time pH (x1 x2) 1 3.5 3.5 3.50 0.06 0.813
Time adsorbent (x1 x3) 1 572.1 572.1 572.12 9.61 0.010
Time MB (x1 x4) 1 31.0 31.0 31.04 0.52 0.485
Time SO (x1 x5) 1 95.9 95.9 95.94 1.61 0.230
pH adsorbent (x2 x3) 1 0.6 0.6 0.61 0.01 0.921
pH MB (x2 x4) 1 27. 6 27.6 27.55 0.46 0.510
pH SO (x2 x5) 1 25.5 25.5 25.49 0.43 0.526
Adsorbent MB (x3 x4) 1 6.2 6.2 6.16 0.10 0.754
Adsorbent SO (x3 x5) 1 26.1 26.1 26.08 0.44 0.522
MB SO (x4 x5) 1 121.2 121.2 121.19 2.04 0.181
Residual error 11 654.7 654.7 59.52
Lack-of-fit 6 160.8 160.8 26.80 0.27 0.928
Pure error 5 493.9 493.9 98.79
Total 31 14521.0
M. Ghaedi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 123 (2014) 402–409 405

5. was obtained to be 96.9%, which is very close to the predicted va-
lue. A similar and rapid adsorption rate was observed for both re-
sponses at the beginning of adsorption process that may be
explained by an increase in the number of active dye binding sites
at adsorbent surface, which would result in an increased concen-
tration gradient between sorbate in the solution and on the adsor-
bent surface. A very rapid adsorption process observed for NiS-NP-
AC is very promising for important application of this adsorbent. It
was observed (see Fig. 3) that with the increase in the adsorbent
amount from 0.005 to 0.025 g, the removal percentage of MB and
SO increased [29–31]. This can be attributed to the increasing sur-
face area of the adsorbent as well as the availability of more
adsorption sites. The adsorption yield (%) decreases after more in-
crease in initial MB concentration which is because of the
saturation of adsorption sites. The high uptake values at high initial
dyes concentrations are due to providing an important driving
force to overcome all mass transfer resistances of dye between
aqueous and solid phases [35–39]. Surface plot of MB removal
(%) vs. adsorbent and MB concentration shows their influences
on the response (see Fig. S4). The presence of SO develops a com-
petition for the adsorption sites on the surface. Some sites are
occupied by second component, especially at their high concentra-
tion. Surface plot of SO removal (%R) vs. adsorbent and time shows
their influences on the response (see Fig. S5).
Adsorption kinetics
The kinetic model for the adsorption of a solute by a solid in
aqueous solution is usually complex. The adsorption rate is
strongly influenced by several parameters related to the state of
the solid (generally with very heterogeneous reactive surface)
and to the physicochemical conditions under which the adsorption
occurs. In the investigation on the processes of the simultaneous
MB and SO adsorption on the adsorbent, the kinetic parameters
are generally helpful for predicting the adsorption rate and give
important information to develop and model the adsorption pro-
cesses. Thus, pseudo-first-order [40], pseudo-second-order [32],
Elovich [41–43] and intraparticle diffusion [44,45] models were
investigated. The consistency between the experimental and the
model-predicted data was investigated by calculating correlation
coefficients (R2
values closer to 1 means more applicability of the
model) and by observing the extent to which the experimental
adsorption capacity is close to the theoretical value. Lagergren
pseudo-first-order model is commonly expressed as follows:
lnðqe qtÞ ¼ ln qe k1t ð5Þ
where qe and qt (mg/g) are the adsorption capacities at equilibrium
and at time t, respectively. k1 is the rate constant of the pseudo-
first-order adsorption (L/min). Using this well-known equation,
the values of k1 and qe were calculated from the slope and intercept
of the plot of log(qe qt) versus t, respectively [42].
The fact that the intercept is not equal to qe means that the reac-
tion is unlikely first-order, regardless of the value of the correlation
coefficient. The initial dye concentration and adsorption rate have
linear relation when pore diffusion limits the adsorption process.
Furthermore, the correlation coefficient (R2
) for each dye is rela-
tively low for most adsorption data, which indicates that the
adsorption of MB and SO onto adsorbent does not follow a first-or-
der reaction. Therefore, it is necessary to fit the experimental data
to another model [46–48]. The adsorption may be described by
pseudo-second-order kinetic model as follows:
dqt
dt
¼ k2ðqe qtÞ2
ð6Þ
t
qt
¼
1
k2q2
e
þ
t
qe
ð7Þ
The plot of log(qe qt) versus t over entire sorption period does
not give a good linear fit. However, the plot of t/qt versus t gives
high correlation coefficient. The values of k2 and equilibrium
adsorption capacity, qe, were calculated from the intercept and
slope of the plot of t/qt versus t, respectively (see Tables S2 and
S3). The R2
values for pseudo-second-order kinetic model were
found to be higher than 0.91 for all amounts of NiS-NP-AC and
all initial dyes concentrations. The increase in the value of k2 with
increasing the adsorbent dosage and initial dyes concentrations,
shows high tendency of the adsorbent for the dyes and diffusion
rate enhancement. The Elovich rate equation, based on the adsorp-
tion capacity, is given as follows [49,50]:
qt ¼
1
b
lnðtÞ þ
1
b
lnðabÞ ð8Þ
The qt is a linear function of ln(t) if the Elovich would apply where
1/b and (1/b)ln(ab) would be obtained from the slope and intercept
Fig. 3. Optimization plot of factors.
406 M. Ghaedi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 123 (2014) 402–409

6. of the plot of the Elovich equation, respectively [11]. These values
are reported in Tables S2 and S3. Another kinetic model for evaluat-
ing the adsorption process is intraparticle diffusion [51]. In this pro-
cess, MB and SO may be transported from aqueous solution to the
adsorbent by intraparticle diffusion. Therefore, this model may be
used to study the rate-limiting step for the adsorption of both dyes
onto NiS-NP-AC. The intraparticle diffusion model is commonly ex-
pressed as follows:
qt ¼ kidt1=2
þ C ð9Þ
The values of kid and C are calculated, respectively, from the
slope and intercept of the plot of qt versus t1/2
(see Tables S2 and
S3) [11]. Generally, the interparticle diffusion model possesses
two parts that are attributed to phenomena such as initial surface
adsorption and subsequent intraparticle diffusion. The sole limit-
ing step of intraparticle diffusion [15,33] requires the respective
plot of qt versus t1/2
to pass through the origin (i.e. the C value to
be zero) [52]. The R2
value (Tables S2 and S3) for this model was
far from the unity, which shows that the intraparticle diffusion
model is not applicable.
At all concentrations and sorbent dosages, the calculated qe val-
ues were mainly closer to the experimental data and the R2
values
for pseudo-second-order kinetic model were larger than that of
pseudo-first-order model. This shows the suitability of the pseu-
do-second-order kinetic model for the MB and SO removal over en-
tire sorption period [53].
Application of multi-component adsorption models to equilibrium
data
A study was undertaken for the removal of MB and SO at vari-
ous initial concentrations in the range of 5–25 mg/L [54–56]. Each
adsorbate has a typical adsorption pattern for a particular adsor-
bent that could be specified with the help of simple equilibrium
models such as Langmuir and Freundlich, which used in the pres-
ent study. The corresponding equations are described as follows
[57]:
Langmuir:
qe ¼
qmklCe
1 þ klCe
ð10Þ
or
Ce
qe
¼
1
klqm
þ
1
qm
Ce ð11Þ
Freundlich:
qe ¼ kf þ cm
e ð12Þ
or
ln qe ¼ ln kf þ n ln ce ð13Þ
The adsorption equilibrium models determine the type of inter-
action between the adsorbate and adsorbent at equilibrium. The
presence of more than one component in an aqueous solution
causes interference and competition for the adsorption sites lead-
ing to a more complex mathematical formulation of the equilib-
rium. Therefore, the relationship between the adsorbed quantity
of one component and the concentrations of all other components
present in the aqueous solution are described by multi-component
adsorption isotherms [28]. Additionally, if the purpose of the work
is to optimize the simultaneous removal of more than one compo-
nent, it is desirable to take into account the effect of such interac-
tions as well as the extent of the adsorption of one component in
the presence of other component(s). In general, the amount of a
component adsorbed may increase, decrease or remain unchanged
in the presence of other component(s). For such complex systems,
equilibrium data need to be modeled using different isotherm
models discussed above.
Non-modified competitive Langmuir model
One of the most widely used models in multi-component sys-
tems is the non-modified Langmuir model [14,16,17,28]. This mod-
el predicts the amount of component ‘i’ adsorbed per unit weight
of adsorbent (qe,i) in the presence of other component(s) at equilib-
rium which is given by (see Table S1):
qe;i ¼
ðQ0kiCe;iÞ
1 þ
X
N
j¼1
kj
Ce;i
gi
! ð14Þ
where Ce,i is the equilibrium concentration of component ‘i’ in a
mixture consisting of N components and the constants Q0 and ki
are the model parameters determined by fitting the single compo-
nent adsorption equilibrium data of component ‘i’ alone to Lang-
muir model. gi is the correction parameter of component ‘i’,
which is the characteristic of each species and depends on the con-
centrations of all other components in the solution. The values of
the correction parameters (i) can be determined from the experi-
mental data on multi-component system. From the Table S1, it is
seen that the non-modified Langmuir which uses the coefficients
from single component Langmuir isotherm could not be used for
predicting qe in case of multi-component adsorption of MB and
SO because of high values of v2
and SD.
Modified competitive Langmuir model
In many cases, single component adsorption isotherm fails to
describe well the interaction between individual components in
the mixture. In those cases, the addition of a correction factor to
the non-modified model may make the model applicable to the
complex adsorption process (see Table S1). The modified Langmuir
model [58–60] is given by:
qe;i ¼
Q0kiCe;i
gi
1 þ
X
N
j¼1
kj
Ce;i
gi
! ð15Þ
Modified extended Langmuir model
The modified extended Langmuir model (MELM) was developed
to describe the simultaneous adsorption of MB and SO by introduc-
ing synergistic efficiency (h) of adsorbates. Assume that synergistic
efficiency (h) arising from the adsorbate–adsorbate lateral interac-
tion is linearly related to the amount adsorbed (Qe) at equilibrium
of the other adsorbate,
h1ðQe2Þ ¼ a1Qe2 þ b1; ð16Þ
h2ðQe1Þ ¼ a2Qe1 þ b2; ð17Þ
where a and b are the constant parameters of synergistic efficiency
(the subscripts 1 and 2 are representative for the MB and SO,
respectively). The amounts of MB (Qe,i) and SO (Qe,j) adsorbed at
equilibrium can be calculated from the following equation (see
Table S1):
qe;i ¼
kiQm;iCe;i
1 þ kl;iCe;i þ kl;jCe;j
1 þ
aiðC0;j Ce;jÞvi
W þ b
ð18Þ
The optimum values of a and b for MELM are listed for each binary-
solute system in Table S1. The facts that the values of v2
and SD for
MELM are much lower than that for other models proved the great-
er validity of the MELM to describe the simultaneous adsorption of
MB and SO on the adsorbent. The synergistic effect can be more
M. Ghaedi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 123 (2014) 402–409 407

7. easily explained if we take into account the chemical characteristics
changes of the adsorbent surface caused by the adsorption of the
dyes. The uptake capacity of NiS-NP-AC found to be 46–52 mg/g
due to multilayer adsorption and to the observed enhancement in
the adsorption of MB onto the adsorbent. For the same reason,
the adsorbed MB molecules induce a remarkable synergistic effect
on the adsorption capacity for SO. Additionally, due to the acid–base
interaction, the electrostatic repulsions among the adsorbed MB
and SO molecules could counteract each other, resulting in a closer
packing of the aromatic molecules on the hydrophobic surface and
thus an increase in the adsorption capacity [61,62]. It is worth to
note that the reasonably high uptake capacity of NiS-NP-AC (46–
52 mg/g) and the very rapid adsorption process (about 5 min) ob-
served for NiS-NP-AC is very promising for important application
of this adsorbent. It is worth to compare this work to what for in-
stance Nassar and Ringsred [63] have done for the adsorption of
Methylene blue from Aqueous Solutions by Goethite Nanoadsor-
bents with the adsorption process within 20 min.
Extended-Freundlich model
The extended Freundlich model [38,64] for binary system is gi-
ven by:
qe;i ¼
KF;iCniþxi
e;i
Cxi
e;i þ y1Czi
e;j
ð19Þ
where KF,1, KF,2, n1 and n2 are the constants of single component Fre-
undlich isotherm model and x1, y1, z1, x2, y2 and z2 are the parame-
ters of extended-Freundlich model for first (MB or SO) and second
(SO or MB) component. It is seen from the Table S1 that the ex-
tended-Freundlich, which uses the coefficients from single compo-
nent Langmuir isotherm, could not be used for the prediction of qe
in case of multi-component adsorption of MB and SO because of
high values of v2
, and SD.
Freundlich–Langmuir (Sips model)
The Sips model is another empirical model for representing the
equilibrium adsorption data. It is a combination of the Langmuir
and Freundlich isotherm models. The Sips model takes the follow-
ing form for single-solute equilibrium data:
qe;i ¼
QmKLF;iC1=ni
e;i
1 þ KLF;iC1=ni
e;i
ð20Þ
Unlike the other above-mentioned adsorption isotherm models,
this model contains three parameters; Qm, KLF and 1/n which can
be calculated by fitting the experimental data to this model (see
Table S1). The Sips model can be extended to describe the multi-
component adsorption equilibrium data [61,62].
qe;i ¼
QmKLF;iC1=ni
e;i
1 þ
X
2
j¼1
KLF;jC1=nj
e;j
ð21Þ
From the Table S1, it is seen that the Sips model could not be used
for the prediction of qe in case of multi-component adsorption of
MB and SO because of high values of v2 and SD [64–67].
Conclusions
Nickel sulfide nanoparticle-loaded activated carbon was syn-
thesized and used as a novel adsorbent for the rapid individual
and simultaneous adsorption of MB and SO. The optimized values
for the factors pH, adsorbent dosage, MB concentration, SO concen-
tration and contact time were found to be 8.1, 0.022 g, 17.8 mg/L,
5 mg/L and 5.46 min, respectively. At this condition, the removal
percentage for each dye was predicted to be 99.9%. A very rapid
adsorption process (5.46 min) by using NiS-NP-AC is very promis-
ing for important adsorption applications.
An empirical extension of a competitive Langmuir model was
proposed to predict the simultaneous adsorption of MB and SO
by fitting to modified-extended Langmuir model. The MELM
parameters indicate that the synergistic coefficient of one adsor-
bate is linearly correlated to the adsorbed amount of the other.
Moreover, the greater synergistic efficiencies of adsorbates are
due to the larger average pore size of adsorbent, which probably al-
lows the movement of MB and SO molecules and the formation of
their lateral acid–base interaction.
Conventional kinetic models were applied and it was seen that
pseudo-second-order equation is suitable to fit the experimental
data. The removal percentage of MB increases as the initial MB
concentration increases by 17.8 mg/L. The adsorption yields (%) de-
creases after more increase in the initial MB concentration. The
presence of the SO causes a competition for the adsorption sites
on the surface and some sites are occupied by the second
component.
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.saa.2013.12.083.
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