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Feb 6, 2016 - Fluoride deficiency may cause dental caries and its excessive use may cause dental disease, and skele- tal fluorosis [3,4]. Fluorosis can cause ...

Journal of Molecular Liquids 216 (2016) 401–410

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Adsorptive removal of fluoride from aqueous solution using single- and multi-walled carbon nanotubes Mohammad Hadi Dehghani a,b, Gholam Ali Haghighat a, Kaan Yetilmezsoy c, Gordon McKay d, Behzad Heibati a,⁎, Inderjeet Tyagi e, Shilpi Agarwal e,f, Vinod Kumar Gupta e,f,⁎⁎ a

Department of Environmental Health Engineering, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran Institute for Environmental Research, Center for Solid Waste Research, Tehran, Iran Department of Environmental Engineering, Faculty of Civil Engineering, Yildiz Technical University, Davutpasa Campus, 34220, Esenler, Istanbul, Turkey d Division of Sustainability, Hamad Bin Khalifa University, Education City, Qatar Foundation, Doha, Qatar e Department of Chemistry, Indian Institute of Technology, Roorkee 247667, India f Department of Applied Chemistry, University of Johannesburg, Johannesburg, South Africa b c

a r t i c l e

i n f o

Article history: Received 22 December 2015 Received in revised form 14 January 2016 Accepted 16 January 2016 Available online xxxx Keywords: Adsorption Fluorine removal SWCNTs MWCNTs Modeling

a b s t r a c t In the present study, defluoridation study of liquid phase with the help of multi-walled carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs) were well investigated and elucidated. The impact of different experimental conditions such as solution pH, initial fluoride concentration, adsorbent dose, and contact time was well studied and optimized for the maximum fluoride removal from water. The experimental data were fitted by the Freundlich, Langmuir and Dubinin–Radushkevich (D–R) isotherm models and the related equilibrium constants were calculated. The results of the isotherm studies showed that fluoride removal by both adsorbents followed the Freundlich isotherm model. Kinetic studies were conducted and the results demonstrated that the experimental data were fitted well with the pseudo-second order kinetic model. Furthermore, two multiple regression-based equations were also derived to model the removal of fluoride from aqueous solutions by the carbon nanotubes. This study demonstrated that the polynomial equations satisfactorily described the behavior of the present defluoridation process for both MWCNTs (R2 = 0.913) and SWCNTs (R2 = 0.941). © 2016 Elsevier B.V. All rights reserved.

1. Introduction Fluoride is one of the halogen elements and exists abundantly in minerals, geochemical deposits and natural water systems and enters in food chains either through drinking water or consuming plants and cereals. It is one of the noxious pollutants that is present in the ground water. Environmental and a range of anthropogenic actions are responsible for the water blemish by fluoride. Effluents waste coming from the industries i.e. industries involved in glass and ceramic production, semiconductor manufacturing, electroplating, coal fired power stations, beryllium extraction plants, brick and iron works, and aluminium smelters can add up the fluoride burden in groundwater [1]. World Health Organization (WHO) guidelines suggest a globalized standard for fluoride in drinking water in the range of 0.5–1.5 mg/L [2]. Fluoride pollution is a global problem in various countries such as the USA, Canada, Brazil, Pakistan, India, Sri Lanka, China, Thailand, Japan, New Zealand, and some countries of Africa and Europe continents. The ⁎ Corresponding author. ⁎⁎ Correspondence to: V.K. Gupta, Department of Chemistry, Indian Institute of Technology, Roorkee 247667, India. E-mail addresses: [email protected], [email protected] (V.K. Gupta).

http://dx.doi.org/10.1016/j.molliq.2016.01.057 0167-7322/© 2016 Elsevier B.V. All rights reserved.

fluoride problem is recognized globally. Fluoride deficiency may cause dental caries and its excessive use may cause dental disease, and skeletal fluorosis [3,4]. Fluorosis can cause weakness of dental and skeletal structure and affect the growth. Those suffering from fluorosis complain of fatigue. Typically the bones of the backbone, neck, hands or legs of the affected person become fragile and lead to deformity. Long term exposure of the elevated level of fluoride may negatively affect nervous development in children, additionally toxic levels of fluoride have been associated with a weakening of bones and an increase in hip and wrist fractures. Consumption of fluoride at levels beyond those used in fluoridated water for a long period of time causes skeletal fluorosis. Skeletal fluorosis is endemic disease in some areas, it is known to cause irritable-bowel symptoms and joint pain. Early stages are not clinically obvious, and may be misdiagnosed as (seronegative) rheumatoid arthritis. As the dental or skeletal fluorosis has no permanent treatment, the only possible remedy is prevention by having the fluoride intake within safe limits. WHO has determined 0.7 mg/L for the optimum range of fluoride to reduce dental caries and to avoid fluorosis in the tropics and up to 1.2 mg/L in cold regions [5]. Several techniques like membrane filtration [6], precipitation [7], nanofiltration [8], ion-exchange [9], electrocoagulation flotation [10], and adsorption [11] have been used for fluoride removal. Among all

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Fig. 1. SEM micrographs of (a) SWCNTs, (b) MWCNTs and TEM micrographs of (c) SWCNTs, (d) MWCNTs, XRD of (e) CNTs and FTIR of SWCNTs and MWCNTs.

the methods, adsorption has been proven to be a low cost and effective process, and is applicable for the removal of fluoride even at low concentrations [12]. Various low cost adsorbents [13–23] have been examined for the removal of fluoride from aqueous solution. Carbon nanotubes (CNTs), such as single-walled carbon nanotubes (SWCNTs) [24] and multi-walled carbon nanotubes and (MWCNTs) [24] have been widely studied in recent years for the removal of different pollutants from water and wastewater [25–27]. However, the potential of CNTs for defluoridation has been rarely investigated. Therefore, the objective of the present study was to get an insight on the fluoride removal from aqueous solution by multiwalled carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs) in batch mode under different experimental conditions. The experimental data was fitted into various kinetic and

isotherm models and also polynomial equations to describe the adsorption process. The results have been thoroughly discussed which would help in the better understanding of defluoridation mechanism by CNTs.

2. Materials and methods 2.1. Reagents and instruments MWCNTs and SWCNTs were used to investigate the adsorption of fluoride from aqueous solution. The adsorbents, SWCNTs and MWCNTs, used in this study, were purchased from the Research Institute of Petroleum Industry (RIPI), Tehran, Iran. A stock solution (100 mg/L) was prepared by dissolving 0.221 g NaF (analytical grade) in 1 L of deionized

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water. All the solutions for fluoride removal experiments were prepared for an appropriate dilution from the stock solution. 2.2. Experimental procedure A specified amount of adsorbent was added to solutions containing fluoride, and adsorption tests were carried out under different conditions (solution pH, contact time and initial concentration of fluoride). Finally, samples were filtered, centrifuged and the concentration of residual fluoride was measured at a maximum wavelength of 570 nm by means of a UV–Vis spectrophotometer Lambda 25 (PerkinElmer, Norwalk, CT, USA). 0.01 M NaOH and/or HNO3 were used to adjust the pH. A mass of 0.5 g of the adsorbent by adding to solutions having 1– 4 mg/L fluoride concentration to determine the maximum adsorption of fluoride by the CNTs. The adsorption capacity, q, mg/g and percentage removal were obtained by using Eqs. (1) and (2): q¼

  C o −C e V M

ð1Þ

  Ce  100% Percentage removal ¼ 1− Co

Fig. 2. Effect of contact time and initial concentration on fluoride adsorption by SWCNTs, and MWCNTs (adsorbent dose 0.5 g/L, pH = 5).

ð2Þ

where Co and Ce (mg/L) are the adsorbate concentrations at the initial time and at a given time t, respectively, V is the volume expressed in L and M is the adsorbent mass expressed in g. 2.3. Analytical methods The surface textural and morphological features of used adsorbent were analyzed using various analytical techniques such as scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD) and Brunauer, Emmett and Teller (BET) analysis. The Fourier transform infrared spectroscopies (FTIR) of the samples were recorded on a Perkin Elmer Spectrum 100 spectrophotometer to investigate the change in the functional groups of the material surface (using a KBr disk technique in the range of 500 to 4000 cm−1). 2.4. Non-linear regression analysis-based modeling approach In the present study, two multiple regression-based equations were derived for multi-walled carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs) for modeling the removal of fluoride from aqueous solutions. For the comparative purpose, the experimental data were evaluated by a licensed multiple regression software package (DataFit® V9.0.59, Oakdale Engineering, PA), containing 298 two-dimensional (2D) and 242 three-dimensional (3D) non-linear regression models. The regression analysis was conducted on the basis of the Levenberg–Marquardt methodology with double precision, as similarly conducted in previous studies [28–34]. The following non-linear convergence criteria were considered suitable for solution preferences: regression tolerance = 1 × 10 − 10, maximum number of iterations = 250, and diverging non-linear iteration limit = 10. In the computational analysis, the stepwise selection procedure (SSP) was implemented as the combination of the forward selection and backward elimination procedures for variable selection process within the framework of

DataFit® software. The SSP begins with a forward step (with no variables in the model). After the forward step, the p values of the variable coefficients are re-examined and any now insignificant variables are removed in a backward step. This process continues until no variables are either added or removed from the model. The SSP is more generally popular than either the forward or backward procedures. The experimental data on the present defluoridation process were imported directly from Microsoft® Excel used as an open database connectivity data source, and then the non-linear regression analysis was implemented. As regression models were solved, they were automatically sorted based on the goodness-of-fit criteria into a graphical interface in the DataFit® numeric computing environment. Moreover, regression variables (β1,β2,β3,β4andβ0), standard error of the estimate (SEE), coefficient of multiple determination (R2), adjusted coefficient of multiple determination (R2a ), and number of non-linear iterations (NNI) were computed to appraise the performance of the regression models. Furthermore, t-ratios and the corresponding p-values were also computed for the appraisal of the significance of the regression coefficients. An alpha (α) level of 0.05 (or 95% confidence) was used to emphasize the statistical significance of the model components.

Table 1 Surface areas and pore parameters of the MWCNTs and SWCNTs. Adsorbent

Inner diameter (nm)

Outer diameter (nm)

Length (μm)

Specific surface area (m2/g)

MWCNTs SWCNTs

– 0.8–1.1

10–30 1–2

10 10

270 700

Fig. 3. Effect of solution pH on the adsorption of fluoride by SWCNTs, and MWCNTs ([fluoride] = 1 mg/L; adsorbent dose = 0.5 g/L and contact time 30 min).

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(Fig. 1c and d), we can say that the CNTs used for the adsorption study are spherical in shape. These spherical particles have a tendency to adhere together and form chains [24]. The X-ray diffraction spectra of CNTs is shown in Fig. 1(e). As shown in Fig. 1e, the peaks at 25 and 43° are related to the graphene structure of carbon nanotubes [24]. The FT-IR spectra of the CNTs are shown in Fig. 1(f). The band observed near 1580 cm− 1 in all samples shows the presence of the cylinder like carbon structure (rolled graphene sheet) [24]. It can be ascribed to the fact that several infrared active modes may have a wave number near 1580 cm− 1 , while the wave number depends on the geometry of the CNTs. Besides this, infrared wave numbers are dependent on the nanotube diameter. The broadness of the band observed at 1580 cm− 1 for MWCNT samples can be explained on the basis of the polydispersity in the geometry of the nanotube [24]. 3.2. Effect of contact time and initial fluoride concentration In order to determine the equilibration time for maximum adsorption of fluoride and to establish the kinetics of the adsorption process, the adsorption of fluoride (at two different concentrations of fluoride (1 and 4 mg/L) at pH 5) on CNTs was studied as a function of contact time and the results are presented in Fig. 2. It can be observed that the removal efficiency of fluoride is rapid in the beginning, and then reaches an equilibrium state after 30 min. This is probably due to the abundant availability of active binding sites on the adsorbent surface, which are gradually occupied with time and adsorption slows down in the later stages, hence initially high rate of adsorption is due to the more number of active sites present on the adsorbent surface, nearly around 30 min it becomes constant due to lesser number of active sites left on the adsorbent surface. [35]. As can be seen in Fig. 2, the percentage removal efficiency decreased with increasing fluoride concentration. These results indicate that energetically less favorable sites became involved when the fluoride concentration is increased. Consequently, Fig. 2 shows that the adsorbents have high removal efficiency for fluoride even at low initial concentrations of fluoride [36]. 3.3. Effect of solution pH To determine the optimum pH for maximum fluoride removal, the equilibrium sorption of fluoride (for an initial concentration of 1 mg/L) was investigated in the pH range 5, 7 and 9, while the other experimental parameters were maintained constant, (temperature: 24 °C and adsorbent dose: 0.5 g/L). The results obtained are presented in the form of graph in Fig. 3, from the results obtained it is clear that the maximum fluoride removal for both adsorbents i.e. SWCNTs and MWCNTs

Fig. 4. Isotherm modeling plots for fluoride adsorption (A) Langmuir, (B) Freundlich and (C) Dubinin–Radushkevich isotherm (D–R).

Table 2 The isotherm parameters and determination coefficients for fluoride adsorption onto MWCNTs and SWCNTs. Model

3. Results and discussion

Langmuir isotherm

3.1. CNTs characterization SEM analysis of SWCNTs and MWCNTs (Fig. 1a and b) revealed that both the adsorbents had porous surface morphology. The specific surface area (by BET method) of SWCNTs and MWCNTs was found to be 700 and 270 m2/g, respectively. Other parameters related to the pore structure and properties are presented in Table 1. Based on TEM images

Freundlich isotherm

Dubinin–Radushkevich

Parameters

MWCNTs

SWCNTs

qmax(mg/g) b (L/mg) RL(L/mg) R2 KF (mg/g (L/mg)1/n) 1/n R2 qm(mg/mg) E(kJ/mol) K R2

2.83 0.353 0.54 0.682 0.462 0.745 0.980 0.83 0.447 1 × 0−7 0.864

2.40 0.415 0.50 0.807 0.570 0.767 0.993 0.97 0.447 1 × 0−7 0.902

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Fig. 5. Kinetics adsorption (A) pseudo-first order by SWCNTs, (B) pseudo-first order for MWCNTs (C) pseudo-second order by MWCNTs, (D) pseudo-second order for SWCNTs, and intraparticle diffusion for fluoride adsorption by (E) SWCNTs and (F) MWCNTs.

was observed at an acidic pH rather than in alkaline pH of the solution. This is due to the fact that there is competition between the hydroxyl groups and fluoride ions for the sorbent active sites, because the surface

sites are positively charged, which leads to the electrostatic attraction between positively charged surface ions and prevailing fluoride ions [12].

Table 3 Pseudo first-order, pseudo-second-order and intra-particle diffusion model constants for fluoride adsorption by CNTs. Pseudo first-order model

Co

MWCNTs

SWCNTs

1 mg/L 2 mg/L 4 mg/L 1 mg/L 2 mg/L 4 mg/L

Intra-particle diffusion model

Pseudo-second-order model

qe,exp. (mg/g)

qe,cal (mg/g)

k1 (1/min)

R2

qe,cal (mg/g)

k2 (g/mg min)

R2

Kp

R2

0.23 0.42 0.89 0.27 0.53 1.11

0.22 0.408 0.855 0.26 0.510 1.09

0.0086 0.0095 0.0121 0.0108 0.0091 0.0078

0.614 0.408 0.712 0.567 0.760 0.796

0.220 0.394 0.888 0.27 0.511 1.091

2.49 2.306 0.67 1.739 0.574 0.336

0.997 0.991 0.998 0.997 0.984 0.997

0.004 0.006 0.016 0.005 0.010 0.021

0.495 0.416 0.495 0.501 0.629 0.577

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Table 4 Non-linear regression-based results for multi-walled carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs). Rank

Regression model

SEE

SR

RSS

R2

R2a

NNI

Modeling of defluoridation process for MWCNTs (Y1) 1 β1X1 + β2X2 + β3X3 + β4X4 + β0 2 exp(β1X1 +β2X2 + β3X3 + β4X4 + β0) 3 β1X1 + β2X2 + β3X3 + β4X4

1.830 1.978 6.391

2.31 × 10−13 −0.816 56.142

177.413 207.432 2205.375

0.913 0.899 0.000

0.907 0.891 0.000

11 4 3

Modeling of defluoridation process for SWCNTs (Y2) 1 β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β0 2 exp(β1X1 +β2X2 + β3X3 + β4X4 + β0) 3 β1X1 + β2X2 + β3X3 + β4X4

2.101 2.354 7.335

−1.88 × 10−13 −1.491 56.825

207.559 260.373 2582.589

0.941 0.926 0.267

0.936 0.920 0.221

5 4 11

SEE, standard error of the estimate; SR, sum of residuals; RSS, residual sum of squares; R2, coefficient of multiple determination; R2a , adjusted coefficient of multiple determination; and NNI, number of non-linear iterations.

The equation is conveniently used in its linear form by taking the logarithm of both sides as:

3.4. Adsorption isotherm experiments After obtaining the optimum conditions (pH, contact time etc.) equilibrium adsorption studies were conducted to achieve the maximum fluoride removal using CNTs and results are presented in Fig. 4A-C. Classical models of superficial adsorption namely Langmuir, Freundlich, and Dubinin–Radushkevich (D–R) isotherm models were applied to the experimental data. The Langmuir model can be expressed as: qe ¼

qm bC e : 1 þ bC e

ð3Þ

It can conveniently be written in a linearized form as follows: Ce 1 1 þ ¼ Ce qe qm b qm

ð4Þ

where qe is the adsorbed amount at equilibrium (mg g−1), Ce is the adsorbate concentration at equilibrium (mg L−1), qm is the maximum adsorption capacity and b is the Langmuir constant related to the energy of adsorption [37]; qm and b can be deduced from the slope and intercept, by plotting Ce/qe versus Ce. The influence of the adsorption isotherm shape can be discussed to examine whether adsorption is favorable in terms of RL, a dimensionless constant referred to as separation factor or equilibrium parameter. RL is defined by the following relationship: RL ¼

1 : 1 þ bC o

ð5Þ

RL values between 0 and 1 indicates favorable adsorption, while RL N 1, RL = 1, and RL = 0 indicate unfavorable, linear, and irreversible adsorption isotherms, respectively [38]. The Freundlich isotherm can be expressed as: qe ¼ K f C 1=n e :

ð6Þ

logqe ¼ logK f þ

1 logce n

ð7Þ

where Kf and n are the Freundlich constants. For favorable adsorption, the value of n should be in the range from 1 to 10 [39]. In order to understand the adsorption type, equilibrium data were tested with the Dubinin–Radushkevich isotherm (D–R) [40]. The linearized D.R. equation can be written as: lnqe ¼ ln qm −Kε2

ð8Þ

where ε is polanyi potential, and is equal to RT ln(1 + 1/Ce), qe is the amount of fluoride adsorbed per unit mass of adsorbents, qm is the theoretical adsorption capacity, Ce is the equilibrium concentration of fluoride, K is the constant related to mean free energy, R is the universal gas constant and T is the absolute temperature (K). The mean free energy of adsorption (E) was calculated from the constant “K” using the relation [40]: E ¼ ð2 KÞ−0:5 :

ð9Þ

It is defined as the free energy change when 1 mol of ion is transferred to the surface of the solid from infinity in solution. The experimental data have been fitted to three isotherm models and the results are presented in Fig. 4 and Table 2. As can be seen from the correlation coefficients (R2), the Freundlich model fit the experimental values better than the other models for MWCNTs and SWCNTs. The 1/n value shown in Table 2 for the Freundlich model indicates that the strength of the adsorption process will be related to the distribution of energy sites. The values of constant RL for the MWCNTs and SWCNTs are 0.54 and 0.5 respectively, which represents the desirable adsorption of fluoride on adsorbent of MWCNTs and SWCNTs [24]. It is also shown in Table 2 that the magnitude of the Langmuir constant ‘b’ for MWCNTs and SWCNTs were 0.353 and 0.415 L/mg, respectively. These b values indicate that the affinity of the SWCNTs for the fluoride is higher than that of the MWCNTs [41,42]. It is shown from

Table 5 Model components and regression variable results obtained from the best-fit (first-order polynomial model) model for multi-walled carbon nanotubes (MWCNTs). Independent and original variables

SEa

t-ratio

Y1 = β1(X1) + β2(X2) + β3(X3) + β4(X4) + β0E(MWCNTs) = (−2.028)(pH) − (0.989)(C0) + (16.701)(M) + (0.163)(t) + 36.122 0.1493 −13.5825 Solution pH (X1 = pH) 0.1988 −4.9758 Initial fluoride concentration (X2 = C0: mg/L) 1.9326 8.6416 Adsorbent dose (X3 = M: g/L) 0.0097 16.8162 Contact time (X4 = t: min) β0 = constant term 1.4676 24.6136 a b

Standard error. p-Values b 0.05 were considered to be significant.

p-Valueb 0.00000 0.00001 0.00000 0.00000 0.00000

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Table 6 Model components and regression variable results obtained from the best-fit (first-order polynomial model) model for single-walled carbon nanotubes (SWCNTs). Independent and original variables

SEa

t-ratio

Y2 = β1(X1) + β2(X2) + β3(X3) + β4(X4) + β0E(SWCNTs) = (−2.569)(pH) − (2.024)(C0) + (25.727)(M) + (0.199)(t) + 41.795 0.1872 −13.7275 Solution pH (X1 = pH) 0.2381 −8.5018 Initial fluoride concentration (X2 = C0: mg/L) 2.3412 10.9888 Adsorbent dose (X3 = M: g/L) Contact time (X4 = t: min) 0.0115 17.4135 1.8023 23.1906 β0 = constant term a b

p-Valueb 0.00000 0.00000 0.00000 0.00000 0.00000

Standard error. p-Values b 0.05 were considered to be significant.

the results in Table 2 that the theoretical value of the adsorption capacity is higher for MWCNTs than SWCNTs, and this is probably due to the higher porosity of MWCNTs. The maximum adsorption capacities of MWCNTs and SWCNTs were found to be 2.83 and 2.4 mg/g, respectively. It was obvious that the MWCNT adsorbent was more effective in removing fluoride from aqueous solutions. This could be due to the complex formation with MWCNTs as referenced earlier but a more likely explanation is the higher availability of internally available adsorption sites on MWCNTs due to the different pore size diameters resulting in a larger internal available surface area than for SWCNTs [43]. The adsorption of fluoride onto carbon is usually by physical adsorption and is mainly dependent on two parameters, the specific surface area and the pore size distribution. In the case of the two CNTs, the SWCNTs have a significantly larger surface area of 700 m2/g but

have a slightly lower maximum fluoride adsorption capacity of 2.4 mg/g. The pore entry diameter limits for the SWCNTs may account for the relatively low fluoride adsorption capacity of this 700 m2/g material. Fig. 4C shows the plot of ln qe against ε2, which was almost linear with a correlation coefficient (R2) of 0.864 and 0.902 for MWCNTs and SWCNTs respectively. The mean free energy evaluated using the D–R model is 0.447 kJ mol−1 for MWCNTs and SWCNTs (Table 2). 3.5. Kinetics studies Various kinetics models (namely, pseudo-first-order (Eq. 10), pseudo-second-order (Eq. 12) and intra-particle diffusion model) were utilized to evaluate the dynamics of adsorption process [44].

Fig. 6. (a) Agreement between the experimental data and the model outputs for MWCNTs (R2 = 0.913), and (b) relationship between the proposed first-order polynomial equation (Y1) and the experimental data obtained for MWCNTs.

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Fig. 7. (a) Agreement between the experimental data and the model outputs for SWCNTs (R2 = 0.941), and (b) relationship between the proposed first-order polynomial equation (Y2) and the experimental data obtained for SWCNTs.

The pseudo-first order kinetics can be described by the following equation [45]:

The pseudo-second order kinetics can be expressed by the following equation [46]:

dqt ¼ k1 ðqe −qt Þ dt

dqt ¼ k2 ðqe −qt Þ2 dt

ð10Þ

ð12Þ

where qe and qt are the amount adsorbed(mg/g) at equilibrium and at time t (min) and k1 is the pseudo-first-order rate constant. After integration at the boundary conditions of qt = 0 at t = 0 and qt = qt at t = t, the linearized equation will be:

where k2 is the pseudo-second-order rate constant (g/mg·min). After integration at the boundary conditions of qt = 0 at t = 0 and qt = qt at t = t, the linearized equation will be

  q k1 t: Log 1− t ¼ − qe 2:303

t 1 1 ¼ þ t: qt k2 qe 2 qe

ð11Þ

Table 7 Comparison table for the removal of fluoride ion using SWCNTs and MWCNTs with different adsorbents. Adsorbent

Adsorption capacity (mg/g)

References

Bleaching powder Lanthanum-modified chitosan Granular red mud Montmorillonite Pyrophyllite Activated kaolinite SWCNTs MWCNTs

0.1308 0.344 0.851 0.263 0.737 0.134 2.4 2.83

[66] [67] [68] [69] [70] [71] Proposed method Proposed method

ð13Þ

The most accurate model was considered based on the regression coefficient (R2) and the experimental qe value obtained. The results of the kinetic adsorption studies are shown in Fig 5. The parameters of the kinetics equations are shown in Table 3. As shown in Table 3, the kinetics of fluoride removal by MWCNTs and SWCNTs followed the pseudo-second order model. It can be also observed from Table 3 that the calculated values, qe,cal of MWCNTs and SWCNTs agreed well with the experimental values, qe,exp, in the case of the pseudo-second order kinetic model. Accordingly, the pseudo-second-order kinetic model fitted well to the kinetic experimental data. These results suggested that the pseudo-second-order adsorption mechanism was predominant and adsorption was controlled by the chemisorption process [47]. In addition, the intra-particle diffusion model was used to investigate the mechanism involved in the adsorption process. Assuming

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that the rate is controlled by pore and intra-particle diffusion, in a nonflow-agitated system the amount adsorbed (qt) is proportional to the square root of time (t1/2), according to the relationship given by Weber and Morris [48]. qt ¼ kp t 1=2

ð14Þ

where qt(mg/g) is the fluoride uptake at time t (min) and kp (mg/g min1/2) is the intra-particle diffusion rate constant. The intra-particle diffusion model [49] was plotted in order to verify the influence of mass transfer resistance on the binding of fluoride to the MWCNTs and SWCNTs (Table 3 and Fig. 5A–F). Thus, the intra-particle diffusion constant, kp (mg/g min1/2) can be obtained from the slope of the plot of qt (uptake at given time, mg/g) versus the square root of time. If this plot passes through the origin, then intra-particle diffusion is the rate controlling step [24]. Fig. 5(e, f) shows the plots of qt versus t1/2, with multilinearity, which implies the process involves more than one kinetic stage (or sorption rates) [49]. The first was related to the initial boundary layer effect binding of fluoride molecules to the MWCNTs and SWCNTs surface and the second and third portions characterize a tendency of fluoride to diffuse in the internal pores and adsorb [49]. Fig. 5(E and F) suggest to the first stage in an external mass transfer adsorption process followed by film or intra-particle diffusion mechanism [50–62]. The value of the rate constant for intra-particle transport increased with the increase in the initial fluoride concentration (Table 3). The plots are linear but do not pass through the origin (Fig. 5(E and F)), indicating that external mass transfer is the main rate controlling step at the initial stage of fluoride removal. However, the lower correlation coefficients and the short time of 30 min to reach equilibrium suggest the mechanism to kinetics controlled rather than diffusion.

409

study, the significance of each coefficient was determined by Student's t-test and p-values, which are presented in Tables 5 and 6. Based on the absolute effects (t-ratio × SE) of the independent variables, adsorbent dose (X3 = M: g/L) had more importance with a weight of about 84% than other variables for the derived first-order polynomial models for both MWCNTs and SWCNTs in modeling of the defluoridation process. This was followed by the solution pH with a weight of about 10.2% and 8.4% for MWCNTs and SWCNTs, respectively. Consequently, the resulting regression models clearly indicated that 4 parameters all contributed to the dependent variable (Y1,2 = E(%): percentage of removal) and that none of them could be eliminated without affecting the outcome of the model. Finally, Figs. 6 and 7 show the agreement between the experimental data and the model outputs for MWCNTs and SWCNTs, respectively. As seen from the relationship between the developed multiple regression-based formulations and the experimental data set, it can be concluded that the proposed polynomial equations satisfactorily described the behavior of the present defluoridation process for different experimental conditions. 3.7. Comparison with other adsorbents The used adsorbent i.e. SWCNTs and MWCNTs had a relatively large adsorption capacity for fluoride ion as compared to some other adsorbents reported in the literature; Table 7 lists the comparison of maximum monolayer adsorption capacity of fluorine on various adsorbents. The adsorption capacity for the proposed method in comparison with all of the adsorbents is preferable and superior to the literature which shows satisfactory removal performance for fluorine as compared to other reported adsorbents [66–71]. 4. Conclusions

In this study, a non-linear regression-based analysis was performed to model the removal of fluoride from aqueous solutions by multiwalled carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs). In this approach, two first-order polynomial models and one exponential model were derived for both MWCNTs and SWCNTs. Results of the non-linear regression analysis are summarized in Table 4. Regression variable results including the standard error of the estimate (SEE), the t-statistics and the corresponding p-values for the best-fit regression model (herein first-order polynomial models) are presented in Tables 5 and 6. The polynomial models (Y1 and Y2 for MWCNTs and SWCNTs, respectively) derived as a function of four input variables [Y1,2 = E(%) = f(solution pH(X1 = pH), initial fluoride concentration (X2 = C0: mg/L), adsorbent dose (X3 = M: g/L), contact time (X4 = t: min)] are expressed as follows:

MWCNTs and SWCNTs were investigated for the removal of fluoride from aqueous solutions. From the BET analysis, it was found that specific surface area of SWCNTs and MWCNTs are 700 and 270 m2/g, respectively. The results showed that fluoride removal increased with contact time at pH 5.0. The removal efficiency of fluoride was rapid in the beginning, and reached equilibrium after 30 min. The Freundlich isotherm model was found to fit well to the experimental data as compared to other applied isotherm models. The maximum adsorption capacity of fluoride adsorbed by MWCNTs and SWCNTs was 2.83 and 2.4 mg/g, respectively. Adsorption processes for the fluoride were found to follow the pseudo-second-order kinetics model for both adsorbents. According to the absolute effects of the independent variables, adsorbent dose has more importance than other variables for the derived first-order polynomial models. The result of this study clearly demonstrated that the polynomial equations satisfactorily described the behavior of the defluoridation process for both MWCNTs and SWCNTs.

Y 1 ðor Y 2 Þ ¼ β1 ðX 1 Þ þ β2 ðX 2 Þ þ β3 ðX 3 Þ þ β4 ðX 4 Þ þ β0

ð15Þ

Acknowledgments

EðMWCNTsÞ ¼ ð−2:028ÞðpHÞ−ð0:989ÞðC 0 Þ þ ð16:701ÞðM Þ þ ð0:163Þðt Þ þ 36:122

ð16Þ

The authors would like to thank Tehran University of Medical Sciences for financial and other supports. There is no conflict of interest declared by the authors.

EðSWCNTsÞ ¼ ð−2:569ÞðpHÞ−ð2:024ÞðC 0 Þ þ ð25:727ÞðM Þ þ ð0:199Þðt Þ þ 41:795

ð17Þ

3.6. Modeling of defluoridation process

It is reported that the t-ratio represents the ratio of the estimated parameter effect to the estimated parameter standard deviation. Moreover, the p-value is used as a useful statistical tool to check the significance of each of the coefficients. The variable with the larger tratio and with the smaller p-value is considered as the more significant parameter in the regression model [63,64]. It is also noted that values that yield Prob(t) factors (or p-values) of greater than 0.9 can be omitted until all remaining factors are calculated at once [63–65]. In the

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