Desalination 278 (2011) 1–9

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Desalination

j ourna l homepage: www.e lsev ie r.com/ locate /desa l

Defluoridation of water using Brushite: Equilibrium, kinetic andthermodynamic studies

M. Mourabet, H. El Boujaady ⁎, A. El Rhilassi, H. Ramdane, M. Bennani-Ziatni, R. El Hamri, A. TaitaiTeam Chemistry and Valorization of Inorganic Phosphates, Department of Chemistry, Faculty of Sciences, 13000 Kenitra, Morocco

⁎ Corresponding author.E-mail address: elboujaadyhicham@yahoo.fr (H. El B

0011-9164/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.desal.2011.05.068

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 April 2011Received in revised form 30 May 2011Accepted 31 May 2011

Keywords:BrushiteFluorideAdsorptionKineticsThermodynamics

In this study, the adsorption potential of Brushite for the removal of fluoride from aqueous solution has beeninvestigated by using batch mode experiments. The effects of different parameters such as pH, adsorbentdosage, initial fluoride concentration, contact time, temperature and co-existing ions have been studied tounderstand the adsorption behavior of the adsorbent under various conditions. The adsorbent has beencharacterized by pHpzc measurement, FTIR, XRD and TEM with EDAX analysis. The Langmuir Freundlich, andTemkin models are found to be the best to describe the equilibrium isotherm data, with a maximummonolayer adsorption capacity of 6.59 mg g−1 at 310 K. Thermodynamic parameters including the Gibbs freeenergy ΔG°, enthalpy ΔH°, and entropy ΔS° have revealed that the adsorption of fluoride ions on the Brushiteis feasible, spontaneous and endothermic. Among the kinetic models tested for Brushite, pseudo-second-order model fits the kinetic data well. It has been found that the adequate time for the adsorption equilibriumof fluoride is only 60 min. The results of this study have demonstrated the effectiveness and feasibility ofBrushite for the removal of fluoride ions from aqueous solution.

oujaady).

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© 2011 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. Materials and method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1. DCPD powder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2. Characterization of the sorbent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3. Adsorption studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.1. Characterization of Brushite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.2. Effect of adsorbent dosage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.3. Effect of initial pH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.4. Adsorption isotherm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.4.1. Langmuir isotherm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.4.2. Freundlich isotherm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4.3. Temkin isotherm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4.4. Dubinin–Radushkevich isotherm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.5. Temperature effect and thermodynamic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.6. Kinetics studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.6.1. Pseudo-first order model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.6.2. Pseudo-second order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.6.3. Intra-particle diffusion model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.7. Effect of anions in the medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 M. Mourabet et al. / Desalination 278 (2011) 1–9

1. Introduction

Fluoride-related health hazards are considered to be a majorenvironmental problem in many regions of the world. Chronic intakeof excessive fluorine can lead to severe permanent bone and jointdeformations of skeletal fluorosis, which is irreversible and has notreatment. Fluoride normally enters the environment and humanbody through water, food, industrial exposure, drugs, cosmetics, etc.However, drinking water is the single major source of daily intake.Taking health effects into consideration, the World Health Organiza-tion has set a guideline value of 1.5 mg L−1 [1] as the maximumpermissible level of fluoride in drinking waters. The same standardsare adopted in Morocco. The fluoride content in many regions ofMorocco greatly exceeds the acceptable standards. The fluoridecontamination is attributed essentially to the phosphate deposit.Consequently, the treatment of fluoride has currently become animportant subject worldwide.

For the removal of the excessive amount of fluoride from drinkingwater, several methods, i.e. ion exchange [2], precipitation [3],Donnan dialysis [4], electrodialysis [5], reverse osmosis [6], nanofil-tration [7], and adsorption, have been investigated.

Among the methods reported adsorption seems to be the effectiveand promising technique for selective fluoride removal. Some of theadsorbents, viz., hydroxyapatite, nano-hydroxyapatite/chitosan [8], amodified Amberlite resin, activated alumina [9], Iron–tin mixed oxide[10], etc.…, have been successfully employed for fluoride removal.

The objective of the present work is to investigate the sorptionpotential of Brushite (CaHPO42H2O, DCPD) for removing fluoride ionsfrom aqueous solution. The Langmuir, Freundlich, Temkin andDubinin–Radushkevich (D–R) models are used to describe equilibri-um isotherms. Kinetic and thermodynamic parameters are alsocalculated to describe the sorptionmechanism of fluoride on Brushite.Furthermore the characterizations of Brushite have been donned byusing XRD analysis, Transmission electron microscopy (TEM) andenergy dispersive X-ray (EDX) analysis, and FTIR spectroscopy.

2. Materials and method

2.1. DCPD powder

The Brushite (DCPD) powders have been prepared by an aqueousdouble decomposition of the salt of calcium and of phosphate salt[11].

A calcium nitrate solution (Ca (NO3)24H2O) (Scharlau,Spain) hasbeen added to ammonium dihydrogen phosphate ((NH4) H2PO4)(Riedel-de Haën, Germany) to an ordinary temperature and a whiteprecipitate appears. After maturation of 2 h, the precipitate hasfiltered and washed with 1 L of distilled water. Finally, the precipitatehas been lyophilized for at last 24 h.

2.2. Characterization of the sorbent

Transmissionelectronmicroscopy(TEM)andenergydispersiveX-ray(EDX) analysis have been performed using an FEI Tecanai G2 (Philips)(120KV). An FTIR spectrum of the samples has been characterized usingVERTEX 70/70v FT-IR spectrometers. An X-ray powder diffraction (XRD)pattern has been analyzed using X'Pert PRO (Germany) X-ray diffrac-tometer with Cu Kα radiation.

The pH of the zero point charge (pHZPC) has been determined byplacing 0.2 g of Brushite glass stopper bottle containing 25 mL of0.01 M NaCl solutions.

The initial pH of these solutions has been adjusted to 4, 4.5, 5, 5.5,6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10 and 11 by either adding 0.1 M NaOH or0.1 M HCl. The bottles have been emplaced incubator shaker at 25 Cfor 48 h, and the final pH of supernatant has been measured. The

ΔpH=pH (final)−pH (initial) have been plotted against the initialpH, the pH at which ΔpH was zero was taken as a pHZPC.

2.3. Adsorption studies

Adsorption studies of fluoride have been investigated by batchexperiments. Stock solution (100 mg L−1) has been prepared bydissolving 0.221 g of anhydrous sodium fluoride in distilled water andmade up to 1 L and it has been further diluted to get the desiredconcentration. All batch experiments have been carried out in 50 mLtube to test. A Brushite sample 0.2 g has been added in 25 mL offluoride solutions. The mixture has been agitated at 400 rpm.Thesolution has then been filtered and the residual fluoride ionconcentration analyzed electrochemically with a fluoride ion-selective electrode (Orion, USA) by the use of total ionic strengthadjustment buffer (TISAB) solution (58 g of sodium chloride, 57 mLof glacial acetic acid and approximately 150 mL of 6 M NaOH in avolume of 1000 mL) to maintain pH5.0 and to eliminate theinterference effect of complexing ions. The fluoride samples and thefluoride standard solutions diluted 1:1 with a total ionic strengthadjustment buffer solution.

The fluoride adsorbed on Brushite has been calculated from thefollowing Eq. (1).

qe = Co−Ceð Þ:V =m ð1Þ

Where qe is the fluoride adsorbed (mg g−1); Co, initial concentra-tion of fluoride (mg L−1); Ce, concentration of fluoride in solution atequilibrium time; V, solution volume (L); m, adsorbent dosage (g).

Adsorption isotherm has been studied at three different temper-atures, 298, 303 and 310 K, on fluoride solutions with varyingconcentrations from 20 to 50 mg L−1 and at natural solution pH(6.8–6.9).

Kinetic studies have been carried at, two different initial fluorideconcentrations (25 and 30 mg L−1), contact time (10–180 min), atnatural solution pH and at 303 K.

3. Results and discussion

3.1. Characterization of Brushite

The TEM image of the synthesized DCPD powder and fluoridereacted DCPD material have been presented in Fig. 1a and b. Thecrystals appear as stretched out tablets of very irregular shapes. EDXspectra confirmed the presence of relevant elements in Brushitebefore (Fig. 1c) and after treatment by the fluoride (Fig. 1d). It clearlyindicated that F− element have been introduced in Brushite afteradsorption. Presence of a minor peak for fluoride in Fig. 1d indicatesthat fluoride is superficially adsorbed on the surface of Brushite.

Fig. 2 shows the IR spectrum of DCPD before the adsorption of F−

ions. In the spectrum of the before DCPD adsorption, the peaks at 563and 580 cm−1 is due to P–O bending vibration, the peaks at 1084 and1129 cm−1 is due to P–O stretching vibration. The infrared peaks at1649 and 3000–3428 cm−1 is due to adsorption water. An absorptionband appears at 901 and 1384 cm−1 which are attributed to the HPO4

2−

ions.Fig. 3 shows the XRD patterns of the DCPD before adsorption of

fluoride ions. The main peaks are characteristic peaks of Brushite.

3.2. Effect of adsorbent dosage

The percent removal varies with different dosages of sorbent, viz.,0.05, 0.1, 0.15, 0.2, 0.25, 0.30 and 0.4 g have been studied to ascertainthe effect of dosage and to optimize the minimum dosage required forbringing down the fluoride level to the tolerance limit with initialconcentration 20 mg L−1, contact time 60 min, natural solution

Fig. 1. (a) pure DCPD (b) Fluorude loaded DCPD (c) EDX before adsorption (d) after adsorption.

3M. Mourabet et al. / Desalination 278 (2011) 1–9

(pH=6.8) and temperature 303 K. The effect of percentage removal offluoride with different sorbent dosages is shown in Fig. 4. Thepercentage removal of fluoride significantly increases with increase insorbent dosage, which is obvious because of the increase in the numberof active sites as the dosage increases. Furthermore, the adsorptioncapacity (qe, mg g−1) value has been decreased for a fixed fluorideconcentration (20 mg L−1) with the increase of dose. The percentage offluoride removal gradually reaches a maximum and remains almostconstant with the increase in dosage of sorbent. Hence, in all thesubsequent experiments 0.2 g of sorbent is fixed as the optimumdosage which can give reasonably good defluoridation efficiency.

3.3. Effect of initial pH

The pH of themedium plays a significant role in fluoride adsorption.The effect of initial pH on fluoride removal by Brushite has been studiedover a broad pH range of 4–11 with adsorbent dose 0.2 g, initialconcentration 25 mg L−1, contact time 60 min and temperature 303 K.As shown in Fig. 5, it can be seen that fluoride adsorption decreases asthe pH increases from 4 to 11. The pH of the equilibrated solutionincreased under an initial acid pH range (pHb6.0), while it decreased

when the initial solution has alkaline (pHN6.0). The effect of pHmay beexplained in terms of pHzpc (zero point of charge) of the adsorbent. Inthe present study, pHpzc has been found to be 6.2. Below pHpzc theDCDP surface is protonated and acquires a positive charge. The decreasein adsorption between pH values of 4.0 and 6.2 is due to the decrease inthe positive surface charge density. Beyond pH 6.2, the surface isdeprotonated and acquires a negative charge, which repels thenegatively charged fluoride ions and consequently adsorption de-creases. The progressive decrease of fluoride uptake at alkaline pH canmainly be due to competition for adsorbent active sites by excessiveamount of hydroxyl ions. However, the details of the effect of pH onfluoride adsorption mechanism need to be further investigated.

3.4. Adsorption isotherm

Adsorption isotherm is the relationship between the adsorbate inthe liquid phase and the adsorbate adsorbed on the surface of theadsorbent at equilibrium at constant temperature.

The equilibrium adsorption isotherm is very important to designthe adsorption systems. For solid–liquid systems, several isotherms

Fig. 2. FTIR spectrum before fluoride adsorption.

4 M. Mourabet et al. / Desalination 278 (2011) 1–9

equations are available. Langmuir [12], the Freundlich [13], theTemkin [14] and the Dubinin–Radushkevich(R-D) [15] models.

3.4.1. Langmuir isothermThe Langmuir adsorption model is based on the assumption that

maximum sorption corresponds to a saturated monolayer of solute onthe sorbent surface. This model also supposes that all the sorptionsites are assumed to be identical, each site retains one molecule of thegiven compound and all sites are energetically and sterically

Fig. 3. XRD pattern before

independent of the sorbed quantity. The linear form of the Langmuirequation can be described by

Ce = qe = Ce = qm + 1 = KLqm ð2Þ

where Ce (mg L−1) is the equilibrium concentration of the sorbate, qe(mg g−1) is the amount of adsorbate per unit mass of adsorbent, qm(mg g−1) and KL (L mg−1) are Langmuir constants related to sorptioncapacity and rate of sorption, respectively.

fluoride adsorption.

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,450

2

4

6

Adsorbent dose (g)

Ad

sorp

tio

n c

apac

ity

(qe(

mg

/g))

40

50

60

70

80

90

100

% R

emo

val

Fig. 4. Effect of adsorbent dosage.

0 1 2 3 4 5 6 7 8 9 100,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0 310 K 303 K 298 K

Ce/

qe

Ce (mg/L)

Fig. 6. Langmuir isotherm model.

Table 1Comparison of monolayer sorption capacities of various adsorbents for fluorideadsorption.

Adsorbent qm(mg/g) Amount ofadsorbents

Reference

Activated alumina 2.41 0.04–0.4 g [9]Montmorillonite 3.36 8 g [17]Magnetic-chitosan 22.49 0.1 g [18]Plaster of Paris 0.36 1 g [19]Geomaterials 15.17 0.4 g [20]

5M. Mourabet et al. / Desalination 278 (2011) 1–9

Fig. 6 represents the experimental data that are fitted by the linearform of Langmiur model, (Ce/qe) versus Ce, at temperature 25, 30 and37 °C. The values of qm and KL have been evaluated from the slope andintercept, respectively, for the three isothermal lines and they arelisted in Table 3. The sorption capacity, qm, which is a measure of themaximum adsorption capacity corresponding to complete monolayercoverage found to be 6.59 mg g−1 for the experiments carried out at37 °C. The values of qm have increased from 6.373 to 6.591 mg g−1,while the solution temperature increased from 30 to 37 °C. We havealso observed that the adsorption coefficient, KL, value which isrelated to the apparent energy of adsorption has also increased from0.373 to 0.566 L mg−1 as the solution temperature increased from 30to 37 °C.

The increase in these values of qm and KL with temperatureindicates that the fluoride ions are favorably adsorbed by Brushite athigher temperatures, which shows that the adsorption process is anendothermic one.

Our experimental data of values qm are compared with otheradsorbents in order to validate Brushite as an adsorbent for fluorideions adsorption. Table 1 shows the value of qm for the adsorption offluoride ions on different adsorbents cited in the literature comparedwith that of the present study. It can be stated that our findings arewell. It should be noted that the values and comparisons reported forfluoride removal capacity have only a relative meaning because ofdifferent testing conditions, type of materials and methods.

3 4 5 6 7 8 9 10 11 123,20

3,25

3,30

3,35

3,40

3,45

3,50

qe(

mg

/g)

pHI

Fig. 5. Effect of initial pH (pHi) on the adsorption of fluoride by the Brushite.

The essential characteristics of the Langmuir isotherm can beexpressed in terms of a dimensionless equilibrium parameter (RL),defined by Weber and Chakravorti [16] as

RL = 1= 1 + KLCo ð3Þ

Where C0 and KL are initial fluoride concentration and theLangmuir isotherm constant. The value of RL indicates the type ofthe isotherm to be either favorable (0bRLb1), unfavorable (RLN1),linear (RL=1) or irreversible (RL=0).

RL values calculated from the present system are presented inTable 2. The RL values lying between 0 and 1 indicate the favorableconditions for adsorption at all the temperatures studied.

Zr-CCB 13.69 0.1 g [21]Iron–tin mixed oxide 10.47 0.25 g [10]Light weight concrete material 5.15 40 g [22]Laterite 0.85 1 g [23]ZICNSC 1.88 0.15 [24]Brushite 6.59 0.2 g Present study

Table 2Dimensionless equilibrium parameter (RL) values for fluoride sorption by Brushite atdifferent temperatures.

Fluoride concentration(mg L−1)

Temperature

25 °C 30 °C 37 °C

20 0.112 0.092 0.08125 0.093 0.075 0.06630 0.078 0.063 0.05535 0.067 0.054 0.04840 0.059 0.048 0.04245 0.053 0.043 0.03750 0.048 0.038 0.034

0,0 0,5 1,0 1,5 2,0 2,50,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

303 K 298 K

qe

LnCe

Fig. 8. Temkin isotherm model.

6 M. Mourabet et al. / Desalination 278 (2011) 1–9

3.4.2. Freundlich isothermThe Freundlich isotherm is the earliest known relationship

describing the sorption equation. The fairly satisfactory empiricalisotherm can be used for non-ideal sorption that involves heteroge-neous surface energy systems. The linearized form of the Freundlichmodel is expressed by the following equation:

ln qe = 1 = nlnCe + lnKF ð4Þ

where KF (mg1−(1/n)L1/ng−1) is roughly an indicator of the sorptioncapacity and n is the sorption intensity. In general, as the KF valueincreases the sorption capacity of sorbent for a given sorbateincreases. The equilibrium data have further been analyzed by usingthe linearized form of Freundlich isotherm, by plotting ln qe versus lnCe (Fig. 7). The calculated Freundlich isotherm constants and thecorresponding coefficients of determination are shown in Table 2. Themagnitude of the exponent n gives an indication on the favorability ofsorption. It is generally stated that the values of n in the range 2–10represent good, 1–2 moderately difficult, and less than 1 poorsorption characteristics [25]. The result shows that the values of nare greater than 2 indicating that the metal is favorably sorbed byBrushite. This is in great agreement with the findings regarding to RLvalue.

3.4.3. Temkin isothermTemkin isotherm, which considers the effects of the heat of

adsorption, decreases linearly with coverage of the adsorbate andadsorbent interactions.

The Temkin isotherm has been used in the form as follows:

qe = RT = btln at + RT = btln Ce ð5Þ

Where bt is the Temkin constant related to the heat of sorption(J mol−1), at is the Temkin isotherm constant (L mg−1), R is the gasconstant (8.314 J mol−1K−1) and T is the absolute temperature (K).The parameters of Temkinmodel are determined by plotting qe versuslnCe (Fig. 8) and are listed in Table 3.

3.4.4. Dubinin–Radushkevich isothermThe Dubinin–Radushkevich (D–R) isotherm is more general than

the Langmuir isotherm, because it does not assume a homogeneoussurface or constant sorption potential. It is valid at low concentrationranges and can be used to describe sorption on homogeneous andheterogeneous surfaces. The D–R equation has the general expression

qe = QD exp −BD□2

� �ð6Þ

0,0 0,5 1,0 1,5 2,0 2,50,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

310 K 303 K 298 K

Ln

qe

LnCe

Fig. 7. Freundlich Isotherm model.

or in the linear form

ln qe = ln QD–BD□2 ð7Þ

Where QD is the theoretical maximum capacity (mol g−1), BD isthe D–R model constant (mol2/kJ2) and □ is the Polanyi potential,which is equal to

□ = RT ln 1 + 1= Ceð Þ ð8Þ

The saturation limit QD may represent the total specific microporevolume of the sorbent. The value of BD is the activity coefficient relatedto mean sorption energy (mol2kJ−2). It is related with head sorptionmean free energy, E (kJ mol−1), defined as the free energy changerequired to transfer one mole of ions from infinity in solution to thesolid surfaces. The relation is as the following:

E = 2BDð Þ−0:5 ð9Þ

The values of QD and BD deduced by plotting ln qe versus □2 (Fig.not showed) and the mean energy of adsorption E are given in Table 3.

The calculated results of the Langmuir, Freundlich, Dubinin–Radushkevich and Temkin isotherm constants are given in Table 3. Itis found that the adsorption of fluoride on the Brushite has correlatedwell with the Langmuir, Freundlich and Temkin equation as comparedto, Dubinin–Radushkevich equation under the concentration rangestudied indicating possibility simultaneous validity of multipleisotherms.

Table 3The value of parameters for each isotherm model used in the studies.

Models T (°K)

298 303 310

Langmuir KL 0.373 0.493 0.566qm 6.373 6.501 6.591R2 0.998 0.998 0.994

Freundlich Kf 2.144 2.353 2.73n 2.512 2.506 3.021R2 0.992 0.995 0.998

Temkin bt 1.737 1.740 2.130at 3.75 4.61 9.67R2 0.996 0.998 0.991

D–R QD 4.595 4.664 4.540BD 0.414 0.281 0.128E 1.098 1.319 1.976R2 0.944 0.939 0.906

Table 4Thermodynamic parameters for fluoride adsorption by Brushite.

T(K) ΔG°(kJ mol−1) ΔH°(kJ mol−1) ΔS°(kJ mol−1 K−1)

298 −22.094303 −23.036 22.791 0.150310 −23.924

7M. Mourabet et al. / Desalination 278 (2011) 1–9

3.5. Temperature effect and thermodynamic parameters

In order to decide the feasibility and spontaneity of the adsorptionprocess the thermodynamic parameters including Gibbs free energychange (ΔG°), enthalpy change (ΔH°), and entropy change (ΔS°) havebeen evaluated. These parameters can be calculated using thefollowing equations;

ΔG- = −RT lnKL ð10Þ

ΔG- = ΔH -−TΔS- ð11Þ

Where KL is the adsorption equilibrium constant obtained fromLangmuir isotherm, T is the temperature in Kelvin and R is theuniversal gas constant (8.314 J mol−1 K).

The values of ΔH° and ΔS° can be obtained from the slope andintercept of a plot of ΔG° against T (Fig. 9). The calculatedthermodynamic parameters are presented in Table 4.

The negative values of ΔG° confirm the spontaneous nature ofsorption of fluoride by Brushite. The value of ΔG becomes morenegative with increasing temperature. This shows that the removalprocess is favored by an increase in temperature. The positive value ofΔH° has showed that the adsorption process is endothermic in nature.

Positive values of ΔH° have also reported for the sorption offluoride by nano-hydroxyapatite/chitosan [8], magnetic-chitosanparticle [18] and lanthanum incorporated chitosan beads [26].

The positive value ofΔS° shows increased randomness at the solid-solution interface during adsorption.

3.6. Kinetics studies

The prediction of adsorption rate gives important information fordesigning batch adsorption systems. Information on the kinetics ofsolute uptake is required for selecting optimum operating conditionsfor full-scale batch process. Fig. 10. shows the plot between theamounts adsorbed, qt (mg g−1) versus time, t (min) for differentinitial solute concentrations. From the figure it has been observed thatqt value has increased with the increase in initial fluorideconcentration.

It can be seen that the adsorption kinetics is very fast. The resultshave shown that a contact time of 60 min is adequate to reachequilibrium and there are no significant increases in the rate ofremoval with further increase in contact time. The kinetics of fluorideadsorption on the DCPD has been determined by using three differentkinetic models, which are pseudo-first order, pseudo-second-orderand intra-particle diffusion models.

298 300 302 304 306 308 310

-24,0

-23,5

-23,0

-22,5

-22,0

Gib

bs

free

en

erg

y ch

ang

e

T(K)

Fig. 9. Van't Hoff plot.

3.6.1. Pseudo-first order modelThis is the first equation for the sorption of liquid/solid system

based on solid capacity [27]. In most cases, the pseudo-first orderLagergren equation does not fit well for the whole range of contacttime. This model may be represented:

dqt = dt = k1 qe–qtð Þ ð12Þ

Eq. (12) can be integrated for following boundary conditions toobtain Eq. (13). t=0, qt=0, t= t, qt=qt

ln qe−qtð Þ = ln qe–k1t ð13Þ

Where, qe is the amount of solute on the surface of the sorbent atequilibrium, (mg g−1), qt is the amount of solute on the surface of thesorbent at time t, (mg g−1), k1 is the equilibrium rate constant ofpseudo-first sorption,(L min−1).

The pseudo-first-order rate constant (k1) and theoretical equilibri-um adsorption capacities (qe) calculated from linear plot of ln (qe−qt)versus t (Fig. not showed), are given in Table 5.

The value of correlation coefficient is 0.992–0.996. Moreover, thevariations between the calculated qe and experimental qe were veryminimal for this model. Therefore we can say that the adsorption offluoride on the Brushite do not follow the pseudo-first-order kineticmodel.

3.6.2. Pseudo-second orderContrary to the first order model, the pseudo-second order model

predicts the behavior over the whole adsorption time and is inagreement with adsorption mechanism being the rate-controllingstep. The pseudo-second order rate equation is expressed as [28]

dqt = dt = k2 qe–qtð Þ2 ð14Þ

0 20 40 60 80 100 120 140 160 180 2002,3

2,4

2,5

2,6

2,7

2,8

2,9

3,0

3,1

3,2

3,3

3,4

3,5

25mg/L 30mg/L

qt(

mg

/g)

t(min)

Fig. 10. Effect of initial concentration on adsorption kinetics of fluoride by Brushite.

Table 5The kinetic parameters obtained for fluoride adsorption on Brushite at differentconcentrations.

Kinetic equations Parameters Initial fluorideconcentration(mg L−1)

25 30

Pseudo-second order k2 (g mg−1 min−1) 0.209 0.172qe,cal (mg g−1) 2.940 3.508qe,ex (mg g−1) 2.897 3.456h (mg g−1 min−1) 0.552 0.470R2 0.999 0.999

Pseudo-first order k1 (min−1) 0.019 0.076qe,cal (mg g−1) 0.950 1.596qe,ex (mg g−1) 2.897 3.456R2 0.996 0.992

Intra-particle diffusion kp(g mg−1 min0.5) 0.043 0.048C (mg g−1) 2.440 2.941R2 0.774 0.773

00,0

0,5

1,0

1,5

2,0

2,5

3,0

qe(

mg

/g)

no salt NaCl Na2SO4

NaNO3

NaHCO3

Fig. 12. Effect of presence of co-ions on fluoride adsorption.

8 M. Mourabet et al. / Desalination 278 (2011) 1–9

Where k2 is pseudo-second order rate constant. After integrationand applying boundary conditions, t=0 to t=t and qt=0 to qt=qt;the integrated form of Eq. (14) becomes

t = qt = 1= k2:q2e + t = qe ð15Þ

The constant k2 is used to calculate the initial sorption rate h, att→0, as follows

h = k2q2e ð16Þ

The graph of t/qt versus t (Fig. 11) for the linear pseudo-second-order model has been plotted, and the second order rate constant k2and maximum adsorption capacity qe have been calculated from theintercept and slope of this graph, respectively (Table 5). Thecorrelation coefficient value is magnificent, and the equilibriumadsorption capacity qe cal (2.94 and 3.508 mg g−1) determined byusing the second ordermodel is nearly the experimentally determinedequilibrium adsorption capacity qe exp (2.897and 3.456 mg g−1).

3.6.3. Intra-particle diffusion modelAccording to the intra-particle diffusionmodel proposed byWeber

and Morris [29], the initial rate of intra-particle diffusion can becalculated by plotting qt against t½

qt = kp tO + c ð17Þ

0 20 40 60 80 100 120 140 160 180 200

0

10

20

30

40

50

60

70 25mg/L 30mg/L

t/q

t

t(min)

Fig. 11. Pseudo-second order plots of Brushite.

Where, qt is amount of solute on the surface of the sorbent at timet, (mg g−1), kp is the intra-particle rate constant (mg g−1 min0.5), t isthe time (min) and c (mg g−1) is a constant that gives an idea aboutthe thickness of the boundary layer. If the Weber–Morris plot of qtversus t0.5 gives a straight line, then the adsorption process iscontrolled by intra-particle diffusion only.

The intra-particle rate constant kp and c parameters obtained fromthe plots of qt versus t½ for the intra-particle diffusionmodel are givenin Table 5. The value of c obtained from intra-particle diffusion modelis not zero and the correlation coefficient is not satisfactory, indicatingthat the intra-particle diffusion may not be the controlling factor indetermining the kinetics of the process.

As a result, we can say that the pseudo-second-order kinetic modelsuggested a good correlation for the adsorption of fluoride on theBrushite contrast to the pseudo-first-order model and intra-particlediffusion model, so pseudo-second-order model is suitable formodeling the adsorption of fluoride on the Brushite.

3.7. Effect of anions in the medium

The dependence of adsorbent capacity of the Brushite in thepresence of other anions which are commonly present in waternamely Cl−, SO4

2−, HCO3− and NO3

− have been investigated with afixed 100 mg L−1 initial concentration of these ions and by keeping25 mg L−1 initial fluoride concentration. As shown in Fig. 12 onlyHCO3

− ions have significant effect on adsorbent capacity of the DCPDand hence a reduction in adsorbent capacity has been observed whichmay be due to the competition effect of HCO3

− with F− in sorptionsites of the sorbent and the presence HCO−3 of increase the pH withconsequent decrease in adsorption capacity.

4. Conclusion

According to the results obtained in the study of the adsorption offluoride onto Brushite, we can conclude that:

• Experimental data have shown a good fit with the Langmuir,Freundlich and Temkin

• EDX analysis confirmed that F− has been adsorbed onto the DCPDparticles.

• Thermodynamic analysis has shown that the adsorption process hasendothermic and spontaneous in nature

• The kinetic study has indicated that the adsorption of fluoride isvery rapid, and the equilibrium has been reached within 60 min.

• The adsorption data have been modeled using the pseudo-first,pseudo-second-order kinetic and Intra-particle diffusion equations.

9M. Mourabet et al. / Desalination 278 (2011) 1–9

It has been shown that the pseudo-second-order kinetic bestdescribes the sorption kinetic.

• The adsorption capacity of the adsorbent for the removal of fluoridehas been compared with other adsorbents reported in the literature.

• As a result, Brushite can be used as an adsorbent for batchadsorption of F− ions from aqueous solution under differentconditions.

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