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Journal of Hazardous Materials 229– 230 (2012) 381– 389

Contents lists available at SciVerse ScienceDirect

Journal of Hazardous Materials

jou rn al h om epage: www.elsev ier .com/ loc ate / jhazmat

inetic modeling for dye removal using polyelectrolyte enhanced ultrafiltration

ourav Mondala, Hedia Ounib, Mahmoud Dhahbib, Sirshendu Dea,∗

Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaLETM, BP.273, 8020 Soliman, Tunisia

i g h l i g h t s

A model for dye removal by polyelectrolyte enhanced ultrafiltration is developed.Equilibrium constants are evaluated.Basis to develop engineered polyelectrolytes for this application.

r t i c l e i n f o

rticle history:eceived 14 April 2012ccepted 9 June 2012vailable online 15 June 2012

a b s t r a c t

A generalized kinetic model is proposed for the first time for dye removal using polyelectrolytes inapplication of polyelectrolyte enhanced ultrafiltration. Three polyelectrolyte-dye systems, reported in theliterature have been taken up for case studies. Different cases, namely, nature of dye and polyelectrolytesystem and their concentration, effect of solution pH and electrolyte concentration have been includedin the general framework of the modeling. The equilibrium constants are evaluated by minimizing the

eywords:olyelectrolyteyeetentionltraftiltrationomplexation constant

errors involved in the measured and experimental values of dye retention data. The matching betweenthe calculated and the experimental data is found to be adequate. A general phase space analysis involvingthe equilibrium constants has also been carried out to determine the region of feasible solution, in orderto facilitate dye removal using engineered polyelectrolyte.

© 2012 Elsevier B.V. All rights reserved.

hase space solution

. Introduction

Waste water from dye processing industries poses a threato environmental degradation. The toxic effect of dyes on thenvironment and human health is significant [1–3]. Removal ofyes has been done primarily through adsorption using differentdsorbents [4–7]. Other techniques involving oxidation [8], nanofil-ration [9], chemical coagulation [10], etc., are also available initerature. In recent years, the formation of polymer-organic com-lexes has gained significant importance. Removal of organics byolymer binding is an attractive alternative in this regard. Poly-lectrolytes are particularly useful for formation of complexes with

variety of molecules ranging from surfactants [11,12], peptides13], metal counterions [14,15], dyes [16–18], etc. Application ofolyelectrolyte in the removal of heavy metals by polyelectrolytenhanced ultrafiltration (PEUF) has a huge potential [19–22]. The

echanism of solute removal by the PEUF process is based on

he principle of complexation of the polymer molecule with theharged solute and retention of the complex using a relatively open

∗ Corresponding author. Tel.: +91 3222 283926; fax: +91 3222 255303.E-mail address: sde@che.iitkgp.ernet.in (S. De).

304-3894/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.jhazmat.2012.06.015

membrane [23–25]. Removal of low molecular weight solutesis possible with membrane filtration using reverse osmosis andnanofiltration. However, these processes are highly energy inten-sive, uneconomical and lack selective removal. On the other hand,the polymer complexes are much selective, larger in size and are,therefore, separated by higher molecular weight cutoff ultrafiltra-tion membrane leading to higher flux and feasibility of operation[26].

The rejection of inorganic ions by PEUF has been theoreti-cally modeled using the thermodynamic principles of reactionequilibrium [27,28] and also by the counterion-condensation phe-nomenon [15,29]. However, interaction of dyes with polymer wasnot yet developed. In the present study, a kinetic model based onthe reaction mechanism of reversible thermodynamics has beenpresented. The effects of the presence of co-ions and solution envi-ronment (pH) have also been analyzed. It is already well knownthat polymer nature [30], presence of salts [31] and changing pH ofthe solution [32] greatly affect the retention of the solutes. In thepresent study, a theoretical model has been developed under a gen-

eralized kinetic framework to predict the retention of polymer-dyecomplex formation. The constants for dissociation and com-plexation formation are optimized by comparing the calculatedretention profile with the experimental data [33,34]. An extensive

3 ous M

mie

2

inacma

(

(

(

((

(

t

L

L

wcttmi

K

K

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Sl

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S

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[

82 S. Mondal et al. / Journal of Hazard

athematical analysis has also been presented to relate anddentify the domains of the feasible solution of the different param-ters for various experimental conditions.

. Theoretical development

The binding of dye to the polymers is modeled as reaction dom-nated phenomenon. The kinetics of reaction greatly influences theature of dye attachment to polymer. Since, the monomer unitctually dissociates and reacts with the dye molecule, the con-entration of the polymer is considered in terms of equivalentonomer concentration. However, the following assumptions are

lso considered in the model description,

1) The ligand groups LH on the polymer chain behave as indepen-dent complexing groups.

2) All the polymer molecules are considered to have similarmolecular weight (molecular weight distribution of the poly-mer is unimodal and very sharp).

3) There is equal probability of attachment of a dye molecule to amonomer at all spatial location of the polymer.

4) Only 1:1 complexes are formed.5) The membrane completely retains the dye-polymer complex.

Hence, degree of dye attachment to the polymer is equivalentto membrane retention.

6) There is no interaction between the membrane and the freedye molecules and they are freely permeable through the mem-brane.

The reaction between the monomer and dye is represented byhe set of equilibrium reactions,

HKa�L + H (1)

+ DK1�LD (2)

here Ka is the dissociation constant and K1 is the complex formingonstant. It should be noted that the ionic charges are omitted, sincehey are not significant with respect to the modeling process. It iso be mentioned here that only the non-protonated form (L) of the

onomer is reactive to the dyes (D) and the protonated form (LH)s inactive. From the principles of thermodynamic equilibrium,

a = [L][H][LH]

(3)

1 = [LD][L][D]

(4)

he total concentration of the monomer and dye at any point ofime of filtration can be defined in terms of the free and boundorms,

L]t = [L] + [LH] + [LD] (5)

D]t = [D] + [LD] (6)

ubstituting the expressions in Eqs. (3) and (4) in Eq. (5), the fol-owing equation is obtained,

L]t = [L] + [L][H]Ka

+ K1[L][D] (7)

ubstituting Eq. (4) in Eq. (6), we obtain,

D] = [D]t

1 + K1[L](8)

he value of free dye molecules (D) is replaced in Eq. (7),

L]t = [L] + [L][H]Ka

+ K1[L][D]t

1 + K1[L](9)

aterials 229– 230 (2012) 381– 389

Since, reaction described in Eq. (1) is in equilibrium, [H] is equiva-lent to [L]. Therefore, Eq. (9) can be modified as,

[L]t = [L] + [L]2

Ka+ K1[L][D]t

1 + K1[L](10)

The only unknown in Eq. (10) is [L] which can be computed bysolving the cubic equation using a numerical scheme. The boundfraction (retention) of the dye is defined as,

R = 1 − [D][D]t

(11)

Using Eq. (8), retention (R) can be expressed as,

R = K1[L]1 + K1[L]

(12)

2.1. Retention of dyes at constant pH solution

The dissociation of the polymer in protonated and in non-protonated forms, and hence retention, is sensitive to theenvironmental conditions. pH of a solution is defined as,

pH = − log[H] (13)

Since, hydrogen ion concentration is related to the pH of a solution,the equilibrium relation stated in Eq. (3) can be written as,

Ka = [L][10−pH][LH]

(14)

Therefore, following similar steps of algebraic manipulation as dis-cussed earlier, the expression for free monomer concentration [L]can be expressed as,

[L]t = [L] + [L][10−pH]Ka

+ K1[L][D]t

1 + K1[L](15)

Eq. (15) can be solved for [L], and the retention is estimated asalready stated, using Eq. (12).

2.2. Effect of presence of co-ion on the retention of dye

In presence of co-ion, apart from two equilibrium reactions asmentioned in Eqs. (1) and (2), there is an additional reaction withthe co-ion to the monomer,

L + SK2�LS (16)

where [S] is the molar concentration of the salt. Therefore, from theprinciples of thermodynamic equilibrium,

K2 = [LS][L][S]

(17)

Since, the monomer in a solution also exists as [LS], Eq. (5) can bemodified as,

[L]t = [L] + [LH] + [LD] + [LS] (18)

Also, considering a mass balance for [LS], we obtain,

[S]t = [S] + [LS] (19)

Similarly, following the steps of algebraic manipulation as shownin Eqs. (7–10), we can obtain,

[L]t = [L] + [L]2

Ka+ K1[L][D]t

1 + K1[L]+ K2[L][S]t

1 + K2[L](20)

It must be noted that Eq. (20) is quartic in nature and has been

solved numerically. Feasibility and stability of the solution of Eq.(20) is analyzed in the next section to obtain the domain of thecomplexation constants (K1 and K2). The retention of dye [D] isonce again obtained with the help of Eq. (12).

ous M

2

2p

(l

�

(˛[

i

�

2c

K

T

[

wct

x

b

[

wep

(

w

c

d

e

It

y

Frhhir

S. Mondal et al. / Journal of Hazard

.3. Feasibility of solution of the cubic and quartic polynomial

.3.1. Analysis of the only polymer-dye interaction (cubicolynomial) without added salt

Considering the case of only interaction of dye with polymer (Eq.10)), the discriminant (�) is expressed as (assuming that equiva-ent monomer concentration [L]t � [D]t)

= (1 + KaK1)2(1 + K1[L]t)2K2

a − 4Ka[L]t(1 + KaK1)3

− 4K1K3a (1 + K1[L]t)

3 − 18K1Ka[L]t(1 + KaK1) − 27K2a K2

1 [L]t

(21)

In general, discriminant (�) of a cubic equation of the formz3 + ˇz2 + �z + ı = 0 is � = 18˛ˇ�ı − 4ˇ3ı + ˇ2�2 − 4˛�3 − 27˛2ı2

35]).Therefore, in order to have three distinct real roots, the following

nequality holds,

< 0 (22)

.3.2. Analysis of the only polymer-dye interaction in presence ofo-ion (quartic polynomial)

For the sake of algebraic simplicity, Eq. (20) is rearranged as,

1K2[L]4 + (K2 + K2 + KaK1K2)[L]3 + [1 + Ka(K1 + K2)

+ KaK1K2([D]t + [S]t − [L]t)] [L]2

+ [1 + K1([D]t − [L]t) + K2([S]t − [L]t)] [L] − Ka[L]t = 0

(23)

he above equation can also be written as,

L]4 + b1[L]3 + c1[L]2 + d1[L] + e1 = 0 (24)

here b1, c1, d1 and e1 can be evaluated by comparing theoefficients from Eq. (23). Eq. (24) can always be transformed intohe form,

4 + cx2 + dx + e = 0 (25)

y substituting

L] = x − b1

4(26)

here c = c1 − 3b21

8 ; d = b31

8 − b1c12 + d1; e = b2

1c1

16 − 3b41

256 − b1d14 +

1.Eq. (23) is biquadratic in nature and can be factorized into the aroduct of two quadratics [36] as,

x2 + px + q)(x2 − px + r) = 0 (27)

here

= q + r − p2 (28a)

= p(r − q) (28b)

= rq (28c)

f we set, y = p2, using Eq. (28), we can obtain a characteristic equa-ion of y,

3 + 2cy2 + (c2 − 4e)y − d2 = 0 (29)

or all positive real solution of x, y must have at least one positiveeal solution. Moreover, since, x is a quartic function and do not

ave more than four solutions (Eq. (27), it is necessary that y shouldave only one real solution (as y = p2). On the other hand, Eq. (29)

s a cubic polynomial in y, hence Eq. (29) has only one positive realoot and two complex conjugate roots. To satisfy the above criteria,

aterials 229– 230 (2012) 381– 389 383

the discriminant (�) of the cubic equation should be negative [37].The discriminant (�) of Eq. (29) is defined as,

� = 32c3d2 + 4c2(c2 − 4e) + 27d4 − 36c(c2 − 4e)d2

− 4(c2 − 4e)3

(30)

Analyzing Eq. (30) it can be concluded that for � < 0, the necessaryand sufficient criterion are,

c2 − 4e > 0 (31)

and,

c > 0 (32)

since, all the coefficients are real. Rewriting Eq. (31) in terms of b1,c1, d1 and e1, we obtain,

c21 − b2

1c1 + 316

b41 + b1d1 − 4e1 > 0 (33)

However, e1 is negative (refer to Eq. (23)), therefore, sufficientcondition for satisfying the inequality in Eq. (33) is

f (c1) = c21 − b2

1c1 + 316

b41 + b1d1 > 0 (34)

Eq. (34) is a quadratic function with respect to c1. The inequality inEq. (33) holds if the polynomial is satisfied at the minimum value,that is f(x) > 0 is always true if f(x)|min > 0. Eq. (34) is minimum atc1 = b2

1/2. Therefore,

f

(b2

12

)= − b4

116

+ b1d1 > 0 (35)

satisfies the condition if there is only one root of y. Since, b1 > 0always (refer to Eq. (23)), Eq. (35) can be modified as,

b31 < 16d1 (36)

In terms of Ka, K1, K2, [L]t, [D]t and [S]t, Eq. (36) can be simplifiedas,

K1K2

(Ka + 1

K1+ 1

K2

)3

< 16Ka [1 + K1([D]t − [L]t) + K2([S]t − [L]t)] (37)

Expressing Eq. (32) in terms of Ka, K1, K3, [L]t, [D]t and [S]t, we get,

Ka([D]t + [S]t − [L]t) >38

(K2

a + 1

K21

+ 1

K22

)− Ka

4

(1K1

+ 1K2

)

−58

(1

K1K2

)(38)

It must be mentioned that between Eqs. (37) and (38), Eq. (38) isthe sufficient criteria to be satisfied for a feasible solution space.Thus, the various constants Ka, K1 and K2 satisfy the inequalitiespresented by Eqs. (22) and (38), for real positive solution of [L].

2.4. Solution of the polynomial equation

The roots of the polynomial equation (Eqs. (10), (15), and (20))were determined by computing the eigen values of the companion

matrix of the coefficients [38,39] using MATLAB. The companionmatrix of a polynomial g(t),

g(t) = tn + un−1tn−1 + ... + u2t2 + u1t + u0 (39)

384 S. Mondal et al. / Journal of Hazardous Materials 229– 230 (2012) 381– 389

yes (a) CV; (b) EBBR and (c) ST.

i

M

ao

2c

tft

S

wfic

3

Efp

3

4wphrScw

3

galo

1.41.21.00.80.60.40.20.00

10

20

30

40

50

60

70

80

90

100

Ret

enti

on o

f C

V (

%)

1

2

symbols: experiment

solid lines: predicted

error bar ± 10%

1: Feed CV concentration - 10 ppm

2: Feed CV concentration - 100 ppm

Symbols: experiment at CV 10 ppm

Fig. 1. Structure of the d

s defined [40] as,

(g) =

⎛⎜⎜⎜⎜⎜⎜⎜⎝

0 0 . . . 0 −u0

1 0 . . . 0 −u1

0 1 . . . 0 −u2

......

. . ....

...

0 0 . . . 1 −un−1

⎞⎟⎟⎟⎟⎟⎟⎟⎠

(40)

The iterative scheme of finding roots of non-linear equations isvoided, since it is computationally time consuming and dependsn the initial guess set of parameters.

.5. Determination of the dissociation (Ka) and complexationonstants (K1 and K2)

The constants are obtained by constrained optimization [41] ofhe retention profiles calculated theoretically and those obtainedrom experiments. A minimization routine is defined by the sum ofhe squares of the retention values,

=n∑

i=1

(Ri − Rexp, i

Rexp, i

)2

(41)

here n denotes the total number of experimental points. The pro-les were optimized considering all the effects of dye retention (pH,o-ions, etc.)

. Experimental details

The experimental findings of PEUF for dyes, crystal violet (CV),riochrome Blue Black R (EBBR) and Saffarin T (ST) have been takenrom literature [33,34]. Some important experimental features areresented here.

.1. Materials

Three different dyes, CV, EBBR and ST having molecular weights,07.9, 416.4 and 350.8 g mol−1, respectively, obtained from Fluka,ere used in the present study. Two water soluble polymers:oly(acrylic acid) (PAA) and poly(ammonium acrylate) (PANH4)aving average molecular weights, 100,000 and 30,000 g mol−1,espectively, obtained from Sigma–Aldrich, were used in the study.odium hydroxide, chloride acid and sodium chloride were pur-hased from Sigma–Aldrich. Retention of PAA with CV and PANH4ith EBBR and ST were studied in the experimental procedure.

.2. Ultrafiltration experiments

Cross-flow membrane filtration was carried out with a tan-

ential cell system Minitan-S purchased from Millipore withn effective filtration area of 30 cm2. Organic regenerated cel-ulose membrane of molecular weight cut-off (MWCO) 10 kDabtained from Millipore was used for all the PEUF experiments. The

PAA concentration (mM)

Fig. 2. Variation of retention of CV with equivalent PAA monomer concentration.

value of linear permeability obtained from pure water fluxes was2.47 × 10−10 m/Pa s. Details of the experimental setup is describedelsewhere [33]. Ultrafiltration experiments were conducted atroom temperature (25 ◦C) and at fixed transmembrane pressureof 2 bar.

3.3. Method and analysis

The concentration of the dyes in the solution was measuredspectrophotometrically. The maximum absorbance of the dyes cor-responds to wavelengths of 590, 518 and 525 nm for CV [42], EBBR[43] and ST [44], respectively. The pH of the solution was main-tained by adding chloride acid or sodium hydroxide solutions.Studies were carried out to see the effect of pH in the range of 2–12.The dye concentration was same, 10 ppm, in all the experiments,for all the different dyes.

4. Results and discussion

4.1. Effect of polyelectrolyte concentration

The structure of three dyes, CV, EBBR and ST is shown in Fig. 1.From this figure, the ionic centers (sites of attachment) of thesedyes are observed. Simulation of polyelectrolyte enhanced ultra-filtration of dye is performed with three different combinations;these are removal of crystal violet (CV) with polyacrylic acid (PAA),Eriochrome Blue Black R (EBBR) and Saffarin T (ST) with polyam-monium acrylate (PANH4). Fig. 2 shows the retention of CV withchange in PAA concentration. The dissociation constant (pKa) ofPAA and the metal complexation constants (log K1) for PAA-CV

system are obtained by minimizing the retention profile of thetheoretical and experimental values. The optimization results arereported in Table 1. It is observed from Table 1, that the value of dis-sociation constant of PAA pKa is 4.8 which is close to that available in

S. Mondal et al. / Journal of Hazardous Materials 229– 230 (2012) 381– 389 385

Table 1Values of the dissociation and complexation constants obtained from simulation.

System Values

pKa log K1 log K2

PAA + CV 4.8 ± 0.1 6.5 ± 0.2 3.7 ± 0.1

lbmacettctciifio

mapibtIrtBwmasopao

Fc

0.50.40.30.20.10.00

10

20

30

40

50

60

70

80

90

100

Ret

enti

on

of

ST

(%

)

PANH4 concentration (mM)

symbols: experiment

solid lines: predicted

error bar ± 10%

1: Feed ST concentration - 10 ppm

2: Feed ST concentration - 100 ppm

Symbols: experiment at ST 10 ppm

PANH4 + EBBR 5.8 ± 0.1 6.0 ± 0.1 4.0 ± 0.2PANH4 + ST 5.8 ± 0.1 6.2 ± 0.1 4.0 ± 0.2

iterature [45]. The change in feed CV concentration is representedy curve 2 in figure which shows that the attachment of dyeolecules is hindered when the dye concentration is increased

t lower PAA concentration (upto 0.4 mM). For the same polymeroncentration upto 0.4 mM, at lower concentration, dye is prefer-ntially adsorbed to the monomer sites of PAA. Since, the numbero attachment sites is much higher compared to relative concentra-ion of the dye and the polymer molecule, beyond a certain polymeroncentration, attachment of dyes is very sharp. This implies thathe electrostatic attraction of the monomer is strong enough toapture the mobile dye molecules. As the polymer concentrationncreases, the mean free path of the dye molecule decreases result-ng in enhanced binding of the dye molecule. This is significantor lower concentration of PAA. At higher concentration, this effects marginal. The simulated data matches with the experimentalbservation within ±3%.

Figs. 3 and 4 shows the effect of two different dyes on the attach-ent to PANH4. Figures show that the modeled parameters (pKa

nd log K1) accurately predict the binding of dye molecules. Com-aring Figs. 3 and 4, it can be observed that the retention of ST

s slightly higher than EBBR, at the same feed concentration ofoth the dyes. This is because the molecular weight of ST is lowerhan EBBR leading to faster mobility and preferential attachment.ncreasing the dye concentration 10 folds significantly changes theate of retention of the dye with PANH4. It must be mentioned herehat the structure of dye molecule also plays a key role in this regard.oth EBBR and ST have four aromatic rings, unlike the CV molecule,hich is responsible for steric hindrance in attachment of theseolecules to the polymer sites. Moreover, presence of unsaturated

mine groups in the ST structure results in multiple resonancetructure, thereby, affecting the charge group attraction. Spatialrientation of such bulky asymmetric molecules, having only one

referential position of attachment is also an important consider-tion in its attachment. It must be mentioned here that the structuref CV is highly symmetric in its spatial arrangement and there is

0.50.40.30.20.10.00

10

20

30

40

50

60

70

80

90

100

Ret

enti

on o

f E

BB

R (

%)

PANH4 concentration (mM)

symbols: experiment

solid lines: predicted

error bar ± 10%

1: Feed EBBR concentration - 10 ppm

2: Feed EBBR concentration - 100 ppm

Symbols: experiment at EBBR10 ppm

1

2

ig. 3. Retention of EBBR with equivalent poly(ammonium acrylate) monomer con-entration.

Fig. 4. Retention of ST with equivalent poly(ammonium acrylate) monomer con-centration.

equal probability of attachment of the molecule with any one ofthe sp2 hybridized nitrogen atoms. It can be qualitatively inferredthat a CV molecule is approximately three times more active thanEBBR in its attachment, which is, in fact reflected through log (K1)values for the two systems. As observed from Table 1, log K1 forCV is highest among three dyes. The other constants for these sys-tems are reported in Table 1. From Figs. 3 and 4, it can be observedthat the simulated data matches with the experimental observationwithin ±3%.

4.2. Effect of solution pH

The next figure (Fig. 5) shows the variation of retention of CVwith change in pH. The dye is completely attached to the monomersbeyond pH 3. In order to enhance the retention, alkaline environ-ment is preferred. As, the hydrogen ion concentration (lower pH)increases, dissociation of the dye and the COOH group of PAA isprevented and that is responsible for lower retention. Since, thepKa value of PAA is in the acidic range, there is complete retentionof the dye at the neutral pH. The sharp transition of dye retention

when pH is increased from 1 to 4 is also observed in another study[46]. Unlike polyethyleneimine (PEI) where the complexation con-stants changes its value with the pH of the solution [47], the rate of

121086420

10

20

30

40

50

60

70

80

90

100

Ret

enti

on

of

CV

(%)

Dis

soci

atio

n f

ract

ion

(%)

pH

symbols: experiment

solid lines: predicted

error bar ± 10%

1

2

1: Retention of CV

2: Dissociated fraction

of PAA

Fig. 5. Retention of CV and dissociation fraction of PAA with pH of the solution. PAAconcentration is 40 ppm.

386 S. Mondal et al. / Journal of Hazardous Materials 229– 230 (2012) 381– 389

1210864200

20

40

60

80

100

Ret

enti

on o

f E

BB

R(%

)

pH

symbol s: exper iment

solid l ines: pr edic ted

error bar ± 10 %

1

Fa

dscDtttosbsdi2s±

imrosnd

FP

50040030020010000

10

20

30

40

50

60

70

80

90

100

Ret

enti

on o

f C

V (

%)

Concentration of NaCl (mM)

symbols: experiment

solid lines: predicted

error bar ± 10%

Fig. 8. Variation of the retention of CV with salt concentration. PAA concentrationis 40 ppm and CV concentration is 10 ppm.

ig. 6. Retention of EBBR with pH of the solution. PANH4 concentration is 40 ppmnd EBBR concentration is 10 ppm.

eprotonation for PAA is only affected by the charge density of theolution and not by the self secondary structural configurations. Thearboxylic groups of PAA are expected to exhibit acidic strength.uring the dissociation of PAA, the ionized carboxylic groups of

he polyacid attract the protons. As a consequence, the deprotona-ion of a functional group depends on the dissociation degree of allhe other groups. Curve 2 shows the trend of fraction dissociationf the polymer molecule with pH of the solution. The polymer dis-ociates significantly (95%) beyond its pKa value. However, it muste noted that, even though the curve shows that below pH 2, dis-ociation is zero (in that retention would also have been zero), thisoes not present the real picture. Actually, the dissociated fraction

s 3–4 orders of magnitude less than 1 in the range of pH less than, which is not apparent from figure (as it has a linear scale). Theimulated data matches with the experimental observation within1%.

Variation of retention of EBBR with solution pH is illustratedn Fig. 6. It shows that retention decreases in the alkaline environ-

ent. The presence of sulphonate group in the EBBR dye molecule isesponsible for this behavior. In the acidic regime, the dissociation

f PANH4 is very minimal (as evident from curve 2 of Fig. 7) whichuggests that binding of EBBR to the monomer sites is dominated byon-electrostatic effects. The rate based kinetic model predicts theecrease of EBBR binding in the alkaline regime, where dissociation

14121086420

20

40

60

80

100

Ret

enti

on o

f S

T(%

)

Dis

soci

atio

n f

ract

ion(%

)

pH

symbols: experiment

solid lines: predicted

error bar ± 10%

1: Retention of ST

2: Dissociated fraction

of PANH4

1

2

ig. 7. Retention of ST and dissociation fraction of PANH4 with pH of the solution.ANH4 concentration is 40 ppm.

of the polymer is complete. With the increase in pH of the solution,the hydroxide groups makes the EBBR molecule more polar (neg-atively charged), leading to like charge repulsion with the COO−

group of the polymer. It must be mentioned that non-bonded inter-action of EBBR is mostly non-electrostatic in nature.

Fig. 7 shows the binding of ST with PANH4 with varying pH ofthe solution. The experimental data at lower pH is not accuratebecause of measurement difficulties at high acidic environment.Also, to maintain low pH environment, there is strong effect of theco-ions added to system which leads to counterion–co-ion inter-action. Figure clearly shows that ST attachment is favored at pHbeyond 5. This can be explained on the basis of the competitionof H+ and ST to be bound to the polymer as a result of protona-tion of the carboxylate groups. Similar behavior was also observedin the case of removal of inorganic ions with PANH4 [5]. The dis-sociation of the polyelectrolyte (PANH4) reaches maximum at pHgreater than 8. As the solution alkalinity increases, the ammoniumgroups detach from the amide functional form and form ammo-nium hydroxide in the solution, resulting in increase in dissociationof the polymer.

0.50.40.30.20.10.00

10

20

30

40

50

60

70

80

90

100

3, NaCl 0.01(M)

2, NaCl 0.001(M)

1, NaCl 0.0001(M)

Ret

enti

on

of

EB

BR

(%

)

Concentration of PANH4 (mM)

1

2

3

symbols: experiment

solid lines: predicted

error bar ± 10%

Fig. 9. Effect of salt concentration on the retention of EBBR.

S. Mondal et al. / Journal of Hazardous Materials 229– 230 (2012) 381– 389 387

0.50.40.30.20.10.00

10

20

30

40

50

60

70

80

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100R

eten

tio

n o

f S

T (

%)

3, NaCl 0.01(M)

2, NaCl 0.001(M)

1, NaCl 0.0001(M)

symbols: experiment

solid lines: predicted

error bar ± 10%

3

2

1

4

pioaTtiSmldcdcdsc

a

Fc

8765432101

2

3

4

5

6

7

log K

1

pKa

1

2

3

4

1: [L]t = 0.1 mM

2: [L]t = 1 mM

3: [L]t = 10 mM

4: [L]t = 100 mM

876543210-3

-2

-1

0

1

2

3

log K

1

pKa

1: log K2 = 1E+03

2: log K2 = 1E+04

3: log K2 = 1E+05

4: log K2 = 1E+06

1

2

34

a

b

Fig. 12. (a) Phase space plot of feasibility solution of polyelectrolyte-dye associa-

Concentration of PANH4 (mM)

Fig. 10. Effect of salt concentration on the retention of ST.

.3. Effect of salt concentration

The effect of co-ions on the retention of the dye (CV) with theolymer (PAA) is presented in Fig. 8. As the salt concentration

ncreases, there is a competitive inhibition occurs between bindingf the dye molecule and the salt to the monomer. However, beyond

certain salt concentration, the retention does not decrease further.his can be explained from the fact that, at a critical salt concen-ration, the attachment sites are completely saturated and theres no further scope of attachment of either the dye or the co-ion.ince, the salts completely dissociate in the solution, in order toaintain electroneutrality of the solution, there is dynamic equi-

ibrium between the relative attachment of dye molecules, salts andissociation of dye molecules and the polymer. There is a signifi-ant deviation of the theoretical prediction with the experimentalata at high salt concentration. This is because that at high saltoncentration, the polymer dissociation is affected by the localevelopment of the charged layer near the monomer attachment

ites owing to distortion of the electric field attraction of the freeounterions [48].

Fig. 9 shows the effect of electrolyte on retention of EBBR. For fixed polymer concentration, retention of dyes decreases due to

0.40.30.20.10.00

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10

15

20

25

30

1.41.21.00.80.60.40.20.0

Concentration of PAA(mM)

Dis

soci

ated

fra

ctio

n o

f th

e poly

mer

(%

)

Concentration of PANH4(mM)

1

2

3

1: CV with PAA

2: EBBR with PANH4

3: ST with PANH4

ig. 11. Dissociation fraction of the polymers interacting with the dyes. Dye con-entration is 10 ppm.

tion and removal. (b) Phase space plot of feasibility solution of polyelectrolyte-dyeremoval in presence of co-ion.

competitive adsorption of co-ions. This trend is clear from the sim-ulation curves 1–3 corresponding to various salt concentrations.As discussed earlier, for a fixed salt concentration, retention of dyeincreases with polymer concentration due to availability of moresites. However, it may be observed from this figure that the experi-mental data upto 0.15 mM of polymer, do not match the simulationresults well. This may be due to the errors involved in the measure-ments.

Fig. 10 shows the variation of the retention profile of ST withvarying polymer concentration in presence of salt (NaCl). At lowsalt concentration (curve 1), the retention profile corroborates withFig. 4. The retention decreases with the salt concentration, butincreases with the polymer concentration. Similar to Figs. 8 and 9,at high salt concentration the theoretical prediction deviates awayfrom the experimental points, as already explained earlier. Thecomplex formation constants (log K2) as observed from Table 1,show similar values for the EBBR-PANH4 and ST-PANH4 system,which suggests that salt attachment to the polymer is hardlyaffected by the presence of counterions in the solution.

Fig. 11 shows a simulated plot of the dissociated fraction of thepolymer for the different polymer-dye systems. The dye concen-tration is fixed at 10 ppm for all the dye considered in this study.

It can be inferred from figure, that dissociation of PAA more thanPANH4, because of lower pKa value of PAA than PANH4. As thepolymer solution increases, the extent of dissociation decreases,

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88 S. Mondal et al. / Journal of Hazard

ecause of lower interaction with the dye molecule and to maintainlectroneutrality of the solution.

The phase space plot or region of feasible solution for the case ofolyelectrolyte and dye without salt and with salt is presented inig. 12(a) and (b), respectively. The curves in Fig. 12(a) are gen-rated from the solution of Eq. (22) in case of without salt forifferent concentration of polymer. The upper region of each curveorresponds to the region of feasible solution. From Figs. 2–4, it isbserved that polyelectrolyte concentration varies between 0.1 and.2 mM. Thus, log K1 and pKa values for different polyelectrolyte-ye combinations should be above curve 1. This is corroboratedy these values presented in first two columns of Table 1. Simi-

arly, the phase space plot for three equilibrium constants K1, K2nd Ka for polyelectrolyte-dye system in presence of salt is pre-ented in Fig. 12(b). The curves are generated from the solution ofq. (38). In this figure also, the feasible range of solution is aboveach curve. From Table 1, it is observed that log K2 values for eachye-polyelectrolyte combination is around 4.0. This corresponds tourve 2 in Fig. 12(b). It is clear that corresponding to curve 2, pKa

nd log K1 values as observed from Table 1, are well within theeasible range of the solution. One important interpretation cane derived from Fig. 12. These figures show the combination ofquilibrium constants for successful attachment of dye moleculeo a polyelectrolyte. Thus, these characteristic curves may be usedo prepare tailor-make polyelectrolytes specifically for a particu-ar dye. These characteristic curves may be useful for preparationf engineered polyelectrolytes in the application of polyelectrolytenhanced ultrafiltration of dye solution.

. Conclusion

The general kinetic model proposed in this work explained thexperimental trends. Effects of polyelectrolyte concentration, pH,nd electrolyte concentration were successfully explained by theodel. The model predictions in most of the cases were well within10% of the experimental data. The dissociation values (pKa) forAA-CV system was the lowest as 4.8 ± 0.1. These values for PANH4-BBR and PANH4-ST systems were 5.8 ± 0.1. The dye complexationonstants (log K1) values for these systems were in the range of.0–6.5 and the salt complexation constant (log K2) in presencef counterions for all the systems were around 4.0. The analysisf phase space plots involving the equilibrium constants provides

basis for preparation of engineered polyelectrolytes to enhanceemoval of a particular dye with extremely high specificity.

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