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Journal of Membrane Science 336 (2009) 128–139

Contents lists available at ScienceDirect

Journal of Membrane Science

journa l homepage: www.e lsev ier .com/ locate /memsci

tudy of polymer–metal ion–membrane interactions in liquid-phaseolymer-based retention (LPR) by continuous diafiltration

anuel Palencia a, Bernabé L. Rivas a,∗, Eduardo Pereira b, Antonio Hernández c, Pedro Prádanos c

Department of Polymer, Faculty of Chemistry, University of Concepción, Casilla 160-C, Concepción, ChileDepartment of Analytic and Inorganic Chemistry, University of Concepción, Casilla 160-C, Concepción, ChileDepartment of Applied Physics, Universidad de Valladolid, Faculty of Science, Real de Burgos s/n, 47071 Valladolid, Spain

r t i c l e i n f o

rticle history:eceived 17 January 2009eceived in revised form 10 March 2009ccepted 16 March 2009vailable online 27 March 2009

eywords:nteraction coefficients

a b s t r a c t

In this work were studied polymer–metal ion–membrane interactions during continuous diafiltration ofdivalent metal ions (Co2+, Ni2+, Cu2+, Zn2+, Cd2+, and Pb2+) using poly(acrylic acid) (PAA) as water solublepolymer by liquid-phase polymer-based retention (LPR) technique at pH 6. Polyethersulfone (PES) mem-branes were used and characterized by different methods (solute rejection test, force atomic microscopy(AFM) and contact angle). Changes on fouled membrane roughness (22.91 ± 2.2) with respect to virginmembrane (7.05 ± 4.6) and changes on contact angle measures (76.0 ± 0.9 and 85.0 ± 2.34 with water) sug-gest an increasing in surface hydrophobicity of PES membrane associated mainly with deposited forming

rue retention coefficientontinuous diafiltrationolymer enhanced ultrafiltrationater soluble polymer

on the surface as results of enhanced in the polymer–membrane interaction throughout proceed filtra-tion. From metal ion concentration data in the permeate throughout filtration experiment polymer–metalinteractions were studied and analyzed by equations based on the combination of molar binding ratioand the consideration of chemical equilibrium between the polymer and metal ions. Membrane–metalion interaction was around 10% for all cations studied, with the following order in the interactions:Ni2+ ≈ Zn2+ > Pb2+ > Co2+ > Cu2+ > Cd2+. A relatively high and specific interaction of the carboxylate groups

as ob

of PAA with metal ions w

. Introduction

Membrane separation processes are very interesting for waterreatment owing to, among other factors, their simplicity of oper-tion and moderate energy consumption. These processes haveound important industrial applications for wastewater purifica-ion, water reuse, and recovery of some valuable materials.

In the case of ultrafiltration, this technique has been foundo be applicable to the treatment of effluents (i.e. wastes fromlectroplating) that contain metal ions if the membrane materialauses appropriate polymer–metal interactions [1–3]. In classicalltrafiltration systems, the membrane works as a molecular sizearrier, but the pore size is too large to retain metal ions except

n their colloidal form [2]. On the other hand, the formation ofigh molecular weight species by complexation with water-solubleacromolecules leads to metal-ion retention and a concentration of

etal solutions in the ultrafiltration unit. Moreover, metal selective

xtraction can be achieved if specific chelating groups are bondedo the polymeric chains [2,3]. This technique has been called inifferent ways: liquid-phase polymer-based retention (LPR) [3,4],

∗ Corresponding author. Fax: +56 41 2245974.E-mail address: brivas@udec.cl (B.L. Rivas).

376-7388/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2009.03.016

served. This interaction showed the order: Cu2+ > Cd2+ > Co2+ > Ni2+ ≈ Zn2+.© 2009 Elsevier B.V. All rights reserved.

polymer assisted ultrafiltration (PAUF) [5], polymer enhanced ultra-filtration [6], polyelectrolyte enhanced ultrafiltration (PE-UF) [7], orsimply, enhanced ultrafiltration [8].

The principle of complexation–ultrafiltration was firstly sug-gested by Michaels in 1968 [2], besides, Blatt et al. presented atheoretical discussion to connect the method of analysis by diafil-tration with continuous ultrafiltration [1,9]. In general, a polymersolution is placed in contact with a metal-ion solution in the feedside of an ultrafiltration system. The metal ion is bonded to thepolymer and retained while the unbonded species (low molecularweight solutes) pass through the membrane [1–9].

Most researches in relationship with the LPR technique havebeen done in order to study the capacity of retention of severalions (i.e. Hg2+, Ni2+, Cu2+, Pb2+, Mn2+ and Zn2+) with different typesof polymers (i.e. polycarboxylic acids, polyphosphonic acids, poly-sulfonic acids and polyamines) [3,5,10–13]. In very few studies, theanalysis included some variables which can affect the ultrafiltrationprocess in the context of LPR experiments (i.e. pressure, tempera-ture, membrane type, and feed circulation rate). Even less studies

focused on the effects of the characteristics and properties of themain components of the system (membrane and polymer) and theirinteractions on the performance of LPR [8,14–18].

There are two methods usually used in LPR: the washing method(with the ionic strength kept constant or not) and the enrichment

mbran

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pm(conm(sa

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2

2

m

R

Ctr

R

wpdtttrtr�

M. Palencia et al. / Journal of Me

ethod [3]. The most used method to study the metal-ion retentionapacity of a polymer in aqueous solution is the washing method,hich is a discontinuous process. In this method, a certain amount

f polymer and metal-ion solutions with known concentrations arelaced in the feed side of a ultrafiltration cell and a water stream isassed through the cell. The theory and mathematical descriptionf the method have been presented by different authors [3,4,19,20].

The enrichment method uses continuous diafiltration [1,9,21].n this case, the macromolecular solution is placed in a stirred cellnd a metal-ion solution is added continuously from a pressurizedeservoir. During the process, the permeate is removed at the sameate, keeping the volume in the feed cell and the polymer concentra-ion constant all the time. When the bonding groups of the polymerre saturated by their interaction with the metal ion in the solution,he maximum retention capacity (MRC) of polymer is reached andhe process cannot continue [1,3,10]. Evidently, the physicochemicalroperties of the polymer and the polymer–metal complexes muste taken into account and their interaction with the membrane sur-

ace is also very relevant. This makes important to analyze how therocess affects the membrane.

The LPR technique should be economically more feasible, if theolymer could be regenerated and reused. Among regenerationethods of the polymeric agent there are: chemical regeneration

protolysis, transcomplexation and redox reaction), electrochemi-al regeneration and thermal regeneration [19]. In this way, newptions of regeneration of chelating groups by using new compo-ents incorporated to the system can be useful to make the processore feasible. A presentation of the different ultrafiltration modes

continuous and discontinuous), a comparison of these modes, andome thoughts about the optimization of them were given by Dutrénd Trägardh [22].

The aim of this work is to study the polymer–metal ion,embrane–metal ion, and polymer–membrane interactions during

he continuous diafiltration of divalent metal ions using poly(acryliccid) (PAA) as the water soluble chelating polymer by LPR tech-ique (enrichment method). This work is a part of a wider research

or the development of an in situ regeneration system of polymerichelating groups into ultrafiltration system to increase the metal-on retention capacity (MRC).

. Theory

.1. Membrane functional characterization

The retention coefficient R is a parameter, depending only on theembrane and solute characteristics, and it is defined as:

= 1 − Cp

Cm(1)

p and Cm being the concentrations of the permeate and directly onhe feed side of the membrane Cp respectively. However, observedetention (R0) can be measured experimentally which is defined as:

0 = 1 − Cp

C0(2)

here, C0 is the concentration of the feed. The concentration–olarization, which is the balance between accumulation and back-iffusion, produces that concentration directly on the membrane athe feed side is different to concentration feed. In order to obtainhe true retention coefficient [1,22–25], flow and permeate concen-

ration of test solutes can be measured either for changing surfaceates on the feed side of the membrane or for different feed concen-rations. Thus, the flow through the membrane, Jv, and the observedetention, R0, should be obtained as a function of recirculation rates,, or feed concentrations, C0.

e Science 336 (2009) 128–139 129

According to the film theory, it is possible to analyze the massbalance in the boundary layer by taking into account convective anddiffusive flows for the solute:

Js = JvC − DdC

dx(3)

Js and Jv are the solute flux and the volume flow, respectively, Dis the solute diffusivity and C is the solute concentration. The soluteflux is Js = JvCp, the boundary conditions in the film layer shouldbe:

x = 0 → C = C0x = ıc → C = Cm

}(4)

ıc being the film thickness. The mass transfer coefficient, Km, acrossthe polarization layer can be calculated as:

Km = D

ıc(5)

Thus, after the integration of Eq. (3):

Jv = Km ln

(Cm − Cp

C0 − Cp

)(6)

The gel layer model considers that the concentration on the mem-brane reaches a limit Cm = Cg for long time. This gel concentrationshould actually depend on the operation conditions. The flowthrough the membrane can be described when this limit has beenreached by

Jv,lim = �P

�(Rm + Rg)= Km ln

(Cg − Cp

C0 − Cp

)(7)

where, � is the solution viscosity, Rm is the intrinsic membraneresistance and Rg is the additional resistance produced by the gellayer [24,25]. Eq. (7) can be written in terms of the retention coef-ficients as:

ln(

1 − R0

R0

)= ln

(1 − R

R

)+ Jv,lim

Km(8)

A plot of ln((1 − R0)/R0) as a function of Jv should give a straight linewhen gelation is reached (i.e. at high volume flows) with a slopegiven by 1/Km and an ordinate intercept of ln((1 − R)/R). In order toget different flows we can change the feed concentration, but it iseasier from the experimental point of view, to change the velocityon the membrane feed surface.

The mass transfer coefficient can be assumed to depend on thevelocity on the membrane surface as:

Km = ˚�ω (9)

where, ω is a constant depending on flow conditions and the lengthof the flow channel on the membrane and ˚ depends both on thegeometry of the channel and on the characteristics of the solutionand the solute diffusivity. Several values for ω can be found in the lit-erature [1] for different conditions of the flow through the channelon the membrane. Then

ln(

1 − R0

R0

)= ln

(1 − R

R

)+ Jv,lim

˚�ω(10)

Thus, if we plot ln((1 − R0)/R0) versus Jv,lim/�ω , it is possible toobtain ˚ from the slope of the straight and R from the ordinateintercept. This allows an evaluation of Cm if C0 is known. The processoutlined here will be applied here to characterize the ultrafiltra-tion membrane used in LPR experiments and is called method of

variation of the surface velocity.

The information on R allows drawing the standard retentioncurves in order to find the real molecular weight cut-off for themembrane [1,24]. In effect, Jw,t being the pure water flux transmit-ted through the fraction of pores that do not reject the solute and Jw

130 M. Palencia et al. / Journal of Membra

Fi

ti

Tpftb

b

B[tmf

2

mr((teem

cogttott

2

f

ig. 1. Scheme of the process of metal-ion retention by an aqueous soluble polymern a ultrafiltration system.

he pure water flux passing through all the pores in the membrane,t is easy to arrive at:

Jw,t = Jv(1 − R)Jw = Jv − Js = Jv(1 − Cp)

}Jw,t

Jw= 1 − R

1 − Cp(11)

his ratio Jw,t/Jw versus Mw gives the accumulated function of fluxassing through the non-rejecting pores and the derivative of this

unction provides the flux transporting molecules of a given Mw

hrough the membrane. A more detailed description has been giveny different authors [26,27].

In order to accomplish the derivation, the following function haseen reported to fit the cumulative data:

Jw,t

Jw= 1

1 + (Mw/B)x (12)

and x are constants to be evaluated from the experimental data26]. On the other hand, the abscissas can be changed from Mw

o pore diameter (dp) by considering the gyration radii, rg,of theolecules of the solutes used in the test and thus getting the dif-

erential pore size distribution from d(Jw,t/Jw)/d(dp).

.2. Liquid-phase polymer-based retention (LPR)

The LPR technique is based on the interaction between the poly-er and the metal ions in aqueous solution and the subsequent

etention by an ultrafiltration membrane of the complexes formedsee Fig. 1). The type of interaction depends on the chemical natureionization potential and electronic affinity) of the polymer func-ional groups. In any case, these interactions are mainly due tolectrostatic forces and the formation of coordinating bonds. How-ver, other phenomena may appear such as the trapping of theetal ions in the bulk of the polymer phase [3].

The variables that affect the polymer/metal ion interaction arelassified into two groups: intrinsic to the polymer (i.e. the naturef the atoms in the backbone chain, the nature of the functionalroups attached to the backbone, the structure and composition ofhe polymer, the molecular weight and the polydispersity, the dis-ance between the functional groups and the backbone, the degreef branching, etc. . .) and extrinsic to the polymer (i.e. charge andype of the metal ion, the pH of the solution, the ionic strength, the

emperature, and the dielectric constant of the medium) [3,12].

.2.1. Metal–membrane interaction coefficientThe metal ions in the cell can appear in three configurations:

ree in the solution or unbounded (Ccf), bound to the polymer (Ccb),

ne Science 336 (2009) 128–139

and linked to the membrane due to rejection and/or sorption. Theconcentration of metal ions in the cell (C0) is given by Cc = Ccf + Ccb.Then the retention of free ions is, R0f:

R0f = 1 − Cp

Ccf(13)

Cp being the concentration of metal ions in the permeate.The general differential mass balance equation in the presence

of polymer can be written as:

Vcd(Ccf + Ccb)

dt= QCr − QCp (14)

Q = dVp/dt, Vc is the volume of the cell, Q is the flow rate, Vp is thepermeate volume and Cr is the reservoir concentration. Vc, Q and Cr

are constants. From Eq. (14), using dt = dVp/Q and considering that1 − R0f is the fraction of metal ions not rejected by the membraneand therefore the real concentration of free ions in the cell is givenby Ccf = Cp(1 − R0f) according to Eq. (13), we obtain:

Vc

1 − R0f

dCp

dVp+ Vc

dCcb

dVp= Cr − Cp (15)

In the case of the enrichment experiments in the absence of poly-mer (Ccb = 0), the permeate concentration should be C∗

p and:

ln

(Cr

Cr − C∗p

)= Vp(1 − Rof )

Vc(16)

Thus a plot of ln[Cr/(Cr − C∗p)] versus (Vp/Vc), yields a straight line

with a slope given by 1 − R0f [21–23]. This coefficient R0f is a mea-sure of the interaction of the metal ions with the membrane.

2.2.2. Metal–polymer interaction coefficientsIn relation to the metal-polymer interaction the bonded ion con-

centration, Ccb, can also be described by

Ccb = r[PT ] (17)

where r is the molar binding ratio (mole of ion bound to one moleof polymer), and [PT] is the total concentration of polymer added.Assuming that there is chemical equilibrium between the polymer(P) and metal ions (M):

P + M ↔ PM (18)

The association constant, Ka, is defined as:

Ka = [PM][P][Mf ]

(19)

where [PM] = Ccb is the metal–polymer complex concentration,[P] the free polymer concentration, and [Mf] = Ccf the free metal ionconcentration. Note that [PT] = [P] + [PM]. Then, according to Eqs.(15) and (19):

r = KaCcf

1 + KaCcf(20)

Note that r is not constant but depends on Ccb. If there were n inde-pendent sites with the same unique intrinsic binding constant, theconcentration Ccb should be n times that resulting from the associ-ation with one single site. Thus, instead of Eq. (20), it is obtained:

r = nKaCcf

1 + KaCcf(21)

Rearranging:

r

Ccf= Kan − Kar (22)

Plotting r/Ccf versus r would result in a line with a slope given by−Ka, and an ordinate intercept equal to −Kan. If there would exist

M. Palencia et al. / Journal of Membrane Science 336 (2009) 128–139 131

F

mwaiw

r

Tcet

mbuau(

3

3

2TwIMTX

PbaTmT(

3s

troscopy (Unicam Solaar M5).

ig. 2. Scheme of the ultrafiltration stirred cell device used for the LPR experiments.

ore than one type of binding sites, the plot should be a curvehose linear portions should refer to different binding sites and

ssociation constants. The value of Ccf is equal to Cp, when theres no retention of free metal ions by the membrane, and Cp/1 − R0f

hen there is some rejection [21].(1 − R0f

Cp

)= Kan − Kar (23)

his relationship allows an evaluation of the interaction coeffi-ients, n and Ka, for a known dependency of r on Cp once R0f has beenvaluated from measurements in the absence of polymer accordingo Eq. (16).

In order to find the molar binding ratio, the general differentialass balance in a diafiltration experiment given in Eq. (15) must

e numerically integrated to obtain Ccb and then Eq. (17) must besed. Ccb can be evaluated from data on the time evolution of Cp

nd Vp if Vc, Cr and R0f are all known. This Ccb relationship allowss to obtain r as a function of Cp, if [PT] is known (according to Eq.17)) in order to get information on n and Ka by Eq. (23).

. Experimental procedure

.1. Reagents

Poly(acrylic acid) was used, PAA, (solution 25%, Aldrich, Mw :50 000 Da, d: 1.267 g/cm3, n20

D : 1.3950) as bonding polymer.he PAA was chosen since its interaction and retention capacityith metal ion has been studied by different techniques [28–30].

n the feed solutions, different nitrates of analytical grade fromerck, with a general expression Mn+(NO3)n·XH2O, were used.

hese included the anions Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Pb2+ withbeing: 6, 6, 2.5, 6, 4 and 0 respectively.

In order to characterize the membrane, polyethylene glycols,EGs, are customarily used, because they are water soluble and cane readily obtained with narrow molecular weight distributionsnd their adsorption is very low on almost all polymer surfaces.he PEGs used here were obtained from Fluka Chemie AG. Theirolecular weights were: 1000, 3000, 6000, 12 000 and 20 000 Da.

hey were used in aqueous solution in a low concentration of 0.10%

w/w) to assure a minimal membrane–solute interaction [24].

It is worth noting that for PEGs with Mw from 300 to5 000 g mol−1, from data reported in the literature [31], it is pos-ible to obtain a relationship for rg as a function of Mw at 25 ◦C

Fig. 3. Scheme of the ultrafiltration parallel plate tangential flow device used for theretention test method to characterize the membrane.

given by

rg = w1

1000(Mw)w2/1000 [×10−9 m] (24)

w1 = 31.63 ± 1.31; w2 = 499.87 ± 0.43 with a correlation coeffi-cient of 0.9999.

3.2. Filtration experiments

Polyethersulfone (PES) disk-shaped (44.5 mm in diameter)membranes with a nominal cut-off of 10 000 Da, manufactured byAmicon Bioseparations (Millipore Co.) were used in all experiments.

In this study two stages were used for filtration experiments:

(a) Retention experiments of divalent metal ions by a PAA solutionby continuous diafiltration and

(b) membrane functional characterization by solute retention testusing a cross-flow ultrafiltration.

3.2.1. LPR experimentsThe aim of these experiments was to obtain the enrichment

curves by using the LPR technique. A solution of 50 mM (in termsof the monomer with molar mass of 72 g mol−1) PAA at pH 6.0 wasplaced inside a stirred ultrafiltration cell whose volume was 25 cm3.The feed was a 2.0 mM solution of metal ion nitrates (nitrates ofCo2+, Ni2+, Cu2+, Zn2+, Cd2+, Pb2+—all present in one single solution)at pH 6.0. pH was adjusted by using HNO3 and NaOH solutions.This pH value was selected in order to get a high interaction andthus high retention as has been reported in these conditions [32].An experimental blank was realized before and after each LPRexperiment. These blank runs consisted in the filtration of the solu-tion of the metal ion at the same experimental conditions but inthe absence of polymer. Before performing each blank–LPR–blankset of experiments, the membrane was washed with bi-distilledwater.

A description of the filtration system used for these measure-ments is shown in Fig. 2. The system was operated at 300 kPaof pressure, by using pressurized nitrogen, and at 80 rpm surfacestirring rate. Permeate fractions were collected and the metal ionconcentrations were analyzed by flame atomic absorption spec-

3.2.2. Membrane characterizationSolute retention tests were realized by cross-flow ultrafiltration

of polyethylenglycol solutions (PEG, 0.1%, w/w) by means of tangen-

1 mbra

tswom

btwwl8ompAf

mta0

3

mD[lrafot

icad

R

wr

3

2tdfch

sbwGaa

32 M. Palencia et al. / Journal of Me

ial flow filtration experiments by using a parallel plate filtrationystem shown in the scheme of Fig. 3. Ultrafiltration experimentsere done with both a virgin membrane and a membrane previ-

usly used in all the LPR experiments, after interacting with all theetal ions and with PAA.

The PEG solutions were pumped tangentially over the mem-rane and recirculated at a range of velocities under a constantransmembrane pressure of 300 kPa. The membrane effective areaas 6.23 × 10−4 m2 and the retentate channel cross-section areaas 2.1 × 10−5 m2. The tangential flows on the membrane active

ayer were: 1.67 × 10−6, 3.33 × 10−6, 5.00 × 10−6, 6.67 × 10−6 and.33 × 10−6 m3 s−1 which are equivalent to recirculation velocitiesf 0.08, 0.16, 0.24, 0.32 and 0.40 m s−1. The permeate flow waseasured by weighting the permeate at given times with a high

recision balance with errors lower than ±1 × 10−7 kg (Sartoriusnalytic A120S). The polymer concentration was measured by dif-

erential refractometry (Atago Differential Refractometer DD-5).Hydrodynamic permeability, also for both virgin and used

embranes, was measured by using bi-distilled water underransmembrane pressures of: 100, 200, 300, 400 and 500 kPa at

tangential flow of 5.0 × 10−6 m3 s−1 (recirculation velocity of.24 m s−1).

.3. Atomic force microscopy

Images of the membranes were obtained by atomic forceicroscopy (AFM) using a Nanoscope IIIA Multimode SPM fromigital Instruments. The Tapping Mode® technique was used

33–35]. In this measurement mode, the cantilever where the tip isocated oscillates with its natural frequency and the sample topog-aphy is obtained from the subsequent changes in the oscillationmplitude. Differences in viscoelastic properties can be detectedrom the changes in the oscillation phase. The tip used had a radiusf curvature of approximately 5 nm and the natural frequency forhe cantilever was 300 kHz.

Roughness plays an important role in the study of surfaces andts thermodynamic description [36,37]. The average roughness (Rq)an be directly obtained from AFM images, by using an appropri-te tool for image analysis, for different explored areas using theefinition expressed by the following equation:

q =

√√√√1n

n∑i=0

(Zi − Zm)2 (25)

here Zm is the mean value of the tip-to-surface distance, Zi over aeference baseline (Z) [35].

.4. Contact angle measurements

The contact angle measurements were carried out by using a FTA00 apparatus both for virgin and fouled membranes. 3 �L drops ofhree liquids with different polarities (water, ethane-1,2-diol andiiodomethane) were deposited one by one on the membrane sur-

ace and the process captured on video format to be analyzed. Theontact angle was measured from digitized pictures by using an “adoc” software of analysis.

In order to obtain more direct quantitative information on theurfaces of the virgin and used membranes, and on the differences

etween them, surface energies and surface energy componentsere calculated from the measurement of contact angles. Theood–van Oss theory (vOGT) [38] can be used to calculate thecid–base components of solid surface free energies [39–41]. In thispproach the work of adhesion of a liquid phase (W) onto a solid

ne Science 336 (2009) 128–139

substrate can be expressed as:

W = �totli (1 + cos �i) = 2(

√�d

li�d

s +√

�+li

�−s +

√�−

li�+

s ) i = 1–3

(26)

where �dli

, �+li

, �−li

, �ds , �−

s , �+s , are dispersive, basic and acidic com-

ponents of the surface free energy of the liquid and the solidrespectively and �tot

li= �d

li+ 2

√�+

li�−

liis the total surface free

energy of the liquid. The three equations described by Eq. (26) canbe solved to evaluate the three unknowns corresponding to thethree parts of the free energy surface for the solid. A more detailedexposition of this theory is given by Letellier et al. [39,40].

It is actually difficult to measure the contact angle accurately, asfar as, the process of wetting when the liquid spreads on a surfaceis affected by some factors such as: the viscosity of the fluid, theroughness and heterogeneity of the surface, the temperature of boththe fluid and the substrate, the volume of the drop deposited and thespecific interactions of the fluid and the surface, etc. [42]. Thereafter,it is only possible to measure an apparent contact angle, which isnot actually that to be used in Eq. (26).

Actually, on a rough surface, the apparent contact angle is relatedto the ideal contact angle by the Wenzel’s equation [37,43,44],

cos �app = �r cos � (27)

where �app is the apparent contact angle, � is the actual Young’scontact angle and �r is the ratio between the actual area, Ar, andthe projected area, Ag:

�r = Ar

Ag(28)

This ratio can be called roughness factor. Recently, several authorshave studied the variation of apparent contact angle with the rough-ness factor and the effect of the scan-size on the determination ofthis factor [36].

4. Results and discussion

The LPR process may be described by stages where the dif-ferent interactions are appearing. In the first stage, only thepolymer–membrane interaction is possible. Given that initially thereare no metal ions, or its concentration remains is relatively low,it seems reasonable to assume that metal ions do not affect thedissociation behavior of polyacid molecules [45]. Subsequentlythe polymer–metal ions interaction is more and more important,and with time we would recognize that it is the polymer–metalcomplexes–membrane interaction which plays a central role simul-taneously with the membrane–metal ion interaction. Of course thismembrane–metal ion interaction is also present in the blank exper-iments when the metal ions are ultrafiltered in the absence ofPAA.

Nevertheless, for the sake of clarity, here we will study theseinteractions in the following order:

1. Polymer–membrane,2. membrane–metal ion,3. polymer–metal ions and4. polymer–metal complexes–membrane.

4.1. Polymer–membrane interaction

In a first stage of LPR experiments, only PAA solution is con-tained in the ultrafiltration cell at low concentrations and low ionicstrength. According to the extended Henderson–Hasselbalch equa-tion, the pH depends on the dissociation grade, ˛, and the apparent

M. Palencia et al. / Journal of Membrane Science 336 (2009) 128–139 133

Fu(

d

p

ˇedrrKcii

uKedr

bfotopah

ihensapa

Table 1Values of R0f for each metal ions studied.

Mn+ R0f

Ri0f

Rf0f

Cu2+ 0.09 0.11Cd2+ 0.08 0.00Zn2+ 0.12 0.12

ig. 4. Possible interactions between PAA and the surface of the PES membranender the experimental conditions of low ionic stretch and slightly acid pH. (a) PES,b) PAA and (c) possible interaction between PES and PAA.

issociation constant of the acid, pKapp, as:

H = pKapp + ˇ log(

˛

1 − ˛

)(29)

is an empirical constant bigger than unity. It accounts for theffect of the strong intramolecular electrostatic forces appearinguring the protonic dissociation of all polyelectrolytes [45–49]. Theelationship given by Eq. (29) is reasonably applicable within a pHange of 4.5–6.5. Intramolecular interactions have also an effect onapp due to the conformational changes they induce [48]. The ionicomposition of the solution (nature and concentration of the saltsn presence) also affects pKapp and ˇ, both of them decrease withncreasing ionic strengths [46,48].

At our experimental conditions pH is 6, and Eq. (29) can besed to obtain a dissociation grade ˛ = 0.97 if we assume thatap = 3.16 × 10−7 M (pKap = 6.5) and ˇ = 2 as suggested by Tomidat al. [29]. Thus, the carboxylic groups of PAA are almost totallyissociated, and the chains of PAA should be extended due to theepulsion of their carboxylate groups.

The adsorption of polyelectrolytes onto a surface is governedy a number of parameters such as: the polyelectrolyte and sur-ace charge densities and their sign, the ionic strength and the pHf the solution. At low ion concentrations, the electrostatic fac-ors dominate the adsorption phenomena of the polyelectrolyten the surface [42]. The zeta potential versus pH studies done onolyethersulfone membranes, which are similar to ours, showedn isoelectric point of 3.1 which means that our membrane shouldave a negative surface charge density at pH 6.0 [50].

The PES polymer has several characteristic functional groupsn its structure (see Fig. 4a). The sulfonyl and ether groups areydrophilic while the phenyl groups are hydrophobic. By resonanceffects increasing positive charges on the carbon atoms and the

egative charge of the oxygen atoms of the sulfonyl groups is pos-ible. The negative charges of the carboxylate groups (see Fig. 4b)re attracted by the positive charges of the benzene rings of thehenyl groups of PES and simultaneously repelled by the oxygentom of PES as it is shown in Fig. 4c. Thus, the electrostatic attrac-

Co2+ 0.10 0.11Ni2+ 0.12 0.05Pb2+ 0.11 0.33

tion between PAA and PES should be very low in the experimentalconditions used in this first stage of LPR process.

4.2. Membrane–metal ion interaction

Given that the metal ions carry positive charges, the PES mem-brane surface can potentially interact with the ions electrostatically.The two oxygen atoms attached to a sulfur atom in the sulfonylgroup of PES are the most probable interaction sites.

As it was mentioned, according to Eq. (16) a plot of ln[Cr/(Cr −C∗

p)] versus Vp/Vc, should result in a straight line with a slope givenby 1 − R0f. This has been done both before and after the membranewas used in the diafiltration experiments with polymer. The cor-responding Ri

0fand Rf

0fare shown in Table 1. These results show

weak interactions between the membrane and all the metal ionsused. Membrane–metal ion interaction was close to 10% for allcations studied (0.08 ≤ Ri

0f≤ 0.12) with the following order in the

interactions:

Ni2+ ≈ Zn2+ > Pb2+ > Co2+ > Cu2+ > Cd2+

After diafiltration experiments, membrane–metal ion interactionchanged its order to:

Pb2+ > Zn2+ > Cu2+ ≈ Co2+ > Ni2+ > Cd2+

With values in the range 0.04 ≤ Rf0f

≤ 0.33.The formation of hydro-gen bonding between water molecules and the sulfonyl groups ofthe PES membrane surface is possible. A lowered diffusive mobilityof H2O molecules near the PES surface due to this type of bondinghas been reported by Ahn et al. based on molecular modeling stud-ies [51]. Oxygen atoms of the sulfonyl groups at the PES membranesurface can participate in hydrogen bonding interactions with sur-face water molecules, what causes hydration and shielding of theirrelatively low negative charge. Thus, the net interaction betweenthe hydrated cations and the PES membrane surface remains weakand the cations could not interact strongly with the surface. Thisshould explain the very low interaction measured for the mem-brane and the metal ions.

Moreover, when the membrane has been already in contactwith PAA, another molecular mechanisms, such as hydrophobic orelectrostatic interactions between the membrane surface and thepolymer, could slightly change the interaction of the metal ionswith this modified membrane surface which should explain thedifferences between the values of Ri

0fand Rf

0f.

4.3. Polymer–metal ions interaction

In our experiments, enrichment was followed until obtaining afiltration factor of 5.3Vp/Vc = 133 cm3/25 cm3 = 5.3 given that over

these ratios, there was a considerable drop of the permeate flow.How and why this happens will be discussed in more detail below,when analyzing the polymer–metal–membrane interactions. In anycase, up to these ratios no precipitation of polymer–metal com-plexes was observed.

134 M. Palencia et al. / Journal of Membrane Science 336 (2009) 128–139

FvC

bbsipirpaaattsot

C

TVp

i

ig. 5. Concentration of Mn+ in the permeate as a function of the filtered volume (Cp

ersus Vp) for the enrichment of metal ions with PAA: (a) Cu2+, Zn2+and Ni2+ and (b)d2+, Co2+ and Pb2+. The dashed line corresponds to Eq. (30) with R0f = 0.

In Fig. 5a and b, Cp is shown versus Vp for the metals used. In theeginning of these experiments it can be seen that all metal ions areeing retained by the polymer and no ion concentration can be mea-ured in the permeate. In effect, when LPR by enrichment is startingt is normal to have a very strong interaction between the weakolyacid and the metal ions in solution. When the amount of metal

ons in the inner cell is high enough, the PAA molecules are satu-ate. At a certain time afterwards metal ions start to appear in theermeate, enrichment curve shows an inflection point after a timend a controlled diffusion process should be occurring if the inter-ctions between the polymer–metal complexes previously formednd new metal ions incorporated to the inner cell are small enougho be considered negligible since amount of functional groups ofhe polymer are available to interact with metal ions is fewer in thistage of the process [21]. In these conditions the metal ions interactnly with the membrane and the process could be described likehat without polymer in the inner cell: i.e. by

∗p = Cr[1 − e(−Vp(1−R0f ))/Vc ] (30)

∗

hat can be obtained by integration of Eq. (15) where Cp andp should be measured from those at the moment when theolymer–metal interaction starts to be negligible.

Eq. (30) is also shown in Fig. 5a and b for R0f = 0, i.e. for zero metalon–membrane interaction. It can be seen, how when the polymer

Fig. 6. Variation of the number of moles of metal bound per polymer mol, r, duringthe filtration process versus the permeate volume.

is present the behavior of C∗p versus Vp after the inflexion point is

quite similar to that shown for the non-polymer experiments. Thiswould mean that an almost pure diffusion process would effectivelyappear at this moment.

Finally, when the polymer molecules are highly saturated, thecarboxylic groups cannot retain new metal ions incorporated in thecell without a considerable decrease of their interaction with watermolecules that surround them ending in a loss of their stability anda substantial decrease in solubility with the subsequent precipita-tion of polymer–metal ion complexes which is observed for highfiltration factors.

The values of r, the number of moles of bonded metal ions permole of polymer can be obtained, as a function of Vp (or equiva-lently of time), as already mentioned, by numerical integration ofEq. (15) and according to Eq. (17). The corresponding curves for allthe metals used are shown in Fig. 6. It is clear that they show twodifferent trends:

(a) A monotonous increase of r with Vp that appears for Cu2+ andPb2+ and

(b) a more complex behavior including an initial increase followedby a posterior decrease that appears for the other metal ions.

In the beginning, the metal ions concentration is low and carboxy-late groups of PAA are available to a possible interaction with metalions. As the time goes on the number of available sites decrease asthey are being occupied. Of course, a maximal r would be reachedwhen the maximum capacity of the polymer is attained. If thereappears an ulterior decrease in r, it could be due to modificationsin the association capacity of the polymer possibly due to confor-mational changes induced in the polymer. At the same time, anion displacement phenomenon could act due to the competition ofions for the accessible sites. Both these factors could contribute toa decrease in r for long times (high Vp). A quantitative predictionof this maximum r and its correlation with the maximum reten-tion capacity of the polymer (MRC) is not an easy matter without adetailed consideration of the possible presence of multiple equilib-riums and the perturbations due to the presence of the membrane.

Note that, in the treatment here presented, description of metalcomplexation by PAA is implicitly assumed that the process is very

fast and therefore membrane performances are not affected sig-nificantly. This is possible since when one amount of metal ionis incorporated from reservoir to the stirred cell, it is diluted inthe internal volume of the cell and, at the same time, solutionin the cell is homogenously mixed permitting a residence time

M. Palencia et al. / Journal of Membrane Science 336 (2009) 128–139 135

mber

ltestvtp

sdmeaatgTdpi

g(NoaoCed

aC

Fig. 7. Determination of association constants and nu

arge enough for metal ions–polymer interaction take place andhis way the rejection is produced. If the residence time is notnough to metal–polymer interaction or if this interaction is nottrong enough, an increasing in the permeated curve is observedo filtration factors very small. From experimental point view someariables as stirring rate and adequate volume should be condi-ions enough to increase residence time and increasing interactionrobability by an adequate mix of the solution in the cell.

It has been often reported that when interactions between wateroluble polymers and metal ions in solution take place by coor-inating bonds, the nature of the metal ions and the effect of pHay induce differences in the retention profiles and selectivity of

qually charged metal ions [30,32]. The carboxylic groups of PAAre expected to exhibit unlike acid strengths. During the dissoci-tion of PAA, the ionized carboxylic groups of the polyacid attracthe protons. As a consequence, the deprotonation of a functionalroup depends on the dissociation degree of all the other groups.he ability of a protonated group (COOH) to complex metal ionsoes not only depend of the stability of the metal–ligand com-lexes but also on the dissociation constant of the ligand which

s important [48].According with Eq. (23), a plot of r(1 − R0f)/Cp versus r should

ive a straight with −Ka as slope and Kan as the ordinate interceptsee Fig. 7). The values for these parameters are shown in Table 2.ote that for Cu2+ two kinds of binding sites should exist as far as thebtained curve shows two approximately linear portions, thereforen overall dissociation constant can be evaluated as the productf the two constants for the detected steps in the dissociation. Tou2+, the plot based in Eq. (23) is an exponential curve and thereforeach linear portion constitutes a different kind of binding sites with

ifferent Ka [21].

On the other hand Ka for Pb2+ has not been calculated because,s can be seen in Fig. 5a and b, most of the experimental values ofp are zero, what causes a divergence in Eq. (23).

Table 2Values of n and Ka for PAA and the metal ions studied.

Mn+ n log Ka

Cu2+ 0.022 3.490.028 2.81

Cd2+ 0.020 3.56Zn2+ 0.017 2.78Co2+ 0.017 3.00Ni2+ 0.013 2.78Pb2+ 0.027 –

of binding sites from Eq. (23) for (a) Ni2+ and (b) Cu2+.

The values of Ka obtained by us show that there is a relativelyhigh and specific interaction of the carboxylate groups of PAA withthe divalent counter ions. This interaction follows the order:

Cu2+ > Cd2+ > Co2+ > Ni2+ ≈ Zn2+

It has been reported that, according to potentiometric titrations inthe presence of metal ion [48], the association constant dependson: the composition of the solution (nature and concentration ofneutral salts), the concentration of PAA, the dissociation coefficientof the polymer (which is linked to the pH and to the potential atthe surface of the poly-ion) and with the possible conformationalchanges of PAA due to its interaction with the metal ions. On theother hand, from ultrafiltration experiments, Tomida et al. [29],noted that the dissociation constant for PAA follows:

Cu2+ > Pb2+ > Zn2+ > Ni2+ ≈ Co2+

Mosqueda et al. [52], showed that the stability of the PAA metalcomplexes follows the order:

Pb2+ > Cu2+ > Cd2+ > Zn2+ > Ni2+ ≈ Co2+

All these series for the association of the PAA–metal ion complexesessentially agree if the relative values of the association constantsare taken into account.

The value of Ka for Cu2+ has been proved to be close thatof Pb2+, and both to be much larger than those for all theother divalent metal ions [29,30]. These features have also beenfound here. Moreover, the order of stability of the polymer–metalcomplexes of Co2+, Ni2+, Cu2+ and Zn2+ established here is sim-ilar to that predicted according to the Irving–Williams series –Zn(II) < Cu(II) > Ni(II) > Co(II) – which is essentially independent ofthe ligand.

The strength of this interaction should be correlated to theenergy of solvation of the cations. Actually, decreasing solvationenergies should correspond to stronger interactions and easiercomplexation with the polymer [53]. The heats of solvation, of themetal ions we studied, are given in Table 3. It is possible to observethat the following order appears:

Pb2+ < Cd2+ < Co2+ < Zn2+ < Ni2+ < Cu2+

Nevertheless, the results on the dissociation constant indicate that

Cu2+ forms more stable complexes with PAA than other ions understudy, which is not in accordance with its very high salvation energy.Moreover Cu+2 and Ni+2 have very similar salvation energies butCu+2 have much higher tendency to form complexes with PAA thanNi+2 [42].

136 M. Palencia et al. / Journal of Membrane Science 336 (2009) 128–139

Table 3Solvation heats of metal ions in aqueous solution, Mn+

(g) → Mn+(aq) at 298.16 K.

These data are based on the assumption that for the reaction H+(g) → H+

(aq), −�Gis 1090.32 kJ/mol and −�S is 0.131 kJ/(◦C mol) [50].

Mn+ −�Gsolv (kJ/mol) −�H (kJ/mol) −�S (kJ/(◦C mol))

Pb2+ 1497.6 1556.6 0.198Cd2+ 1801.9 1882.6 0.273Co2+ 2006.9 2106.6 0.335ZNC

tcsso

sNpecs

P

4

edTiifchiPs

iPPbtffdo

TMP�

M

M

12

n2+ 2028.3 2121.2 0.312i2+ 2068.5 2171.4 0.345u2+ 2087.3 2175.2 0.309

This can be explained by using the ligand field theory given thathe Cu2+ ion presents a distorted Jahn–Teller effect [54]. In the pro-ess of complex formation, with bidentate ligands, the Cu2+ useshorter and stronger bonds, and so form complexes that are moretable than those of Ni2+ [54]. Note that, for Cu2+, it was possible tobtained two values of n; i.e. two kinds of adsorption sites.

From the values of Ka it is possible to predict how certain ionshould be displaced by others among these studied. In particular,i2+, Co2+ and Zn2+ with a lower value of Ka should be easily dis-laced by other ions with higher Ka (Cu2+, Cd2+ or Pb2+). The orderstablished for the dissociation and complex stability could also beorrelated with the order in the permeate concentration as can beeen in Fig. 5a and b, which corresponds to retentions in the order:

b2+ > Cu2+ > Cd2+ > Zn2+ > Co2+ > Ni2+

.4. Polymer–metal complexes–membrane interaction

A decrease in permeability of the membrane after retentionxperiments was observed. The permeability for pure water (hydro-ynamic permeability) decreased from 0.0036 to 0.0012 m/(s bar).his decrease in the volume flow of pure water is caused by the foul-

ng of the membrane due to the specific physical and/or chemicalnteractions between the membrane and the PAA–metal complexesormed. In the case of the Cu2+ and Pb2+ ions, it can also be partlyaused by a partial precipitation during the process. Actually, thisas been reported for these ions during ultrafiltration experiments

n presence of PAA and other metal ions – Co2+, Ni2+, Zn2+, Cu2+ andb2+ for [PAA]/[Mn+] = 33 [29]. The intensity of these phenomenahould determine the rate and extent of the resulting fouling.

The mass transfer coefficient Km has been measured for increas-ng recirculation speeds � and for several molecular weights Mw ofEGs. The corresponding values are shown in Table 4 for the virginES membrane (PESm) and for the fouled one (PESm/PAA). It cane seen how an increase of Mw affects less to the Km for PESm/PAAhan for PESm. These reductions in the values of K and its range

m

or the same molecular weights are a direct consequence of theouling produced during LPR and mean that there is an appreciableecrease of the effective cut-off of the membrane and a narrowingf the corresponding distributions. In effect these features can be

able 4ass transfer coefficient for PEGs of different molecular weights calculated for

ESm and PESm/PAA at three values of � (�1 = 0.40 m s−1, �2 = 0.24 m s−1 and3 = 0.08 m s−1).

ass transfer coefficient (Km) (x10−6 m s−1)

w (g/mol) PESm PESm/PAA

�1 �2 �3 �1 �2 �3

1 000 115.07 97.22 67.673 17.89 15.13 10.513 000 81.13 68.54 47.709 16.49 13.92 10.266 000 78.03 65.91 45.88 9.83 8.31 5.802 000 24.96 21.08 14.694 8.68 7.32 5.120 000 23.65 20.00 13.919 7.41 6.26 4.34

Fig. 8. Differential pore fraction and accumulated fraction of flux passing throughthe non-rejecting pores versus the pore diameter for PESm and PESm/PAA.

seen in Fig. 8 where the pore size distributions obtained from thesedata on Km are shown.

The contact angle measurements provide information on thehydrophobicity and hydrophilicity of the membrane surface. Thedirectly obtained contact angles, �app, for each membrane (PESmand PESm/PAA) are given in Table 5. Of course, as mentioned, theseresults can be improved by taking into account the roughness of themembrane surface that can be measured by AFM.

In AFM images, the formation of deposits on the membrane sur-face was observed (see Fig. 9). It is clearly seen that the structure ofthe fouled membranes is quite different of that of the virgin mem-brane. This confirms that there is an important deposition on thesurface of the membrane. This has a sure effect on the membraneroughness. This parameter is scale dependent due to the fractalbehavior of the surfaces, which makes difficult to compare resultswith those reported in the literature due to the inconsistency ofthe methods applied [43]. Here we decided to use, for comparison,the roughness as obtained from scanned areas of 1.0 �m2 becauseat this scale there is still resolution enough but macroscopic fea-tures, not attributable to the material of the membrane, are notconsidered [36].

The roughness obtained was 7.05 ± 4.6 for PESm and 22.91 ± 2.2for PESm/PAA. On the other hand, the corresponding average rough-ness factor was 1.03 ± 0.017 and 1.30 ± 0.113 respectively. These �r

factors were averaged from the values obtained from AFM imageswith nominal projected topographic areas of 0.25, 1.0, 6.25 and100 �m2. Thus, from the direct measurements of �app and these�r, the actual or Young contact angles � were obtained as shown inTable 5.

In general, higher contact angles with water mean that the sur-face is more hydrophobic. Equivalently, for liquids with low polarity,smaller � values correspond to higher wettability [42]. In our case, �remains almost constant for the less polar liquid (diiodomethane)

while it increases for ethylene glycol and significantly for water.This indicates an increase in hydrophobicity of the surface of PESmafter fouling. The hydrophobic character the PESm surface can beexplained by the presence of benzene rings in the structure of PES

Table 5Directly measured and Young’s contact angles for virgin membrane (PESm) and PESmembrane used in LPR experiments (PESm/PAA) for the three liquids used.

Liquid Contact angle (�app) Young’s angle (�)

PESm PESm/PAA PESm PESm/PAA

Water 75.6 ± 0.94 83.5 ± 3.05 76.0 ± 0.9 85.0 ± 2.34Ethylene glycol 56.1 ± 1.50 64.7 ± 0.84 57.2 ± 1.44 70.8 ± 0.62Diiodomethane 58.8 ± 1.75 53.4 ± 5.02 59.8 ± 1.68 62.7 ± 3.49

M. Palencia et al. / Journal of Membrane Science 336 (2009) 128–139 137

Fig. 9. AFM images of PESm (A1, A2, A3) and PESm/PAA (B1, B2, B3) for surfaces with areas of 1, 25 and 100 �m2.

Table 6Surface free energy data (� s) and its components calculated for each membrane. Dispersive component (�d

s ), acid and basic components (�+s and �−

s ) and non-dispersivecomponent (�nd

s ).

Membrane Components of surface free energy (mJ/m2) � s (mJ/m2)

�ds �−

s �+s �nd

s

PP

mtfmm

mcimcnaL

blsTi

toptf

ESm 28.7 ± 1.0 1.0 ± 0.7ESm/PAA 27.0 ± 0.9 12.5 ± 3.3

olecule that overrides the hydrophilic character attributable tohe sulfonyl and ether groups. The increase in hydrophobicity afterouling would mean that the foulant is probably deposited on the

embrane and shields the polar groups of the membrane lettingainly exposed the hydrophobic backbone of PAA.

The values of �s and their components were calculated fromeasurements of � obtained and these are shown in Table 6. The

hanges in the surface energy after of the fouling appear mainlyn the polar component showing a increasing in a factor approxi-

ately of 12.5 both for �+s , �−

s and �nds . It can be seen that the polar

omponent (non-dispersive) changes largely probably due to sig-ificant adjusting in the hydrogen bridges and in the electron-donornd electron-acceptor interaction forces due to fouling during thePR experiments.

Recently, Anh et al. [51] did not observe any significant contri-ution of hydrophobic interactions between a PES membrane and

ow molecular weight acids. They used a highly hydrophilic sub-tance, similar in this aspect to PAA in the absence of metal ions.hus probably are these metal ions which should play a central role

n the changes of hydrophobicity.An increase in metal ions concentration leads to a screening of

he charges along the PAA chain; for this reason, the importancef electrostatic attraction or repulsion decreases. A weakly chargedolyelectrolyte experiences less segment to segment repulsion andhe formation of loops and tails of largely uncharged sections isavored [55]. Thus, divalent ions could cause membrane fouling by

10.1 ± 1.2 6.4 ± 0.1 35.1 ± 0.9125.4 ± 24.3 79.2 ± 18.1 106.2 ± 18.9

enhancing the aggregation of PAA molecules in solution rather thanby binding the carboxylate groups of the PAA directly to the sulfonylgroups of the PES membrane during the LPR experiments. Conse-quently the partially neutralized PAA–Mn+ complex may be moreeasily adsorbed at the membrane surface than negatively chargedPAA molecules.

Other possibility is the formation of binding bridges between thegroups of PAA and those of PES on the membrane. Referring to thispossibility it should be taken into account that it has been provedthat the membrane–ion interaction is low. In any case it still remainspossible that this interaction could be powered by the presence ofthe PAA molecules. Hence, the fouling could be caused by both themechanisms: (1) the metal ions-mediated PAA aggregation in solu-tion and (2) by stronger PAA–surface interactions in the presence ofdivalent metal ions. Consequently, an additional resistance to flowthrough membrane is observed and some membrane propertiesare modified (for example permeability, hydrophobic/hydrophilicrelation, roughness and pore size distribution).

5. Conclusions

Four mechanisms of interaction appear in LPR according themetal ion present in the inner cell. In the first stage of LPR experi-ments by the enrichment method, only the soluble polymer (PAA)and membrane ultrafiltration (PES) are present and interact in theinner cell. A second stage starts with the addition of metal ions to the

1 mbrane Science 336 (2009) 128–139

sttacwV(i(pdsrbf

dbaTbocimcwimt

A

CNafAPfiA

D solute diffusivity (m2 s−1)Km mass transfer coefficient (m s−1)Mw molecular weight (g mol−1)Jw,t pure flux transmitted through the non-rejecting

fraction of pores (m s−1)Jw pure water flux (m s−1)dp pore diameter (m)rg gyration radii (m)Ar area of the topography imagine (m2)Ag geometrically projected area (m2)−�Gsolv heat of solvation (kJ/mol)−�H enthalpy of solvation (kJ/mol)−�S entropy of solvation (kJ/(◦C mol))Rq average roughness (m)

Greek symbols� recycling rate (m s−1)ıc film thickness of the boundary layer (m)� solution viscosity (Pa or kg m−1 s−1)ω constant associated to Reynolds number˚ factor of the mass transfer coefficient ((m s−1)1−ω)˛ dissociation grade� contact angle (radians)�Y Young’s contact angle (radians)ϕr roughness factor� surface energy (mJ m−2)

Subscriptsc cellr reservoirp permeatef freeb bondeds solidli liquid

Superscripts+ acidic component− basic componentsl solid–liquidsv solid–vapord dispersive component

38 M. Palencia et al. / Journal of Me

ystem and while its concentration is low in the cell. In this stage,he enrichment curve is seen to remain relatively flat. Afterwardshe enrichment curve goes up as metal ions cross the membranend appear in the permeate. This third stage starts when the pro-ess begins to be mainly controlled by diffusion. This should happenhen there is saturation (a plateau in the corresponding r versus

p curve) or a decrease in the capacity of association of the polymerdecrease in the r versus Vp curve). In these conditions, the metalon–membrane interaction should, in a first approximation, by Eq.30). The maxima could be caused, as our results suggest, by dis-lacements in the polymer–metal complex reaction of formationue the lack in the stability of the polymer–metal links. This lack oftability could be due to conformational and structural changes as aesult of the saturation of the polymer. A four stage should be possi-le when MRC is obtained and a horizontal line should be observedor very high permeate volumes.

An increase of surface hydrophobicity and roughness and aecrease of effective cut-off of the membrane were observed toe main surface changes of PES membrane when PAA is useds soluble polymer in LPR experiment by enrichment technique.hese changes can lead to relevant limitations to the LPR processefore reaching the theoretical MRC as decreasing permeabilityr precipitation of polyacid could take to place. In effect, largeoncentrations of the divalent ions would eventually cause the foul-ng of the membrane by enhancing the aggregation of the PAA

olecules in solution. This could be due to the screening of theharges along the PAA chain. In this case the short range forcesould cause aggregation and, consequently, the partially neutral-

zed PAA–Mn+ complexes should be more easily adsorbed at theembrane surface. The metal ions-mediated forces could also con-

ribute to enhance aggregation and fouling.

cknowledgements

The authors thanks to FONDECYT (Grant No. 1070542) andIPA the financial support; M. Palencia, acknowledges to “Comisiónacional de Investigación, Ciencia y Tecnología” (CONYCT-Chile)nd “Centro de Investigación de Polímeros Avanzados” (CIPA-Chile)or funds received in the realization of his doctoral formation.. Hernández and P. Prádanos acknowledge the Spanish CICYT-lan Nacional de I+D+I and the Junta de Castilla y León fornancing this research through the projects BU-03-C3-2 (INNOVIN-LCOHOLGRADE) and CTQ2006-0165, respectively.

Nomenclature

N mol number (mol)C concentration (mmol L−1)V volume (L)R0f apparent retention coefficientR true rejention coefficientQ Caudal (g s−1 or m3 s−1)r molar binding ratioPT total concentration of polymer (molar concentration

of monomérica unit, mmol L−1)Ka association constant (L mol−1)n number of independent sites with only one intrinsic

binding constantJv flow through membrane (m3 s−1)Js flow of solute through membrane (m3 s−1)

C0 feed concentration (mmol L−1)Cm membrane surface concentration (g m−3)Cg membrane surface concentration in the gel layer

model (mol m−3)

nd polar component

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