Research Article Liquid-Phase Polymer-Based Retention: Theory, …downloads.hindawi.com/journals/jchem/2015/965624.pdf · 2019-07-31 · Research Article Liquid-Phase Polymer-Based

Research ArticleLiquid-Phase Polymer-Based Retention Theory Modeling andApplication for the Removal of Pollutant Inorganic Ions

Manuel Palencia

Department of Chemistry Faculty of Natural and Exact Science University of Valle Cali Colombia

Correspondence should be addressed to Manuel Palencia manuelpalenciacorreounivalleeduco

Received 10 December 2014 Accepted 9 February 2015

Academic Editor Marinos Pitsikalis

Copyright copy 2015 Manuel Palencia This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The aim of this work is to give the theoretical background of liquid-phase polymer-based retention (LPR) technique provide acomplete model of separation process and evaluate its application for the removal of pollutant inorganic ions (PIIs) from aqueoussolutionThus fundaments of LPRmodeling by washing method from the ion distribution in active and passive zones are specifiedand its application was evaluated for cadmium removal using poly(sodium styrene sulfonate) as water-soluble polymer (WSP)LPR simulations were performed using a semiempirical description from data of concentration filtration factorm and retentioncoefficients It is concluded that semiempirical simulation of PII retention by WSP can be performed from a small amount ofexperimental data using the described modeling In addition new approximations associated with molecular structure of polymershould be performed and linked to parameters of LPR experiments

1 Introduction

The aim of this work is to give the theoretical backgroundof LPR technique provide a complete model of separa-tion process and evaluate its application for the removalof pollutant inorganic ions (PIIs) from aqueous solutionThus to start it is important to indicate that membraneseparation processes are very attractive for waste pollutantnatural and drinking water treatment due to their simplicityof operation and moderate energy consumption [1 2] Inthe case of ultrafiltration (UF) this technique has beenapplied to the treatment of effluents that contain particulatematerials dissolved species with high molecular weight andmetal ions when a strength membrane-metal interactionis present [1ndash5] In UF systems the membrane acts as aporous barrier at molecular level but the pore size is toolarge that it is not possible to retain dissolved inorganicions unless these are present in a colloidal form On theother hand the addition of water-soluble high molecularweight species to the UF unit with a strength polymer-ioninteraction leads to ion retention by the formation of newmacromolecular species which can be easily retained by size-exclusion mechanism Moreover metal selective extractioncan be achieved if specific chelating or ionic groups are

bonded on the polymeric chains [3 5] This technique hasbeen named in different ways liquid-phase polymer-basedretention (LPR) [3 5 6] polymer assisted ultrafiltration(PAUF) [7 8] ultrafiltration-complexation [9ndash13] polymeror polyelectrolyte enhanced ultrafiltration (PE-UF) [14ndash18]or simply enhanced ultrafiltration [19 20]

The principle of LPR was firstly suggested by Michaels in1968 and Blatt et al (1968) presented a theoretical discussionto connect the method of analysis by diafiltration with con-tinuous ultrafiltration [20] Geckeler et al (1986) carried outthe first experimental advances and analytical applicationsrelated to this technique [6 21 22] Later many researchgroups have worked on the evaluation and descriptionof retention properties of different water-soluble polymers(WSPs) for environmental and analytical applications [5 21ndash30] it is important to highlight the works done by Rivaset al related to the modeling and development of newexperimental configurations and novel applications of thistechnique [3 31 32]

2 LPR Theory and Modeling

LPR technique is a hybrid membrane separation methodwhich combines UF membranes with WSPs in order to

Hindawi Publishing CorporationJournal of ChemistryVolume 2015 Article ID 965624 9 pageshttpdxdoiorg1011552015965624

2 Journal of Chemistry

H2O(reservoir tank)

Ultrafiltration membrane

H2O + PII (excess)(permeate)

WSP-PII WSP + PII

(a)

(reservoir tank)

Ultrafiltration membraneH2O + PII (excess)

(permeate)

H2O + PII

WSP + PII WSP-PII

(b)Pr

essu

re sy

stem Elution solution

Reservoir tankFiltration unit

MembraneStirringsystem

Collected samples(permeate)

WSP-PII solution

(c)

Figure 1 Description of LPR technique by washing method (a) and enrichment method (b) and schematic representation of experimentaldevice (c)

separate low molecular weight species dissolved in aqueoussolution [5] Thus a WSP solution and a metal ion solutionare contacted in the feed-side of an UF system the metalions are consequently bonded to the polymer and newmacromolecular species are formed and retained by a size-exclusion mechanism while the unbounded species witha diameter smaller than cutoff diameter of the membranepasses to the permeate stream [5 20]

Usually LPR technique can be applied by two operationmethods (1) the washing method or elution method (withthe ionic strength kept constant or not) which is the mostusedmethod to study the PIIrsquos retention capacity of a polymerin aqueous solution and is a discontinuous separation processand (2) the enrichment method or concentration methodwhich is a continuous separation process [5] In the washingmethod a certain amount of polymer and PII solutions withknown concentrations are placed in the feed-side of an UFcell and a water stream is passed through the cell [5 22 25]On the other hand for the application of the enrichmentmethod the WSP solution is placed in a stirred cell and a PIIsolution is added continuously from a pressurized reservoirHowever when the bonding groups of theWSP are saturatedby their interactionwith the PII in the solution themaximumretention capacity (MRC) of polymer is reached and the pro-cess cannot continue [5 20] Evidently the physicochemicalproperties of the WSP and the polymer-metal complexes

must be taken into account and their interaction with themembrane surface is also very relevant During the retentionand separation process by LPR the permeate is removed atthe same rate keeping the volume in the feed cell and thepolymer concentration constant all the time [20] Reviewson LPR technique have been performed by Geckeler et al[6 21 22] andmost recently by Rivas et al [3 5] (see Figure 1)

TheLPR technique can be visualized like cyclic separationprocess and thus it should be economically more feasiblewhenWSP can be regenerated and reused Among regenera-tion methods of theWSP are the chemical methods (protoly-sis transcomplexation and redox reaction) electrochemicalmethods and thermal methods [3] In this way new optionsof regeneration of chelating groups by using new componentsincorporated to the system can be useful to make the processmore feasible

The LPR technique either by washing method or byenrichment method is based on the interaction between theWSP and the PIIs in aqueous solution and the progressiveretention by anUFmembrane of the new species formed [20]The type of interaction depends on the chemical nature ofthe WSP functional groups In any case these interactionsare mainly due to electrostatic forces and the formationof coordinating bonds The variables that affect the WSP-PII interaction are classified into two groups intrinsic tothe polymer (ie the nature of the atoms in the backbone

Journal of Chemistry 3

chain the nature of the functional groups attached to thebackbone the structure and composition of the polymerthe molecular weight and the polydispersity the distancebetween the functional groups and the backbone the degreeof branching etc) and extrinsic to the polymer (ie chargeand type of the metal ion the pH of the solution the ionicstrength the temperature and the dielectric constant of themedium) [3 5 6 12]

From a molecular point of view PII retention by WSPduring the application of LPR technique can be understoodfrom the description of three types of main interactions(1)WSP-PII interaction (2) membrane-PII interaction and(3) WSP-membrane interaction [20] Commonly WSP-PIIinteraction has been the attention focus in many researcheswhere it is assumed that retention capacity of polymer is veryhigh in comparison with retention capacity of the membraneand in consequence membrane is assumed to be inert inmany cases

If WSP and PII solutions are contacted the ion distribu-tion in the UF cell is governed by the WSP-PII interactionsand the electrostatic attraction between WSP chains and PIIin solutions can be discussed by counterion condensationtheory (CCT) [33 34] There are several approaches todescribe counterion condensation in WSP solutions by cellmodels In the first approach two-state model or two-zonemodel proposed by Oosawa and Manning the counterionsare separated into ldquofreerdquo and ldquocondensedrdquo Free counterionscan explore the solution volume (external zone) and thecondensed counterions are located within a small volumesurrounding the polymer backbone which is assumed tobe rodlike (polymer domain or internal zone) [35 36]Thus during LPR technique by washing method PIIs aredistributed in the external and internal zones of a WSPsolution and only PIIs distributed in the external zone can beeluted from UF cell to permeate stream On the other handduring LPR technique by enrichment method PIIs are addedto the external zone and transported to internal zone as PIIconcentration in the external zone is continuously increasedIn this case concentration of PIIs in the permeate dependson their distribution between the external and internal zones[31]

As modeling strategy LPR system can be described asa group of four independent regions contacted with a fifthldquopassiverdquo region [31]The regions considered are (1) reservoir(which is a passive component in the washing method butin other operation modes such as the enrichment method itshould be considered) (2) solution bulk (which is the fractionof the solution where metal ions are not affected by the inter-action with some retainer component of the cell which canbe for exampleWSP ormembrane) (3) permeate (this is thefraction of solution which can pass through the membraneand corresponds only to solvent and solutes distributed inthe solution bulk) (4) membrane surface (which is based inthe adsorption process on polymeric surfaces and retentionproperties of polymer in solid phase when an aqueous streamis passed through it) and (5) polymer domain (which is theregion where the strongly interacting counterions with thepolymer are distributed) [31] If the membrane is consideredto be an inert component and the polymer is not present in

the cell (blank experiment) then regions 1 2 3 and 4 can beconsidered under a hydrodynamic control and system canbe described from filtration theories when the polymer ispresent and membrane is not inert regions 2 4 and 5 areassumed to be controlled by two factors a hydrodynamiccontrol resulting from its interaction with regions 1 3 and4 and a physicochemical control related to the WSP-PII andmembrane-PII interactions

Under the consideration of ion distribution interactingregions the filtration cell is like a continuously stirred tankreactor and therefore it is identical in design requirementsto the batch reactor except for the introduction of a constantflow of feed and a constant removal of reactor contents sothat the reactant volume in the reactor remains constantThus the filtration cell is inherently a steady state reactorThis is accomplished by keeping the volume temperaturefeed rate and pressure of the filtration cell constant duringthe experiment

To describe the LPR technique by ldquoion distributionmodelrdquo for washing method system retention (119877syst) is theresult of PII transport between regions 2 rarr 4 (from bulk ofsolution to membrane surface) and between regions 2 rarr 5(from bulk of solution to polymer domain) at 119905 = 0 Ina long enough time (if 119905 rarr infin then 119865 rarr infin 119865 isdefined to be the ldquofiltration factorrdquo and is equal to the volumeof permeate 119881119901 divided by solution volume in the cell119881119888) a new distribution of PII in the system is obtained Inthis case retention by the polymer is the fraction of PIIdistributed in the polymer domain (119877pol) and retention bythemembrane is the fraction of PIIs distributed in the surfacepolymer (119877119898) which cannot be eluted by continuous additionof solvent from reservoir in the experimental conditionsof pressure temperature pH ionic strength polymer-metalratio and so forthThus different situations can be analyzed(1) modeling of inert system (2) membrane-PII interactionparameter (modeling of blank experiment) (3) WSP-PIIinteraction parameter (modeling of LPR in presence of WSPconsidering the membrane as an inert component) and (4)WSP-membrane-PII interaction parameters [31]

For the first case modeling of inert system if an inertsystem is considered then PIIs can be distributed in regions 2and 3 In this case from the following mass balance

119873119888 = 1198730 minus 119873119901 (1)

where 119873119888 and 119873119901 are the number of moles distributed inregions 2 and 3 respectively and 1198730 is the number of molesinitially placed in the cell Since 119889119873119888 = 119881119888119889119862119888 and 119889119873119901 =119889(119881119901119862119901) = 119881119901119889119862119901 + 119862119901119889119881119901 it is obtained that

minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 (2)

where 119862119888 and 119862119901 are cell and permeate concentrationsrespectively Since the mathematical expression described by(2) relates three interdependent variables 119889119862119888 119889119862119901 and 119889119881119901the assumption of a linear approximation is useful in order toobtain an analytical resolving of (2) Thus for small values ofΔ119865 (where Δ119865 = 119865119899 minus 119865119899minus1 for the 119899th fraction recollected ofpermeate) it can be assumed that

119889119862119888 = 120572119889119862119901 (3)


120572 being an empirical parameter which describes the relativechanges of 119862119888 and 119862119901 as functions of 119865 By considering of alinear dependence 119862119888 and 119862119901 from (2) and (3)

119889119862119901

119889119881119901=minus119862119901

120572119881119888 + 119881119901 (4)

Resolving and evaluating for boundary conditions at 119905 = 0and 1199051 (at 119905 = 0 119862119901 = 1198620 and 119881119901 = 0 at 1199051 119862119901 = 119862119901 and119881119901 = 119881119901) are obtained

119862119901

1198620=120572119881119888

120572119881119888 + 119881119901=120572

120572 + 119865 (5)

where 119862119901 and 119881119901 in terms of LPR experiments are given by

119862119901 =1

119881119901

119899

sum119894=1

(119862119901119894119881119894)

119881119901 =

119899

sum119894=1

119881119894

(6)

where 119881119894 and 119862119901119894 are the volume and the concentration ofeach one of the permeate fractions recollected

Note that 120572 can be easily calculated from experimentalmeasures Thus one value of 120572 can be obtained from a plotof 119862119888 versus 119862119901 For the situation where 119862119888 is not linearwith respect to 119862119901 several values of 120572 can be assigneddepending on the selection of approximately linear rangesdefined according to the experimental data

For the second case membrane-metal interaction param-eter (modeling of blank experiment) for blank experimentPIIs can be distributed in regions 2 3 and 4 since membraneis not assumed to be an inert component of the systemDescribing the PII adsorption on the membrane surface bymeans of Donnanrsquos equilibrium given by

Mn+(sol) 999448999471 Mn+

(membrane) (7)

the followingmembrane-PII interaction constant (119896119898) can bedefined

119896119898 =119862119898

119862119888=119873119898119881119888

119873119888119908119898 (8)

where119862119898 is the number of PII moles adsorbed (119873119898) per unitof membrane mass (119882119898) Thus 119896119898 is defined to be equal todistribution coefficient analogously to the strategy used todescribe the affinity between PII and polymeric resin [16]

From (8) it is concluded that119889119873119898 = 119896119898119908119898119889119862119888 where119873119898is the number of moles in region 4 Thus from mass balancein regions 2 3 and 4 the following relation is obtained

minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 (9)

By (3) and (9)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896119898119908119898) 120572 + 119881119901 (10)

Note that implicitly it was assumed that retention propertiesof membrane are not affected by the elution of PIIs in theother regions This assumption is strongly dependent onnature of membrane-PII interaction However for high levelsof membrane-PII interaction can be appropriate since theadsorption on membrane surface will be favored and for lowlevels of membrane-PII interaction the membrane can beconsidered an inert component In consequence the modelconsiders that the initial concentration of PII in the cell at119905 = 0 is modified by membrane-PII interaction and thereforean effective initial concentration 1198620 can be obtained

Resolving and evaluating for boundary conditions at 119905 = 0and 1199051

119862119901

1198620=(1 + 119896119898119908119898119881119888

minus1) 120572

(1 + 119896119898119908119898119881119888minus1) 120572 + 119865

=120572120579119898

120572120579119898 + 119865 (11)

where 120579119898 can be defined as a system interaction parametergiven by 120579119898 = 1 + 119896119898119908119898119881119888

minus1For the third case WSP-PII interaction parameter (mod-

eling of LPR in presence of WSP considering the membraneas an inert component) it is seen that it corresponds to onetypical assumption done for LPR in retention experimentsThis situation is achieved as a result of adequate selection ofthe material of the membrane or by control of the experi-mental conditions (eg pH and ionic strength) Accordingto the proposedmodel PIIs can be distributed in regions 2 3and 5 and the polymerWSP-PII interaction constant (1198961) canbe described throughDonnanrsquos equilibriumbetweenpolymerdomain and bulk of solution according to Manningrsquos theorywhich is given by

Mn+(sol) 999448999471 Mn+

(polymer) (12)

Thus 119896pol can be defined as

1198961 =119862pol

119862119888=119873119887

119862119888119881pol (13)

From (13) it is concluded that 119889119873119887 = 119896pol119881pol119889119862119888 where 119873119887is the number of moles in region 5 and 119881pol is the volume ofpolymer domain Frommass balance in regions 2 3 and 5 thefollowing relation is obtained

minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896pol119881pol119889119862119888 (14)

By (3) and (14)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896pol119881pol) 120572 + 119881119901 (15)

Solution of (15) is analogous to (10) and therefore

119862119901

1198620=(1 + 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896pol119881pol119881minus1119888) 120572 + 119865

=120572120579pol

120572120579pol + 119865 (16)


Table 1 Values of 119877pol and 119862in for removal of PIIs (PSSNa-Cd) [20 23 27 36]

119862in (mmolL) 018 036 089 134 223 356 445119877pol () 610 567 470 412 351 309 280

where 120579119901 can be defined as a system interaction parametergiven by 120579pol = 1 + 119896pol119881pol119881

minus1

119888

Finally for WSP-membrane-PII interaction parametersPIIs can be distributed in regions 2 3 4 and 5 and 1198961 and 119896119898can be described through Donnanrsquos equilibriums given by (7)and (12) assuming that these interactions can be consideredto be independent that is to say retention properties relatedto one specific interaction are not affected by the occurrenceof the otherThus the change of number of moles distributedin regions 4 and 5 is given respectively by 119889119873119898 = 119896119898119908119898119889119862119888and 119889119873119887 = 119896pol119881pol119889119862119888 therefore

minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 + 119896pol119881pol119889119862119888

(17)

And it can be obtained that

119889119862119901

119889119881119901=

minus119862119901

(1 + 119896119898119908119898 + 119896pol119881pol) 120572119881119888 + 119881119901 (18)

Solution of (18) is analogous to (10) and (15) and therefore

119862119901

1198620=(1 + 119896119898119908119898119881

minus1

119888+ 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896119898119908119898119881minus1119888+ 119896pol119881pol119881

minus1119888) 120572 + 119865

=120572120579

120572120579 + 119865 (19)

where 120579 = 1 + 119896119898119908119898119881minus1

119888+ 119896pol119881pol119881

minus1

119888

3 Materials and Methods

31 Reagents and Filtration Unit In order to evaluate theLPR modeling commercially available poly(sodium styrenesulfonate) (PSSNa Aldrich) was used as WSP Cadmiumnitrate (analytical grade fromMerck) was used to prepare thePII solutions WSP and PIIs were selected because sufficienttheoretical and experimental data related to LPR techniqueare available from previous publications Polyethersulfone(PESm) disk-shaped membranes (Biomax PBGC nomi-nal molar mass cutoff of 10 kDa Amicon Bioseparations-Millipore Co) were used in all experiments Experimentswere performed in a stirred-cell filtration unit (Milliporemodel 8050) The components and operation modes of thefiltration systemhave been described in previous publications[20] and include a reservoir tank filtration cell magnetic stir-ring system ultrafiltration membrane and pressure system(Figure 1(c))

32 Experimental Procedure

321 Retention of PIIs by the Washing Method In eachexperiment 10mL of a 20mmolL WSP solution was mixedwith 10mL of a 374mmolL PIIs solution The workingpH (20 35 and 50) operating pressure and stirring ratewere 60 300 kPa and 200 rpm respectivelyThese operatingconditions have been previously established [19 20 31] Per-meate fractions with a volume of 20mL were collected andthe PII concentration was measured by atomic absorptionspectroscopy (AAS Unicam Solaar M5) A blank experimentwas performed using the same experimental conditions

322 Semiempirical Simulation of LPR Experiments Exper-iments were simulated from the experimental data obtainedin Section 321 and by using (19) By combining 119877syst for thewashing method (119877syst = 1 minus 119862119901119865119862

minus1

in ) and (19) 119877syst can beexpressed as a function of the model parameters

119877syst = 1 minus1205721205791198620

(120572120579 + 119865)119862in119865 (20)

Consequently the retention for infinite dilution (119877infin for119865 rarr infin) was calculated according to

119877infin = lim119865rarrinfin119877 = 1 minus

1205721205791198620

119862in (21)

where 1198620 and 120579 were calculated using experimental dataand linearizing (19) The parameter 120572 was determined by thelinear correlation of experimental data using (3)

323 Simulation of LPR Experiments from Retention ValuesLPR experiments were simulated from membrane and WSPdata previously published [20 23 31]These data are summa-rized in Table 1

4 Results and Discussion

41 Description of LPR Experiments from Experimental Dataand Semiempirical Simulation The effect of (6) on thebehavior of experimental data can be easily evidenced (seeFigure 2) Thus data denoted to be ldquoardquo correspond to theaverage concentration values of permeate fractions collectedin the tubes whereas data denoted as ldquobrdquo correspond toeffective concentration values in the permeate This firstobservation suggests that the experimental data report ofLPR by washing method should be done using the accu-mulated concentrations instead of partial concentrations Itis clear that curve ldquoardquo is strongly affected by the experimentaldesign of the experiments (note that for 200mL in ldquoardquo


000

002

004

006

008

010

012

014

0 50 100 150 200 250Volume of permeate (mL)

[Cd2

+]

(mm

olL

)

(a)

000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)(b)

Figure 2AverageCd2+ concentration values of permeate fractions collected in the tubes (a) and effective concentration values in the permeateaccording to (6) (b)

0

5

10

15

20

25

30

35

40

45

50

0 2 4 6 8Filtration factor (F)

1Cp

(Lm

mol

)

y = mx + by = 626x + 289

r2 = 09991

(a)

00

05

10

15

20

25

30

35

40

000 002 004 006 008 010 012 014

Supposed behavior(A)Experimental behavior (B)

(A)

(B)

Cc

(mm

olL

)

Cp (mmolL)

(b)

Figure 3 Description of experimental data by (19) (a) and evaluation of (3) from experimental data (119862119888 and 119862119901)

apparently the PII concentration in the aqueous effluent hasbeen completely eliminated however from curve ldquobrdquo it can beseen that PII concentration in the effluent is relatively high incomparison with initial concentration) Thus apparently PIIconcentration could be identified to be zero when really thisis not like that

It can be seen that experimental data are satisfactorilydescribed by linear form of (19) (see Figure 3(a)) However itis clear that experimental error should beminimized in orderto obtain an adequate value of 1198620 On the other hand it can

be seen that the product 120572120579 can be easily determined from119887119898 (intersection at the119910-axis divided by slope)Thoughwithinformation obtained from experimental data a simulationbased on (19) can be performed the parameter 120579 includes allinformation about interactions associated with the WSP-PIImembrane-PII and WSP-membrane-PII interactions

From Figure 3(b) it can be seen that (3) is not the betterapproximation for the description of relation between119862119901 and119862119888 This supposition only is valid for short ranges of 119865 and itsevaluation is required depending on each systemunder study


00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5 6 7

(B)

(A)

Filtration factor (F)

Rsy

st

(a)

094

095

096

097

098

099

100

0 1 2 3 4 5 6 7Filtration factor (F)

Rsy

st

Experimental dataSimulation from (19)

(b)

Figure 4 (a) Retention profiles for PSSNA-Cd and blank experiment (A and B resp) and (b) semiempirical modeling of retention profilefrom experimental data by (19)

00

01

02

03

04

05

06

07

08

09

10

0 2 4 6 8 10


(A)(B)(C)(D)(E)(F)(G)

Rsy

st

(a)

00

02

04

06

08

10

0 1 2 3 4 5

(A)(B)

(C)(D)

(E)(F) (G)

Rsy

st

Simulated retentionExperimental retention

Cin (mmolL)

(b)

Figure 5 (a) Retention profiles and (b) modeling of 119877pol for PSSNA-Cd from 119862in and 119877pol data Initial concentration values were 018 (A)036 (B) 089 (C) 134 (D) 223 (E) 356 (F) and 445 (G)

In consequence it is concluded that it is required to know anadequate value of 120579 and analyze the interaction parameters bynew approximations

Retention profiles for PSSNA-Cd and blank experimentare shown in Figure 4(a) In addition from Figure 4(b) it canbe seen that (19) can simulate adequately the retention profilefrom experimental data (semiempirical modeling) Howeverwhen retention by WSP (119877pol) at 119865 = 67 is compared with119877infin it is concluded that 119877pol lt 119877infin (119877pol = 965 and 119877infin =959) thus by modeling of LPR experiments more preciseformulations of WSP necessary to remove an amount of PIIcan be performedwhen amore significant difference between119877pol and 119877infin is evidenced

42 LPR Simulation from Retention Values In order to simu-late the retention profiles for different values of 119862in and usingretention values previously published it is necessary to definesome model parameters Thus it is clear that by definition1198620 can be determined from (1 minus 119877pol)119862in however it wasnoted that for experiments described in the previous sectionthis is not completely valid therefore a correction factor wasrequired and this was determined by comparison of 1198620 with(1 minus 119877pol)119862in thus the correction factor calculated was 218and 1198620 used for each simulation was calculated to be 218(1 minus 119877pol)119862in

Retention profiles are shown in Figure 5(a) and thevariation of 119877infin is shown in Figure 5(b) It can be seen


that the model permits the description of retention profilesand the projection of new profiles from a small number ofexperiments and experimental data

On the other hand the need to use a correction factoris supported in the fact that the comparison of experimentalresults with theoretical predictions reveals only a partialagreement and the need to define explicitly the product120572120579 and to refine the knowledge of changes of 120572 duringthe elution However it is suggested that the differencesbetween experiment and modeling are a result of variationin the experimental conditions which are not consistent withtheoretical assumptions (ie conformational changes ofWSPin solution volume measures with a low precision initialtime to achieve the equilibrium pressure polydispersity ofthe polymer chains and changes of ionic strength during theelution can affect the capture of experimental data)

5 Conclusions

A complete modeling of LPR technique by washing methodis described from the PII distribution in regions (retainerelements and passive zones) of the UF system in conse-quence semiempirical simulation of PII retention by WSPcan be performed from a small amount of experimentaldata In addition it is concluded that it is required toknow adequate values of 120579 and 120572 as well as to analyze theinteraction parameters by new approximations associatedwith molecular structure of polymer

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by internal funding of the Univer-sity of Valle

References

[1] MCheryanUltrafiltration andMicrofiltrationHandbook Tech-nomic Publishing Company Lancaster Pa USA 1998

[2] G Kang and Y Cao ldquoApplication and modification ofpoly(vinylidene fluoride) (PVDF) membranesmdasha reviewrdquo Jour-nal of Membrane Science vol 463 pp 145ndash165 2014

[3] B L Rivas E D Pereira and I Moreno-Villoslada ldquoWater-sol-uble polymer-metal ion interactionsrdquo Progress in Polymer Sci-ence vol 28 no 2 pp 173ndash208 2003

[4] Z Berk Membrane Processes Food Process Engineering andTechnology 2nd edition 2013

[5] B L Rivas E D Pereira M Palencia and J Sanchez ldquoWater-soluble functional polymers in conjunction with membranesto remove pollutant ions from aqueous solutionsrdquo Progress inPolymer Science vol 36 no 2 pp 294ndash322 2011

[6] K E Geckeler E Bayer B Y Spivakov V M Shkinev andG A Vorobrsquoeva ldquoLiquid-phase polymer-based retention a newmethod for separation and preconcentration of elementsrdquoAnalytica Chimica Acta vol 189 pp 285ndash292 1986

[7] R Molinari T Poerio and P Argurio ldquoChemical and opera-tional aspects in running the polymer assisted ultrafiltrationfor separation of copper(II)-citrate complexes from aqueousmediardquo Journal of Membrane Science vol 295 no 1-2 pp 139ndash147 2007

[8] E Katsou S Malamis and K J Haralambous ldquoIndustrialwastewater pre-treatment for heavymetal reduction by employ-ing a sorbent-assisted ultrafiltration systemrdquo Chemosphere vol82 no 4 pp 557ndash564 2011

[9] R Molinari S Gallo and P Argurio ldquoMetal ions removalfrom wastewater or washing water from contaminated soil byultrafiltration-complexationrdquoWater Research vol 38 no 3 pp593ndash600 2004

[10] B Chaufer and A Deratani ldquoRemoval of metal ions bycomplexation-ultrafiltration using water-soluble macromole-cules perspective of application to wastewater treatmentrdquoNuclear and Chemical Waste Management vol 8 no 3 pp 175ndash187 1988

[11] Y R Qiu L J Mao and W H Wang ldquoRemoval of manganesefrom waste water by complexation-ultrafiltration using copoly-mer of maleic acid and acrylic acidrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 24 no 4 pp 1196ndash1201 2014

[12] K R Desai and Z V P Murthy ldquoRemoval of silver fromaqueous solutions by complexation-ultrafiltration using anionicpolyacrylamiderdquoChemical Engineering Journal vol 185-186 pp187ndash192 2012

[13] J Shao S Qin J Davidson W Li Y He and H S ZhouldquoRecovery of nickel from aqueous solutions by complexation-ultrafiltration process with sodium polyacrylate and polyethyl-eniminerdquo Journal of HazardousMaterials vol 244-245 pp 472ndash477 2013

[14] A Tabatabai J F Scamehorn and S D Christian ldquoEco-nomic feasibility study of polyelectrolyte-enhanced ultrafiltra-tion (PEUF) for water softeningrdquo Journal of Membrane Sciencevol 100 no 3 pp 193ndash207 1995

[15] R Camarillo A Perez P Canizares and A de Lucas ldquoRemovalof heavy metal ions by polymer enhanced ultrafiltration Batchprocess modeling and thermodynamics of complexation reac-tionsrdquo Desalination vol 286 pp 193ndash199 2012

[16] P Canizares A Perez R Camarillo and R Mazarro ldquoSimulta-neous recovery of cadmium and lead from aqueous effluents bya semi-continuous laboratory-scale polymer enhanced ultrafil-tration processrdquo Journal of Membrane Science vol 320 no 1-2pp 520ndash527 2008

[17] J Sabate M Pujola and J Llorens ldquoSimulation of a continuousmetal separation process by polymer enhanced ultrafiltrationrdquoJournal of Membrane Science vol 268 no 1 pp 37ndash47 2006

[18] J Llorens M Pujola and J Sabate ldquoSeparation of cadmiumfrom aqueous streams by polymer enhanced ultrafiltration atwo-phase model for complexation bindingrdquo Journal of Mem-brane Science vol 239 no 2 pp 173ndash181 2004

[19] S Ahmadi B Batchelor and S S Koseoglu ldquoRemoval of toxicheavy metal ions from metal finishing industry effluents bymicellar enhanced ultrafiltration technologyrdquo Journal of Haz-ardous Materials vol 28 no 1-2 p 225 1991

[20] M Palencia B L Rivas E Pereira A Hernandez and PPradanos ldquoStudy of polymer-metal ion-membrane interactionsin liquid-phase polymer-based retention (LPR) by continuousdiafiltrationrdquo Journal of Membrane Science vol 336 no 1-2 pp128ndash139 2009


[21] K E Geckeler ldquoPolymer-metal complexes for environmentalprotection Chemoremediation in the aqueous homogeneousphaserdquo Pure and Applied Chemistry vol 73 no 1 pp 129ndash1362001

[22] K E Geckeler V M Shkinev and B Y Spivakov ldquoLiquid-phasepolymer-based retention (LPR)mdasha new method for selectiveion separationrdquo Separation and purification methods vol 17 no2 pp 105ndash140 1988

[23] Y Uludag H O Ozbelge and L Yilmaz ldquoRemoval of mercuryfrom aqueous solutions via polymer-enhanced ultrafiltrationrdquoJournal of Membrane Science vol 129 no 1 pp 93ndash99 1997

[24] V M Shkinev V N Gomolitskii B Y Spivakov K E Geckelerand E Bayer ldquoDetermination of trace heavy metals in watersby atomic-absorption spectrometry after preconcentration byliquid-phase polymer-based retentionrdquo Talanta vol 36 no 8pp 861ndash863 1989

[25] S Ahmadi B Batchelor and S S Koseoglu ldquoThe diafiltrationmethod for the study of the binding ofmacromolecules to heavymetalsrdquo Journal ofMembrane Science vol 89 no 3 pp 257ndash2651994

[26] S D Alexandratos and X Zhu ldquoHigh-affinity ion-complexingpolymer-supported reagents immobilized phosphate ligandsand their affinity for the uranyl ionrdquo Reactive and FunctionalPolymers vol 67 no 5 pp 375ndash382 2007

[27] W M Anspach and J A Marinsky ldquoComplexing of nickel(II)and cobalt(II) by a polymethacrylic acid gel and its linearpolyelectrolyte analogrdquo Journal of Physical Chemistry vol 79no 5 pp 433ndash439 1975

[28] K H Choo S C Han S J Choi et al ldquoUse of chelatingpolymers to enhance manganese removal in ultrafiltration fordrinking water treatmentrdquo Journal of Industrial and EngineeringChemistry vol 13 no 2 pp 163ndash169 2007

[29] D Zamariotto B Lakard P Fievet andN Fatin-Rouge ldquoReten-tion of Cu(II)ndash andNi(II)ndashpolyaminocarboxylate complexes byultrafiltration assisted with polyaminesrdquo Desalination vol 258no 1ndash3 pp 87ndash92 2010

[30] L Dambies A Jaworska G Zakrzewska-Trznadel and B Sar-towska ldquoComparison of acidic polymers for the removal ofcobalt from water solutions by polymer assisted ultrafiltrationrdquoJournal of Hazardous Materials vol 178 no 1ndash3 pp 988ndash9932010

[31] M Palencia B L Rivas and E Pereira ldquoPolymer-enhancedultrafiltration counterion distribution and its relation withthe divalent metal-ion retention properties by sulfonic acidpolyelectrolytesrdquo Polymer Bulletin vol 67 no 7 pp 1123ndash11382011

[32] M Vera M Palencia and E Enrique Combatt ldquoEstudio de lacapacidad de retencion de boro disponible en suelos mediantemembranas funcionales con cadenas de poliolesrdquoRevista TemasAgrarios vol 19 no 1 pp 98ndash107 2014

[33] A Deshkovski S Obukhov and M Rubinstein ldquoCounterionphase transitions in dilute polyelectrolyte solutionsrdquo PhysicalReview Letters vol 86 no 11 pp 2341ndash2344 2001

[34] A V Dobrynin ldquoEffect of counterion condensation on rigidityof semiflexible polyelectrolytesrdquoMacromolecules vol 39 no 26pp 9519ndash9527 2006

[35] G S Manning ldquoCounterion binding in polyelectrolyte theoryrdquoAccounts of Chemical Research vol 12 no 12 pp 443ndash449 1979

[36] G S Manning ldquoLimiting laws and counterion condensation inpolyelectrolyte solutions 7 Electrophoretic mobility and con-ductancerdquo Journal of Physical Chemistry vol 85 no 11 pp 1506ndash1515 1981

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


H2O(reservoir tank)

Ultrafiltration membrane

H2O + PII (excess)(permeate)

WSP-PII WSP + PII

(a)

(reservoir tank)

Ultrafiltration membraneH2O + PII (excess)

(permeate)

H2O + PII

WSP + PII WSP-PII

(b)Pr

essu

re sy

stem Elution solution

Reservoir tankFiltration unit

MembraneStirringsystem

Collected samples(permeate)

WSP-PII solution

(c)

Figure 1 Description of LPR technique by washing method (a) and enrichment method (b) and schematic representation of experimentaldevice (c)

separate low molecular weight species dissolved in aqueoussolution [5] Thus a WSP solution and a metal ion solutionare contacted in the feed-side of an UF system the metalions are consequently bonded to the polymer and newmacromolecular species are formed and retained by a size-exclusion mechanism while the unbounded species witha diameter smaller than cutoff diameter of the membranepasses to the permeate stream [5 20]

Usually LPR technique can be applied by two operationmethods (1) the washing method or elution method (withthe ionic strength kept constant or not) which is the mostusedmethod to study the PIIrsquos retention capacity of a polymerin aqueous solution and is a discontinuous separation processand (2) the enrichment method or concentration methodwhich is a continuous separation process [5] In the washingmethod a certain amount of polymer and PII solutions withknown concentrations are placed in the feed-side of an UFcell and a water stream is passed through the cell [5 22 25]On the other hand for the application of the enrichmentmethod the WSP solution is placed in a stirred cell and a PIIsolution is added continuously from a pressurized reservoirHowever when the bonding groups of theWSP are saturatedby their interactionwith the PII in the solution themaximumretention capacity (MRC) of polymer is reached and the pro-cess cannot continue [5 20] Evidently the physicochemicalproperties of the WSP and the polymer-metal complexes

must be taken into account and their interaction with themembrane surface is also very relevant During the retentionand separation process by LPR the permeate is removed atthe same rate keeping the volume in the feed cell and thepolymer concentration constant all the time [20] Reviewson LPR technique have been performed by Geckeler et al[6 21 22] andmost recently by Rivas et al [3 5] (see Figure 1)

TheLPR technique can be visualized like cyclic separationprocess and thus it should be economically more feasiblewhenWSP can be regenerated and reused Among regenera-tion methods of theWSP are the chemical methods (protoly-sis transcomplexation and redox reaction) electrochemicalmethods and thermal methods [3] In this way new optionsof regeneration of chelating groups by using new componentsincorporated to the system can be useful to make the processmore feasible

The LPR technique either by washing method or byenrichment method is based on the interaction between theWSP and the PIIs in aqueous solution and the progressiveretention by anUFmembrane of the new species formed [20]The type of interaction depends on the chemical nature ofthe WSP functional groups In any case these interactionsare mainly due to electrostatic forces and the formationof coordinating bonds The variables that affect the WSP-PII interaction are classified into two groups intrinsic tothe polymer (ie the nature of the atoms in the backbone










119873119888 = 1198730 minus 119873119901 (1)


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 (2)


119889119862119888 = 120572119889119862119901 (3)



119889119862119901

119889119881119901=minus119862119901

120572119881119888 + 119881119901 (4)


119862119901

1198620=120572119881119888

120572119881119888 + 119881119901=120572

120572 + 119865 (5)


119862119901 =1

119881119901

119899

sum119894=1

(119862119901119894119881119894)

119881119901 =

119899

sum119894=1

119881119894

(6)




Mn+(sol) 999448999471 Mn+

(membrane) (7)


119896119898 =119862119898

119862119888=119873119898119881119888

119873119888119908119898 (8)



minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 (9)

By (3) and (9)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896119898119908119898) 120572 + 119881119901 (10)



119862119901

1198620=(1 + 119896119898119908119898119881119888

minus1) 120572

(1 + 119896119898119908119898119881119888minus1) 120572 + 119865

=120572120579119898

120572120579119898 + 119865 (11)




Mn+(sol) 999448999471 Mn+

(polymer) (12)


1198961 =119862pol

119862119888=119873119887

119862119888119881pol (13)


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896pol119881pol119889119862119888 (14)

By (3) and (14)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896pol119881pol) 120572 + 119881119901 (15)


119862119901

1198620=(1 + 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896pol119881pol119881minus1119888) 120572 + 119865

=120572120579pol

120572120579pol + 119865 (16)



119862in (mmolL) 018 036 089 134 223 356 445119877pol () 610 567 470 412 351 309 280


minus1

119888


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 + 119896pol119881pol119889119862119888

(17)


119889119862119901

119889119881119901=

minus119862119901

(1 + 119896119898119908119898 + 119896pol119881pol) 120572119881119888 + 119881119901 (18)


119862119901

1198620=(1 + 119896119898119908119898119881

minus1

119888+ 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896119898119908119898119881minus1119888+ 119896pol119881pol119881

minus1119888) 120572 + 119865

=120572120579

120572120579 + 119865 (19)

where 120579 = 1 + 119896119898119908119898119881minus1

119888+ 119896pol119881pol119881

minus1

119888






minus1


119877syst = 1 minus1205721205791198620

(120572120579 + 119865)119862in119865 (20)



1205721205791198620

119862in (21)






000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)

(a)

000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)(b)


0

5

10

15

20

25

30

35

40

45

50


1Cp

(Lm

mol

)

y = mx + by = 626x + 289

r2 = 09991

(a)

00

05

10

15

20

25

30

35

40

000 002 004 006 008 010 012 014


(A)

(B)

Cc

(mm

olL

)

Cp (mmolL)

(b)







00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5 6 7

(B)

(A)


Rsy

st

(a)

094

095

096

097

098

099

100


Rsy

st


(b)


00

01

02

03

04

05

06

07

08

09

10

0 2 4 6 8 10


(A)(B)(C)(D)(E)(F)(G)

Rsy

st

(a)

00

02

04

06

08

10

0 1 2 3 4 5

(A)(B)

(C)(D)

(E)(F) (G)

Rsy

st


Cin (mmolL)

(b)









5 Conclusions




Acknowledgment


References















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










119873119888 = 1198730 minus 119873119901 (1)


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 (2)


119889119862119888 = 120572119889119862119901 (3)



119889119862119901

119889119881119901=minus119862119901

120572119881119888 + 119881119901 (4)


119862119901

1198620=120572119881119888

120572119881119888 + 119881119901=120572

120572 + 119865 (5)


119862119901 =1

119881119901

119899

sum119894=1

(119862119901119894119881119894)

119881119901 =

119899

sum119894=1

119881119894

(6)




Mn+(sol) 999448999471 Mn+

(membrane) (7)


119896119898 =119862119898

119862119888=119873119898119881119888

119873119888119908119898 (8)



minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 (9)

By (3) and (9)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896119898119908119898) 120572 + 119881119901 (10)



119862119901

1198620=(1 + 119896119898119908119898119881119888

minus1) 120572

(1 + 119896119898119908119898119881119888minus1) 120572 + 119865

=120572120579119898

120572120579119898 + 119865 (11)




Mn+(sol) 999448999471 Mn+

(polymer) (12)


1198961 =119862pol

119862119888=119873119887

119862119888119881pol (13)


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896pol119881pol119889119862119888 (14)

By (3) and (14)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896pol119881pol) 120572 + 119881119901 (15)


119862119901

1198620=(1 + 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896pol119881pol119881minus1119888) 120572 + 119865

=120572120579pol

120572120579pol + 119865 (16)



119862in (mmolL) 018 036 089 134 223 356 445119877pol () 610 567 470 412 351 309 280


minus1

119888


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 + 119896pol119881pol119889119862119888

(17)


119889119862119901

119889119881119901=

minus119862119901

(1 + 119896119898119908119898 + 119896pol119881pol) 120572119881119888 + 119881119901 (18)


119862119901

1198620=(1 + 119896119898119908119898119881

minus1

119888+ 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896119898119908119898119881minus1119888+ 119896pol119881pol119881

minus1119888) 120572 + 119865

=120572120579

120572120579 + 119865 (19)

where 120579 = 1 + 119896119898119908119898119881minus1

119888+ 119896pol119881pol119881

minus1

119888






minus1


119877syst = 1 minus1205721205791198620

(120572120579 + 119865)119862in119865 (20)



1205721205791198620

119862in (21)






000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)

(a)

000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)(b)


0

5

10

15

20

25

30

35

40

45

50


1Cp

(Lm

mol

)

y = mx + by = 626x + 289

r2 = 09991

(a)

00

05

10

15

20

25

30

35

40

000 002 004 006 008 010 012 014


(A)

(B)

Cc

(mm

olL

)

Cp (mmolL)

(b)







00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5 6 7

(B)

(A)


Rsy

st

(a)

094

095

096

097

098

099

100


Rsy

st


(b)


00

01

02

03

04

05

06

07

08

09

10

0 2 4 6 8 10


(A)(B)(C)(D)(E)(F)(G)

Rsy

st

(a)

00

02

04

06

08

10

0 1 2 3 4 5

(A)(B)

(C)(D)

(E)(F) (G)

Rsy

st


Cin (mmolL)

(b)









5 Conclusions




Acknowledgment


References















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119889119862119901

119889119881119901=minus119862119901

120572119881119888 + 119881119901 (4)


119862119901

1198620=120572119881119888

120572119881119888 + 119881119901=120572

120572 + 119865 (5)


119862119901 =1

119881119901

119899

sum119894=1

(119862119901119894119881119894)

119881119901 =

119899

sum119894=1

119881119894

(6)




Mn+(sol) 999448999471 Mn+

(membrane) (7)


119896119898 =119862119898

119862119888=119873119898119881119888

119873119888119908119898 (8)



minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 (9)

By (3) and (9)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896119898119908119898) 120572 + 119881119901 (10)



119862119901

1198620=(1 + 119896119898119908119898119881119888

minus1) 120572

(1 + 119896119898119908119898119881119888minus1) 120572 + 119865

=120572120579119898

120572120579119898 + 119865 (11)




Mn+(sol) 999448999471 Mn+

(polymer) (12)


1198961 =119862pol

119862119888=119873119887

119862119888119881pol (13)


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896pol119881pol119889119862119888 (14)

By (3) and (14)

119889119862119901

119889119881119901=

minus119862119901

(119881119888 + 119896pol119881pol) 120572 + 119881119901 (15)


119862119901

1198620=(1 + 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896pol119881pol119881minus1119888) 120572 + 119865

=120572120579pol

120572120579pol + 119865 (16)



119862in (mmolL) 018 036 089 134 223 356 445119877pol () 610 567 470 412 351 309 280


minus1

119888


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 + 119896pol119881pol119889119862119888

(17)


119889119862119901

119889119881119901=

minus119862119901

(1 + 119896119898119908119898 + 119896pol119881pol) 120572119881119888 + 119881119901 (18)


119862119901

1198620=(1 + 119896119898119908119898119881

minus1

119888+ 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896119898119908119898119881minus1119888+ 119896pol119881pol119881

minus1119888) 120572 + 119865

=120572120579

120572120579 + 119865 (19)

where 120579 = 1 + 119896119898119908119898119881minus1

119888+ 119896pol119881pol119881

minus1

119888






minus1


119877syst = 1 minus1205721205791198620

(120572120579 + 119865)119862in119865 (20)



1205721205791198620

119862in (21)






000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)

(a)

000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)(b)


0

5

10

15

20

25

30

35

40

45

50


1Cp

(Lm

mol

)

y = mx + by = 626x + 289

r2 = 09991

(a)

00

05

10

15

20

25

30

35

40

000 002 004 006 008 010 012 014


(A)

(B)

Cc

(mm

olL

)

Cp (mmolL)

(b)







00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5 6 7

(B)

(A)


Rsy

st

(a)

094

095

096

097

098

099

100


Rsy

st


(b)


00

01

02

03

04

05

06

07

08

09

10

0 2 4 6 8 10


(A)(B)(C)(D)(E)(F)(G)

Rsy

st

(a)

00

02

04

06

08

10

0 1 2 3 4 5

(A)(B)

(C)(D)

(E)(F) (G)

Rsy

st


Cin (mmolL)

(b)









5 Conclusions




Acknowledgment


References















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119862in (mmolL) 018 036 089 134 223 356 445119877pol () 610 567 470 412 351 309 280


minus1

119888


minus119881119888119889119862119888 = 119881119901119889119862119901 + 119862119901119889119881119901 + 119896119898119908119898119889119862119888 + 119896pol119881pol119889119862119888

(17)


119889119862119901

119889119881119901=

minus119862119901

(1 + 119896119898119908119898 + 119896pol119881pol) 120572119881119888 + 119881119901 (18)


119862119901

1198620=(1 + 119896119898119908119898119881

minus1

119888+ 119896pol119881pol119881

minus1

119888) 120572

(1 + 119896119898119908119898119881minus1119888+ 119896pol119881pol119881

minus1119888) 120572 + 119865

=120572120579

120572120579 + 119865 (19)

where 120579 = 1 + 119896119898119908119898119881minus1

119888+ 119896pol119881pol119881

minus1

119888






minus1


119877syst = 1 minus1205721205791198620

(120572120579 + 119865)119862in119865 (20)



1205721205791198620

119862in (21)






000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)

(a)

000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)(b)


0

5

10

15

20

25

30

35

40

45

50


1Cp

(Lm

mol

)

y = mx + by = 626x + 289

r2 = 09991

(a)

00

05

10

15

20

25

30

35

40

000 002 004 006 008 010 012 014


(A)

(B)

Cc

(mm

olL

)

Cp (mmolL)

(b)







00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5 6 7

(B)

(A)


Rsy

st

(a)

094

095

096

097

098

099

100


Rsy

st


(b)


00

01

02

03

04

05

06

07

08

09

10

0 2 4 6 8 10


(A)(B)(C)(D)(E)(F)(G)

Rsy

st

(a)

00

02

04

06

08

10

0 1 2 3 4 5

(A)(B)

(C)(D)

(E)(F) (G)

Rsy

st


Cin (mmolL)

(b)









5 Conclusions




Acknowledgment


References















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)

(a)

000

002

004

006

008

010

012

014


[Cd2

+]

(mm

olL

)(b)


0

5

10

15

20

25

30

35

40

45

50


1Cp

(Lm

mol

)

y = mx + by = 626x + 289

r2 = 09991

(a)

00

05

10

15

20

25

30

35

40

000 002 004 006 008 010 012 014


(A)

(B)

Cc

(mm

olL

)

Cp (mmolL)

(b)







00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5 6 7

(B)

(A)


Rsy

st

(a)

094

095

096

097

098

099

100


Rsy

st


(b)


00

01

02

03

04

05

06

07

08

09

10

0 2 4 6 8 10


(A)(B)(C)(D)(E)(F)(G)

Rsy

st

(a)

00

02

04

06

08

10

0 1 2 3 4 5

(A)(B)

(C)(D)

(E)(F) (G)

Rsy

st


Cin (mmolL)

(b)









5 Conclusions




Acknowledgment


References















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


00

01

02

03

04

05

06

07

08

09

10

0 1 2 3 4 5 6 7

(B)

(A)


Rsy

st

(a)

094

095

096

097

098

099

100


Rsy

st


(b)


00

01

02

03

04

05

06

07

08

09

10

0 2 4 6 8 10


(A)(B)(C)(D)(E)(F)(G)

Rsy

st

(a)

00

02

04

06

08

10

0 1 2 3 4 5

(A)(B)

(C)(D)

(E)(F) (G)

Rsy

st


Cin (mmolL)

(b)









5 Conclusions




Acknowledgment


References















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




5 Conclusions




Acknowledgment


References















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Documents

Research Article Liquid-Phase Polymer-Based Retention: Theory, …downloads.hindawi.com/journals/jchem/2015/965624.pdf · 2019-07-31 · Research Article Liquid-Phase Polymer-Based