• Aucun résultat trouvé

NRC Publications Archive Archives des publications du CNRC

N/A
N/A
Protected

Academic year: 2021

Partager "NRC Publications Archive Archives des publications du CNRC"

Copied!
9
0
0

Texte intégral

(1)

Publisher’s version / Version de l'éditeur:

Journal of Membrane Science, 401-402, 15 May 2012, pp. 89-96, 2012-02-06

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

https://nrc-publications.canada.ca/eng/copyright

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la

première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.

Questions? Contact the NRC Publications Archive team at

PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.

NRC Publications Archive

Archives des publications du CNRC

This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.

For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.

https://doi.org/10.1016/j.memsci.2012.01.033

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

Chiral separation with molecularly imprinted polysulfone-aldehyde

derivatized nanofiber membranes

Sueyoshi, Yuuki; Utsunomiya, Akira; Yoshikawa, Masakazu; Robertson,

Gilles P.; Guiver, Michael D.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

NRC Publications Record / Notice d'Archives des publications de CNRC:

https://nrc-publications.canada.ca/eng/view/object/?id=b7efc168-7dc6-4e45-a453-fa922aee9161

https://publications-cnrc.canada.ca/fra/voir/objet/?id=b7efc168-7dc6-4e45-a453-fa922aee9161

(2)

ContentslistsavailableatSciVerseScienceDirect

Journal

of

Membrane

Science

j our na l h o me p ag e :w w w . e l s e v i e r . c o m / l o c a t e / m e m s c i

Chiral

separation

with

molecularly

imprinted

polysulfone-aldehyde

derivatized

nanofiber

membranes

夽夽

Yuuki

Sueyoshi

a

,

Akira

Utsunomiya

a

,

Masakazu

Yoshikawa

a,∗

,

Gilles

P.

Robertson

b

,

Michael

D.

Guiver

b

aDepartmentofBiomolecularEngineering,KyotoInstituteofTechnology,Matsugasaki,Kyoto606-8585,Japan

bInstituteforChemicalProcessandEnvironmentalTechnology,NationalResearchCouncilofCanada,Ottawa,Ontario,CanadaK1A0R6

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received15December2011

Receivedinrevisedform25January2012 Accepted28January2012

Available online 6 February 2012 Keywords:

Electrospraydeposition Chiralseparation Membrane Molecularimprinting

Molecularlyimprintednanofiber membrane

Nanofiberfabric Opticalresolution

a

b

s

t

r

a

c

t

Molecularly imprinted membranes (MIPMs) and molecularly imprinted nanofiber membranes (MINFMs)were prepared from polysulfone with aldehyde (PSf-CHO-05 or PSf-CHO-10) and N-␣-benzyloxycarbonyl-d-glutamicacid(Z-d-Glu)orN-␣-benzyloxycarbonyl-l-glutamicacid(Z-l-Glu)as aprintmolecule.Thosetwotypesofmolecularlyimprintedmembrane,suchasMIPMsandMINFMs, incorporatedtheenantiomer,ofwhichabsoluteconfigurationwassameasthatoftheprintmolecule, inpreferencetothecorrespondingantipode.Inotherwords,themembranesimprintedbythed-isomer preferentiallyadsorbedthed-isomerandviceversa.Thosetwotypesofmembraneshowedchiral sep-arationabilitybymembranetransport.Againstexpectation,transportoftheenantiomerpreferentially adsorbedinthemembranewasretarded,inotherwords,theenantiomerlessadsorbedinthe mem-branewasselectivelytransported.Thefluxesthroughthemolecularlyimprintednanofibermembranes gaveonetotwoordersofmagnitudehigherthanthoseofusualmolecularlyimprintedmembranes with-outdepressionofpermselectivity.Thepresentstudydemonstratedthatmolecularlyimprintednanofiber membranegavehighfluxwithoutdepressionofpermselectivity.Abreakthroughinmembraneseparation wouldberealizedbyadoptingmolecularlyimprintednanofibermembranes.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Membraneseparation(transport)isexplainedbyacoupleof mechanism,suchasincorporationofpermeantintoagiven mem-braneanddiffusion(migration)ofpermeantwithinthemembrane fromthefeedsidetothepermeateside [1–3].Inthecase of a membranetransportthroughanon-porousmembrane,such trans-port mechanism is called solution-diffusion mechanism, while thatthroughaporousmembrane,ifapproved,partition-diffusion mechanism.Diffusionofpermeantwithinthemembranewould bedominantlydeterminedbyitsdimensionand/orshape.From this,thecontrol ofpermselectivityby usingdifferencein diffu-sivity wouldbeintrinsically limited. Againstthis, incorporation ofpermeantintoagivenmembraneistheoreticallyexpectedto varyfromnaughttoinfinity.Inordertoimprovepermselectivity ofmembranes,introductionofmolecularrecognitionsites,which rigorouslydiscriminatethetargetsubstrateandothers,intoagiven membraneiscrucial.

Atime-consuming,costly,andawkwardexperimentalworkis requiredtointroducemolecularrecognitionsitesintopolymeric

夽 NRCCPublicationNo.53064. ∗ Correspondingauthor.

E-mailaddress:masahiro@kit.ac.jp(M.Yoshikawa).

membranes.Against this,molecularimprintingtechnique [4–7]

wouldintroducemolecularrecognitionsitesintopolymeric mem-braneswithoutsuchaneffortmentionedaboveandisperceived tobeoneofthemostfacilewaystogivepolymericmembranes substrate specificity [8–11]. Among molecularimprinting tech-niques, an alternative molecular imprinting is a facile way to introducemolecularrecognitionsitesintopolymericmembranes. Thealternativemolecularimprintingcanbetakenasanextension ofMichales’study[12],whichwasthefirstapplicationof molec-ularimprintingtomembraneseparation.Applyinganalternative molecularimprinting,anypolymericmaterials,suchassynthetic polymers [13], oligopeptide derivatives [14,15], derivatives of natural polymers[16], and naturalpolymers[17] were directly convertedintomolecularlyimprintedmembranes.Inmembrane separation,notonlypermselectivitybutalsofluxisanimportant membraneperformance.Inasense,thedevelopmentofseparation membraneswithhighfluxismoreimportantthanthatwithhigh permselectivity.However,inmembraneseparation,afluxandthe correspondingpermselectivityoftenshowatrade-offrelationship. Membranologistshaveperceivedthatitisanunsolvedproblem inmembraneseparationtosimultaneouslyenhancebothfluxand permselectivity.

Membraneformofnanofibermat,whichisfabricatedby elec-trospraydeposition,isexpectedtosolveatrade-offrelationship inmembraneseparation,sincenanofibermatsgivehighersurface

0376-7388/$–seefrontmatter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2012.01.033

(3)

90 Y.Sueyoshietal./JournalofMembraneScience401–402 (2012) 89–96

areaandhigherporosity[18–22].Electrosprayednanofiber mem-braneswithmolecularrecognitionsiteswerefirstfabricatedfrom polyallylamine and poly(ethylene terephthalate) adopting 2,4-dichlorophenoxyaceticacidasaprintmoleculebyanalternative molecularimprinting[23].Thisprovedthatanalternative molecu-larimprintingisasuitablemethodtoobtainnanofibermembranes bearingmolecularrecognitionsitesdirectlyfrompolymeric mate-rials.Simultaneouslyapplyinganelectrospraydepositionandan alternativemolecularimprinting,molecularlyimprintednanofiber membranescanbefabricatedfromjustpolymersolutionwitha printmoleculewithease.Nanofibermembraneswithmolecularly imprintednanoparticleswerealsofabricatedbyelectrospray depo-sitionofpoly(ethyleneterephthalate)andmolecularlyimprinted nanoparticles[24,25].Thosematerialswereapplicableto solid-phaseextractorandsensorchipforthedetectionofagiventarget molecule.

The recognition of a target molecule by nanofiber fabrics with molecular recognition sites corresponds to the incorpo-ration of the permeant into the membrane in a membrane transport system. If the membrane diffusion process within the membrane and dissociation of a target molecule from a molecularrecognitionsite or release of it from the membrane are accompanied with molecular recognition process, a mem-brane transport process witha higher flux would be attained. To this end, nanofiber membranes with molecular recognition sites, which are called molecularly imprinted nanofiber mem-branes,werefabricatedbysimultaneouslyapplyinganalternative molecular imprinting and an electrospray deposition [26–28]. Those studies revealed that molecularly imprinted nanofiber membranes gave high flux without depression of permselec-tivity. A breakthrough in membrane separation was attained, in other words,there wasfound one of promising and simple ways to solve a trade-off relationship in membrane separa-tion.

In theprevious study[26],molecularly imprinted nanofiber membranesfrompolysulfonewithcarboxylicacidasafunctional moietybearingoxygenatomwasinvestigated.Aldehydegroupis anotherfunctionalmoietybearingoxygenatom.Itisinterestingto studytheeffectoffunctionalmoietyonchiralseparationability. To this end, in the present study, polysulfone with aldehyde group (PSf-CHO) was adopted as membrane materials. In the presentstudy,molecularlyimprintednanofibermembranesand usual molecularly imprinted membranes were fabricated from PSf-CHOand printmolecule, suchas N-␣-benzyloxycarbonyl-d-glutamic acid (Z-d-Glu) or N-␣-benzyloxycarbonyl-l-glutamic acid (Z-l-Glu), and their membrane performances of adsorption selectivity, permselectivity, and flux were studied.

2. Experimental 2.1. Materials

Polysulfoneswithaldehyde(PSf-CHO),withdegreeof substitu-tionof0.50(PSF-CHO-05)and1.00(PSf-CHO-10)(Scheme1)were preparedbythemodificationofPSfUdelP-3500(BPAmoco)as reportedpreviously[29].

N-␣-benzyloxycarbonyl-d-glutamic acid (Z-d-Glu) or N-␣-benzyloxycarbonyl-l-glutamic acid (Z-l-Glu), purchased from WatanabeChemicalIndustries,Ltd.(Hiroshima,Japan),wasused asaprintmoleculewithoutfurtherpurification.d-Glutamicacid (d-Glu), l-glutamic acid (l-Glu), sodium azide, copper sulfate, and ethanol were obtainedfrom commercialsources and used as received. N,N-Dimethylformamide (DMF) and tetrahydrofu-ran(THF)werepurifiedbytheconventionalmethod[30].Water

Scheme1.Chemicalstructuresofpolysulfonewithaldehydegroup(PSf-CHO)and printmolecule(Z-d-GluorZ-l-Glu).

purifiedwithanultrapurewatersystem(SimpliLab,MilliporeS.A., Molsheim,France)wasused.

2.2. Preparationofmolecularlyimprintedmembranes

Usualmolecularlyimprintedmembraneswerepreparedfrom THFsolution,containingtheimprintingcomponents.Moleratio of0.50forprintmoleculetoconstitutionalrepeatingunitof PSf-CHOinthemembranepreparationprocesswasstudied.A200mg ofquantityofPSf-CHOandaprescribedamountofprintmolecule, Z-d-GluorZ-l-Glu,wasdissolvedin3.0cm3ofTHF.Theamountof Z-Gluwas61.61mgforthepreparationofmolecularlyimprinted membrane from PSf-CHO-05 and 59.78mg for that from PSf-CHO-10,respectively.TheTHFsolutionthuspreparedwaspoured into 89mm diameter flat laboratorydish, and the solvent was allowedtoevaporateatambienttemperaturefor24h.The result-ingmembranewasfurtherdriedat50◦Cfor2h.Afterdrying,the printmoleculewasextractedfromtheresultantmembranebya largevolumeof50vol.%aqueousethanolsolutionuntiltheprint moleculewashardlydetectableinaqueousethanolsolutionbyUV analysis.Inthepresentstudy,mostofaddedprintmoleculewas leachedfromthemembranes.

2.3. Fabricationofmolecularlyimprintednanofibermembranes Inthepresentstudy,themolecularimprintingratio,whichwas themoleratioofprintmoleculetoconstitutionalrepeatingunitof PSf-CHOinthemembranepreparationprocesswasfixedtobe0.50 sothattheresultscanbecomparedwiththoseofusualmolecularly imprintedmembranes.MixtureofDMFandTHF(DMF/THF=2/1 (vol./vol.))was adoptedas solventand the polymer concentra-tionwasfixedat12.0wt.%inthepresentstudy.EsprayerES-2000 (FuenceCo.Ltd.,Japan)wasadoptedastheelectrospray deposi-tiondevice.Polymersolutioncontainingeither oneoftheprint moleculeswaselectrosprayedatambienttemperatureusingan appliedvoltageof25kVformolecularlyimprintednanofiber mem-branesor15kVforcontrolnanofibermembranes.Thesyringeused inthepresentstudyhadacapillarytipof0.52mmdiameter.The feedingratewas3.0mm3forthemolecularlyimprintedmembrane and5.0mm3forthecontrolnanofibermembrane,respectively.A groundedaluminumfoilusedasacounterelectrodewasplaced 10cmfromthetipofthecapillary.

(4)

Themorphology,diameter,andthicknessoftheelectrosprayed nanofibermembranesweredeterminedwithHitachiS-3000 scan-ningelectronmicroscope(SEM).Asmallsectionofthemembrane was placed on the SEM sample holder. The fiber diameter of nanofibermembranewasdeterminedusingImageJsoftware pro-grambymeasuringatleast30fibersfromeachSEMimage. 2.4. Adsorptionselectivity

Themembranesampleswereimmersedinaracemicmixture ofGlu,whichwasthesameracemicmixturestudiedinthe mem-branetransportability(i.e.,a50vol.%aqueousethanolsolutionof racemicGlu,withconcentrationof1.0×10−3moldm−3)andthe mixturewasallowedtobeequilibratedat40◦C;0.02wt.%sodium azide was added asa fungicide. Quantitative measurements of aliquotsofthesolutionattheinitialstageandafterequilibrium hadbeenreachedweremadeusingHPLCemployingaChiralpak MA(+)column(50mm×4.6mm(i.d.))(DaicelChemicalInd.Ltd.). TheamountofGluinthesupernatantsubtractedfromtheamount initiallyinthesolutiongavetheamountofGluadsorbedinthe membrane.

TheadsorptionselectivitySA(i/j)isdefinedas SA(i/j)= (i-Glu)/(j-Glu)

[i-Glu]/[j-Glu] (1)

where(i-Glu)and[i-Glu]aretheamountofi-Gluadsorbedinthe membraneandconcentrationinthesolutionafterequilibriumhad beenreached,respectively.

2.5. Adsorptionisothermsofd-Gluandl-Glu

Themembranesampleswereincontactwithvarious concentra-tionsofpured-Gluorl-Glusolutionandallowedtobeequilibrated at40◦C.Thequantitativeanalysesweredoneasdescribedabove. TheconcentrationofGluin themembrane[i-Glu]m or[j-Glu]m (i=D,j=Lori=L,j=D)wasdeterminedadoptingtheamountof Gluadsorbedinthemembraneandthevolumeofmembranephase, includingthatofmembraneandthatofsolutioninthemembrane.

2.6. Enantioselectivemembranetransport

Amembranewithanareaof3.0cm2wastightlysecuredwith Parafilmbetween two chambersof a permeationcell. The vol-umeofeachchamberwas40.0cm3.AracemicGlusolutionwas placedintheleft-handsidechamber(L-side)anda50vol.% aque-ousethanolsolutionintheright-handsidechamber(R-side).Each concentrationofracemicGluwas1.0×10−3moldm−3.Transport experimentswerecarriedoutat40◦Cwithstirring.Analiquotwas drawnfromthepermeatesideateachsamplingtime.Theamount ofd-andl-Glu transportedthroughthemembranewere deter-minedbyHPLCasdescribedabove.

Theflux,J(molcmcm−2h−1),isdefinedas J=Qı

At (2)

whereQ[mol]istheamountoftransportedGlu,ı[cm]the mem-branethickness,A[cm2] theeffectivemembranearea,andt [h] meanstime.

Thepermselectivity˛i/jisdefinedasthefluxratio,Ji/Jj,divided bytheconcentrationratio[i-Glu]/[j-Glu]

˛i/j= Ji/Jj

[i-Glu]/[j-Glu] (3)

Fig.1.SEMimagesofZ-d-Gluimprintednanofibermembrane(MINFM-10-D)(a), controlnanofibermembrane(MINFM-10-C)(b),andZ-l-Gluimprintednanofiber membrane(MINFM-10-L)(c).

3. Resultsanddiscussion

3.1. Morphologyofmolecularlyimprintednanofibermembranes TheSEMimagesoftheelectrosprayednanofibermembranes formPSf-CHO-10areshowninFig.1.ThosefromPSf-CHO-05also

(5)

92 Y.Sueyoshietal./JournalofMembraneScience401–402 (2012) 89–96

gavesimilarSEMimages.Inallnanofibermembranesinthepresent study,beadsarehardlyobserved.

Table1 summarizesmembrane thicknessofeach membrane studiedinthepresentstudyandfiberdiameterofeachnanofiber membrane. In the membrane code, MINFM denotes “molecu-larly imprinted nanofiber membrane” and MIPM “molecularly imprintedmembrane”,respectively.Inthemiddletwodigitinthe membrane code,05 denotes that themembrane was prepared fromPSf-CHO-05,in otherwords,thedegree ofsubstitution of PSf-CHObeing0.50,and 10wasfromPSf-CHO-10,respectively. Asforthelastalphabetinthemembranecode,D,C,andLmean d-isomerimprinted,control,andl-isomerimprintedmembrane, respectively.

3.2. Adsorptionselectivity

Adsorptionselectivityofmolecularlyimprintedandmolecularly imprintednanofiber membranes wasstudied adopting racemic mixtureofGlu’sasmodelracemates.Resultsaresummarizedin

Table2.Asexpectedfrompreviousstudies[13–16,26,27],the mem-branes imprintedby Z-d-Glu,incorporated d-Gluin preference tothe corresponding l-Glu and vice versa. In other words,the membranesimprintedbythel-isomerpreferentiallyadsorbedthe l-isomer.Asanticipated,controlmembranes,whichwereprepared fromPSf-CHOwithoutprintmolecule,hardlyshowedadsorption selectivity.Fromtheseresults,itwasconcludedthatZ-d-Gluand Z-l-Gluworkedasaprintmoleculeinthepresentstudy,aswell. Theadsorptionselectivityofthepresent molecularlyimprinted membranesmightbeexpressedbymolecularrecognitionsitesin themembrane,whichwereconstructedbythepresenceofprint moleculeduringthemembranepreparationprocess.Inthenext section,substratespecificityofthosemolecularrecognitionsites wasstudied.

3.3. Adsorptionisotherms

Itisinterestingtostudythesubstratespecificityofthe molecu-larrecognitionsitesinthemolecularlyimprintedandmolecularly imprintednanofibermembranes.Tothisend,adsorptionisotherms ofd-Glu and l-Glu for thosemembranes wereinvestigated. As anexample,theadsorptionisotherms ofmolecularlyimprinted nanofibermembranesfromPSf-CHO-10areshowninFig.2.The adsorptionisothermofl-GlufortheZ-d-Gluimprintednanofiber membrane(MINFM-10-D)andthatof d-Gluforthe MINFM-10-Lare straight lines passingthrough origin,implying that those enantiomerswereadsorbedinthemembranewithoutanyspecific interactionwiththemembrane,inotherwords,thosewere non-specificallyadsorbedinthemembranes.Adsorptionisothermsfor othermembranes,suchasmolecularlyimprintednanofiber mem-branesfromPSf-CHO-05,andmolecularlyimprintedmembranes fromPSf-CHO-05and PSf-CHO-10, alsogave similaradsorption isothermsasshowninFig.2.

TheadsorptionisothermofGlunon-specificallyadsorbedinthe membranecanberepresentedbythefollowingequation:

[j-Glu]m=kA[j-Glu] (4)

where[j-Glu]mdenotes theconcentrationofj-Gluin the mem-brane,whichwasnon-specificallyadsorbedinthemembrane,kA isadsorptionconstant,and[j-Glu]meanstheconcentrationof j-Gluinthesolutionequilibratedwiththemembrane.Ontheother hand,theadsorptionisothermofd-GluinMINFM-10-Dandthat ofl-Glu inMINFM-10-L, whichwere preferentiallyadsorbedin themembrane, gave complicated profiles. Those isotherms are dualadsorptionisotherms,whichconsistofnon-specific adsorp-tionandadsorptiononthespecificrecognitionsites,whichwere

constructedduringthemembranepreparationprocessbythe pres-enceof a print moleculeof Z-d-Gluor Z-l-Glu.Theadsorption isothermforGluspecificallyincorporatedintothemembranecan berepresentedbythefollowingequation:

[i-Glu]m=kA[i-Glu]+KS[Site]0[i-Glu]

1+KS[i-Glu] (5)

where[i-Glu]mdenotes theconcentrationof i-Gluin the mem-brane,whichwasspecificallyincorporatedinthemembrane,KSis theaffinityconstantbetweenmolecularrecognitionsiteandi-Glu, [i-Glu]meanstheconcentrationofi-Gluinthesolutionequilibrated withthemembrane.

TwoparametersinEqs.(4)and(5),whichweredeterminedtofit eachadsorptionisothermbest,aresummarizedinTable3together withthoseforothersstudiedinthepresentstudy.Asforthe con-centrationofmolecularrecognitionsites,whichwereconstructed bytheprint molecules,inthemembrane, thoseformolecularly imprintednanofibermembranesareslightlylowerthanthosefor usualmolecularlyimprintedmembranes.Thisleadstothe spec-ulationthat the amountof print molecule, which workedas a printmoleculetomemorizemolecularmemoryduringmembrane preparationprocess,forthepreparationofmolecularlyimprinted nanofibermembranewasslightlylowerthanthatforusual molecu-larlyimprintedmembrane.Suchphenomenawerealsoobservedin thestudyofmolecularlyimprintednanofibermembranesfrom cel-luloseacetate(CA)[27].ComparingPSf-CHOmolecularlyimprinted nanofibermembraneswiththoseofCAones,moreamountofprint moleculeworkedwellintheelectrospraydepositionprocessof PSf-CHOthanthatofCA.Inthepresentstudy,smallamountofprint moleculewaselectrosprayedsolelytowardthecounterelectrodeof groundedaluminumfoilaccompanyingnoPSf-CHOmolecule.This mightbeduetothedifferenceinaffinityconstantKSforthose mem-branes.Moreprecisediscussionaboutthispointwillbedescribed later.

Inthepreviousstudy[27,31],theaffinityconstantwasobserved toincrease withthedecrease in molecularimprintingratio; in otherwords,atthelowermolecularimprintingratio,more func-tionalgroupsinthecandidatepolymerinteractedwithoneprint molecule,resultinginahigheraffinityconstant.Similar phenom-ena were also observed in the present study, and the affinity constants for the molecularly imprinted nanofiber membranes gavehighervaluesthanthoseoftheusualmolecularlyimprinted membranes.

Asdescribedintheintroduction,apartofthemotivationtostart thepresentstudywashowthedifferenceinfunctionalgroupwould affectthemembrane performances. Tothis end, in thepresent study,polysulfonewithaldehydegroup(PSf-CHO)insteadof car-boxylicacidwasadoptedasamembranematerial.Thedetermined parameters for adsorption equations for PSf-CHO molecularly imprintedmembranesareagainsummarizedinTable4together withthoseforPSf-COOHmolecularlyimprintedmembranes.Inthis table,theparametersforthemolecularlyimprintedmembranes fromPSf-CHO-10withDSof1.00aresummarized,sincethedegree ofsubstitutionofPSf-COOHmembranesbeing0.88[13].Inthe con-structionofmolecularrecognitionsitesfromPSf-COOH,carboxylic acidmoietyandsulfonegroupmightcontributetorecognize align-mentofthefunctionalmoietiesoftheprintmoleculeviahydrogen bond.InthecaseofPSf-CHO,justsulfonegroupmightcontributeto recognizethealignmentofthefunctionalmoieties.Ifsuch specu-lationmentionedaboveisaproperone,themolecularrecognition abilityoftheformedrecognitionsitesfromPSf-CHOislessthan thatfromPSf-COOH.Againstanticipation,theaffinityconstantsof PSf-CHOmembranewerehigherthanthoseofPSf-COOH.Inthe presentcase,shapememoryabilityofPSf-CHOshouldbebetter thanthatofPSf-COOH,whichmightbedominantlydependenton vander Waalsinteraction. Thisledtothedifferencein affinity

(6)

Table1

Membranethicknessandfiberdiameterofvariousmembranesinthepresentstudy.a

DS Membrane Membranethickness(␮m) Fiberdiameter(nm)

0.50 MINFM-05-D 200 269±170 MIPM-05-D 51 MINFM-05-C 175 564±333 MIPM-05-C 30 MINFM-05-L 129 280±218 MIPM-05-L 30 1.00 MINFM-10-D 135 177±64 MIPM-10-D 50 MINFM-10-C 50 189±85 MIPM-10-C 30 MINFM-10-L 100 165±105 MIPM-10-L 58

aMINFM,molecularlyimprintednanofibermembrane;MIPM,molecularlyimprintedmembrane.

Table2

Adsorptionselectivityofmolecularlyimprintedandmolecularlyimprintednanofibermembranes.a

DS Membrane (d-Glu)/mem.(mol/g-mem.) (l-Glu)/mem.mol/g-mem. SA(D/L) SA(L/D)

0.50 MINFM-05-D 2.26×10−4 1.63×10−4 1.39 0.72 MIPM-05-D 8.92×10−5 7.06×10−5 1.26 0.79 MINFM-05-C 1.48×10−4 1.48×10−4 1.00 1.00 MIPM-05-C 6.77×10−5 6.79×10−5 1.00 1.00 MINFM-05-L 1.44×10−4 1.85×10−4 0.78 1.28 MIPM-05-L 6.95×10−5 8.34×10−5 0.83 1.20 1.00 MINFM-10-D 3.03×10−4 2.31×10−4 1.31 0.76 MIPM-10-D 9.10×10−5 7.01×10−5 1.30 0.77 MINFM-10-C 1.97×10−4 1.97×10−4 1.00 1.00 MIPM-10-C 6.92×10−5 6.92×10−5 1.00 1.00 MINFM-10-L 2.61×10−4 4.10×10−4 0.64 1.57 MIPM-10-L 7.32×10−5 9.69×10−5 0.76 1.32

aMolecularimprintingratio,(Z-Glu)/(PSf-CHO)=0.50.

Fig.2.Adsorptionisothermsofd-Gluandl-GluinthenanofibermembraneimprintedbyZ-d-Glu(MINFM-10-D)(a)andthenanofibermembraneimprintedbyZ-l-Glu (MINFM-10-L)(b).

Table3

Parametersofadsorptionisothermsformolecularlyimprintedmembranes(MIPM)andmolecularlyimprintednanofibermembranes(MINFM).a Z-d-Gluimprintedmem. Z-l-Gluimprintedmem.

MIPM-10-D MINFM-10-D MIPM-10-L MINFM-10-L

kA 5.3×102 7.3×102 5.4×102 6.9×102

[Site]0(moldm−3) 2.0×10−1 1.5×10−1 1.6×10−1 1.5×10−1

KS(mol−1dm3) 1.3×104 2.2×104 1.7×104 2.0×104

Z-d-Gluimprintedmem. Z-l-Gluimprintedmem.

MIPM-05-D MINFM-05-D MIPM-05-L MINFM-05-L

kA 5.4×102 6.5×102 5.7×102 5.6×102

[Site]0(moldm−3) 1.5×10−1 1.5×10−1 1.6×10−1 1.4×10−1

KS(mol−1dm3) 1.4×104 1.9×104 1.4×104 1.8×104 aThemolecularimprintingratios(PrintMolecule)/(PSf-CHO),forthosemembraneswerefixedtobe0.50.

(7)

94 Y.Sueyoshietal./JournalofMembraneScience401–402 (2012) 89–96 Table4

Parametersofadsorptionisothermsformolecularlyimprintedmembranes(MIPM)fromPSF-CHO-10andPSf-COOH.a

Z-d-Gluimprintedmem. Z-l-Gluimprintedmem.

MIPM-10-D PSf-COOHb MIPM-10-L PSf-COOHb

kA 5.3×102 1.7×103 5.4×102 1.8×103

[Site]0(moldm−3) 2.0×10−1 4.2×10−1 1.6×10−1 4.2×10−1

KS(mol−1dm3) 1.3×104 7.9×103 1.7×104 7.9×103 aThemolecularimprintingratios(PrintMolecule)/(PSf-CHO)or(PrintMolecule)/(PSf-COOH),forthosemembraneswerefixedtobe0.50.

b DS=0.88;citedfromthepreviousstudy.

constantKS forthosetwotypesofmolecularlyimprinted mem-brane(Table5).

3.4. Chiralseparation

Fromtheadsorptionstudy,thosetwotypesofmembrane in thepresentstudywereexpectedtoshowchiralseparation abil-ity. To this end, chiral separation ability for those membranes wasinvestigated.Inthepresentstudy,concentrationgradientwas adoptedas a driving force for membrane transport. The trans-port of racemic Glu’s through the control membranes, suchas MIPM-10-Cand MIPM-05-C, washardlyobserved. Other mem-branes transported racemic mixture of Glu’s. As an example, time-transportcurvesofd-Gluandl-Gluthroughthemolecularly imprintednanofibermembranes,MINFM-10-DandMINFM-10-L, areshown inFig.3.Againstexpectation basedontheprevious results[26,27],MINFM-10-Dmembrane,whichwasimprintedby thed-isomerandpreferentiallyadsorbedthed-isomer,transported l-Gluinpreferencetothecorrespondingd-Gluandviceversa.Such transport phenomena were oftenobserved in chiral separation

[15,32–37].RetardedtransportofGlupreferentiallyincorporated intothemembranemightbebecauseofarelativelystrong interac-tionbetweenthemembraneandGluselectivelyadsorbed.

Inmembraneseparation,notonlypermselectivitybutalsoflux isanimportantmembraneperformance.Inasense,development ofamembranewithhighfluxismoreimportantthanthatwith highpermselectivity.Fromthisitisnecessarytocompare mem-braneperformancesofthepresentmembraneseachother.Inorder tocomparemembrane performanceofflux,themolarmobility, u(molcmcm−2J−1h−1),forGluforeachmembraneisasuitable parameter.FromNernst–Planckequation,afluxcanberepresented bythefollowingequation[38]:

J=−ucRT



dlnc dx



+



zF RT





d dx



+



v

RT





dP dx



(6)

whereJdenotesthesumofd-Gluandl-Glufluxes,cisthe concen-trationofeachGluinthefeedside,Rmeansuniversalgasconstant, T denotes absolute temperature, dc/dx is the concentration gradientatthatpoint,zisvalenceofpermeant,FmeanstheFaraday constant,d/dxdenoteselectricalpotentialgradientatthatpoint,

v

ispartialmolarvolumeofpermeant,anddP/dxisthepressure

gradientatthatpoint,Inthepresentstudy,membranetransport experimentswerecarriedoutunderisothermalandisobar condi-tions;andaconcentrationgradientwasadoptedasadrivingforce formembranetransport.Fromthese,thefluxinthepresentstudy canberepresentedbyjustfirstterminEq.(6).Thereforethemolar mobilitywasdeterminedbythefollowingequation:

u=− J/cRT

d lnc/dx (7)

Themolar mobility isdefined as themobility and issimply thefluxperunitmembranearea,perunitmembranethickness, perunitconcentration,andperunitdrivingforce.Inthe calcula-tionofthechemicalpotentialduetotheconcentrationgradient, theconcentrationof Glu in thepermeateside wasdetermined tobe 1.0×10−8moldm−3,since thelowest limit of the detec-tionofGluinthepresentstudywastheconcentrationofaround 1.0×10−8moldm−3.Inthetable,arelativemobilityisalsoshown forconvenience.Intheupperpartofthetable,ofwhichdataare membraneperformancesforthemembranesfromPSf-CHO-10,the relativemolarmobility,whichisrelativetoMIPM-10-L,isgiven; andinthelowerpartofthetable,therelativemolarmobility,which isrelativetoMIPM-05-L,isalsogiven.

Fluxvaluesforthemolecularlyimprintednanofibermembranes wereonetotwoordersofmagnitudehigherthanthoseforusual molecularlyimprintedmembranes.Comparingwiththeprevious resultsof molecularly imprinted nanofiber membranes [26,27], thepresent nanofiber membranesgave similarmolar mobility. Inthecaseofmolecularlyimprintednanofibermembranesfrom

Fig.3. Time–transportcurves of racemic Glu’sthrough the molecularly imprinted nanofiber membranes,MINFM-10-D (a)and MINFM-10-L (b) ([d-Glu]L,0=

(8)

Table5

Resultsofchiralseparationwithmolecularlyimprintednanofibermembranes(MINFMs)andmolecularlyimprintedmembranes(MIPMs).

Membrane Z-d-Gluimprintedmembrane Z-l-Gluimprintedmembrane

˛L/D uc ˛D/L uc MINFM-10a 1.24 1.15×10−9 1.20 1.67×10−9 (28) (41) MIPM-10a 1.20 4.20×10−11 1.20 4.10×10−11 (∼1) (1) MINFM-05b 1.12 7.00×10−9 1.20 2.20×10−9 (231) (72) MIPM-05b 1.25 6.64×10−11 1.16 3.05×10−11 (2.2) (1)

aFiguresinparenthesesaretherelativevalues;theuvalueforMIPM-10imprintedbyZ-l-Glubeingsetasunity. bFiguresinparenthesesaretherelativevalues;theuvalueforMIPM-05imprintedbyZ-l-Glubeingsetasunity. c u=(−J/C)/(d/dx)[{(molcmcm−2h−1)/(molcm−3)}/(Jmol−1cm−1)=molcmcm2J−1h−1].

PSf-COOH, the molar mobility was determined to be around 5.3×10−9(molcmcm2J−1h−1).

The permselectivities for the present molecularly imprinted nanofiber membraneswere not sohighcomparingwith mem-branespreviouslyreported[39–41].Thepermselectivityisthought to be greatly dependent on adsorption selectivity. From this, enhancementofadsorptionselectivityisindispensablesothata givenmolecularlyimprintednanofibermembranecangivehigher permselectivity.Theremightbefollowing plausiblemethodsto enhancepermselectivity:(1)anincreaseinsurfacearea (surface-to-volumeratio)bynarrowingdiameterofmolecularlyimprinted nanofibermembrane,(2)localizationofmolecularrecognitionsites onthesurfaceofnanofiber,whichwouldbefabricatedbyadopting coaxial,two-capillaryspinneret[19,42–46],or(3)applyingahigher molecularimprintingratio.Thosethreetypesofmethodwilllead toanincreaseinconcentrationofmolecularrecognitionsiteinthe membrane.

In the membrane separation, a flux and the corresponding permselectivityoftenshowatrade-offrelationship.Againstthis,as reportedinthepreviousstudies[26,27],theenhancementofflux withoutdepressionofpermselectivitywasrevealedinthepresent study.Inotherwords,molecularlyimprintednanofibermembranes havepotentialtosimultaneouslyenhancethroughput(flux)and permselectivity.

4. Conclusions

Molecularly imprinted membranes (MIPMs) and molecu-larlyimprintednanofiber membranes(MINFMs) wereprepared from polysulfone with aldehyde (PSf-CHO-05 or PSf-CHO-10) and N-␣-benzyloxycarbonyl-d-glutamic acid (Z-d-Glu) or N-␣-benzyloxycarbonyl-l-glutamicacid(Z-l-Glu)asaprintmolecule. Those two types of molecularly imprinted membrane, such as MIPMsandMINFMs,incorporatedtheenantiomer,ofwhich abso-luteconfigurationwassameasthatoftheprintmolecule,in prefer-encetothecorrespondingantipode.Inotherwords,themembranes imprintedbythed-isomerpreferentiallyadsorbedthed-isomer andviceversa.Thosetwotypesofmembraneshowed permselectiv-ity.Againstexpectation,transportoftheenantiomerpreferentially adsorbedinthemembranewasretarded,inotherwords,the enan-tiomerlessadsorbedinthemembranewasselectivelytransported. Thiscanbeexplainedbyarelativelystronginteractionbetween membraneandtheenantiomerpreferentiallyincorporatedintothe membrane.The fluxesthoughthemolecularly imprinted mem-branesgave one totwoordersof magnitudehigherthan those of usualmolecularly imprintedmembraneswithout depression ofpermselectivity.Asprovedinthepreviousstudies,thepresent studyalsorevealedthat molecularlyimprintednanofiber mem-branesgavehighfluxwithoutdepressionofpermselectivity.The

emergenceofmolecularlyimprintednanofibermembranewould solveatrade-offrelationshipinmembraneseparation.

References

[1]H.Winston,K.K.Sirkar(Eds.),MembraneHandbook,Chapmann&Hall,New York,1992.

[2] M.Mulder,BasicPrinciplesofMembraneTechnology,KluwerAcademic Pub-lishers,Dordrecht,1996.

[3]R.W.Baker,MembraneTechnologyandApplications,2nded.,JohnWiley& Sons,WestSussex,2004.

[4] R.A.Bartsch,M.Maeda(Eds.),MolecularandIonicRecognitionwithImprinted Polymers(ACSSymposiumSeries703),ACS,Washington,DC,1998. [5]B.Sellergren(Ed.),MolecularlyImprintedPolymersMan-madeMimicsof

Anti-bodiesandtheirApplicationsinAnalyticalChemistry,Elsevier,Amsterdam, 2001.

[6]M.Komiyama,T.Takeuchi,T.Mukawa,H.Asanuma,MolecularImprinting, Wiley-VCH,Weinheim,2003.

[7]C.Alexander,H.S.Andersson,L.I.Andersson,R.J.Ansell,N.Kirsch,I.A.Nicholls, J.O’Mahony,M.J.Whitcombe,Molecularimprintingscienceandtechnology:a surveyoftheliteraturefortheyearsuptoandincluding2003,J.Mol.Recognit. 19(2006)106–180.

[8]M.Yoshikawa,in:R.A.Bartsch,M.Maeda(Eds.),MolecularandIonic Recogni-tionwithImprintedPolymers(ACSSymposiumSeries703),ACS,Washington, DC,1998,p.170.

[9]S.A.Piletsky,T.L.Panasyuk,E.V.Piletskaya,I.A.Nicholls,M.Ulbricht, Recep-torandtransportpropertiesofimprintedpolymermembranes—areview,J. Membr.Sci.157(1999)263–278.

[10] M.Yoshikawa,Molecularlyimprintedpolymericmembranes,Bioseparation10 (2002)277–286.

[11]M.Ulbricht,Membraneseparationsusingmolecularlyimprintedpolymers,J. Chromatogr.B804(2004)113–125.

[12]A.S.Michaels,R.F.Baddour,H.J.Bixler,C.Y.Choo,Conditionedpolyethylene asapermselectivemembrane,Ind.Eng.Chem.ProcessDes.Dev.1(1962) 14–25.

[13] M.Yoshikawa,J.Izumi,T.Ooi,T.Kitao,M.D.Guiver,G.P.Robertson, Car-boxylatedpolysulfonemembraneshavingachiralrecognitionsiteinduced byanalternativemolecularimprinting technique,Polym.Bull.40 (1998) 517–524.

[14]M.Yoshiakwa,J.Izumi,T.Kitao,S.Sakamoto,Molecularlyimprintedpolymeric membranescontainingDIDEderivativesforopticalresolutionofaminoacids, Macromolecules25(1996)8197–8203.

[15]M.Yoshikawa,J.Izumi,Chiralrecognitionsitesconvertedfromtetrapeptide derivativesadoptingracematesasprintmolecules,Macromol.Biosci.3(2003) 487–498.

[16]M.Yoshikawa,T.Ooi,J.Izumi,Alternativemolecularlyimprintedmembranes fromaderivativeofnaturalpolymer,celluloseacetate,J.Appl.Polym.Sci.72 (1999)493–499.

[17]M.Yoshikawa,K.Kawamura,A.Ejima,T.Aoki,S.Sakurai,K.Hayashi,K. Watan-abe,GreenpolymersfromGeobacillusthermodenitrificansDSM465—candidates formolecularlyimprintedmaterials,Macromol.Biosci.6(2006)2010–2215. [18]C.Burger,B.S.Hsiao,B.Chu,Nanofibrousmaterialsandtheirapplications,Annu.

Rev.Mater.Res.36(2006)333–368.

[19]A.Greiner,J.G.Wendorff,Electrospinning:afascinatingmethodforthe prepa-rationofultrathinfibers,Angew.Chem.Int.Ed.46(2007)5670–5703. [20]K.Yoon,B.S.Hsiao,B.Chu,Functionalnanofibersforenvironmental

applica-tions,J.Mater.Chem.18(2008)5326–5334.

[21]B.Chu,B.S.Hsiao,Theroleofpolymersinbreakthroughtechnologiesforwater purification,J.Polym.Sci.B:Polym.Phys.47(2009)2431–2435.

[22] S.Agarwal,J.H.Wendorff,A.Greiner,Chemistryonelectrospunpolymeric nanofibers:Merelyroutinechemistryorarealchallenge?Macromol.Rapid Commun.31(2010)1317–1331.

(9)

96 Y.Sueyoshietal./JournalofMembraneScience401–402 (2012) 89–96

[23]I.S.Chronakis,B.Milosevic,A.Frenot,L.Ye,Generationofmolecularrecognition sitesinelectrospunpolymernanofibersviamolecularimprinting, Macro-molecules39(2006)357–361.

[24]I.Chronakis,A.Jakob,B.Hagström,L.Ye,Encapsulationandselective recog-nitionofmolecularlyimprintedtheophyllineand17␤-estradiolnanoparticles withinelectrospunpolymernanofibers,Langmuir22(2006)8960–8965. [25]K.Yoshimatsu,L.Ye,J.Lindberg,I.S.Chronakis,Selectivemolecular

adsorp-tionusingelectrospunnanofiberaffinitymembranes,Biosens.Bioelectron.23 (2008)1208–1215.

[26] M.Yoshikawa,K.Nakai,H.Matsumoto,A.Tanioka,M.D.Guiver,G.P.Robertson, Molecularlyimprintednanofibermembranesfromcarboxylatedpolysulfone byelectrospraydeposition,Macromol.RapidCommun.28(2007)2100–2105. [27]Y.Sueyoshi,C.Fukushima,M.Yoshikawa,Molecularlyimprintednanofiber membranesfromcelluloseacetateaimedforchiralseparation,J.Membr.Sci. 357(2010)90–97.

[28] M.Yoshikawa,A.Tanioka,H.Matsumoto,Molecularlyimprintednanofiber membranes,Curr.Opin.Chem.Eng.1(2011)18–26.

[29] M.D.Guiver,H.Zhang,G.P.Robertson,Y.Dai,Modifiedpolysulfones.III. Syn-thesisandcharacterizationofpolysulfonealdehydesforreactivemembrane materials,J.Polym.Sci.A:Polym.Chem.39(2001)675–682.

[30] J.A.Riddick,W.B.Bunger,T.K.Sakano,OrganicSolvents,4thed.,JohnWiley& Sons,NewYork,1986.

[31]K.Taniwaki,A.Hyakutake,T.Aoki,M.Yoshikawa,M.D.Guiver,G.P. Robert-son,Evaluationoftherecognitionabilityofmolecularlyimprintedmaterials bysurfaceplasmonresonance(SPR)spectroscopy,Anal.Chim.Acta489(2003) 191–198.

[32]T. Kakuchi, T. Takaoka, K. Yokota, Polymeric chiral crown ethers. VI. Opticalresolutionof␣-aminoacidbypolymersincorporating 1,3:4,6-di-O-benzylidene-d-mannitolresidues,Polym.J.22(1990)199–205.

[33]T.Masawaki,M.Sasai,S.Tone,Opticalresolutionofaminoacidbyan enantios-electiveultrafiltrationmembrane,J.Chem.Eng.Jpn.25(1992)33–39.

[34]T.Aoki,S.Tomizawa,E.Oikawa,Enantioselectivepermeationthrough poly{␥-[3-(penramethyldisiloxanyl)propyl]-l-glutamate}membranes,J.Membr.Sci. 99(1995)117–125.

[35]S.Tone,T.Masawaki,K.Eguchi,Theopticalresolutionofaminoacidsbyplasma polymerizedterpenemembranes,J.Membr.Sci.118(1996)31–40. [36]M.Yoshikawa,J.Izumi,T.Kitao,Alternativemolecularimprinting,afacileway

tointroducechiralrecognitionsites,React.Funct.Polym.42(1999)93–102. [37] M.Yoshikawa,T.Fujisawa,T.Kitao,Molecularlyimprintedpolymeric

mem-braneshavingEFFderivativesasachiralrecognitionsite,Macromol.Chem. Phys.200(1999)1458–1465.

[38]S.G.Schultz,BasicPrinciplesofMembraneTransport,CambridgeUniversity Press,Cambridge,1980.

[39]N.M. Maier, W. Lindner, Chiral recognition applications of molecularly imprinted polymers: a critical review, Anal. Bioanal. Chem. 389 (2007) 377–397.

[40] R.Xie,L.-Y.Chu,J.-G.Deng,Membranesandmembraneprocessesforchiral resolution,Chem.Soc.Rev.37(2008)1243–1263.

[41] A.Higuchi,M.Tamai,Y.-A.Ko,Y.Tagawa,Y.-H.Wu,B.D.Frteeman,J.-T.Bing,Y. Chang,Q.-D.Ling,Polymericmembranesforchiralseparationof pharmaceuti-calsandchemicals,Polym.Rev.50(2010)113–143.

[42] Z.Sun,E.Zussman,A.L.Yarin,J.H.Wendorff,A.Greiner,Compoundcore–shell polymernanofibersbyco-electrospinning,Adv.Mater.15(2003)1929–1932. [43]D.Li,Y.Xia,Directfabricationofcompositeandceramichollownanofibersby

electrospinning,NanoLett.4(2004)933–938.

[44]S.Ramakrishna,K.Fujihara,W.-E.Teo,T.-C.Lim,Z.Ma,AnIntroductionto ElectrospinningandNanofibers,WorldScientific,NewJersey,2005. [45]D.Li,J.T.McCann,Y.Xia,Useofelectrospinningtodirectlyfabricatehollow

nanofiberswithfunctionalizedinnerandoutersurfaces,Small1(2005)83–86. [46]H.Matsumoto,A.Tanioka,Functionalityinelectrospunnanofibrous mem-branes based on fiber’s size, surface area, and molecular orientation, Membranes1(2011)249–264.

Figure

Fig. 1. SEM images of Z-d-Glu imprinted nanofiber membrane (MINFM-10-D) (a), control nanofiber membrane (MINFM-10-C) (b), and Z-l-Glu imprinted nanofiber membrane (MINFM-10-L) (c).
Fig. 2. Adsorption isotherms of d-Glu and l-Glu in the nanofiber membrane imprinted by Z-d-Glu (MINFM-10-D) (a) and the nanofiber membrane imprinted by Z-l-Glu (MINFM-10-L) (b).
Fig. 3. Time–transport curves of racemic Glu’s through the molecularly imprinted nanofiber membranes, MINFM-10-D (a) and MINFM-10-L (b) ([d-Glu] L,0 = [l- [l-Glu] L,0 = 1.0 × 10 − 3 mol dm − 3 ).

Références

Documents relatifs

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des

We review the relative entropy method in the context of first-order hyperbolic systems of conservation laws, in one space-dimension.. We prove that contact discontinuities in full

It was shown by Valiant, Skyum, Berkowitz and Rackoff [23] that arithmetic circuits of polynomially bounded size and degree can be transformed into circuits of polylogarithmic depth

As games offer the opportunity to design complex and situated learning situations, Game- Based learning fits with curricula based on a Competency-Based Approach to teaching.. A

promotions d'étudiants (de l'ordre d'un peu moins de 400) tiennent alors dans un seul amphithéâtre, ce qui permet au moins de réaliser correctement la forme du cours magistral,

En 2007-2008, l’Institut National de Recherche Pédagogique (INRP), au travers de l’équipe EducTice, en partenariat avec les Institut de Recherche sur

The example we give is taken from Corollary 4 in [3]: the authors provide a set of parametrized inputs to prove that, in base 2 and assuming that the precision is even, the

A introdução das tecnologias da informação e da comunicação na educação (TICE) como suportes didáticos exige uma nova leitura dos papéis dos sujeitos