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Diffusion

By Russell Henderson,2014-07-06 15:04
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Diffusion

    Diffusion

    d"?J.ofChem.Eng.,8(2)146153(2000)

    DiffusionCoefficientsof/-LysineHydrochlorideand

    Solutionsat25C

    MAPeisheng(沛生),wuY(ia(吴艳霞),LIUYunqi(~]耘畦),XIAShuqian(淑倩)

    andLIShufen(李淑芬)

    CollegeofChemicalEngineeringandTechnology,TianjinUniversity,Tianjin300072,China

    AbstractThediffusioncoefficients''of/-lysinehydrochlorideand/-argininehydrochlorideintheiraqueoussolu-

    tionsat25~Cweredeterminedbythemetallicdiaphragmcellmethodwhichischaracterizedbyaccuracy,promptness

    andconvenience.Meanwhile.thedensitiesandviscositiesofthesolutionswerealsodetermined.Basedonallthese

    dataasemi.empiricalmodelforcorrelatingthedi

    sioncoefficientsofsolidorganicsaltsintheiraqueoussolutions

    at25.ewasproposed.Thefittingresultofthismodeliscomparativelysatisfactory.Comparedtoaformermodel,

    GordonMode1.thismodelcanavoidanumberofdicultiesandarduouswork.

    Keywordslyrsinehvdrochloride,argininehydrochloride,disioncoefficient,metallicdiaphragmcellmethod,

    semi-empiricalmodel

    1INTRoDUCTIoN

    Diffusiontoecientsareveryimportantbasicdatafor

    researchandapplicationinchemicalengineering.Be-

    causeofthecomplexstructureofliquid,theresearch

    onliquiddiffusiontoecientisfarfrommaturity.The

    determineddatafoCUSonthesystemsthatconsist oforganicsoluteandsolventwithsmallandsimple molecules.Thedataforlargemoleculesoforganicso- lutearescarce,especiallythosefororganicsolidones intheiraqueoussolutions.Asaminoacidmedicines, ZlysinehydrochlorideandZargininehydrochlorideare widelyusedfortreatingavarietyofdiseases,sothe researchontheirdiffusioncoecientsintheiraque-

    oussolutionsisveryimportantbothintheoreticaland practicalaspects.

    Diaphragmcellmethodischaracterizedbyaccu

    racyandconvenienceandoftenemployedinmeasur- inshqmddie.soncoefficient.Previouslythemicro- porousdiaphragmwasmadeofsinteredglass,and itgenerallytooktwoorthreedaystofinishadif- fusionexperiment.Byusingamicroporousmetallic diaphragminsteadofsinteredone,theexperimental timewasshortenedto2hoursorso[1J.Inthiswork. themicroporousmetallicdiaphragmcellwasemployed tomeasurethediffusioncoecientsofZ.1ysinehy-

    drochlorideandlargininehydrochlorideintheiraque- oussolutionsat25oC.Meanwhile,theirdensitiesand viscositieswerealsodetermined.

    Basedontheexperimentaldataasemi.empirical modelispresentedtocorrelatethediffusioncoeffi- cientsoforganicsaltsintheiraqueoussolutions. 2EXPER.IMENTAL

    2.1Materials

    ThereagentsareZlysinehydrochloride.Zarginine

hydrochloride.sucroseandpotassiumchloride.Z

    lysinehydrochloride(99.85%)WasmadeinTianjin AminoAcidCompany,andl-argininehydrochloride (99.4%)wasimportedfromKyowaAminoAcidCom

    panyinJapan.Thepuritiesofsucroseandpotassium chloridemadeinChinaare99.9%.

    Allmeasurementsfordensitywereperformedwith pycnometersintriplicate.Thepycnometerswerecali

    bratedwithdouble-distilledwaterat25.Cassuming thedensitytobe0.9970x10.kg?m_..Theviscosity wasmeasuredintriplicatewithUbbelohdeviscome- ter.

    Twomicroporousmetallicdiaphragmcellswere usedtomeasuredisiontoecient.Thediaphragm

    cellisshowninFig.1.ThediaphragmismadeofNi, 40ininindiameterand0.1nlnlinthickness.Theaver

    agediameterofthemicroporesis5x100nlin.Thedi.

    aphragmdividesthecellintotwocompartments.Each compartmentshasavolumeofabout35cm3andcon. tain,qastirrerofglasstube.withadianleterof3mm andalengthslightlylessthanthediameterofthedi. aphrm.Insideeachstirrerissealedanironwire. Thethicknessofthewireandthetubewallsareso adjustedthatthestirrerintheuppercompartment sinkswhiletheloweronefloats.Drivenbytherotat. ingpermanentmagnetmountedaroundthecell,the stirrersrotateandwipebothsidesofthediaphragm Received1998.10-16.accepted1999-09-23. 'Towhomcorrespondenceshouldbeaddressed.

"Inthisatticlethediffusioncoefficientreferstothemutualdiflusioncoecient

DiffusionCoefficientsofl-LysineHydrochlorideand/-ArginineHydrochloride

    twiceperrevolutionofthemagnet,soastostirthe stagnantflowlayeronthediaphragmandpromote thediffusion.0nthetopofeachcompartmentisa rubberstopper.Acapillaryisthroughtheupperone toadaptthevariationofsolutionvolumeduringthe diffusion.Afteracertaindisiontimetheconcen-

    trationvariationofthesolutionineachcompartment ismeasured,andthentheintegraldiffusioncoefficient attheaverageconcentrationcanbedetermined. Figure1Metallicdiaphgramdiffusioncell 2.2Experimentalprocess

    Firstthecellconstantsofthediaphragmswere tested.Forthediaphragmcellmethod,theintegral diffusioncoefficientisshownas[2]

    --

    .:1-

    n

    (1)

    whereistheconstantofthediaphragmcellandcan- notbeobtaineddirectly.Subscripts'2'and'1'refer 147

    totheupperandthelowercompartmentsrespectively, '0'and'f'refertotheinitialandfinalstatesrespec- tively.isusuallytestedthroughasubstancewhose disioncoe~cientsareknown.Generallyanaqueous solutionofpotassiumchlorideat25.Cischosen.Ac-

cordingtoRefs.[1,3,4,stirringrateof70revolutions

    perminutewasadoptedforexperiment,andadiffu- siontimewas1.5hours.Inthisstudy,thevaluesof are5.14cm2and6.60cmforZlysinehydrochloride

    andZargininehydrochloride,respectively. Therearealreadyanumberofreliablediffusion coefficientsofsucroseinitsaqueoussolutionsat25.C. Soitischosenfortestingthereliabilityofthemetallic diaphragmcel1.Thecomparisonbetweentheexperi- mentalandtheliteraturederentialdiffusioncoeffi-

    cientsofsucroseisshownink1.Theresultindi- catedthattwometallicdiaphragmcellsarereliable. Thentheexperimentonllysinehydrochlorideand

    Zargininehydrochloridecanbeperformed.Aftera solutionwithacertainconcentrat;ionwasprepared, itsdensityandviscosityat25weredeterminedby usingpycnometerandUbbelohdeviscometerrespec- tively.Thentheintegraldiffusioncoecientwasde-

    termined.Twosolutionswithlittledmrenceincon- centrations,wereselected.Becausethedensityin- creasedwiththeconcentrationofsolution,thesolu- tionwithhigherconcentrationwaspouredintothe lowercompartmentofthediffusioncellsoastoelim- inatetheinfluenceofthegravityondiffusion. Table1Comparisonbetweentheexperimentalandtheliteraturediffusioncoefficientsofsucr

    ose

    ?Pet.IslP646Table171a.

    ..Pet.5P647Table378.

    ChineseJ.Ch.E.8(2)146(2000)

148ChineseJ.Ch.E.(Vo1.8,No.2)

    2.3Experimentalresults

    (1)Thedensitiesandtheviscositiesoftheaque- oussolutionsofZlysinehydrochlorideandZarnine

    hydrochlorideat25?weredetermined.Thedataare

    showninTable2.Thedensityofeachsolutionwas fittedintoequationsoftheform

    P=?AjC(n=12??)

    j=1

    (2)

    whereCismolarity,Pisin103kg.m3.Asforvis

    cosity,itsrelativevaluesneededbythesemiempirical

    modelwerefittedtoequationsoftheform =

    1+?BjC=12??)

    J=1

    (3)

    where7}rreferstotherelativeviscosityofthesolu- tionwithrespecttotheviscosityofwaterat25.C. InEqs.(2)and(3),coefficientsAjandcanbeob_ talnedbythemethodofleastsquares.Theirvalues arelistedin1[le3andTab1e4respectively. (2)Theintegraldiffusioncoefficientsoftheaque- oussolutionsofZlysinehydrochlorideandZarginine

    hydrochlorideat25?weredetermined.Therelation betweentheintegralandthed'erentialdusionco-

    ecientscanbeexpressedast

    D=CM2——CM1(4)

    whereCM2,CM1aretheaverageconcentrationinthe upperandlowercompartmentsrespectively.Thedif-

    ferentialdiffusioncoefficientD(C)canbeshownas D(c)=?u+1)AjC

    j=o

    CombiningEq.(4)andEq.(5),theresultis

    D=

    cM2cMl

    (5)

    ?Aj(c~+2一嗽)(6)

    j=O

    ThroughEq.(6)thepolynomialcoefficientsAjin Eq.(5)canbeobtainedbythemethodofleastsquare. Thediffusioncoefficientsofthetworeagentsareshown inTable5andthepolynomialcoefficientsinEq.(5) areshowninTble6.

    (1)zlysinehydrochlorideandzargininehy

    drochloridewilldissociateintheiraqueoussolutions, soinfactthediffusionisionicdiffusion,notmolecular diffusion.HoweveraccordingtoRef.f61whenthereis noexternalelectricfieldthediffusionof11typeof

    electrolytecanbeseenasmoleculardiffusion.The reasonsarethatwhenthecurrentiszeroananion andacationattracttightlyeachotherandthatwhen thereexistonlytwokindsofionscarryingopposite charge,theionsdmseatthesamerate.Hence,the aqueoussolutionofZlysinehydrochlorideorZarginine

    hydrochloridecanbeseenasabinarydiffusionsystem. Table2Densitiesandviscositiesoftheaqueous solutionsofI-lysinehydrochlorideandl-arginine hydrochlorideat25~C

    Table3CoefficientsAjinEq?(2)

DiffusionCoefficientsof/-LysineHydrochlorideandl-ArginlneHydrochloride

    Table4CoefficientsBjinEq?(3)

    149

    Table5Thediffusioncoefficientsof/-lysinehydrochlorideand/-argininehydrochlorideat25

    ~C

    Table6ThepolynomialcoefficientsAjinEq.(5) f2)Indilutesolutionstheresistancefordiffusion comesmainlyfromtheinteractionbetweensoluteand solvent.Withtheincrementofconcentration.theel- fect,ondiffusion,oftheinteractionbetweensolutes increases.Thiscanbeseenfromthetendencythalt diffusioncoefficientsaresuccessivelydecreasingwith theincrementofsolutionviscosity.

    (3)Byextrapolatingthecurveofdiffusioncoefl~- cientVS.molaritytothepointwheremolaxityiszero, thediffusioncoefl~cientatinfinitedilutionD0canbe obtained.ThevalueofD0ofZ.1ysinehydrochlorideis 12.97×106cm2.sl,andtheoneofjargininehy_

    drochlorideis10.04×106cm2.s-1.FromStokeS-

    Einsteinequation,

    DAB=kT/(61r~or)

    wherekisBoltzman'Sconstant,0istheviscosityof

    thesolvent,andristheradiusofsolventmolecule.It Canbeseenthatthesmallerthevolumeofthediffusing entity,thehigherthevalueofthediffusioncoefficient ChineseJ.Ch.E.8(2)146(~-ooo)

150ChineseJ.Ch.E.(Vo1.8,No.2)

    (ininfinitedilutesolution).Thestructuresof/-lysine

    hydrochlorideandl-arglninehydrochlorideare H2N(cH2)4CHcOOH

    I

    NH2?HCl

    lysinehydrochloride

    H2NCH-NH(cH2)3cHCOOH

    lI

    NH2NH2?HC1

    argininehydrochloride

    ThechainofZargininehydrochlorideislonger.sothe volumeofitsdiffusionentityislargerthanthatof Zlyslnehydrochloride.0ntheotherhand.Zlysine

    hydrochloridehasmoresidechainswhicharedisad- vantageoustoitsdiffusion,soitsvalueofD0issmaller thanthat0flysinehydrochloride.

    3SEMI-EMPIRICALMoDEL

    3.1Model

    BasedontheattemptofOnsagerandFuoss,

    GordonMpresentedthefollowingequationforcorre- latingthediffusioncoefficientsofelectrolyteinaque- oussolutions

    .=[](7)

    wherelisthepotentialofthesoluteinsolution,and Doisthediffusioncoefficientatinfinitedilution.Do isgivenbytheNernstrelation

    ..=2RT()(8)

    whereFisFaraday'sconstant,Ulandu2arethemo- bilitiesatinfinitedilutionofanionandcation,respec

    tively.

    Eq.(7)consistsessentiallyofthreegroupoffac-

    tors.ThefirstoneisDo/2RT,thesecondisather- modynamicgroup.ffact.COu1

    ,andthethirdisa

    'mobility'groupoffactors(/).Howeverthereare

    somedifBcultiesinapplyingthisequation.First,it isverydimculttoobtainthevalueofDo.Tocom- puteitfromtheNernstrelationneedsdeterminingt'l andu2.Ifitisobtainedbyextrapolatingthecurveof diffusioncoecientvs.molarityonthebasisofase- riesexperimentaldatatoinfinitedilution,Eq.(7)loses itssignification.Secondly,inordertocalculatethe thermodynamictermaseriesofactivitycoefficients orvaporpressuresshouldbedetermined,whichisan arduouswork.

    Hence,toavoidevaluatingDoandtestingactivity coefficientY,aseml-empiricalmodelisproposed.On June,2000

    themicroscale,viscosityreflectstheeffectsofmolecu- laxmotionandinteraction,andtheresistanceagainst moleculardiffusion.Therefore,viscosityisanimpor- tantfactorforcorrelatingdiffusioncoecients.With

    thesemi-empiricalmodelthediffusioncoefficientat anyconcentrationpointwithintherequiredrangecan beobtainedaslongasthecurveofviscosityvs.mo- laritywithintherangeisknownandthedi~usionc ecientatagivenconcentrationisdetermined.The semiempiricalmodelwasdefinedas

    D=A1)](9)

    whereAl,A2andA3areparameters,Disthediffu-

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