An Introduction to Chromatographic Separations對色譜分離的介紹

AnIntroductiontoChromatographicSeparations1AnIntroductiontoChromatographicSeparationsItwasMikhailTswett,aRussianbotanist,in1903whofirstinventedandnamedliquidchromatography.Tswettusedaglasscolumnfilledwithfinelydividedchalk(calciumcarbonate)toseparateplantpigments.Heobservedtheseparationofcoloredzonesorbandsalongthecolumn,hencenamechromatography,whereGreakchromameanscolorandgrapheinmeanswrite.

234Thedevelopmentofchromatographywasslowforreasonstobediscussedlaterandscientistswaitedtoearlyfiftiesforthefirstchromatographicinstrumenttoappearinthemarket(agaschromatograph).However,liquidchromatographicequipmentwithacceptableperformancewasonlyintroducedabouttwodecadesaftergaschromatography.56GeneralDescriptionofChromatographyInachromatographicseparationofanytype,differentcomponentsofasamplearetransportedinamobilephase(agas,aliquid,orasupercriticalfluid).Themobilephase(alsocalledeluent)penetratesorpassesthroughasolidorimmisciblestationaryphase.Solutes(eluates)inthesampleusuallyhavedifferentialpartitioningorinteractionswiththemobileandstationaryphases.Sincethestationaryphaseisthefixedonethenthosesoluteswhichhavestrongerinteractionswiththestationaryphasewilltendtomoveslower(havehigherretentiontimes)thanotherswhichhavelowerornointeractionswiththestationaryphasewilltendtomovefaster.7Therefore,chromatographicseparationsareaconsequenceofdifferentialmigrationofsolutes.Itshouldberememberedthatmaximuminteractionsbetweenasoluteandastationaryphasetakeplacewhenbothhavesimilarcharacteristics,forexampleintermsofpolarity.However,whentheirpropertiesaresodifferent,asolutewillnottendtostayandinteractwiththestationaryphaseandwillthusprefertostayinthemobilephaseandmovefaster;apolarsolventandanonpolarstationaryphaseisagoodexample.8Accordingtothenatureofthemobilephase,chromatographictechniquescanbeclassifiedintothreeclasses:Liquidchromatography(LC)Gaschromatography(GC)Supercriticalfluidchromatography(SFC)Otherclassificationsarealsoavailablewherethetermcolumnchromatographywherechromatographicseparationstakeplaceinsideacolumn,andplanarchromatography,wherethestationaryphaseissupportedonaplanarflatplate,arealsoused.9ElutionChromatographyThetermelutionreferstotheactualprocessofseparation.Asmallvolumeofthesampleisfirstintroducedatthetopofthechromatographiccolumn.Elutioninvolvespassingamobilephaseinsidethecolumnwherebysolutesarecarrieddownthestreambutonadifferentialscaleduetointeractionswiththestationaryphase.Asthemobilephasecontinuestoflow,solutescontinuetomovedownwardthecolumn.Distancesbetweensolutebandsbecomegreaterwithtimeandassolutesstarttoleavethecolumntheyaresequentiallydetected.

1011Thetimeasolutespendsinacolumn(retentiontime)dependsonthefractionoftimethatsolutespendsinthemobilephase.Assolutesmoveinsidethecolumn,theirconcentrationzonecontinuestospreadandtheextentofspreading(bandbroadening)dependsonthetimeasolutespendsinthecolumns.Factorsaffectingbandbroadeningareveryimportantandwillbediscussedlater.Thedarkcolorsatthecenterofthesolutezonesintheabovefigurerepresenthigherconcentrationsthanareconcentrationsatthesides.Thiscanberepresentedschematicallyas:1213ChromatogramsTheplotofdetectorsignal(absorbance,fluorescence,refractiveindex,etc..)versusretentiontimeofsolutesinachromatographiccolumnisreferredtoasachromatogram.Theareasunderthepeaksinachromatogramareusuallyrelatedtosoluteconcentrationandarethusveryhelpfulforquantitativeanalysis.Theretentiontimeofasoluteisacharacteristicpropertyofthesolutewhichreflectsitsdegreeofinteractionwithbothstationaryandmobilephases.Retentiontimesservequalitativeanalysisparameterstoidentifysolutesbycomparisonwithstandards.14MigrationRatesofSolutes

Theconceptswhichwillbedevelopedinthissectionwillbebasedonseparationofsolutesusingaliquidmobilephaseandanimmiscibleliquidstationaryphase.Thiscaseisparticularlyimportantasitisadescriptionofthemostpopularprocesses.15DistributionConstantsSolutestravelinginsideacolumnwillinteractwithboththestationaryandmobilephases.If,asisourcase,thetwophasesareimmiscible,partitioningofsolutestakesplaceandadistributionconstant,K,canbewritten:K=CS/CM (1)Where;CSandCMaretheconcentrationsofsoluteinthestationaryandmobilephases,respectively.Ifachromatographicseparationobeysequation1,theseparationiscalledlinearchromatography.InsuchseparationspeaksareGaussianandindependentoftheamountofinjectedsample16Thetimerequiredforananalytetotravelthroughthecolumnafterinjectiontilltheanalytepeakreachesthedetectoristermedtheretentiontime.Ifthesamplecontainsanunretainedspecies,suchspeciestravelswiththemobilephasewherethetimespentbythatspeciestoexitthecolumniscalledthedeadorvoidtime,tM.Soluteswillmovetowardsthedetectorindifferentspeeds,accordingtoeachsolute’snature.17ChromatographyRetentionTimes

tM=retentiontimeofmobilephase(deadtime)tR=retentiontimeofanalyte(solute)tR’

=timespentinstationaryphase(adjustedretentiontime)L=lengthofthecolumn18Chromatography:Velocities

Linearrateofsolutemigration!Velocity=distance/timelengthofcolumn/retentiontimesVelocityofsolute:Velocityofmobilephase:19averagelinearvelocityofasolute,v,canbewrittenas:

v=L/tR (2)Where,ListhecolumnlengthandtRistheretentiontimeofthesolute.Themobilephaselinearvelocity,u,canbewrittenas:u=L/tM (3)

Thelinearvelocityofsolutesisafractionofthelinearvelocityofthemobilephase.Thiscanbewrittenas:v=u*molesofsoluteinmp/totalmolesofsolute20Chromatography

Velocity/RetentiontimeandKc21Thiscanbefurtherexpandedbysubstitutionforthemolesofsoluteinmp,CMVM,andthetotalnumberofmolesofsolute,CMVM+CSVS.v=u*CMVM/(CMVM+CSVS)DividingbothnominatoranddenominatorbyCMVMwegetv=u*1/(1+CSVS/CMVM) (4)

Now,letusdefineanewdistributionconstant,calledthecapacityorretentionfactor,k’,as:k’=CSVS/CMVM=KVS/VM (5)22Substitutionof1,2and5inequation4weget:L/tR=L/tM*{1/(1+k’)}

Rearrangementgives:tR=tM(1+k’) (6)Thisequationcanalsobewrittenas:k’=(tR–tM)/tM

23TheSelectivityFactorFortwosolutestobeseparated,theyshouldhavedifferentmigrationrates.Thisisreferredtoashavingdifferentselectivityfactorswithregardtoaspecificsolute.Theselectivityfactor,a,canbedefinedas:

a=kB’/kA’ (7)Therefore,acanbedefinedalsoas:a=(tR,B–tM)/(tR,A–tM) (8)

FortheseparationofAandBfromtheirmixture,theselectivityfactormustbemorethanunity.24TheShapesofChromatographicPeaks

Chromatographicpeakswillbeconsideredassymmetricalnormalerrorpeaks(Gaussianpeaks).Thisassumptionisnecessaryinordertocontinuedevelopingequationsgoverningchromatographicperformance.However,inmanycasestailingorfrontingpeaksareobserved.

2526Gaussianpeaks(normalerrorcurves)areeasiertodealwithsincestatisticalequationsforsuchcurvesarewellestablishedandwillbeusedforderivationofsomebasicchromatographicrelations.Itshouldalsobeindicatedthatassolutesmoveinsideacolumn,theirconcentrationzonesarespreadmoreandmorewherethezonebreadthisrelatedtotheresidencetimeofasoluteinachromatographiccolumn.27PlateTheorySolutesinachromatographicseparationarepartitionedbetweenthestationaryandmobilephases.Multiplepartitionstakeplacewhileasoluteismovingtowardstheendofthecolumn.Thenumberofpartitionsasoluteexperiencesinsideacolumnverymuchresemblesperformingmultipleextractions.Itmaybepossibletodenoteeachpartitioningstepasanindividualextractionandthecolumncanthusberegardedasasystemhavinganumberofsegmentsorplates,whereeachplaterepresentsasingleextractionorpartitionprocess.

28Therefore,achromatographiccolumncanbedividedtoanumberoftheoreticalplateswhereeventuallytheefficiencyofaseparationincreasesasthenumberoftheoreticalplates(N)increases.Inotherwords,efficiencyofachromatographicseparationwillbeincreasedastheheightofthetheoreticalplate(H)isdecreased.

29ColumnEfficiencyandthePlateTheory

IfthecolumnlengthisreferredtoasL,theefficiencyofthatcolumncanbedefinedasthenumberoftheoreticalplatesthatcanfitinthatcolumnlength.Thiscanbedescribedbytherelation:

N=L/H30TheplatetheorysuccessfullyaccountsfortheGaussianshapeofchromatographicpeaksbutunfortunatelyfailstoaccountforzonebroadening.Inaddition,theideathatacolumniscomposedofplatesisunrealisticasthisimpliesfullequilibriumineachplatewhichisnevertrue.Theequilibriuminchromatographicseparationsisjustadynamicequilibriumasthemobilephaseiscontinuouslymoving.

31DefinitionofPlateHeightFromstatistics,thebreadthofaGaussiancurveisrelatedtothevariances2.Therefore,theplateheightcanbedefinedasthevarianceperunitlengthofthecolumn:H=s2/L (9)Inotherwords,theplateheightcanbedefinedascolumnlengthincmwhichcontains34%ofthesoluteattheendofthecolumn(asthesoluteelutes).Thiscanbegraphicallyshownas:3233Thepeakwidthcanalsoberepresentedintermsoftime,t,where:t=s/v (10)t=s/(L/tR) (11)Thewidthofthepeakatthebaseline,W,isrelatedtotbytherelation:W=4twhere96%ofthesoluteiscontainedunderthepeak.s=Lt/tRs=LW/4tR

(12)34s2=L2W2/16tR2s2=HLH=LW2/16tR2

N=16(tR/W)2 (13)

Also,fromstatisticswehave:W1/2=2.354t (14)s2=LH35s=Lt/tRs=L(W1/2/2.354)/tRs2=L2(W1/2/2.354)2/tR2 (15)Substitutioninequation9gives:LH=L2(W1/2/2.354)2/tR2H=L(W1/2/2.354tR)2N=L/HN=5.54(tR/W1/2)2 (16)36AsymmetricPeaks

Theefficiency,N,canbeestimatedforanasymmetricchromatographicpeakusingtherelation:

37N=41.7(tR/W0.1)2/(A/B+1.25) (17)

Drawahorizontallineacrossthepeakataheightequalto1/10ofthemaximumheight.WhereW0.1=peakwidthat1/10height=A+B38BandBroadening

Apartfromspecificcharacteristicsofsolutesthatcausedifferentialmigration,averagemigrationratesformoleculesofthesamesolutearenotidentical.Threemainfactorscontributetothisbehavior:39LongitudinalDiffusionMoleculestendtodiffuseinalldirectionsbecausethesearealwayspresentinaconcentrationzoneascomparedtotheotherpartsofthecolumn.

ThiscontributestoHasfollows:

HL=K1DM/V

Where,DMisthediffusionofsoluteinthemobilephase.Thisfactorisnotveryimportantinliquidchromatographyexceptatlowflowrates.40ThiscontributestoHasfollows:

HL=K1DM/V

Where,DMisthediffusionofsoluteinthemobilephase.Thisfactorisnotveryimportantinliquidchromatographyexceptatlowflowrates.41ResistancetoMassTransferMasstransferthroughmobileandstationaryphasescontributestothistypeofbandbroadening.

1.StationaryPhaseMassTransfer

Thiscontributioncanbesimplyattributedtothefactthatnotallmoleculespenetratetothesameextentintothestationaryphase.Therefore,somemoleculesofthesamesolutetendtostaylongerinthestationaryphasethanothermolecules

42Quantitatively,thisbehaviorcanberepresentedbytheequation:

Hs=K2ds2

V/Ds

WheredsisthethicknessofstationaryphaseandDsisthediffusioncoefficientofsoluteinthestationaryphase.43MobilePhaseMassTransferSolutemoleculeswhichhappentopassthroughsomestagnantmobilephaseregionsspendlongertimesbeforetheycanleave.Moleculeswhichdonotencountersuchstagnantmobilephaseregionsmovefaster.Othersolutemoleculeswhicharelocatedclosetocolumntubingsurfacewillalsomoveslowerthanotherslocatedatthecenter.Somesoluteswhichencounterachannelthroughthepackingmaterialwillmovemuchfasterthanothers.

44HM=K3dp2V/DM

Wheredpistheparticlesizeofthepacking.45MultiplePathEffects

Multiplepathswhichcanbefollowedbydifferentmoleculescontributetobandbroadening.Sucheffectscanberepresentedbytheequation:

HE=K4dp

46Theoverallcontributionstobandbroadeningarethen,

Ht=HL+HS+HM+HE

Where;Htistheoverallheightequivalenttoatheoreticalplateresultingfromthecontributionsofthedifferentfactorscontributingtobandbroadening.

Ht=k1dp+k2DM/V+K3ds2

V/Ds+K4dp2

V/DM

Ht=A+B/V+CSV+CMV

47H=A+B/V+CV

Itturnedoutthatresistancetomasstransferterms(K3ds2

V/DsandK4dp2

V/DM)aremostimportantinliquidchromatographyandthusshouldbeparticularlyminimized.Thiscanbedoneby:DecreasingparticlesizeDecreasingthethicknessofstationaryphaseWorkingatlowflowratesIncreaseDMbyusingmobilephasesoflowviscosities.48Ontheotherhand,thelongitudinaldiffusionterm(k2DM/V)isthemostimportantoneingaschromatography.Reducingthisterminvolves:WorkingathigherflowratesDecreasingDMbyusingcarriergasesofhigherviscosities49Van-DeemterEquationFromtheabovementionedcontributionstobandbroadening,thefollowingequationwassuggestedtodescribebandbroadeninginliquidchromatography(LC)

H=A+B/V+CV

Where;Arepresentsmultiplepatheffects,B/Vaccountsforlongitudinaldiffusion,andCVaccountsforresistancetomasstransfer.ThefigurebelowshowsaplotofHagainstthedifferentfactorsintheequation5051Theoptimumflowratecanbefoundbytakingthefirstderivativeofequation23.

dH/dV=O-B/V2+C

VisoptimumwhendH/dV=O,therefore, C=B/V2optimum

Voptimum={B/C}1/2 (24)

Thistheoreticallycalculatedvelocityisalwayssmallandinpracticealmosttwiceasmuchasitsvalueisusedinordertosavetime.52TherelationofHandtheflowrateofthemobilephaseishighlydependentonparticlesize.Hwillbecomealmostindependentonflowrateatverysmallparticlesize.Inthiscase,fasterseparationscanbeachieved,usinghigherflowrates,withoutaffectingH,andthusbandbroadening.Thefigurebelowshowssuchaneffect:Particlesizeandflowrate5354ResolutionOneofthebasicandmostimportantcharacteristicofachromatographicseparationisundoubtedlytheresolutionterm.Resolutionbetweentwochromatographicpeaksisameasureofhowwellthesepeaksareseparatedfromeachother,whichistheessenceoftheseparationprocess.Resolutionofthetwopeaksinthefigurebelowaredifferentandonefindsnotroubleidentifyingthatthelowerchromatogramhasthebestresolutionwhilethetoponehastheworstresolution:55Chromatography:PeakResolutionPoorresolutionMoreseparationLessbandspread5657Chromatography

DeterminingtheNumber

ofTheoreticalPlatesW1/258Resolutioncanbedefinedfromthefollowingfigureas:59R=DZ/(WA/2+WB/2)=2DZ/(WA+WB) (18)

R=2(tR,B–tR,A)/(WA+WB) (19)

ForaseparationwhereWA=WB=W,wecanwrite:

R=(tR,B–tR,A)/W However,wehavetheequation:N=16(tR/W)2,orforpeakBwehave:W=4tR,B/N1/260R=(N1/2/4)(tR,B–tR,A)/tR,BWecannowsubstitutefortheretentiontimeusingtheequationderivedearlier:tR=tM(1+k’)Thuswehave:

R=(N1/2/4){(tM(1+kB’)-tM(1+kA’))/tM(1+kB’)}Rearrangementgives:R=(N1/2/4)(kB’–kA’)/(1+kB’)61DividingbothnominatoranddenominatorbykB’:R=(N1/2/4)(1–kA’/kB’)/{(1+kB’)/kB’}However,a=kB’/kA’R=(N1/2/4)(1–1/a)(kB’)/(1+kB’)

R=(N1/2/4){(kB’)/(1+kB’)}{(a–1)/a)} (21)62Therefore,resolutioncanbeviewedasacompositecontributionofthreeterms:

a.

EfficiencytermwhereRisproportionaltoN1/2b.

RetentiontermwhereRisproportionaltok’/(1+k’)whichsuggeststhattheretentionparametershouldbeoptimized.Avaluefork’intherangefrom5-10ispreferredassmallervalues(lowretention)resultsinbadresolutionwhileaveryhighk’valuemeansverylongretentionwithexceedinglysmallimprovementsinresolution:6364Thesedatacanbebetterviewedasaplotwhereask’wasincreased,almostaplateauwasrealized.

65TheoverlapoftwoGaussianpeaksofequalareaandamplitude,atvariousvaluesofresolution(R)ispresentedbelow:

(a)R=0.50

Overlapoftwopeaks=16%

(c)R=1.00

Overlapoftwopeaks=2.3%

(d)R=1.50Overlapoftwopeaks=0.1%c.

Resolutionisdependentonaselectivityterm{(a–1)/a)}.Astheselectivityisincreased,resolutionincreasesaswell.Whena=1,resolutioniszero.

66EffectofOtherParametersonResolutiona.Theresolutionofacolumnisproportionaltothesquarerootofitslengthsince

N=L/HETP.

R=(L1/2/4H1/2){(kB’)/(1+kB’)}{(a–1)/a)} (22)b.Retentiontimeasrelatedtoresolutioncanbeobtainedbythefollowingtreatment:N=L/HtM=NH/u67tR,B=tM(1+kB’)tR,B=(NH/u)(1+kB’)

N=16R2{(1+kB’)/kB’}2{a/(a-1)}2

Substitutiongives:tR,B=(16R2H/u){(1+kB’)3/kB’2}{a/(a-1)}2

Therefore,onecanalsowrite:tR,A/tR,B=RA2/RB2

68Toobtainahighresolution,thethreetermsmustbemaximised.AnincreaseinN,thenumberoftheoreticalplatescansimplybedonebylengtheningthecolumn.Thisleadstotwoopposingeffectswhereresolutionisincreasedbutatthesametimethiscausesanincreaseinretentiontimeandthusincreasedbandbroadening.Inaddition,alongercolumnmaynotalwaysbeavailable.Analternativeistoincreasethenumberofplates,theheightequivalenttoatheoreticalplatebyadjustingelutionvariables(mobilephasecomposition),andotherfactorsaffectingselectivity.69ChromatographicRelationships70Itisoftenfoundthatbycontrollingthecapacityfactor,k',separationscanbegreatlyimproved.Thiscanbeachievedbychangingthetemperature(inGasChromatography)orthecompositionofthemobilephase(inLiquidChromatography).71Whenaisclosetounity,optimisingk'andincreasingNisnotsufficienttogivegoodseparationinareasonabletime.Inthesecases,aisincreasedbyoneofthefollowingprocedures:1.

Changingmobilephasecomposition2.

Changingcolumntemperature3.

Changingcompositionofstationaryphase4.

Usingspecialchemicaleffects(suchasincorporatingaspecieswhichcomplexeswithoneofthesolutesintothestationaryphaseoruseofsurfactants)72TheGeneralElutionProblemLookatthechromatogrambelowinwhichsixcomponentsaretobeseparatedbyanelutionprocess:

73Itisclearfromthefigurethattheseparationisoptimizedfortheelutionofthefirsttwocomponents.However,thelasttwocomponentshaveverylongretentionandappearasbroadpeaks.Usingamobilephasecompositionthatcanoptimizetheelutionofthelasttwocompoundswill,unfortunately,resultinbadresolutionoftheearlierelutingcompoundsasshowninthefigurebelowwherethefirsttwocomponentsarecoelutedwhiletheresolutionofthesecondtwocomponentsbecomestoobad:7475Onecanalsooptimizethe

separationofthemiddletoocomponentsbyadjustingthemobilephasecomposition.Inthiscase,achromatogramliketheonebelowcanbeobtained:76However,inchromatographicseparations,weareinterestedinfullyseparatingallcomponentsinanacceptableresolution.Therefore,itisnotacceptabletooptimizetheseparationforasinglecomponentwhiledisregardingtheothers.Thesolutionofthisproblemcanbeachievedbyconsecutiveoptimizationofindividualcomponentsastheseparationproceeds.Inthiscase,themobilephasecompositionshouldbechangedduringtheseparationprocess.

77First,amobilephasecompositionsuitablefortheseparationofthefirstelutingcomponentisselected,andthenthemobilephasecompositionischangedsothatthesecondcomponentisseparatedandsoon.Thechangeinmobilephasecompositioncanbelinear,parabolic,step,oranyotherformula.Thechromatographicseparationwherethemobilephasecompositionischangedduringtheelutionprocessiscalledgradientelution.Aseparationliketheonebelowcanbeobtained:7879QualitativeAnalysisUsually,theretentiontimeofasoluteisthequalitativeindicatorofaspecificanalyte.Theretentiontimeofananalyteisthuscomparedtothatofastandard.Ifbothhavethesameretentiontime,thismaybeagoodindicationthattheidentityoftheanalyteismostprobablythatofthestandard.However,therecanbeimportantuncertaintiessincesomedifferentcompoundshavesimilarretention.Insuchcases,itisnotwisetousetheretentiontimeasaguaranteedmarkeroftheidentityofcompound,exceptincaseswherethesamplecompositionisknown.

80Developmentinqualitativeanalysisinchromatographyinvolvesuseofdetectorsthatcangivestructuraldetailsofsolutes,likediodearray,Fouriertransforminfrared,massspectrometers,etc.Insuchcases,qualitativeanalysiswithhighdegreeofcertaintycanbeaccomplished.Itshouldthereforebeclearthatasimilarretentiontimeofacomponentandstandard