i I POLYMER BRANCHING MEASUREMENTS IN MODEL SYSTEMS BY GPC/LALLSNISCOMETRY David J. Strumfels*, ElizabethCohn-Ginsberg, T. M. Bender, DanielA. Saucy Rohm and Haas Co. 727 NorristownRoad, Spring House, PA 19477 REVIEW Size ExclusionChromatography(SEC; alsoknown as Gel Permeation Chromatography,or GPC), iswell established as atechnique to fractionate .pol¥i_e:_s and to determine polymer molecularweights 1. Traditionally, these twin aspectsof SEC have been treated as essentiallyequivalent. However, it should beemphasizedthat thefractionationof a polymerin a gel permeationcolumnis notby molecularweightbut by hydrodynamicvolume,and that the molecular weightdeterminationis a data analysistechnique which requiresstandardsof the same compositionand structure as the polymerbeinganalyzed. In other words,traditional SEC usingsimple refractiveindexdetectioncan give only limitedinformationabout a polymer,and this only under limitedconditions. The developmentof in-line detectors that are sensitiveto molecularweight and/or structure has both refined and expandedthe usefulness of SEC as a tool for characterizingpolymers2. Such detectorsfall intotwo basic categories: light scattering detectors, such as the Low Angle Laser LightScatteringphotometers (LALLS) builtby Chromatix, and the MultiAngle Laser Ught Scattering photometer(MALLS) by Wyatt Technologies;andcapillaryviscometers,suchas those built byViscotek and Waters Associates. These detectors, eitheralone or in combination,can give molecularweightand structureinformationabout polymers,withoutthe use of standards andcalibrations3. At the Rohm and Haas research laboratorieswe have an SEC system with in- line lightscattering (LALLS KMX-6 by Chromatix)and viscosity(Model 100 by Viscotek)detectors,in additionto a refractive index (Waters 410) detector.
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iI
POLYMER BRANCHING MEASUREMENTS IN MODELSYSTEMS BY GPC/LALLSNISCOMETRY
David J. Strumfels*,ElizabethCohn-Ginsberg,T. M. Bender,DanielA. Saucy
Rohm andHaas Co.727 NorristownRoad,
Spring House, PA 19477
REVIEW
Size ExclusionChromatography(SEC; alsoknown as Gel Permeation
Chromatography,or GPC), is well establishedas a techniqueto fractionate
.pol¥i_e:_sand to determine polymer molecularweights1. Traditionally,these twin
aspectsof SEC have been treated as essentiallyequivalent. However, it should
be emphasizedthat the fractionationof a polymerin a gel permeationcolumnis
notby molecularweightbut by hydrodynamicvolume,and that the molecular
weightdeterminationis a data analysistechniquewhich requiresstandardsof
the same compositionand structure as the polymerbeinganalyzed. In other
delayvolumesand band broadeningneedsto be evaluated. A seriesof
monodispersedstandards,with known,uniformdegrees of branching,is
desirableinthe evaluationof the variablesof the system. Suchstandardsare
difficultto obtain however. Anotherapproachis to evaluatethe variables
individually,and use erroranalysisto determinethe precisionof branching
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=.
Figure 1 showsthe configurationof the system. Note that all three detectorsareconnected inseries, withthe refractiveindexdetectorat the end. An alternative
configurationuses a flow splitbefore or after the lightscatteringdetector,sothat
the viscosityand refractiveindexdetectorsare in a parallelconfiguration;this is
to preventdisruptionsin the refractive indexbaseline,whichwouldresultfrom
incompletepurgingof the viscometersolventreservoirs.Accuratedetermination
of detectorvolume off'setsis complicatedby thisconfigurationhowever. We
have obtainedbetter resultswithoutsplittingthe flow. This may be due to our
use of continuouslydistilledTHF as the onlymobilephase for the system;the
exclusiveuse of such a well purifiedanddegassedsolventshouldavoidthe
problemof solvent mixingdue to incompletelypurged reservoirs.
Data collectionis via NelsonAnalyticalsoftwarerunningon a Hewlett-Packard
1000 seriescomputer,and data analysisis performedby in-housesoftwareon a
separate HP-IO00 computer. "Absolute"molecularweightsare calculatedfromthe LALLSoutput,and intrinsicviscosities([11])are calculatedfromthe
viscometeroutput. The softwarealsocalculatesmolecularweightsusingeither
straightSEC (log MW versusretentionvolume)or universalcalibration( log(MWo[TI])versusretentionvolume). Concentrationdata are determinedfrom the
refractive indexdetector.
The combinationof these detectorsonan SEC system ailows usto examine
branchingin polymers. A branchedpolymerhas a smaller hydrodynamicvolume
than a linearpolymerof the same compositionand molecularweight. Fromtherelationship4
HydrodynamicVolume(HV) = MW • [11] (1)
we see that,at equal molecularweight, the branchedspecieswill have a lower
intrinsicviscositythan the linear. Givenmolecularweightdata fromthe LALLS,
the viscometeroutput can be usedto measure this reductionin hydrodynamicvolume.
We can usethis relationshipbetweenHV and MW to lookat branchingin a
qualitativeway, by comparingthe Mark-Houwinkplotsof a branchedpolymer
and its linearanalogue. A Mark-Houwinkplot is a log-logplotof intrinsic
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is quite large compared to the error in [_]. This is explained by notingthat, in
measuringe¢and K, one plotslog ([TI])versuslog (MW) overthe MW rangeof
interest. Log (K) is thusan extrapolatedvalue (at log (MW) = 0); smallerrorsin(_will therefore lead to largererrorsin log(K), and consequently,in K.
In orderto improvethe precisionof the SEC and henceuniversalcalibration
calculations,we exploredthe effect of morefrequentcalibrationsof the system.The resultsof these calculationsare summarizedin Table 2. "WeeklyCal." uses
the calibrationcurve for all the runs,as describedabove. "DailyCal." usesa
differentcalibrationfor each day;thiscalibrationis generatedfrom the first run of
the day usingthe LALLSand viscositydata.
The improvementin the precisionof the molecularweightcalculationsfrom
"Weekly Cal." to "DailyCal." demonstratesthat the clayto day variationis
significantcompared to the run to runvariationwithina singleday. It shouldbe
possibleto do even better however,as the runto runvariationinthe LALLSand
the viscositydetectorscontributesto the errorin the "DailyCal." calibrations.
The situationis also artificialfor a pure SEC systemwhich, lackingmolecular
weight sensitivedetectors,useseithera set of narrowstandardsof known
molecularweights,or a broad MWD standardwitha knowndistribution,to
generate the calibration.
In orderto evaluate the data as thoughthey came from a pure SEC system,i.e.,
to eliminatethe variabilityin the LALLSandviscositydata, the MW and [11]
distributionsof a runchosen for calibrationwere adjustedto matchthe "true"distributionof the standard; i.e., the distributionas determinedone time and
taken as a constant. This resultsin "Dally Cal. A" in whichthe precisionis
considerablyimprovedover the unadjustedcalibrations('Daily Cal.').
The precisionof g factor measurements,and hence branching,depends in parton the methodusedto calculate them. In our system,[_] values for the linear
polymerare nottaken directlyfrom the viscometeroutput, but are calculated
usingthe Mark-Houwinkrelationship;combining(2) and (3)
gMW= [[TI]B,Mw/(K*MW(X')]1/E (5)
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q
" . This method is valid onlyinthe regionwhere K and o_are invariantwithrespect
to molecularweight; i.e., where the Mark-Houwinkplotis a straightline. 'Ifconstantvalues of c¢and K are used,this methodleaves as the mainsourceof
errorinthe g factorcalculationsthe variationof [TI]with respectto MW inthe
branchedpolymer. We evaluatedthis runto runvariationfor all fourstandards
by selectingthree molecularweightsintheir distributionsand interpolatingthe
[q]sat these molecularweightsfor each data file. The resultsare summarized inTable 3, along with the calculatedg factors(whichusess = 1.0). These results
suggestthat we can performbranchingmeasurementswith goodprecision.
II. Evaluationof Unear/Star-Shaped Polystyrene Mixtures.
Polymers with differentamountsof branchingwere simulatedby mixinga linear
polystyrene(NBS-706 from the NationalBureauof Standards)witha six-armed
star-shapedpolystyrene(Lot 71520 from Polysciences).Two mixtures,withthe
proportions2:1 (weight.weight)linear:starand 1:2 linear:star,were freeze-driedfrom benzene, and run alongwiththe pure linearand star polymers.
Figure5 containsthe refractive index, LALLS, and viscositychromatogramsfor
the four sample runs. Note that 71520 hastwo peaks;the peakelutingat 21-22ml isthe linear arm fromwhichthe star is constructed. Thislinear armalso
contaminatesthe two mixtures.
Figure6 containsthe Mark-Houwinkplots for the polystyrenes. Aswe are
interestedonly in the portionof the data wherethe linearandstar polystyrenes
co-elute,the plotsare limitedto the molecularweightrange from approximately1.75E+5 to 6.00E+5 daltons. In thisregion,the Mark-Houwinkplot forNBS-706
is sufficientlystraightto permitthe calculationof [q] usingKand oz.
The plotsdemonstrate the generalprinciplesoutlinedinthe reviewsection;
increasingthe amountof star polymerresultedin lower intrinsicviscositiesateach molecularweight inthe distributions.Anotherpointof interestis the flat
slopeof the plotfor the star polymer. The model for branchingin starpolymerspredictsthat the numberof armsis a functionof the [11]B/[1]]Lratio. If 71520 is a
pure hexafunctionalstar, its Mark-Houwinkplotshouldbe parallelto the plotfor1
linear polystyrene; i.e., they should bothhave the same values for (z. The flati
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value of the slope is alsoinconflictwiththeoriesof dilutepolymersolutions,whichpredictsthat o¢cannothave a valueless than 0.5.
To allowa morepertinentevaluationof the system'ssensitivityto branching,g
factor and functionalityplotswere constructedusingthe molecularweightandI
intrinsic viscosity distributions.Functionalitiesfor the star polymerwerecalculatedusingthe relation3
Forthe gstarfactorcalculations,s was determinedby forcingthe g derived
weightaverage functionalityof the starto agree withthe functionalitycalculated
by dividingthe weightaveragemolecularweightof the star bythe weightaverage molecularweightof the lineararm:
functionality= Mwstar/Mwarm (7)
This yieldedan s valueof 1.21, fora functionalityof 6.0. This methodof
determining_ is a reasonableapproximationonly if boththe starand lineararm
haverelativelynarrowdistributions. It can be tested by repeatingthe
determinationusingnumberaverages: the g derivednumberaverage
functionalityof the starshouldagree withthe functionalitycalculatedby dividingthe numberaverage molecularweight of the star by the arm. In the case of
71520, the differencebetweenthetwo functionalitycalculationswas
approximately5%.
Rgures 7 and 8 containthe respectiveg factor and functionalityplotsfor the two
mixturesplusthe unmixedstar and linearpolymers. Some discussionis
requiredhere. There are several methodsfor synthesizingstar polymers.8The
traditionalmethodinvolvesanionicpolymerizationof the arm, followedby
terminationwitha nucleusof the desiredfunctionality. This methodof synthesiswilloften result inan averagefunctionalitylessthan that of the nucleus,due to
incompleteconversion;the importantpointhowever,is that functionalitygreater
than that of the nucleusis notpossible,unlessadditionalbranchingoccursinthearm or metal-halogenexchangesbetweenthe polymerchains andthe nuclei
resultin couplingsto formhighermolecularweight/functionalityspecies. In the
3o
case of anionically polymerizedpolystyrenehowever,the chemistrydoes notlead to longchainbranching,while the couplingreactionwouldlead to a different
distributionthan that observed. Therefore, if 71520 was preparedin this
manner, usinga hexafunctionalnucleuswith a highdegree of conversion,we
shouldnot expectfunctionalitiesgreaterthan six, or muchvariationin the
71520's molecularweight range (excludingthe linearportion,whichis around69K daltons), fromlessthan three arms/moleculeto almostten.
An alternativepreparationof star polymersalso hasas its firststage the anionicpolymerizationof monomerto the arm; instead of a nucleusof known
functionalityhowever,terminationis by additionof divinylbenzene(or anotherdifunctionalmonomer). The polymerizationof DVByieldsthe nucleiabout which
the star polymerforms. As the functionalityof these nucleiwillnotbe
monodispersed,the resultingstar will reflect thisdispersity,inboth its molecular
weight and functionalitydistributions.The variationinfunctionalityshown in
Figure 8 suggeststhat 71520 was, in fact, preparedby the lattermethod.
If 71520 was preparedin thismanner, itwouldexplainthe flatslopeof its Mark-
Houwink plot: as it is nota chemicallyand structurallyhomogeneousmaterial,neither cxnorK determinedinthis manner is meaningful.
There are also severalpossiblereasonswhythisvariationcould be an artifact of
the data. One possibilityis systemband broadening. Bandbroadening,as it
resultsin spreadingof the lightscatteringand viscosityenvelopes,reducesthe
slope of the Mark-Houwinkplot. This effect increasesas the dispersityof the
polymerdecreases;i.e., giventwo polymersof differentdispersities,equal band
broadeningwill reducethe slope of the broader polymerlessthan that of the
narrower. As the starpolymer in ourwork is narrowerthan the linear,thiswould
result in a smallerslopefor the star relativeto the linearpolymer. This inturnwould cause the [TI]B/[TI]Lratioto decrease with increasingmolecularweight,
thus raisingthe calculatedfunctionality.
Our softwareallowscorrectionof the raw data for bandbroadening,using
mathematicaldeconvolution9.The model used for the chromatographicpeakshape is the exponentiallymodifiedGaussian
t
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X ! (8)
in which a is the standarddeviationof the Gaussiancomponentof the peak, and
is the exponentialmodifierwhich determinesthe peak tailing. These
(thesame oneused to measure the detectoroffsets),and usingthe algorithmsin
the literature. The rawdata are correctedby transformingthem via a Fourier
transform intothe frequencydomain, dividingthem bythe transformof the band
broadeningenvelopedevelopedfromthe parameters,and back transformingthem intothe time domain:
(1) Raw Datatime--> (FFT) --> Raw Datafrequency
(2) a,_ --> Band BroadeningEnvelopetime-->(FFT) --> Envelopefrequency
(3) Raw Datalrequency/ Envelopelrequency--> DeconvolutedDatafrequency(4) DeconvolutedDatafrequency-> (reverse FFT) --> DeconvolutedDatatime
Once the data are corrected, the molecularweight/intrinsicviscosity/branchingcalculationsare repeated. Figure 9 plotsthe functionalitydistributionof the
deconvolutedstardata versusthe uncorrecteddistributiontaken from Figure8.
It appears that bandbroadeningalone does notfullyaccountforthe variation in
the stars functionality,althoughthere issome contribution.Therefore, weexploreda secondpossibilityfor this variation,whichis that the detectoroffsets
calculated from the monodispersedpolystyreneare erroneousor invalid. Like
band broadening,incorrectoffsetswill affectthe Mark-Houwinkplotslope,with
the magnitudeof the effect dependinguponthe dispersityof the polymer. Thus,by alteringthe viscosity - lightscatteringoffset,we canforce the linear and star
polymersto have the same o:;that is, to make their Mark-Houwinkplotsparallel.
Figure 10 is a plotof the deconvoluteddata, withthe newoffset. To test the
validityof thisoffset,we recalculated the Mark-Houwinkparameters for the linearpolystyrene. These calculationsyieldan ¢ of 0.862, anda K of 1.82E-5, neither
of which is inthe rangeof acceptable values for thispolymerin THFg.
Furthermore,as the parameters calculatedby usingthe originaloffsetsare
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withinthe acceptable ranges, it appears likely that these offsetsare correct.
Figure11 compares the experimentally determined functionality plotsof the twomixtures with theoretical predictions. The theoretical predictions are constructed
by combining molecular weight and viscosity data, point by point, from the
unmixed star and linear polymer data files, in proportions that correspond to theunmixed polymers' respective concentrations in the actual mixtures. The
excellent agreement between the two plots demonstrates that the detectors are
not sensitive to interactions between the linear and star materials in solution; that
is, as is well known, weight average molecular weight and intrinsic viscosity aremass additive properties of polymers.
CONCLUSIONS
SEC combined with in-line light scattering and viscometry has been usedat
Rohm and Haas for several years as a method of detecting polymer branching;however, as standards with known amounts of branching have not been
available, the technique lacked quantitative evaluation. By analyzing known
mixtures of a linear and star polystyrene, we have shown that the technique is
capable of quantization. The results of the reproducibility study suggest thatgood precision should be obtainable.
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