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

words,traditionalSEC usingsimple refractiveindexdetectioncan giveonly

limitedinformationabout a polymer,and thisonlyunder limitedconditions.

The developmentof in-linedetectors that are sensitiveto molecularweightand/orstructurehas both refinedand expandedthe usefulnessof SEC as a tool

for characterizingpolymers2. Such detectorsfall intotwo basiccategories: light

scatteringdetectors,such as the Low AngleLaser LightScatteringphotometers

(LALLS)builtby Chromatix,and the MultiAngleLaser Ught Scattering

photometer(MALLS) by Wyatt Technologies;andcapillaryviscometers,suchas

those built byViscotek and Waters Associates.These detectors, eitheraloneor

incombination,can give molecularweightandstructureinformationabout

polymers,withoutthe use of standardsandcalibrations3.

At the Rohm and Haas research laboratorieswe have an SEC system with in-

line lightscattering(LALLS KMX-6 by Chromatix)andviscosity(Model 100 by

Viscotek)detectors,in additionto a refractive index (Waters 410) detector.

i

In the initialdata analysis,molecularweightdistributionswere calculatedfrom

LALLSand refractive indexdata, and intrinsicviscositydistributionsfromviscometerand refractive indexdata. Bothsetsof calculationswere done in

accordwiththe manufacturers'literature.The volumeoffsetsbetweenthe

detectorswere measured from the peakpositionsof a monodispersedmolecular

weightpolystyrene(Polymer Laboratories,Mp 68000 daltons,Mw/Mn 1.04); thismeasurementassumed a constantflowrate.

In thisstudy, we also evaluated the precisionof standardSEC and the universal

calibrationtechnique6,7 for measuringmolecularweights. For the SEC and

universalcalibrationcalculationsa calibrationforthe columnsetwas required.

Undernormaloperations,a calibrationisgeneratedeitherby runninga setof

narrowmolecularweightdistribution(MWD)standards,or by runninga single

broadMWD standard whichencompassesthe molecularweightrange of

interest;a table of Iog(MW) (SEC) or Iog(MW*[11])(universalcalibration)versus

retentionvolume is then produced. Sincethisstudywas concernedonlywith

precision,the calibrationwas generatedby electronicallysummingall the raw

data intoa singledata file,and creatingd_ributions fromthiselectronic

compositeusingLALLS andviscosity(Figure4). Usingthiscalibration,

molecularweightdistributionsof the standardswere calculated,usingboththe

standard SEC and universalcalibrationmethods. Finally,the Mark-Houwink

parameters,o¢and K, were calculatedforeachstandard runby plottingIog([11])

versusIog(LALLSMW); fromthe logformof the Mark-Houwinkequation,¢zis

the slopeof the fit line, while K is the antilogof the intercept.

The precisionof the varioustechniquesis summarizedin Table 1. The errors

are percentrelativestandard deviation. There is a dramatic lossof precisionin

the weightaverage molecularweightdata inproceedingfrom a purely

instrumentaltechnique(LALLS)to a calibratedtechnique(SEC), and finally,to a

combinationof the two (SEC/viscos_ or universalcalibration). The poorer

precisionof the universalcalibrationmolecularweightswas notsurprising,as

thistechniquecombines the errorsof SEC withthose of viscometry. Error

analysisshowedthat SEC is the majorcontributorto the overall error inthe

universalcalibrationtechnique.

The viscositydata requiresome explanation. The errorin the measurementof K

24

measurements. This approachistime consuminghowever.

Our approachto the problem,therefore,was twostaged: first,we evaluated the

reproducibilityof the fundamentalmeasurementsof the system, usinga set of

linear polystyrenestandards;second, we preparedquantitativemixturesof a

linearanda star-shaped polystyrene,andcompared the molecularweightand

branchingdistributiondata from these mixtureswithdistributionstheoretically

calculatedusingthe data from the pure linearandbranchedpolystyrenes.

EXPERIMENTAL

I. Reproducibilityof MW and [_ measurements.

Molecularweight and intrinsicviscositydatawere gatheredon a set of four

American PolymerStandardspolystyrenestandardsof labeledweightaverage

molecularweights190000, 234000, 253000, and 280000 respectively. The

polydispersityof the standardsrangedfromtwo to three. Each standard was

preparedinduplicate. The followingsequenceof runswere then made sixtimes

overa period of eightdays:

01: PS-190000 Prep #102: PS-234000 Prep #103: PS-253000 Prep #104: PS-280000 Prep #105: PS-190000 Prep #206: PS-234000 Prep #207: PS-253000 Prep #208: PS-280000 Prep #209: PS-190000 Prep #110: PS-234000 Prep #111: PS-253000 Prep #112: PS-280000 Prep #113: PS-190000 Prep #214: PS-234000 Prep #215: PS-253000 Prep #216: PS-280000 Prep #2

Thus, a total of 96 runs were made, 24 per standard, and 12 per standard prep.

25

viscosity([11])versusmolecularweight (MW); it is describedby the equation

log [11]= log K + o¢• log MW (2)

Since a branchedpolymerhas a lower[11]than its linearanalogue, differencesin

branchingwill show upin comparisonsof their Mark-Houwinkplots(Figure2).

Quantitativemeasurementsof branchingcan be obtainedfrom g factors5. A g

factoris the ratio of a branchedpolymermolecule'sunperturbedmeansquared

radiusof gyrationto that of a linearpolymerwiththe same compositionand

molecularweight.

g = <S2>o,B/<S2>o,L (3)

g factors can be usedto calculate eitherthe numberof branchpointsin the

polymerchain or the functionalityof the branchpoints. These calculationsuse

modelswhich relatethe g factorto the type of branching;e.g., random branchingwith eithertri or tetra-functionalbranchpoints,star, or comb (Figure 3).

Experimentally,g factors can be calculatedfrom molecularweight andviscositymeasurementsusingthe relation3

g = (HVB,Mw/HVL,MW)1Is = ([TI]B,MW/[TI]LMW)I/s (4)

where [TI]B,MWis the intrinsicviscosityof the branchedpolymer,and [TI]L,MWof

the linear speciesat the same molecularweight. _ dependsuponthe modelof

branchingbeing assumed,as well as upon experimentalfactors such as solvent

and temperature.

Usinga systemof the typedescribedabove, it shouldbe possibleto provide

suchquantitative information,notonlyfor the whole polymer,but also asa

functionof the molecularweightdistribution. In practice, the sensitivityof the

systemto experimentalvariablessuchas detectorreproducibility,inter-detector

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

26

=.

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

27

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)

28

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

29

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

gstar= 6*functionality/[(functionality+l).(functionality+2)] (6)

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

functionality. Yet Figure8 showsconsiderablevariationinfunctionalityacross

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

31

X ! (8)

in which a is the standarddeviationof the Gaussiancomponentof the peak, and

is the exponentialmodifierwhich determinesthe peak tailing. These

parametersare measuredby runninga monodispersedpolystyrenestandard

(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

32

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.

33

REFERENCES

1. W.W. Yau, J. J. Kirkland, and D. D. Bly,Modern Size Exclusion Liquid

Chromatography, Wiley, New York, 1979.

2. H.G. BarthandW. W. Yau, International GPC Symposium

Proceedings, MilliporeCorporation,1989, 26.

3. Th. G. Scholte,Developments in Polymer Characterization - 4, J. V.

Dawkins,ed., AppliedScience,New York, 1983, 1.

4. T.G. Foxand P. J. Rory,J. Am. Chem. Soc., 1951, 73, 1904.

5. B.H. Zimmand W. H. Stockmayer,J. Chem. Phys., 1949, 17, 1301.

6. H. Benoit, Z. Grubisic,and R. Remmp, J. Poly. ScL, 1967, B5, 753.

7. A. Weissand E. Cohn-Ginsberg,Polymer Letters, 1969, Vol.7, 379.

8. B.J. Bauerand L J. Fetters,Rubber Chem. Techn., 1978, 51,406.

91 W.W. Yau,Analytical Chemistry, 1977, 49, No. 3, 395.

10. J. Brandrupand E. H. Immergut,Polymer Handbook, 3rd Ed., Wiley,New York, 1989.

34

i

1 ,-,(Waters

S,Jll _6._-__Ir . (G_o. 231.)]

LALLS Viscosity (Waters 410Detector Detector(KMX-6) (Viskotek100) RI Detector

Interfacesto datacollectionsystem

(Nelson/HP-1000) Backto

Still

nningNelsondataI Interfaceto da,=,reductionsystem HP-IO00 computer I

I runningin-housedataIIlection software (In-houseon HP-IO00) reductionsoftware

Rgure 1. GPC/LALLS/VLscosity Set Up

linear polymerpolymer

logM]

log MW

FK3ure 2. Mark-Houwink Plot .

(

35

STARBRANCHING

_._ ,,_ COMBBRANCHING

.,_.,v

RANDOMBRANCHING(tri-functional)

RANDOMBRANCHING(tetra-functional)

Figure3. BranchingModels

36

INTEGRATED GPCIVISCOS.

SI"D. PREP LALLS Mw GPC Mw Mw_+03) (E+03) (E+03)

PS-190K 1 191 +/- 1.8% 195 +/- 3.8% 192 +/- 6.1%2 187 +/- 2.0% 193 +/- 4.1% 191 +/- 7.3%

BOTH 189 +/- 2.1% 194 +/- 3.9% 191 +/- 6.6%

PS-234K 1 231 +/- 2.8% 235 +/- 3.7% 230 +/- 6.5%2 233 +/- 2.7% 236 +/- 4.1% 232 +/- 7.1%

BOTH 232 +/- 2.7% 236 4-/- 3.9% 231 +/- 6.7%

PS-253K 1 260 +/- 2.5% 268 +/- 3.8% 264 +/- 9.3%2 259 +/- 2.7% 261 +/- 4.2% 257 +/- 5.3%

BOTH 260 +/- 2.5% 264 +/- 4.1% 261 +/- 7.3%

PS-280K 1 275 +/- 1.8% 284 +/- 3.9% 272 +/- 6.5%2 274 4-/- 2.3% 280 +/- 3.9% 275 4-/- 8.3%

BOI'H 274 +/- 2.0% 282 +/- 3.9% 274 +/- 7.3%

TOTALSRSD (%) 2.3 3.9 7.2

INTRINSIC

STD. PREP VISCOSITY ALPHA K(dUg) (E-04)

PS-190K 1 .657 +/- 1.2% .715 +/- 1.5% 1.182 +/- 13.6%2 .652 +/- 1.0% .693 +/- 2.4% 1.588 +/- 21.6%

BOTH .654 +/- 1.2% .704 +/- 2.5% 1.385 4-/- 24.2%

PS-234K 1 .741 +/- 1.2% .715 +/- 2.7% 1.131 +/- 22.9%2 .744 +/- 1.2% .713 +/- 2.9% 1.317 +/- 26.4%

.742 +/- 1.2% .714 +/- 2.8% 1.238 +/- 26.3%

PS-253K 1 .810 +/- 1.5% .700 +/- 3.9% 1.546 +/- 40.2%2 .795 +/- 1.1% .697 +/- 4.6% 1.626 +/- 39.0%

BOTH .803 +/- 1.6% .698 +/- 4.2% 1.586 +/- 38.7%

PS-280K 1 .875 +/- 0.7% .698 +/- 2.0% 1.510 +/- 15.5%2 .859 +/- 1.9% .714 +/- 2.9% 1.239 +/- 27.1%

BGI'H .868 +/- 1.6% .706 +/- 2.7% 1.375 +/- 22.9%

TOTALS .706+/-3.1% 1.392+/-30.5%RSD (%) 1.4 3.I 30.5

Table 1. GPC/LALLS/Viscosity Resultsfor POlystyreneMixtures

WEEKLY CAL. DAILY CAL.STD. PREP GPC _ GPC Mw

(_+03) ¢E+03)

PS-190K 1 195 +/- 3.8% 190 +/- 2.8%2 193 +/- 4.1% 188 +/- 3.1%

BOTH 194 +/- 3.9% 189 +/- 2.9%

PS-234K 1 235 +/- 3.7% 231 +/- 3.0%2 236 +/- 4.1% 233 +/- 3.3%

BOTH 236 +/- 3.9% 232 +/- 3.1%

PS-253K 1 268 +/- 3.8% 259 +/- 3.0%2 261 +/- 4.2% 252 +/- 3.1%

BOTH 264 +/- 4.1% 255 +/- 3.3%

PS-280K 1 284 ./- 3.9% 274 +/- 1.5%2 280 +/- 3.9% 270 +/- 1.7%

BOTH 282 +/- 3.9% 272 +/- 1.7%

TOTALS

RSD (%) 3.9 2.8

DALLY CAL. ASTD. PREP GPC Mw

(E+03)

PS- 190K 1 189 +/. 1.9%2 187 +/- 1.0%

BOTH 188 +/- 1.5%

PS-234K 1 231 +/.2.3%2 231 +/.2.6%

BOTH 23] +/. 2.5%

PS-253K I 254 +/-1.6%2 247 +/- 1.8%

BOTH 251 +/-2.1%

PS-2|0K I 271 +/-1.3%

2 266 +/-0.8_i BOTH 269 +/- 1.5_:!

TOTALS

f RSD(%) 1.9I

Table 2. ComDarison of Different CalibrationTect_niques

39

TARGET MW INTRINSICSTD. (LALLS) RETENTION TIME VISCOSITY G FACTORS

('1 0-3) (minutes) (dl/g)

PS-190K 100 21.15 +/- 0.28 0.445 +/- 2.17 0.990 +/- 2.17%200 20.40 +/- 0.25 0.734 +/- 1.04 1.001 +/- 1.04%300 19.93 +/- 0.25 0.976 +/- 0.87 0.999 +/- 0.87%

PS-234K 150 20.74 +/- 0.31 0.594 +/- 2.45 0.968 +/- 2.45%250 20.15 +/- 0.29 0.857 +/- 1.66 0.998 +/- 1.66%350 19.74 +/- 0.30 1.087 +/- 1.22 0.998 +/- 1.22%

PS-253K 150 20.72 +/- 0.35 0.599 +/- 2.35 1.001 +/- 2.34%250 20.13 +/- 0.33 0.857 +/- 1.47 0.998 +/- 1.47%350 19.72 +/- 0.35 1.087 +/- 1.69 0.999 +/- 1.69%

PS-280K 200 20.40 +/- 0.25 0.742 +/- 1.70 1.012 +/- 1.70%300 19.93 +/- 0.26 0.991 +/- 1.04 1.015 +/- 1.04%

400 19.56 +/- 0.28 1.216 +/- 1.26 1.017 +/- 1.26%

'I'OTAI_RSD (%) 0.29 1.58 2.9

Table 3. Reproducibility of g Factor Measurements

4o

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2.00E-01

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z 5oE01 I 1 I I I I5.20E+00 5.30E+00 5.40E400 5.50E_00 5.60E+00 5.70E+00 5.80E+00

Log Molecular Weight

Figure 6. Mark-Houwink Plots of Polystyrenes

42

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5.2 5.3 5.4 5.5 5.6 5.7 5.8

Log Molecular Weight

' Figure7. g FactorPlotsof Polystyrenes

43

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10

0

9

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Log Molecular Weight

Figure8. FunctionalityPlotsofPolystyrenes

44

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Log Molecular Weight

Figure9. FunctionalityPlotsofStarPolystyrene

45

V

0.300"

0

0.200" 0

• LINEAR •

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Log Molecular Weight

Figure10. Mark-HouwinkPlotsofPolystyrenes-- NewVI-RIOffset

46

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LOG MW

Figure11. TheoreticalVersusExperimentalFunctionalities

I

47

• _ _ --.=,z_.-i_...%_cb_ _._,i