, ' 90-

SEC-VISCOMETRY-RIGHT ANGLE LIGHT SCATTERING(SEC-VISC-RALS)

M.A. HaneyViscotek Corporation1032, RussellDrivePorter, TX 77365

C. Jackson and W.W. Yau1

E.I. du Pont de Nemours and CompanyCentral Research and DevelopmentExperimental StationP.O. Box 80228Wilmington, DE 19880-0228

ABSTRACT

The two types of light scattering photometers currently being usedfor on-line size-exclusionchromatographic (SEC) polymer detection are thelow-angle laser lightscattering (LALLS)photometer and the multi-angle laserlight scattering photometer (MALLS). In both of these approaches, theattainment of the zero degree forward light scattering intensity is thetargeted goal for the experimental determination of polymer molecularweight. However, for molecules with dimensions small in comparison to thewavelength of the incident light (D < 1/20_ wavelength)the angular variationof the scattered light becomes too smallto measure, and the light scatteredat a right-angle (90°), to the incident beam may be used to determinemolecular weight. With the addition of an on-line viscometer, the molecularweight of molecules with dimensions larger than 1/20 thof the wavelengthof the incident light may be determined using the right-angle method. In theproposed method, the scattered intensity is corrected for angularasymmetry by using the combined measurementsof intrinsic viscosity and

i 90° light-scattering intensity to estimate the molecular radius, and thus theexpected scattering asymmetry. This molecular weight method providesincreased precision over lower angle measurementsdue to the high signal-to-noise of the right-angle scattering intensity, and is accurate to within a

1Technical consultant to Viscotek Corp., Porter, TX.

• _ " 49

few percent for all spherical and linearflexible chain molecules. The conceptand the computer algorithm used are discussed. Data obtained using alaser light scattering detector as Well as right angle scattering from afluorescence detector are presented.

INTRODUCTION

The light scattered by a polymer molecule in dilute solution in theforward direction of the incident beam is proportional to the polymermolecular weight [1]. Two methods are currently used to estimate thisintensity in conjunction with SEC.The scattered intensity at angles close tothe forward direction of the incident beam is practically the same as at zerodegrees. Thus a measurement of the light scattered at, typically 7°, can beused to estimate molecular weight [2]. The second method takes advantageof the fact that the angular distribution of the scattering from a polymersolution is a monotonic function of angledescribed by the form factor, P(e).Measurements of the scattered intensityat a number of angles, generallyin the range 30 - 150°, are used to extrapolate to the zero degree intensity.Furthermore, in some cases, the variation of the scattered intensity withangle can be used to determine the molecular radius of gyration [3]. Thisangular variation of the scattered light is caused by destructive interferencebetween light scattered from different segments of the same molecule. Asa result, the scattered intensity decreases with increasing angle. The initialslope of the scattered intensity as a function of sin2(e/2) is proportional tothe square of the radius of gyration. Figure 2 shows such a plot for aflexible chain molecule with a root-mean-square radius of gyration of 33 nm.

Recently, a method for determiningpolymer molecular weight usingthe scattering at 90° was described [4]. When the maximum distancebetween two points of the molecule is less than 1/20th of the incidentwavelength ( e.g., 20-25 nm, depending on solvent refractive index, for the632.8 nm band of a helium-neon laser, this corresponds to a radius ofgyration of about 10 nm for a flexible chain molecule ) the asymmetry in thescattered intensity cannot be detected. Under these conditions, thescattered intensity at any angle is the same as at zero degree, and may beused equally well to determine molecular weight.

The method was demonstrated for a variety of biopolymers [4]. Forsome compact proteins of molecular weights up to 1 x 106,the radius ofgyration is so small that the difference between zero and 90° scattering isoften less than 1%. A standard fluorescence detector was used as a lightscattering monitor by setting the emissionmonochrometer wavelengthequalto that of the excitation monochrometer wavelength. Using a wavelength of

5O

467 nm the signal to noise level in the light scattering signal wascomparable to that from the UV concentration detector. An excellent linearrelationship (correlation coefficient = 0.9998) was found between thescattered light intensity and the literature molecular weights for a series ofbiopolymers with molecular weights ranging from 29,000 to 1,000,000g/mol. In addition to the simplicity of the apparatus and data handling, themethod has the advantage that the signal at 90° is much less prone tonoise caused by dust particles, column particulates, etc. than the lightscattering signals from lower angles. The 90° scattering measurement giveshigher signal to noise than both the low angle measurement used byLALLS, and the 0° extrapolation used by MALLS. Furthermore, the right-angle measurement does not require the refraction corrections required atother detection angles, or the problem of normalizing multiple detectorsinherent in MALLS.

The combination of SEC with an on-line viscometer and a lightscattering detector (LALLS or MALLS) gives highly precise measurementsof molecular weight, intrinsic viscosity and radius distributions of a polymersample [5]. Because the method relies on direct measurement of physicalproperties of the eluting sample, it is insensitiveto many adverse variationsin SEC experimental conditions such as changes in flow rate, bandbroadening, column degradation, etc. The molecular weight and intrinsicviscosity at each slice can be used to calculate the hydrodynamic radius,and for linear flexible chain molecules the radius of gyration. The combinedSEC-Visc-RALS instrument thus provides a very desirable method forstudying polymer conformation and branching.

For flexible linear polymers, the SEC-Visc-RALSmethod provides alow-cost, reliable measurement of the radius of gyration. In addition, SEC-Visc-RALS gives improved measurement capability for small molecular sizesover SEC-MALLS.The measurement has a wide size range and is precise.

The capability of SEC-Visc-RALS is extended to a wider range ofmolecular shapes and sizes by the following computer algorithm: this isdone by repeatedly using the intrinsic viscosity and the right-angle lightscattering intensity to estimate the size of the molecule, and then using thesize value to correct for the angular asymmetry in scattered intensity [8].

In our software we have implemented the following steps to correctfor the light scattering asymmetry. The raw data consists of signals from theconcentration detector, the viscometer and the right-angle scatteredintensity for each chromatogram slice.

1. Initially, the angular scattering function, P(e), is assumed to be equal

51

to 1 at 90°, and an initial molecular weight, Me=, is calculated for eachchromatogram slice from the light scattering intensity, R(e = 90o),measuredat 90°. Typical SEC concentrations, c, which are low, allow us to neglect theeffect of the second virial coefficient, and write,

M=,-R(o=9°_) (1)K*¢

where K* is an opticalconstantdependent on the solvent refractive index,the polymerspecificrefractiveindexincrement,and the wavelengthof theincidentlight.

2. The radius of gyration, R_=,is calculatedfrom the Flory-Foxequationassuminga linearflexiblechainmolecule.Usingthe above Me=valuefor themolecularweightand the measuredintrinsicviscosity,[n], foreach slice,weobtain,

RFF _ - _

where _ is the Flory viscosityconstant.

3. The valueof the asymmetryfunctioncorrespondingto the calculatedradiusof gyrationfor each slicethen is used to correct for the asymmetryand providea new estimateof molecularweightfrom the 90° signal. ThecompleteP(e) functionderivedby Debyefor a flexiblecoil is used,avoidingany systematic errors caused by unconstrainedextrapolation from apolynomialleast-squaresfit,

P(e)=_(e-'+x-l) (3)x"

where

4_n= ,.=smO (4)

where no is the solvent refractive index, and Io is the wavelength of the

52

• .,(. "

incident light.

4. A new estimate of molecular weight is calculated from,

M= M_ (5)P(O=9oD

5. Steps 2 to 4 are repeated using the new estimateof molecular weightuntil the molecular weight values no longer change significantly. This usuallyrequires three iterations.

The algorithm can be improved to take into account the differentdegrees of expansion of the polymer chain described by the Ptitisyn-Eisnermodification of the Flow-Fox equation [7]. After the molecular weight valuesare determined ineach step, the Mark-Houwink exponent relating molecularweight to intrinsic viscosity is calculated and used to modify the calculationof the radius of gyration. This step has little effect on the final molecularweight, but does improve the estimate of radius of gyration. However, thesample must have some polydispersity to enable the Mark-Houwinkexponent to be calculated. Again it is noted that this software approachgives the radius of gyration only when the sample is a linear flexible chainstructure. Otherwise, the method provides a measurement of an apparenthydrodynamic radius of the molecule.

A more general version of the algorithm uses the radius of anequivalent sphere for the asymmetry correction. In this case thehydrodynamic radius is estimated from the measured value and thescattering function for a sphere is used to correct for the scatteringasymmetry. Such a model can be applied to any molecular conformation aswell as branched molecules. The range of validity is currently beinginvestigated.

EXPERIMENTAL

Data were collected on two separate systems. One using a MALLSdetector and the other using a fluorometer as the LSdetector. The SEC anddetector configuration is shown in Fig. 2. In the first system three PL gel 5/_mmixed-bed linearcolumns were used (Polymer Labs,Amherst, MA). Therefractometer was a Waters _(Waters Associates, Milford, MA). Themulti-angle laser light scattering d_{ector was a Model F laser photometer

f

53

(Wyatt Technology Corporation, Santa Barbara CA) with a helium-neonlaser ( 632.8 nm wavelength ) as the incident light source. The viscometerwas a Model 110 (Viscotek Corporation, Porter TX). The mobile phase wastoluene at 30°C. The broad molecular weight standard was polystyrene 706(National Institute of Standards and Technology, Bethseda MD).

The second system consisted of three TSKgel PW columns, 2500,3000, and 5000 ('l'osoHaas, Philadelphia, PA).The concentration detectorwas a Knauer refractometer. The 90° scattered light intensity was measuredon a Hitachi F-1050 Fluorescence Spectrophotometer (Hitachi Ltd., Tokyo,Japan) with both the emission and the excitation wavelengths set to 300nm. The viscometer was a Model 110 (Viscotek Corporation, Porter TX).The mobile phase was water. The samples used were poly(ethylene oxide),(American Polymer Standards, Mentor, OH) and dextran (PharmaciaCorporation, Uppsala, Sweden) molecular weight standards.

RESULTS

Figure 3 compares the radius of gyration calculated by using theFlory-Fox equation using intrinsicviscosityand molecular weight valuemeasured by MALLS,comparedto that measuredusingonlySEC-MALLSresultsfor polystyrene706. The two setsof data agree withinexperimentalerror. The increased precision of the SEC-Visc-LS integration in themeasurementfor the lowerhalfof the distributionisclearlyapparent. Figure4 showsthe plotof molecularweightagainstelutionvolumefor polystyrene706. The lowerlineshowsthe initialmolecularweightestimate,from the 90°scatteringuncorrectedfor angularasymmetry.The higher line showsthefinal molecularweight calculatedusingthe correctionalgorithm. Figure 5compares the molecularweightcalculatedby extrapolationfrom multi-anglemeasurementsto thatobtainedby the LS-asymmetrycorrected right-angledetermination. The values are the same across the molecular weightdistribution,and the improvedsignal-to-noiseof the right-anglemethod isapparent at the low molecularweight end of the MWD.

Figures6 and 7 showthe LSand RI chromatogramsobtainedfromthe second systemusingthe fluorometeras a right-anglelightscatteringdetector. Fig. 6 showsa PEO standard( MW = 10,000 ) and Fig. 7 showsa T-500 dextran (nominalMW = 500,000 ) respectively.The signal-to-noiselevel of the light-scatteringsignal is comparableto the RI, showingthat thedetector is sensitiveenoughfor SEC sampleconcentrations.Also note theasymmetricalshapeof the LSchromatogramfor the dextranT-500 sample.The slightshoulderon the left-hand-sideof the peak could be caused by

54

branching or ion exclusion of dextran containing carboxylic acidfunctionality. This feature would have been present but unnoticeable withconventional SEC using only an RI detector. Even without making acorrection for scattered intensity asymmetry, this apparent branching canbe detected by the right-angle light scattering detector.

To illustratethe applicability ofthe LS-asymmetrycorrection for RALS,the algorithm was evaluated using literature experimental values ofmolecular weight, intrinsic viscosity and radius of gyration for differentmolecular conformations from the literature [8,9,10]. Measurements madeunder both good solvent, and e conditions were used. The measured radiusof gyration and molecular weight were used to determine the 90° intensityby means of the angular scattering function for the appropriateconformation. Then this value was used as an initial molecular weightestimate and was corrected using the intrinsic viscosity and the modifiedFlory-Fox equation. The molecular weights calculated using the right-anglescattering and the intrinsic viscosity are shown in Table I, along with thepercentage difference from the experimental values. As expected, theaccuracy of the estimated molecular weights is well within the experimentalerrors for flexible coils and spherical molecules with molecular weights upto many millions. For rod-shaped polymers the Flory-Fox relation breaksdown for molecular weights above a few hundred thousand. In fact thevalues obtained by successive iterationsfail to converge for data from DNA.

If additional information is knownabout the molecular conformationthen this can be used to select the appropriate model for the asymmetrycorrection. As mentioned above, for polydisperse samples, the Mark-Houwink exponent can be used to determine conformation, and in the caseof branched samples the g' factor canbe used to determine the relationshipbetween radius of gyration and intrinsicviscosity [11]. When the appropriateequations for the intrinsic viscosity and scattering function of rigid rods areused in the calculation, the resultsin Table I are improved. Thus if themoleculesare knownto be rod shaped,or if this can be determinedfromthe relationshipof the 90° molecularweight to intrinsic viscosity, thecorrespondingtheoreticalmodelcan be usedto calculatemolecularweightvalues.Similarlyfor the sphericalmoleculesinTable I, if the moleculeswereknown to be so compact the estimateof molecularweight from the 90°scatteringcouldbe used,as it isclearthatmakingan asymmetrycorrectionin this case actually increasesthe error inthe molecularweight estimate.

For branched polymers, the Rory-Fox equation is no longerapplicable, as the Floryviscosityconstantfor the branched polymer willdifferfrom that for the linearform. Howeverunlessthe molecule is highly

55

branched ( > 50 branch points per molecule ) or highly uniform ( e.g., starshaped polymers ) the error in the calculated molecular weight is generallyless than experimental errors. This is due to a number of reasons. Firstly,the calculated radius of gyration is proportional to the cube root of theinverse of the Flory constant, so errors are greatly reduced in the radiusvalue. Secondly, the asymmetry correction to the molecular weight value isgenerally small ( < 30% for all flexible coil examples in Table I ), so that anyerror in the estimated asymmetry is again reduced in the final estimate ofmolecular weight. Finally, for a given molecular weight, the effect ofbranching is to reduce the radius of gyration, tending more to a compact,spherical conformation than a random coil. As a result the correctionrequired for a branched polymer is always less than for it's linear form atthe same molecular weight. This can be seen in Fig. 8 where the viscositybranching factor, g', for an experimental branched polymer is shown as afunction of molecular weight. The branching factor calculated from the LS-asymmetry corrected right-angle light scattering molecular weight gives thesame result as that calculated using the multi-angle molecular weight. Theweight-average number of branches per molecule is 20.

SUMMARY

The method of molecular weight determination using a right-anglelight scattering detector can be greatly extended by using an on-lineviscometer. The intrinsic viscosity can be used with the right-angle scatteredintensity to correct for any angular asymmetry in the scattering if such acorrection is needed. The results show that for flexible random coil andspherical molecular configurations, the molecularweight results are accurateup to molecular weights of many millions. In addition for random coilconfigurations, the correct radius of gyration is determined. For rod-shapedmolecules, the method can calculate molecular weights within 5% accuracyfor rod lengths below 85 nm( Rg = 25 nm). For branched molecules, theerrors in molecular weight determination are negligible for moderatedegrees of random branching. Thus, for the majority of commerciallyimportant polymers the incorporation of a right-angle light scatteringdetector into a SEC system with an on-line viscometer provides a simpleand economical way of adding absolute molecular weight determination tothe system.

56

REFERENCES

[1] Kratochvil,P.,Classical light scattering from polymer solutions, Elsevier,Amsterdam 1987.[2] Ouano, A.C., and W.J. Kaye, J. Polym. Sci., Part A-l, 12 : 1151 (1974)[3] Wyatt, P.J., C. Jackson and G.K. Wyatt, Am. Lab., 20(5), 86 (1988),Am. Lab., 20(6) 108 (1988).[4] Jones, R., G. Dollinger, R. Cunico, and M. Kunitani, poster presentationat Pittsburgh Conference, Chicago, March 4-8, 1991.[5] Jackson, C., Barth, H.G., and Yau, W.W., Waters' International GPCSymposium Proceedings 1991.[6] Rory, P.J., Principles of polymer chemistry, Cornell University Press,Ithaca, New York 1953 Ch. 7.[7] Ptitsyn, O.B., and Y.E. Eizner, Sov. Phys. Tech. Phys. 4, 1020 (1960)[8] Tanford, C.C., Physical chemistry of macromolecules, Wiley, New York1961.[9] Davidson, N.S., LJ. Fetters, W.G. Funk, N. Hadjichristidis, and W.W.Graesley, Macromolecules, 20, 2614 (1987)[10] Brandrup, J., and E.H. Immergut, eds., Polymer Handbook, 3rd ed.,Wiley, New York 1989.[11] W.H. Stockmayer, personal communication.

TABLE IEvaluation of Algorithm for Molecular Weight Determination by

RALS with Asymmetry Correction

Literaturevalues CalculatedvaluesMW Rg [11] P(90°) MW %

(g/mol) (nm) (dl/g) (g/tool) difference

Random coil molecules

Polystyrene 51,000 8 0.29 0.98 51,000 0 %

Polystyrene 420,000 19 0.52 0.95 415,000 -1%(e conditions)

Poly(methyl 680,000 36 1.34 0.70 682,000 0%methacrylate)

Polyisoprene 940,000 48 4.6 0.56 945,000 0 %-70% cis

Spherical molecules

Bovineserum 66,000 3 0.036 1.00 66,000 0 %albumin

Bushystunt virus 10,700,000 12 0.034 0.98 11,200,000 + 5%

Rod-shsped molecules

Poly-_-benzyl 130,000 26 1.25 0.91 125,000 - 4%-L-glutamate

Myosin 493,000 47 2.17 0.74 425,000 - 14%

DNA 4,000,000 117 50 0.35 5,600,000 + 40%

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FIGURE 1. Debye plot of reduced Rayleigh ratio as a function of angle.

Solvent.__ I Injection SECReservoir 0.2p Filter Valve Columns

Pump

Refractometer Viscometer LS Detector

_o,,,.to- 1 I I I ISolvent,,ow i 1Detector Computer for DataOutput Acquisition and Analysis

FIGURE 2. Schematic of the SEC-Visc-LS instrument.

59

LO0• 0

LS-VIS RADIUSOF GYRATION/ X

i,_._ _ / \

,.'_. ".'."• / _ \ ._" ..:... _:

t0.0 - "__,

i. 000 I I I I I Ii9 2 i 23 25 27 29 3 i

ELUTZON VOLUHE

FIGURE 3. Radius of gyration as a function of elution volume forpolystyrene 706 measured by SEC-Visc-RALS and SEC-MALLS. The concentration profile of the sample is also shown.

LSASYMMETRYCORRECTEDMWREFRACTOMI=/_-H

ixi0=6 - J5"

INmAL MWESTIMATEtxtO*5-

,,._, .-.

...t

: ;: • • 2,:4,:.ixt0"4 " ...... ,_..,,-.

• .'_. . ..?- ; "..

_;._'.-.::.'.

... . .

1000 1 i i J10 t2 t4 i6

FIGURE 4. Initialmolecular weight (MW) values, calculated form the 90 °scattering, and asymmetry corrected MW values, as a functionof elution volume for polystyrene 706• Note the increasing

asymmetry correction with increasing MW.

6O

. __ -$

tx10_6

,._ MALLS MW..

ix10"5 -

VISC-RALS MW

_000. I I I I = =t9 2! 23 25 27 29 " 3!

ELUTION VOLUME

FIGURE 5. Molecular weight values measured by SEC-MALLS and SEC-Visc-RALS for polystyrene 706. Note the close agreement for

_.oo all MW fractions. (The results are slightly offset for illustrative

purposes), oU__CHROHATOGRAH

o_,,_ �/Z.o0RALS . _""_ IREFRACTOMETER

_" _..00

e_

J

_L I I ".--"-_ . ,•000 : --: • " : ' : : : : " : : :t4.0 _.7.0 ;20.0 23.0 26.0 29.0

RETV0L(_}FIGURE 6. RALS and RI chromatograms for 10,000 g/mol PEO standard.

61

VISCOTEKCORP. UCAL3._1 _ 031_191it:31F'_.LENJO_E: Trr_O-A RUNi_ 30On=3 ¢o15

6.00

DUALC_OMATOBRAM

6.00

REFRACTOMETER

4:00

Z

--).

2.00.--JUJCC "_

!•000 _ _ _ _ _

14.0 17.0 20.0 23.0 26.0 29.0

BETVOL (ml)

FIGURE 7. PALS and RI chromatograms for T-500 dextran. Note theshoulder on the left-hand-side of the LS trace.

62

:+

SEC-Visc-LS Branching Report

s,,,-= DETECTOR SIGNALS w MARK-HOUWINK PLOT

0,0 I0

RALS VISC ..

{ =

LINEAR POLYMER ." .-:"

///: f...1"

._.-I ,' .'BRANCHED POLYMER

4.0 i i * O.ll i30 _ 40 N M issr4 I=111 smlo'l

volvu lel4ali_ lespt

.. BRANCHING FACTORsJ

Sample File : ti-tGa._4Samcle lO : B_anched Polymer s.oContro2 File : tJ-18a.,5Control IO : Linear Polymer to

8ranching factor g" = 0.60 ;- ..

%°11.4

IJ

O.IIulr4 --in .rl

llillP

FIGURE 8. Branching report showing the branching factor, g', as afunctionof molecularweightmeasuredusingSEC-Visc-RALS.TheMark-Houwinkplotforthelinearcounterpartisalsoshownin the top rightbox.

i

63• _+ ++ . • •

_" "" • _ " - "+; i_+: +_:+-_,,,+......... - ' " - " " -" '" ' " "': " :, _+".+, " "+""_'':.'" """'_ ": ''+' " +":':"'__'