DETERMINATION OF BRANCHING IN BIOPOLYMERS BY SIZEEXCLUSION CHROMATOGRAPHY WITH LIGHT SCATTERING(MALLS), VISCOSITY, AND REFRACTIVE INDEX DETECTION

WILLIAM S. BAHARY AND MICHAEL P. HOGAN

UNILEVER RESEARCH, U.S.EDGEWATER, N. J. 07020

The objective of this work was to assess the methods for determining thedegree of long chain branching in polysacchaddes by the light scattering andviscosity techniques in combination with size exclusion chromatography (SEC).The samples used were branched dextrans and the reference linear polymers werepullulans. The first method involved determining the ratio of the radii of gyrationfor branched and linear polymers having the same molecular weight by SEC withmulti angle laser light scattering (MALLS) In the second and third methods,branching was determined by the ratio of the intrinsic viscosities of branched andlinear polymer having the same molecular weight for the SEC slices as well as forthe whole polymer, using different values for the structure and solvent factor, s.The average frequencies obtained for long chain branching for the whole polymersby lightscatteringas wellas byviscometryandfor the slicesby viscometryagreedwell with each other and withthose reportedfrom methylationand NMR studies,about 7.5 per 1000 anhydroglucoseunits. It was concluded that the use ofSEC/MALLS/IV is a powerful tool to determine quantitativelyand confirm thedegree of longchainbranchingin polysaccharides.

Key Words: SEC, Light Scattering, Viscometry, Branching,Polysaccharides,Biopolymers.

INTRODUCTION

Althoughnumerousstudiesof longchainbranchinginpolymershavebeenpublished, the use of aqueous size exclusion chromatography (SEC) incombinationwith multi-anglelaserlightscattering(MALLS) andviscositydetectionis relatively new(1-3). Kuo et al. (4-5) as well as Styfing, Armonas, and Hamielec(6) determinedthe degree of chainbranchingin polyvinylacetatesusingSEC withviscosity and differential refractive index (RI) detectors. Pang and Rudincharacterizedthe degree of longchainbranchingin low densitypolyethylenesasa function of molecularweight using SEC with low angle laser light scattering(LALLS), viscosityand RI detectorsand comparedtheir resultswith those from

215

,_,..

,.° i g,

NMR (7). Lesec et al. studied the degree of branching in model star-branchedcopolymersof polymethylmethacrylateand poly-t-butylacrylateusing SEC withLALLS, viscosityand RI detection(8). Yu and Rollingsapplied SEC/LALLS todeterminethe molecularweight,molecularweightdistribution(MWD), and degreeof branchingin polysaccharidesin 0.5N NaOH aqueous solution(9). Huber alsocharacterized the branching in hydroxyethyl starches in 0.05M NaCI usingSEC/LALLSanddiscussedthetype of branchingqualitatively(10). Allof the abovemethodsassumedthe applicabilityof universalcalibration.

In our previouspaper, pullulansand dextranswere characterized by sizeexclusionchromatography(SEC), with multiangle laser lightscattering(MALLS),intrinsicviscosity(IV), andrefractiveindex (RI) detectionintermsof theirabsolutemolecularweight distributions,Mark-Houwinkrelationships,and radius-molecularweightrelationshipswhichdescribedthe conformationalcoefficientsaswell as thedegree of chain branching in dextrans in a qualitative manner (11). With theabove system, it is also possibleto determinethe degree of longchainbranchingin polymersquantitativelybyseveralapproachesbased onthe ratioof the intrinsicviscositiesof branchedand linearpolymersas well as the ratioof radiiof gyrationwhich is not possiblewith the LALLSsystem, since LALLSdoes not providetheangular dependence of scattered lightand the radius of gyration.Accordingly,itwas the objective of this work to assess the various techniques available in aSEC/MALLS/IV system to determine the degree of long chain branching indextransquantitavelyand comparethe resultsobtainedwiththose from NMR andmethylationstudies.

Since the molecular radii and molecular weights could be determineddirectly,no assumptionsabout the validityof universalcalibrationhadto be made.Thiswas importantinthe currentworkbecausethe characterizationofbiopolymersin aqueousmedia hasthe additionalcomplexityoverorganicSEC due to samplesupport interactions.These includehydrogenbonding,hydrophobicinteractions,complex formation, ion exclusionof like charges, as well as ion inclusionfromDonnan equilibriumof charged macromolecules.These interactions can modifyfrom idealitythe size exclusionbehaviorof the sample and have been describedbefore (11-14). Because of these complications,the applicabilityof universalcalibrationin aqueousmedia needsto be verified for each individualcase (15).

THEORETICAL CONSIDERATIONS

The equationsfordeterminingthe degreeof longchainbranchingare basedon the theorythat branchingdecreases the radiusof gyrationof a polymerchainat constant molecularweight. The branching parameter g is defined from therandom flight model by the square of the ratio of the radii of gyration (R) ofbranched and linear polymers havingthe same molecularweight (1, 16):

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, o' i

2

g = _ at constant MW 1<It >L

Furthermore, g can be relatedto the parameter from the hydrodynamicproperties,g', defined as the ratio of intrinsic viscosities of the branched and linear polymerat constant molecular weight and is about equal to g¢ (1):

¢g' = _ = g at constant MW 2

where _ is the branching structure and solvent factor and has different valuesaccording to various models (1, 17). The values are as follows:

¢ = 3/2 Flory - Fox model (18-19) 3= 1/2 Zimm and Kilb model (20) 4= 3/4 Roovers (1), Bohdanecky (21), in general 5

Historically, if the Flory-Fox equation, [ _ ] = $ R _/M, is valid for branchedpolymers, then the exponent in eqn. 2 is 3/2, and the 3/2 rule is obtained (19, 22).In 1959, Zimm and Kilb recommended a value of 1/2 based on their bead and

string model and usin_ their normal coordinate calculation method (20). Theydemonstated that the g J2rule gave more accurate values for the degree of chainbranching for star shaped polymers under theta conditions. In good solvents, thevalue of the exponent was about one. Berry, Hobbs and Long demonstrated theapplicability of the g_2rule to comb type polymers (23). The applicability of the 1/2and 3/2 rules was tossed back and forth until Berry suggested that the value of theexponent might be variable, depending on the polymer and branching type (24,25). More recently, Bohdanecky (21) and Roovers (1) recommended the 3/4 rulefor general use. Once _ is known, the number of long chain branches permolecule (B) can be calculated for different branching types from publishedequations (1, 16, 20). For example, for random trifunctionai branching inpolydisperse samples B is related to the branching parameter g by the followingequation (20, 22):

n 611 .,2+B_1R.h.r(2+B)1r_+B1/21 4, 6gw--'_L-_v-_"l ",,'L(2+8)1/2_B1/2J-,J

In this work, three experimental methods based on solution properties areassessed and compared with the NMR and methylation techniques. The firstmethod is based on the ratio of the mean-square radii obtained from SEC/MALLSfor the whole polymer as described in eq. 7:

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t

1. g (LS, whole) = _ (LS) at constant MW 7,R'., (LS)

In order to determine the degreeof long chainbranchingby thisapproach, whatis needed is the radiusof gyrationand molecularweight for the whole branchedsampleaswell as the radius-molecularweightrelationfor the correspondinglinearpolymerfrom which the radiusof the linear polymerhavingthe same molecularweight and compositionas the branchedpolymercan be calculated.

The second methodisbasedonthe ratioof intrinsicviscositiesof branchedand linear sample havingthe same molecularweightas obtainedfrom SEC andviscometryaccordingto eq. 8:

E2. g' (IV, whole) = [_ ]b = g at constantMW 8

where F.is equal to 3/4 or 312for the polymerstested. In thiscase, the intrinsicviscosityand molecularweightof the whole branchedpolymeris requiredas wellas the intrinsicviscosity-molecularweight relation for the corresponding linearpolymer.

The third method is based on the ratio of intrinsicviscositiesof thechromatographicslices of the branched and linear samples having the samemolecularweight, as obtainedfrom SEC and viscometry,eq. 9:

8

3. g'_ (IV, slices) = [_ ]b,i _- gi at constantMW 9[ ],,i

In this case also, the intrinsicviscosityand molecularweight of the slicesof thebranched polymer as well as the viscosity-molecularweight relation of thecorrespondinglinear polymerare required. The _values are the same as before.It should be noted that in the first two methods, g was calculated manually,whereas in the third,the g_were obtained from the Viscoteksoftware.

From methylationand sequential analysisstudies of Larm et al. (26), andNMR studies of Wolfromet al. (27) as well as of Colsonet al. (28), the degree oftotal branchingin dextransis about5% or 50 branchesper 1000 anhydroglucoseunits(AGU). Since 40% of the side chainsare one unitlong,and about45% aretwo unitslong,then about 15 % of the branchescontainmore than two units(29).Assumingthat longchainbranchesmay be consideredto consistof morethan twounits, then there are 7.5 longchain branches per 1000 AGU's in dextrans. Ifequations7-9 are validand the experimentsare accurate, thenthe degreeof longchainbranchingobtained by all four methodsshouldagree.

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In theory, two other methods are available to determine long chainbranching.One is based on the giobtainedfrom SEC slicesand lightscatteringto determine molecularradii for each slice. Some data and software difficultieswere encountered with this method which are being discussed with WyattTechnology. The othertechniqueis calledthe massmethodand is based on theratio of molecularweights of linear and branched polymersat constant elutionvolume (3, 7, 9, 30). This methodis basedon the validityof universalcalibrationfor the linear and branchedsamples. Sincein this experiment,the dextransandpullulans were run at different dates, the universal calibration plots for bothsamplesdid notcoincide,sothatthisapproachcouldnotbe assessedat thistime.

EXPERIMENTAL

Materials. Standard pullulanshavingweight average molecularweights(<Mw>'s) of 48.0, 100, 186, 380 and 853 kDa with a polydispersity(Mw/Mn) ofabout 1.1 were obtained from J. M. Science (Buffalo, NY). Standard dextranshaving <Mw>'s of 97, 165, 325, 750 and 1750 kDa with a polydispersityof about1.6 were obtained from American Polymer StandardsCorp. (Mentor, OH). Thechemical structures of these polymers are displayed in Figure ! and show theprimarilyo_- 1,4 and a - 1,6 linear linkages of pullulansas well as the e¢- 1,6linear and 0¢- 1,3 branches of dextrans. It is assumed that the pullulansaresuitablelinearreferencepolymersfor the dextrans. The waterusedto prepare themobilephase was grade 1, 18 megohm-cmpurifiedwiththe BarnsteadNanopureRII apparatus. The other materialswere reagentgrade.

EouiDment. The liquid chromatographwas a Waters 150C ALC/GPCoperatedat 30°C equippedwith4 TSK PW columns(Table I). AWyattTechnologyCorp. (Santa Barbara, CA) modelDawnRF MALLS photometerwas used with aUniphase (San Jose, CA) argon ion laser model 2011 Using the 514.5 nmwavelength light.The viscositydetector was Viscotekmodel 100 (Porter,"IX) andthe differentialrefractometerof the 150C ALC/GPC was used as the RI detector.TheViscoteksoftwareemployedwas UnicaP 4.05 andthe Dawn SoftwareManualVersion 1.01 was used.

Procedure_. The detectors were connected in series in the followingsequence: SEC-MALLS-viscometer-RI-waste. This configurationwas used onrecommendationof Wyatt Corp. in order to maximizethe RI signal of the verydilutesolutionsand to ascertain that both the LS and RI detectors observe thesame mass in solution. The detailsof the experimentalconditionsare displayedinTable I. The mobilephase employedwas aqueous0.1M. NaNO3with 0.025MKH2PO4 and was clarifiedby filtrationwith 0.22 micronGS type cellulosenitratefilters (Millipore Corp., Bedford, MA.) and the polymer solutionswere filteredthrough0.45 microndisposablenylon66 syringefilters(Altec,Deerfield, II1.).Light

219

scattering,intrinsicviscosity(IV), andconcentrationchromatogramswereobtainedand analyzed as describedbelow. The MALLS was calibratedwith HPLC gradetoluene. The normalizationconstantsand the delay volumes were determinedwith a 23 kDa pullulanhavinga nominalradiusof about 5 nm as a standard. TheRI constant,which relatesthe RI unitsto sample concentration,was determinedby the dn/dc methodof Wyatt Technology.

Refractive Index Increment. The refractiveindexdifferential,dn/dc,wasdetermined with an Optilab model 903 (Wyatt Technology)at a wavelength of514.5 nm.The value used for pullulansand dextrans as displayedin Table I was0.147 ml/g, the same as that obtainedin 0.2M NaNO3 and discussedbefore (11).It was in linewith other reportedvalues.

Safety Pre¢e_tions. When usingthe argon-ionlaser, severalprecautionsshouldbe followed. Some of these include: 1) Never look directlyintothe mainlaser beam, 2) avoid contactwith the highvoltages of the laser head or powersupply,and 3) use properdisposalproceduresfor brokenor defective lasertubes.The Uniphaselaser manual shouldbe consultedand followedcarefully.

RESULTS

The resultsfor the MW, IV, androot-mean-square(RMS) radiiof the variousdextrans and pullulansobtainedby the detectors after fractionationby SEC arepresentedat first in order to assesstheir accuracy.

Figure 2 illustrates Mark-Houwink plots for pullulans in terms of theexperimental andsuppliervaluesforthe molecularweightand intrinsicviscosities.The equations obtainedare as follows:

For pullulans:Experimental (0.1M NaNO3, 0.025M KH2PO4@pH 7):

[_1] = 1.70 X 10 "4M o.718 10

Supplierdata (0.05M Na_SO4):

[11] = 2.22 X 10"4M °'6"_ 11

Figure 3 illustrates Mark-Houwink plots for dextrans in terms of theexperimentalandsuppliervalues for the molecularweightand intrinsicviscosities.The equationsobtained for the same two solventsas above are as follows:

For dextrans:Experimental: [TI] = 4.76 X 10 -3M 0.344 12

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t

Supplier data: [11] = 1.13 X 10 -2M O._Te 13

Figures 4 and 5 display the double logarithmic plots of the RMS radii versus Mwfor pullulans and dextrans, respectively, and the equations from the experimentalplots are as follows:

For pullulans: R = 5.04 X 10-2 M o.48 14For dextrans: R = 1.12 X 101 MO._ 15

The theoretical values of the radii in the Figures were calculated from the Ptitsyn-Eisner equation as described previously (11,31, 32):

[11]M = • (1 - 2.637 + 2.861,2)(6 1/2ag )3 16

where • = 2.86 exp 23, 1'= (2a - 1)/3, and "a" is the Mark-Houwinkexponent.

In Figure6, the Mark-Houwinkplots of experimentalvalues for pullulansand dextrans are compared and they demonstrate the lower intrinsicviscosityvalues obtainedfor the dextransrelativeto the pullulans.

In Figure7, the experimentalRMS radii vs MW data for the pullulansanddextransisplottedand furtherdemonstratethe lower radiifor the dextransrelativeto those for the pullulans.The lowerintrinsicviscositiesand radiifor the dextransis a reflectionof the degree of long chainbranchingwhich can be calculatedasdescribedabove.

In Figure8, the branchingparameter "g" for five dextrans obtainedby thethree proceduresis plottedas a functionof molecularweight: 1) g(LS, whole) wasobtained from the ratio of radii of gyration obtained from the light scatteringdetectorfor the wholedextransample relativeto that of pullulan,2) g'(IV, 3/2 rule)was obtainedfrom the viscositydetector for the whole polymeraccordingto the312 rule, and 3) g'(IV, 3/4 rule) was obtained from the viscositydetector for thewhole polymeraccordingto the 3/4 rule. It is observedthat the g valuesobtainedfrom lightscatteringand viscometryare in good agreement when the 3/2 rule isappliedbutthe agreementis poorwhenthe 3/4 rule isapplied.The 1/2 rulewouldyieldeven poorer agreement.

Figure 9 displaysa semi-logplot the g factor obtained from the intrinsicviscosity of the SEC slicesversus the MW usingthe 312 rule. The value of thebranching parameter decreases with molecular weight for each sample asexpected.

The branchingfrequency;L,definedinterms of the numberof branchesper1000 anhydroglucoseunits (AGU), and calculated from eq. 17 is displayed inFigure 10:

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, ° •

2,,= RU * Bw * 1000/MW 17

where RU is the mass of an AGU, which is 162 in this case, Bw is the weightaverage number of trifunctionalbranchesper molecule obtained from the g_ofFigure 9 and eq. 6. Althoughthe branchingfrequency increases with MW asexpected, the higher MW fractions exhibit a lower branching frequency, asexplained below,

In Figure 11, the branchingfrequencies obtained for the various dextransamples by lightscattering for the whole samples and viscometryfor the wholesamples as well as for slices are compared to that obtained from NMR andmethylation studies. The latter is depicted by the solid line at 7.5 long chainbranches per 1000 AGU. It is observed that the values obtained by lightscattering, viscometry,and chemicalmethodsare in the same range.

DISCUSSION

Mark-Houwink Plots, For pullulans, the constants K and a in theexperimental Mark-Houwink equation 12 are in line with those reported by,Tsujisakaand Mitsuhashi(33) as wellas Kawaharaet al. (34) inwater, 2.36 x 10"and 0.66, respectively,and by Baharyet al. in0.2M NaNO3, 4.22 x 10 4 and 0.64(11). The higherintrinsicviscositiesinsodiumnitrateand the phosphatebufferaswell as the higherexponentin the phosphatebuffer suggestthat these are bettersolventsfor pullulanthan water. The values of the exponentcorrespondsto thatexpected for a random linear coil polymer,about 0.5-0.8 dependingon solventpower (35).

For linear fractionsof dextrans in water, Sentiet al. reportvalues of 97.8x 10"3and 0.50 for the Mark-Houwinkconstants,and for brancheddextransthevalue of the exponentwas 0.20 (36). Cerney et al. reportvaluesof 10.3 x 10 3and 0.25 for brancheddextransin methanol/water(37). The resultsof thiswork =are in linewith those reportedfor dextransandthe exponentcorrespondsto thatfor a highlybranched coil, about 0.0-0.5 (35).

The conformationalcoefficients,0.45 and 0.36, obtainedfromthe doublelogarithmicplotsof RMS radiiVs Mw for pullulansand dextrans,respectively,areinagreement withthose reportedbyJackson,Nilssonand Wyatt in 0.15M sodiumnitrate, 0.45 and 0.36 (38). The value obtained for pullulan is in the rangeexpected for linear polymercoils,0.5-0.6. and the one for dextrancorrespondstothe value expected for highly branched coil, 0.33-0.5, as expected. Thesecomparisonsconfirmthe accuracy of the experimentaldata and impartcredenceto the branchingdeterminationsand the assumptionsmade as describedbelow.

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Assumptions end Branchina. In calculatingthe degree of long chainbranchingin dextrans using pullulan as a reference linear polymer, four mainassumptionswere made so that their validityneeds to be examined. The firstassumptionwas that pullulanis a suitable linear reference for dextran. Pullulanhas primarilylinear (_ - 1,4 linkages with some o_- 1,6 ones and all are in adifunctionallinear configurationwhereas dextran contains primarily (_ - 1,6linkageswithsome trifunctionaJ¢x- 1,3 linkagesas branchpoints. It is thereforereasonable to assume that the RMS radius of a completely a - 1,6 linkedpolysaccharidewould be close to that of pullulanfor a given molecularweight,sincethe enchained monomerlengthsare about the same. Hence pullulanis asuitable reference as the branchingresultssuggest.

The second assumptionrefersto the use of equation6, whichrelatesg tothe number of trifunctionalbranch points in a polydispe'rsesample. Since thebranch pointsin dextran B-512 is trifunctionaland the samples are polydisperseaccordingto the SEC chromatogramsand to Figure 9, this assumption is alsojustified.

The thirdassumptionisthat longchainbranchescorrespondto greaterthantwo AGU's. From NMR and SEC studieswith polyethylene,a longchainbranchmay be consideredto consistof a minimumof 6-12 carbonatoms (7, 39). Sincethe lengthof each AGU is about5-6 A, two AGU's are expectedto correspondtoabout 6-12 carbon atoms. Therefore the average frequency of long chainbranching in dextrans is 7.5 branches of over two units per 1000 AGU's asdisplayedin Figure 11 (29).

The fourthassumptionis that solventeffectsare small sincethe equationrelatingthe ratioof the radiiof gyrationto g is defined for theta conditions. IntheSEC experimentsgenerallygoodsolventsare required. Fortunately,usinga goodratherthana thetasolventhaslittleeffectonquantitativebranchingdeterminations(1, 3).

Oneapparentanomalymaybe the increaseinthe branchingfrequencywithmolecularweightwithineach fraction as shown in Figure10, butthe decrease invaluewith molecularweightforthe highermolecularweightsamples, as displayedin Figures10 and 11. This may be explained in terms of the procedureused toprepare the samples. Upon fractionalprecipitation,the branched moleculesaremore solublethan the linear ones for a given molecularweight, and thereforeremain in solution. For this reason, the lower molecularweight fractionshave ahigherlevelof branchingandare morepolydispersewith respectto branchingandmolecularweight than the highermolecularweight samples (Figure 10).

Based on these assumptions,the branchingfrequencies obtainedfor thedextransamples of thiswork and illustratedin Figure 11, ranged from 2-10 and

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bracket the 7.5 obtainedfromNMR, methylationandsequential degradation, whichis encouraging.A value of _ of 3/2 for dextran is reasonableas the branchingisextensive and dendriticrather than star shaped and a good solvent was usedinstead of a theta one, both of whichwould enhance its value (1, 3).

Since the dextran samples were prepared by fractionation,and all thefractionationdata is not available, it is not possible to calculate the averagebranchingfrequency for native dextran from this work. However, these resultsconfirm the accuracy of the data, verify the validityof the assumptions, andenhance confidence in polymer solution theory with respect to branching inpolysaccharides. It appears that SECIMALLSNiscometry is a powerful tool todetermine quantitativelyand confirm the degree of long chain branching inpolymerswithout any assumptionsabout the validity of universal calibrationinaqueous media.

CONCLUSION

Reliable Mw, intrinsicviscosities,and RMS radii for dextransand pullulanswere obtained. The degree of longchainbranchingin dextransfromSEC/MALLSfor whole polymerswas in good agreement with values reported by NMR andmethylation. The degree of longchain branchingobtainedfrom SEC/viscometryfor whole polymers or for SEC/viscometryslice method agreed with expectedvalues when the value of the branching structure s used was 3/2. It wasconcluded that the use of SEC/MALLS/IV is a powerful tool to determinequantitativelyandconfirm the degree of longchainbranchingin polysaccharides.

ACKNOWLEDGEMENT

The authorsare gratefulto UnileverResearchfor permissionto publishthiswork.

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5. C. Kuo, T. Provder, M. Koehler,and A. Kah, Am.Chem. Soc. Symo. Ser.,No. 352, T. Provder, ed., 130 (1987).

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(Academic, New York, 1993), pp 400-425.30. Wyatt Technology Corp., DawnR Light Scattering Manual (1993), Santa

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(Wiley, New York, 1979), p.35.32. O. Ptitsyn, and Y. Eisner, Soy. Phys. T_h. Phys.,4, 1020 (1960).33. Y. Tsujisaka, M. Mitsuhashi In Industrial Gums; 3rd ed., R. Whistler, J.

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34. K. Kawahara, K. Ohta, H. Miyamoto, and S. Nakamura,Polymers,_ 335 (1984).

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• -t

LIST OF FIGURES

Figure 1. Chemical structures of linear pullulan and branched L.mesenteroidesB-512 dextran.

Figure 2. Mark-Houwink plots for pullulan samples using experimental andsupplierdata. See text for solvents.

Figure 3. Mark-Houwinkplots for dextran samples using experimental andsupplierdata. See text for solvents.

Figure 4. Double logarithmicplotsof RMS radiusversus molecularweight ofpullulansbased on SEC/lightscatteringdata and as calculatedwiththe Ptitsyn-Eisnerequation.

Figure 5. Double logarithmicplotsof RMS radiusversus molecularweight ofdextrans based on SEC/lightscatteringdata and as calculatedwiththe Ptitsyn-Eisnerequation.

Figure 6. Comparisonof experimental Mark Houwink plots for dextran andpullulansamples.

Figure 7. Comparisonof doublelogarithmicplotsof RMS radiusvs molecularweight for dextranand pullulansamples.

Figure 8. Semi-logarithmicplots of the branching parameter "g" versusmolecularweight for whole dextran samples obtained from lightscattering and viscosity detectors after size exclusionchromatography.

Figure 9. Semi-logarithmicplots of the branching parameter "gi (IV, slice)"versusmolecularweightfor "slices"of five dextran samplesobtainedfrom viscosityand Viscoteksoftware after SEC.

Figure 10. Semi-logarithmicplots of branchingfrequency _. versus molecularweight for slices of five dextran samples. The ;L were calculatedfromvalues of g_(IV, slice)usingequation6 for Bw and equation 17relating ;L to Bw.

Figure 11. Comparisonof the average branchingfrequencies obtainedfor fivedextransamples usingthe three solutionmethodsof this workwiththe value obtained for native dextran by chemical and NMRmethods.

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Table I

EXPERIMENTAL CONDITIONS FOR SEC/LS/IV

Liquid Chromatograph Waters 150C ALC/GPC

Detection 1. WyattTechnologyDawn-F MALlwith ArgonIon Laser @ 514.5 nrr

2. ViscotekDifferentialViscometer3. DifferentialRefractive Index

Columns TSK 7.5 mm x 30 cm columns1. G2500 PW (lx104d, 100A'2. G3000 PW (lxl0Sd, 200A:3. G4000 PW (3xl0Sd, 500A:4. G5000 PW (lxl 0ed, 1000_

Temperature 30°C for GPC and viscometryRT for Dawn-F

Flow Rate 1 ml/min

Sample Concentration 1-4 mg/ml

Injection volume 0.1 mi

Mobile Phase 0.1 M NaNO3 and 0.025M KH2PO4@ pH 7 in water.

dn/dc @ 514.5 nm 0.147 ml/g

Samples Pullulans (Standards)Dextrans (Standards)

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Figure 1

Structure of PullulanI

H2 C.H2OH .CH2OH

OH OH HO_H C.H2OH .CH2OH2

H H O

Io_ HO O I O

OH OH OH n

L.mesenteroides B-512F dextran

.I_H2 ICH 2 /CH2 /CH2

Branch o HO -O H 'H v HO I O

OH OH I OH OHI

0_ /i_o _/__-H (x - 1,3 BranchHO I O HO OOH OH

FigUre 2

Mark-Houwink Plot for Pullulan10

o_ (exp.) = 0.718..................................................................................................................................................... _ .......................................................................................

o_ (suppl.) = 0.654 l.

i !,-., 1

"_'"0.5

0.3 _ .............. Suppllerr ExpeiimentalE_............. t_il......................................................................................

0.1 ' ! ' ' '30,000 50,000 100,000 200,000300,000 500,000 1,000,00(

Mol. Wt. <Mw>

Figure 3 .,

Mark-Houwink Plot for Dextrans

5 i ' " i '3 (z (suppl.)= 0.278: ....................,_..........' .............................................................t,_,..............................................................................................................2 O_(exp.) = 0._44 .....................................!................................

It-_

• " I _........!

_" 0.5 ' .,' I ,I -

0.3 ....... ,_ i w i.......!................................................Sup..":plierExperimental !

0.2 .................. Val_Jes..............:Valdes , ,' I s

0.1 ' '100;000 200,000 500,000 1,000,000 2,000,00

Mol. Wt. <Mw>

Figure 4

Radius of Gyration vs Mw for Pullulans5O

Slope (Theor.) = 0.576Slope (Exp.) = 0 48030 " ..........

I'o

_E"20 ....e-

n-

10l

Theoretical Experimental_ e ,

i

I I I I ; I I I I I

,000 50,000 100_000 200,000 300,000 500,000 1,000,001

Molecular Weight <Mw>

Figure 5

Radius of Gyration vs Mw for Dextrans5O

Slope (theor.) = 0.43730 + I

Slope (exp.) = 0.41220 ....

E_.Io •

i

5 .......Th++retiC+il........Exp+i_im+i_t_il.....................................................................................Values (P-E) Values

:3 +--II-- " ............•

+t

; i i

50,000 100,000 200,000 500,000 1,000,000 2,000,000

Molecular Weight <Mw>

• • . '

Figure 6

Mark-Houwink Plot forDextrans and Pullulans

5 . _ . i •! ....................... _ ........ _. .I ...................................

_ . 1 i i3 . _............_................................................................i..............................................j..............._............i................2 ...................... i............................................i........_............i.................................................

$,

Ii

01 'I , I !

50,000 100,000 200,000 500,000 1,000,000 .2,000,00I_/Inl I/II_ ._1_/I,,,..

Figure 7b

Radius of Gyration vs Mol. Wt.for Dextrans and Pullulans

50

10 ........ _ ..............................................E

I

50,000 100,000 200;000 500,000 1,000,000 2,000,00Mol. Wt. <Mw>

Flgure 8

Branching Parameter "g" for Dextransfrom LS and IV (Whole)

J

0.8 l l I

g(LS, Whole) g(IV, 3/2 Rule) g(IV, 3/4 Rule)|

0.6

E

_04. ...... _ --133C

o 0.2

I,,,,,,

m

050,000 100,000 200,000 500,000 1,000,000 2,000,000

Molecular Weight <Mw>

--4t

Figure 9

g Factor Plot for Dextmns(givs iw)

tO .g - -

°. ,--

97KFO

"_ O .OO - "

X

G .OO - ""

L-

o - _ 165K_--\ \. 750K

\ "_ \ , 1750KIt 4.gg - -

2 .00 ....

Loa Mw

• r B

Figure 10

Branching Frequency for Dextmns(k,vs Mw)

4 .gg

q 97Ko 3.go - - _. = RU • Bw • 1000/MwX

.1_ °

1750K

• . _ _._ _. I..

J Figure 11

i Comparison of Branching Frequency for_ Polydisperse Samples (Bw Method)o 100 ....o LS, Whole

--- 50 "IV, 3/2 rule

o>, 30 Whole.t_.

20 ...... IV, 3/2 rule

I_" _ SlicesP 10 -""- _-_ " " _-U.. :. .._'___--_ .__._._ " ' Expected

" _ _ ...-. . LCB Freq 7._5

- -_'J. -___ _......__ _ "'

i E II i

¢: 3 - ' . .;--_ _-.__ '•=., , ,, "---.____m ,

oo' ;ooooo_ooooo' ;ooooo''0', O} , , , ' ," 1', 0 ,000 2,000,000 5,000,000

_, _ <Mw> of Dextran