Effects of matrix-assisted laser desorption/ionization experimental conditions on quantitative...
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Effects of matrix-assisted laser desorption/ ionization experimental conditions on quantitative compositional analysis of ethylene oxide/propylene oxide copolymers Rui Chen 1 , Nan Zhang 1 , Amy M. Tseng 2 and Liang Li 1 * 1 Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2 2 Nalco Chemical Company, Naperville, IL 60563, USA Matrix-assisted laser desorption/ionization (MALDI) mass spectrometry has the potential to become a valuable tool for the compositional analysis of copolymers. For a copolymer composed of structurally very similar building blocks with minor chain length changes, one would expect the relative peak intensities observed in the MALDI mass spectra to reflect its composition, at least within a narrow mass range. However, we show that variations in experimental conditions in MALDI can have a significant effect on the mass spectral appearance of a copolymer. The effects of concentration, laser power, type of matrices and solvents on mass spectra of an ethylene oxide/propylene oxide copolymer are illustrated. These somewhat surprising results show that great care needs to be exercised when interpreting copolymer spectra for compositional analysis, even for copolymers with structurally similar monomers. This work also points out that further studies are needed to better understand and optimize spectral acquisition conditions for reliable copolymer compositional analysis by MALDI. Copyright # 2000 John Wiley & Sons, Ltd. Received 18 August 2000; Revised 18 September 2000; Accepted 2 October 2000 Matrix-assisted laser desorption ionization (MALDI) mass spectrometry has been demonstrated to be a powerful tool for providing accurate average molecular weights of many narrow polydispersity polymers. 1 For number-average (M n ) and weight-average (M w ) molecular weight calculation of a polymer, MALDI mass spectra are first normalized and the relative peak intensities of oligomer ions are used to represent relative abundances of oligomer molecules in the polymer. Although there are potentially a number of experimental parameters that can affect the appearance of a mass spectrum, and hence M n and M w results, many of these parameters can be controlled. 1–3 For example, the type of solvent can influence the mass spectral data; 4–8 however, as long as we avoid the use of nonsolvents in sample preparation, reproducible mass spectra and reliable M n and M w values can be obtained. 7 The possibility of obtaining accurate M n and M w data suggests that oligomers with minor chain length variations within a narrow mass range should have similar overall analytical response. In a quantitative sense, each individual oligomer in a narrow polydispersity homopolymer can play the role of an internal standard for relative quantitation of the other oligomers. This is not surprising in light of the fact that oligomers have the same backbone structures with only minor variation in the number of repeat units. Of course, for a broad polydispersity polymer, there is a large variation in the number of repeat units that cover a broad mass range. Mass discrimination can take place, resulting in poor representa- tion of actual oligomer distribution in a MALDI spec- trum. 2,3 One of the great strengths of MALDI is its ability to generate compositional information on a polymeric ma- terial. Determination of copolymer composition represents an important area of applications that capitalizes on this unique strength. 9–33 However, the requirement for quan- titative compositional analysis of a copolymer by mass spectrometry is much more stringent than average mol- ecular weight determination. A copolymer is composed of different building blocks that may give different overall detection responses. 19 Thus, relative peak intensities from different building blocks in a mass spectrum may not reflect the true copolymer composition. Quantitative analysis of copolymer composition by MALDI has been demonstrated in a limited number of systems with varying degrees of success. For example, Abate et al. demonstrated that the relative amounts of hydroxybutyrate and hydroxyvalerate in a random copoly- mer, poly(b-hydroxybutyrate-co-b-hydroxyvalerate), deter- mined by MALDI, agree with those expected from theory. 10 Wilczek-Vera et al. have shown that, for diblock copoly- mers of poly(a-methylstyrene)-b-polystyrene, the mole fraction of poly(a-methylstyrene) determined by MALDI is similar to that obtained by NMR and GPC as well as from reagent ratio calculation. 16 The assumption of uniform response from structurally very similar polystyrene and polymethylstyene seems to be valid in this case. On the other hand, for copolymers with greater monomer structural differences, compositional analysis by MALDI can be problematic. For example, for diblock copolymers of poly(a-methylstyrene)-b-poly(4-vinylpyridine), the mole fraction of poly(a-methylstyrene) determined by MALDI can be quite different from that obtained by other methods. 31 A bias in MALDI data was also reported for compositional analysis of copolymers of methyl meth- *Correspondence to: L. Li, Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2. E-mail: [email protected] Contract/grant sponsor: Nalco Chemical Co. Copyright # 2000 John Wiley & Sons, Ltd. RAPID COMMUNICATIONS IN MASS SPECTROMETRY Rapid Commun. Mass Spectrom. 14, 2175–2181 (2000)
Transcript of Effects of matrix-assisted laser desorption/ionization experimental conditions on quantitative...
Effects of matrix-assisted laser desorption/ionization experimental conditions onquantitative compositional analysis of ethyleneoxide/propylene oxide copolymers
Rui Chen1, Nan Zhang1, Amy M. Tseng2 and Liang Li 1*1Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G22Nalco Chemical Company, Naperville, IL 60563, USA
Matrix-assisted laser desorption/ionization (MALDI) mass spectrometry has the potential to become avaluable tool for the compositional analysis of copolymers. For a copolymer composed of structurally verysimilar building blocks with minor chain length changes, one would expect the relative peak intensitiesobserved in the MALDI mass spectra to reflect its composition, at least within a narrow mass range.However, we show that variations in experimental conditions in MALDI can have a significant effect on themass spectral appearance of a copolymer. The effects of concentration, laser power, type of matrices andsolvents on mass spectra of an ethylene oxide/propylene oxide copolymer are illustrated. These somewhatsurprising results show that great care needs to be exercised when interpreting copolymer spectra forcompositional analysis, even for copolymers with structurally similar monomers. This work also points outthat further studies are needed to better understand and optimize spectral acquisition conditions for reliablecopolymer compositional analysis by MALDI. Copyright # 2000 John Wiley & Sons, Ltd.
Received 18 August 2000; Revised 18 September 2000; Accepted 2 October 2000
Matrix-assisted laser desorption ionization (MALDI) massspectrometry has been demonstrated to be a powerful toolfor providing accurate average molecular weights of manynarrow polydispersity polymers.1 For number-average (Mn)and weight-average (Mw) molecular weight calculation of apolymer, MALDI mass spectra are first normalized and therelative peak intensities of oligomer ions are used torepresent relative abundances of oligomer molecules in thepolymer. Although there are potentially a number ofexperimental parameters that can affect the appearance ofa mass spectrum, and hence Mn and Mw results, many ofthese parameters can be controlled.1–3For example, the typeof solvent can influence the mass spectral data;4–8however,as long as we avoid the use of nonsolvents in samplepreparation, reproducible mass spectra and reliable Mn andMw values can be obtained.7 The possibility of obtainingaccurate Mn and Mw data suggests that oligomers withminor chain length variations within a narrow mass rangeshould have similar overall analytical response. In aquantitative sense, each individual oligomer in a narrowpolydispersity homopolymer can play the role of an internalstandard for relative quantitation of the other oligomers.This is not surprising in light of the fact that oligomers havethe same backbone structures with only minor variation inthe number of repeat units. Of course, for a broadpolydispersity polymer, there is a large variation in thenumber of repeat units that cover a broad mass range. Massdiscrimination can take place, resulting in poor representa-tion of actual oligomer distribution in a MALDI spec-trum.2,3
One of the great strengths of MALDI is its ability togenerate compositional information on a polymeric ma-terial. Determination of copolymer composition representsan important area of applications that capitalizes on thisunique strength.9–33 However, the requirement for quan-titative compositional analysis of a copolymer by massspectrometry is much more stringent than average mol-ecular weight determination. A copolymer is composed ofdifferent building blocks that may give different overalldetection responses.19 Thus, relative peak intensities fromdifferent building blocks in a mass spectrum may not reflectthe true copolymer composition.
Quantitative analysis of copolymer composition byMALDI has been demonstrated in a limited number ofsystems with varying degrees of success. For example,Abate et al. demonstrated that the relative amounts ofhydroxybutyrate and hydroxyvalerate in a random copoly-mer, poly(b-hydroxybutyrate-co-b-hydroxyvalerate), deter-mined by MALDI, agree with those expected from theory.10
Wilczek-Veraet al. have shown that, for diblock copoly-mers of poly(a-methylstyrene)-b-polystyrene, the molefraction of poly(a-methylstyrene) determined by MALDIis similar to that obtained by NMR and GPC as well as fromreagent ratio calculation.16 The assumption of uniformresponse from structurally very similar polystyrene andpolymethylstyene seems to be valid in this case. On theother hand, for copolymers with greater monomer structuraldifferences, compositional analysis by MALDI can beproblematic. For example, for diblock copolymers ofpoly(a-methylstyrene)-b-poly(4-vinylpyridine), the molefraction of poly(a-methylstyrene) determined by MALDIcan be quite different from that obtained by othermethods.31 A bias in MALDI data was also reported forcompositional analysis of copolymers of methyl meth-
*Correspondence to: L. Li, Department of Chemistry, University ofAlberta, Edmonton, Alberta, Canada T6G 2G2.E-mail: [email protected]/grant sponsor: Nalco Chemical Co.
Copyright# 2000 John Wiley & Sons, Ltd.
RAPID COMMUNICATIONS IN MASS SPECTROMETRYRapid Commun. Mass Spectrom.14, 2175–2181 (2000)
acrylateandn-butyl methacrylate.17Servaty andco-workersdemonstratedthat quantitative compositional interpretationcould be diffi cult with MALDI data alone for poly(di-methylsiloxane)-co-poly(hydromethysiloxane).29 In addi-tion, they noted that the laser power could affect therelative peak intensities in the MAL DI spectrum of thecopolymer.29
The goal of our researchis to developa mass spectro-metric approach that will provide rapid and accuratequantitative compositional information on copolymers.Ofparticular interestis the compositional analysisof ethyleneoxide (EO)/propylene oxide (PO) copolymers.34 Thestructurally similar EO and PO polymers are expected tohave very similar detection responses.For example, amixture of well-blendedpoly(ethylene glycol) and poly-(propylene glycol) homopolymers of similar molecularweights showssimilar detection efficiencies.However, wefind that experimental conditions in MALDI can signifi-cantly influence the massspectral appearanceof EO/POcopolymers.This work hasimplicationsfor the practice ofusing MALDI asa tool for deducingquantitative composi-tion information on EO/PO copolymers, and likely othertypes of copolymersaswell.
EXPERIME NTAL
Materials and reagents
The EO/POcopolymer usedin this studywasfrom NalcoChemical Co. (Naperville, IL, USA). NMR resultsindicate
that the sample contains4 wt% EO and 96 wt% PO. all-trans-Retinoic acid (RA), dithranol and 2-(4-hydroxyphe-nylazo)benzoicacid(HABA) werepurchasedfrom AldrichChemical Co(Milwaukee,WI, USA). HPLCgradeacetone,methanol and tetrahydrofuran (THF) were from Fisher(Mississauga, ON, Canada). All chemicals were usedwithout further purification.
MALDI- TOFMS
The dried-droplet method was employed in all samplepreparation.Briefly, sample solution wasmixedwith 0.1Mmatrix/THF solution atdifferentratios. Thereafter, a0.5-mLaliquot was deposited onto a stainless-steelsampletarget.Unlessspecified,amatrixsolution of 0.1M RA in THF wasused in all experiments. The laser power was adjustedslightly above the thresholdof the desorption/ionizationprocessexcept in the lasereffect study, in which the laserpowerwasvariedandis indicatedby the laserindex (LI).
MALDI experiments were carried out using a PEBiosystems Voyager laser desorption/ionization time-of-flight (TOF) massspectrometer(Framingham,MA, USA)equippedwith a 337-nmpulsed nitrogen laser. Ions weredetectedby thereflectron TOF.All spectraweretheresultsof signal averaging of between 100 and 200 shots andcalibratedexternally usingpeptidemixtures.All datawerereprocessedusing the Igor Pro Software package(Wave-Metrics, Lake Oswego, OR, USA) and no backgroundsubtraction wasperformed.
Figure 1. (A) MALDI-TOF massspectrumand(B) expandedspectrumof anEO/POcopolymer.all-trans-Retinoicacid wasusedasthe matrix.
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2176 MALDI ANALYSIS OF COPOLYMERCOMPOSITION
RESULTS AND DISCUSSION
Figure 1(A) shows the mass spectrum of the EO/POcopolymer studied in this work. The expanded spectrumin a massrangethat coversone repeat patternof peaksisshown in Fig.1(B). A repeatpattern consistsof four clustersof peaks that arise from several series of distributionsrepresenting different PO andEO compositions aswell asdifferent end-groups. This EO/PO copolymer wasinitiated
with a mixture of long-chainalcohols,C18H37O- (C18)andC16H33O- (C16).Thegeneralformula is asfollows:C18-orC16-[CH2-CH(CH3)-O]n-[CH2-CH2-O]m-H, where n andmcorrespondto the PO and EO numbers in the structuralformula, respectively.
Al l peaksdetected in MALDI spectraare Na� adductpeaks. This is confirmed by adding KCl to the samplepreparationandobserving themass shift resultingfrom thereplacementof Na� by K�. Theadditionof 1% (vol) 0.1MNaCl to thesamplealiquot did not alter themassspectrumshown in Fig. 1, indicatingthat thesample itself containsalargeamountof sodiumsalt.Theeffectsof differenttypesofmetal ions on the massspectral appearance arenot studiedin this work.
Table 1 lists the peak assignments for the 12C isotopepeaksshownin Fig. 1(B). Peakcluster a consistsof twooligomers.Sincetheyhavethesamemass,thereis only oneisotopepatterndisplaying at least five discernablepeaks.Cluster b is from four oligomers, with a 2-Da massdifference between two pairs of possible formulae, andshows seven major peaks from these two overlappingisotope patterns. Clusters g or d are also from twooverlappingisotopepatterns,displayingsevenpeaks.
Since the relative amountsof all theseoligomers canaffect the properties of this copolymer, quantitative
Table 1. Assignmentof major peaksshownin Fig. 1(B)
Peakcluster Exptl. mass Formula Calcdmass
a 1470.2 18PO� 3EO�C18 1470.120PO� 1EO�C16
b 1484.3 19PO� 2EO�C18 1484.121PO�C16
1486.1 16PO� 6EO�C18 1486.118PO� 4EO�C16
g 1498.2 20PO� 1EO�C18 1498.11500.2 17PO� 5EO�C18 1500.1
19PO� 3EO�C16d 1512.2 21PO�C18 1512.2
1514.3 18PO� 4EO�C18 1514.120PO� 2EO�C16
Figure 2. ExpandedMALDI-TOF massspectraobtainedby usingdifferentmatrices:(A) low massand(B) high massregionof the copolymerdistribution.The copolymersamplewasmixed with0.1M matrix/THF solution in 1:10 volume ratio. The laser power usedwas at the desorption/ionizationthreshold(LI=�1750).
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informationon the copolymer composition would be veryuseful for studiesof the relationship between structure/compositionandpolymeractivity.34MALDI canpotentiallyprovide the quantitative information. A fundamentalrequirement for generating quantitative results is that theMALDI spectramust reflect the actual composition of acopolymer. Before one can establisha relation betweencompositionandrelative peakintensitiesin MALDI spectra,it is crucial to ensure that the MALDI spectracan bereproducibly obtained. Understanding how spectra can beaffectedby the experimental conditionsis clearly the firststep in developing a mass spectrometric approach forcompositionalquantitation.ForthisEO/POsample,thetypeof matrix and solvent used for sample preparation, theanalyte and matrix ratio and the laser power can have a
significant effect on massspectral appearance, as demon-stratedbelow.
Figure2 showstheeffectof matrix onMALDI spectraoftheEO/POcopolymer.Thepeakintensitiesarenormalizedto clustera. Table 2 lists the relative peak intensities oftheseclusters. The experimental variation among repeatexperiments undera specificmatrix condition is generallylessthan2% relative standard deviation(RSD). The largevariationshownin Table2 is clearly statistically significant,indicating thatthetypeof matrixusedcanaffecttherelativeintensitiesof theseoligomers.In addition, theextent of thispeak intensity variation is massdependent. The relativeintensity changes are smaller as massesof the oligomersincrease.This canbe seenby comparing thespectrashownin Figs2(A) and2(B). Thisobservationsuggeststhat,asthepolymerchainlength increases,theMALDI responsesfromdifferent componentsbecome moreuniform. In our earlierwork with poly(ethyleneglycol), weshowedthatthetypeofmatrix can affect the MALDI mass resolution andsensitivity.35 The relative peak intensity changes in thecopolymer spectraarelikely dueto thedifferentdegreesofsensitivityvariationresponding to the changeof matrix.
Theeffectof solventonmassspectral patternsis showninFig. 3. Using RA as the matrix and various solvents forsample preparation, the mass spectral variation is quite
Table 2. Relative peak ratios among the 12C peaksfrom differentclustersobtained by using different matrices
a/a b/a g/a d/a
RA 1 0.26 0.54 0.65HABA 1 0.38 0.64 0.62Dithranol 1 0.50 0.80 0.85RSD 0 31.5% 20.0% 17.7%
Figure 3. ExpandedMALDI-TOF massspectraobtainedby usingdifferent solvents:(A) low massand (B) high massregion of the copolymerdistribution. all-trans-Retinoic acid was usedas thematrix. The copolymersamplewasmixed with 0.1M matrix solution in different solventsin 1:15volumeratio. The laserpowerusedwasat thedesorption/ionization threshold(LI =�1750).
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significant. For example, when methanol is used, theoligomers with lower numbersof EO units (see peakslabeled as L in Fig. 3(ii)) are detectedwith much higherrelative intensities, compared to those using THF as thesolvent (Fig. 3(iii)) . The extent of the solvent effect is alsomass dependent (see Figs 3(A) and 3(B)). Acetone,methanol andTHF areall goodsolventsfor thecopolymer.Polymer precipitation prior to matrix crystallization is notexpected. However, the morphology of matrix crystalsformed is dependent on the type of solvent(s)used.7 It isknown that analyte distribution can be affected by thecrystal morphology.36 Thus the solvent effect observed inthis copolymer analysis is likely due to the differenceinpolymer incorporation and distribution in the matrixcrystals. Other more uniform samplepreparation methodssuchaselectrospray37,38may overcome this solventeffect.
It is interestingto notethatthereseemsto beacorrelationbetween the polarity of the solventand the relative signalintensities of peak L. The order of polarity is methanol> acetone> THF. The spectraof the copolymer obtainedby using methanol asthesolventshowa moreintensepeakL thanthose obtainedwith acetone(seeFig. 3). TheuseofTHF generatesspectra with very low intensity for peakL.Among all the ‘good’ solvents, polarity match between
analyte andsolventmay play an importantrole in the finalspectral appearance.Thegenerality of this observation, andany possible correlationbetweenthe propertiesof solventandanalyte, will be investigated in the future.
The mostsignificant peakintensity variationis showninFig. 4, where the analyteto matrix ratio is changed. Lowanalyte concentrationfavorsthe detection of peakslabeledas L. The massdependenceof this concentration effect isshown by comparing Fig. 4(A) with Fig. 4(B). The exactcauseof theconcentration effectis difficul t to ascertain.It isplausible that ion suppression is reduced as analyteconcentration decreases, resulting in an increase in signalintensitiesof theminor components (i.e.,peaksL). We notethat the minor components are completely suppressedthroughoutthe entire massregion studied for the samplepreparedat the ratio of 1:10.
Finally, Fig. 5 shows the laser dependenceof massspectral patternsfor the copolymer. Some variations inrelative intensity are observedbut the magnitude of thevariationis notasgreat asthosedueto theeffectsof matrix,solventandanalyteconcentration. In thehigh mass region,the relative intensity changesare barely noticeable. Notethat the useof excessively high laserpower shouldalwaysbe avoided in MALDI analysis of a polymer to avoid
Figure 4.ExpandedMALDI-TOF massspectraobtainedby usingdifferentanalyteconcentrations:(A) low massand(B) high massregionof thecopolymerdistribution.all-trans-Retinoicacidwasusedas the matrix. The numbershownrefersto the volumeratio of the copolymersampleand0.1M matrix/THF solution. The laser power usedwas at the desorption/ionizationthreshold(LI =�1750).
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MALDI ANALYSIS OF COPOLYMER COMPOSITION 2179
detector saturation. In the caseof analysis of a copolymer,detector saturation will resultin under-determinationof themajor components, since the signals from the majorcomponentswill becomesaturatedfirst.
CONCLUSIONS
We haveshownthat thetypeof matrix andsolvent, analyteconcentration,andlaserpower canaffect themassspectralappearance of an EO/PO copolymer. Since quantitativecomposition analysis of a copolymer relies on the useofrelative peakintensities, themass spectralpattern variationcan certainly alter the composition results. The EO/POcopolymer examined in this work is composedof structu-rally similar monomers.For othertypes of copolymer withgreater variability in monomer structures, even largerspectral variations are expected. It is clear that a betterunderstanding of how experimentalparameters affect themassspectral pattern will facilitatethesearchfor conditionsunder which reproducible results can be obtained. Oncereproduciblespectra canbeobtained,onecanthenexplorethe useof other techniquessuchas NMR to correlatetherelative peakintensitiesin MALDI massspectrawith actualcopolymercomposition.A validatedMALDI method would
provideameansof accurateandrapidanalysisof copolymercomposition.
Acknowledgements
This researchwasfundedby the ResearchAnalytical DepartmentofNalcoChemicalCo.,Naperville,IL, USA.
REFERENCES
1. Nielen MWF. MassSpectrom.Rev.1999;18: 309.2. SchriemerDC, Li L. Anal. Chem.1997;69: 4169.3. SchriemerDC, Li L. Anal. Chem.1997;69: 4176.4. SchriemerDC, Li L. Anal. Chem.1996;68: 2721.5. Dogruel D, Nelson RW, Williams P. Rapid Commun.Mass
Spectrom.1996;10: 801.6. ChenHR, GuoBC. Anal. Chem.1997;69: 4399.7. Yalcin T, Dai YQ, Li L. J.Am.Soc.MassSpectrom.1998;9: 1303.8. Hanton SD, Cornelı́o Clark PA, OwensKG. J Am. Soc. Mass
Spectrom.1999;10: 104.9. DanisPO,Karr DE. Org. MassSpectrom.1993;28: 923.
10. AbateR, Ballistreri A, MontaudoG, GarozzoD, ImpallomeniG,CritchleyG, TanakaK. RapidCommun.MassSpectrom.1993;7:1033.
11. MontaudoG, GarozzoD, MontaudoMS, Puglisi C, SamperiF.Macromolecules1995;28: 7983.
12. PaschH, RodeK. J. Chromatogr. A 1995;699: 21.13. Kalinoski HT, HargissLO, ShayBJ, SchuylPJW.In Proc. 43rd
Figure 5. ExpandedMALDI-TOF massspectraobtainedby usingdifferent laserpower:(A) lowmassand(B) high massregionof thecopolymerdistribution.all-trans-Retinoicacidwasusedasthe matrix. The copolymersamplewasmixed with 0.1M matrix/THF solution in 1:100volumeratio.
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2180 MALDI ANALYSIS OF COPOLYMERCOMPOSITION
ASMSConf. MassSpectrometryand Allied Topics, Atlanta, GA,1995;755.
14. SchaerM. In Proc.43rd ASMSConf.MassSpectrometryandAlliedTopics, Atlanta,GA, 1995;948.
15. Vitalini D, Mineo P, Bella SD, Fragala I, Maravigna P,Scamporrino,E. Macromolecules1996;29: 4478.
16. Wilczek-VeraG, DanisPO,EisenbergA. Macromolecules1996;29: 4036.
17. SuddabyKG, Hunt KH, HaddletonDM. Macromolecules1996;29: 8642.
18. LaceyMP, KeoughT, PanY, ArmstrongMP, Fritz MD. In Proc.44th ASMSConf.MassSpectrometryand Allied Topics, Portland,OR, 1996;908.
19. SchriemerDC,Whittal RM, Li L. Macromolecules1997;30: 1955.20. WangYF, PaventiM, Hay AS. Polymer1997;38: 469.21. HaddletonDM, Maloney DR, SuddabyKG, Clarke A, Richards
SN. Polymer1997;38: 6207.22. GoldschmidtRJ,OwenKG, HantonSD.In Proc.45th ASMSConf.
Mass Spectrometryand Allied Topics, Palm Spring, CA, 1997;1106.
23. Guttman CM, Blair WR, Danis PO. J. Polymer Sci. Part B:PolymerPhys.1997;35: 2409.
24. ScrivensJ,JacksonT, QuinnS,CarterJ,CritchleyG, Brown J. InProc. 46th ASMSConf. Mass Spectrometryand Allied Topics,Orlando,FL, 1998;1189.
25. Yoshida S, YamamotoS, TakamatsuT. Rapid Commun.MassSpectrom.1998;12: 535.
26. Van Rooij GJ,DuursmaMC, de KosterCG, HeerenRMA, BoonJJ,SchuylPJW,van derHageERE.Anal. Chem.1998;70: 843.
27. FranckeV, Rader HJ, GeertsY, Mullen K. Macromol. RapidCommun.1998;19: 275.
28. MontaudoMS, Puglisi C, SamperiF, MontaudoG. Macromol-ecules1998;31: 8666.
29. ServatyS, Kohler W, Meyer WH, RosenauerC, SpickermannJ,RaderHJ, WegnerG, Weier A. Macromolecules1998;31: 2468.
30. Wallace WE, Guttman CM, Antonucci JM. J. Am. Soc. MassSpectrom.1999;10: 224.
31. Wilczek-Vera G, Yu YS, Waddell K, Danis PO, EisenbergA.RapidCommun.MassSpectrom.1999;13: 764.
32. Allgaier J,Martin K, RaderHJ,Mullen K. Macromolecules1999;32: 3190.
33. Yu D, Vladimirov N, FrechetJMJ. Macromolecules1999; 32:5186.
34. Nace VM (ed). Nonionic Surfactants PolyoxyalkyleneBlockCopolymers. Marcel Dekker:New York, 1996.
35. Whittal RM, SchriemerDC, Li L. Anal. Chem.1997;69: 2734.36. Dai YQ, Whittal RM, Li L. Anal. Chem.1996;68: 2494.37. HenselRR, King R, OwensKG. In Proc. 43rd ASMSConf.Mass
SpectrometryandAllied Topics, Atlanta,GA, 1995;947.38. AxelssonJ,HobergAM, WatersonC, Myatt P,ShieldGL, Varney
J, HaddletonDM, Derrick PJ. Rapid Commun.MassSpectrom.1997;11: 209.
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