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tetrafunctional) of branch points. This is defined in terms of another branching factor, g¼ Rg2 b Rg 2 l M (28) where Rg 2 is the mean-square radius of gyration. For different branching architectures, gcan be related to the number of branches per molecule (4). This branching factor gis related to the intrinsic viscosity branching factor g 0 by g 0 ¼g e (29) whereeisastructure factor notspecified by thetheory.Typical values for erange from 0.5 to 1.5. Experimentally determined values for avariety of polymer– solvent systems have been tabulated (68). Because of the uncertainty in eand because SEC measurements are always made in good solvents, whereas gis defined for uconditions, there is too much uncertainty to use g 0 toobtain the number of branch points per molecule. In many cases, only the branching ratio g 0 isreported,whereit servesasausefulmeasureoftherelativedegree ofbranching and is auseful parameter for comparing variations among polymer samples. Kuo et al. (34) used this method to study randomly branched and star polystyrene, as well as branched polyvinyl acetate. Figure 11 shows the Mark– Houwinkplotsforthelinearandbranchedpolystyrenesandaplotofthebranching index g 0 for the branched polystyrene as afunction of molecular weight. As expected, g 0 for randomly branched polystyrene decreases with increasing molecular weight. Siochi et al. (69,70) used this method to study model graft polymethylmethacrylatesandfoundthatinthiscase,g 0 increasedwithincreasing molecular weight. They speculated that this was possibly caused by adifference between macromer and the backbone monomer polymerization kinetics. Notethattheintrinsicviscosity-molecularweightdataforthecorresponding linear polymerarerequired tocalculateg 0 .Ideallythisshouldbedeterminedfrom alinear sample analyzed by SEC-viscometry.Alternatively,literature values for the Mark–Houwink parameters for the linear polymer may be used. If neither of these data are available, the least branched sample or asecondary linear standard can be used as the control. Table 2lists selected references on the use of SECviscometry for branching studies. 4.1.4 Mark–Houwink Coefficients An important application of SEC-viscometry in conjunction with universal calibration is to determine the Mark–Houwink coefficients for a given polymer © 2004 by Marcel Dekker, Inc.
Figure 11 (A) Mark–Houwink plot of log [h] vs. log M for a linear and a branched polystyrene. (B) Plot of branching index g 0 as a function of molecular weight for the randomly branched polystyrene. (From Ref. 34, with permission from the American Chemical Society.) system. The coefficients can provide information about solvent quality and molecular conformation. In addition, once the coefficients for apolymer–solvent system are known, that polymer can then be characterized using conventional universalcalibrationwithoutanon-lineviscometer.AllreferenceslistedinTable1 report the Mark–Houwink coefficients for the systems studied. © 2004 by Marcel Dekker, Inc.
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MARCEL DEKKER Handbook of Size Excl
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CHROMATOGRAPHIC SCIENCE SERIES A Se
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60. Modern Chromatographic Analysis
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Preface to the Second Edition Gel p
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Preface to the First Edition Molecu
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Contents Preface to the Second Edit
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17. Size Exclusion Chromatography o
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James F. Curry Analytical Departmen
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Iwao Teraoka, Ph.D. Othmer Departme
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The graphical data display typicall
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polymer molecule can elute. The tot
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individual states) allowed to them.
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unsaturation while the IR detector
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Sampleconcentrationshouldbeminimize
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averagesdefinedintermsofthemolecula
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information regarding appropriate M
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Analytical. Two models, the KMX-6 a
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Figure 6 Overlay of time-sliced pea
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accurately for very large and very
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4 GENERAL REFERENCES The interested
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46. TA Chamberlin, HE Tuinstra. US
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materials are commercially availabl
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Table 1 Commercial Column Packing M
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necessarily comparable. For this re
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adjusted such that the pore size di
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narrowmolecular weight range, indiv
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Figure 8 Effect of particle size on
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Figure 9 SEC calibration using poly
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Table 4 Typical Eluent Systems for
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Figure 12 Analysis of poly-2-vinyl
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24. E Meehan, S O’Donohue. The ro
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into accepted laboratory techniques
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Table 1 Trace Metal Impurities in C
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mass and biological activity, for m
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Experimental efficiency vs. velocit
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Table 3 Properties of SEC Silica Ge
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operate at aflow rate that can easi
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Figure 3 Efficiency of amide-bonded
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mechanically stable packing materia
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Figure 5 Pore size distributions of
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Figure 6 Separation of polystyrenes
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60-120 A ˚ are large enough to be
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Table 6 Selected Silica-Based Colum
Page 87 and 88: Table 7 Separation Ranges for Polym
Page 89 and 90: the decline in permeability is perm
Page 91 and 92: sample components can be varied by
Page 93 and 94: Figure 10 Diol bonding reactions. I
Page 95 and 96: ecause of the higher relative molec
Page 97 and 98: valuesfork1,k2,anda,theunknownmolec
Page 99 and 100: water-soluble and detergent-soluble
Page 101 and 102: the importance of secondary retenti
Page 103 and 104: discussed in Table 8(33). Based on
Page 105 and 106: individual dispersion processes ins
Page 107 and 108: The detector time constant can dist
Page 109 and 110: 5.3 Mobile Phase A mobile phase is
Page 111 and 112: less steep and still linear at high
Page 113 and 114: 35. P Bristow, J Knox. Chromatograp
Page 115 and 116: 112. K Gooding, K Lu, G Vanecek, F
Page 117 and 118: for branched polymers or copolymers
Page 119 and 120: Figure 1 “Bridge design” flow-r
Page 121 and 122: Figure 3 A light-scattering photome
Page 123 and 124: Figure 5 SEC universal calibration
Page 125 and 126: where hn is the hydrodynamic volume
Page 127 and 128: It should be noted that dn=dc also
Page 129 and 130: sensitivity for many samples compar
Page 131 and 132: that is, log[h] vs. logM,generated
Page 133 and 134: Figure 8 Effect of band broadening
Page 135 and 136: Table 1 Measurement of Molecular We
Page 137: Figure 10 Differential refractomete
Page 141 and 142: Table 3 Measurement of Molecular We
Page 143 and 144: size information is derived from un
Page 145 and 146: Table 5 Molecular Weight Distributi
Page 147 and 148: By measuring the scattered intensit
Page 149 and 150: 8 APPENDIX: INSTRUMENT COMPANIES 8.
Page 151 and 152: 53. G Marot, J Lesec. J Liq Chromat
Page 153 and 154: 125. D Slootmaekers, JAPP Van Dijk,
Page 155 and 156: 200. JG Bindels, GJJ Bessems, BM De
Page 157 and 158: possibly with hydrodynamic volume (
Page 159 and 160: An insurmountable limitation of SEC
Page 161 and 162: to sDR(V) when either nPS ¼nPB ¼c
Page 163 and 164: 1,4-trans;and8%1,2-vynil.TheglobalC
Page 165 and 166: The goal is to find the MWD and CCD
Page 167 and 168: As expected, pS is closer to the no
Page 169 and 170: Figure 3 Example 3: MWD and BD of a
Page 171 and 172: 9. BH Zimm, WH Stockmayer. The dime
Page 173 and 174: 45. RO Bielsa, GR Meira. Linear cop
Page 175 and 176: solubility properties. They are use
Page 177 and 178: determination of the absolute molec
Page 179 and 180: Figure 4 Result of the PBT analysis
Page 181 and 182: Figure 8 Result of natural spider s
Page 183 and 184: 7 Size Exclusion Chromatography of
Page 185 and 186: As pointed out earlier, rubber must
Page 187 and 188: Table 2 Various Solvents and Operat
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Figure 2 Typical GPC calibrations w
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© 2004 by Marcel Dekker, Inc. Figu
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Natural and Synthetic Rubbe177 vari
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Another example, shown in Fig. 5 (3
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APPENDIX: SEC CONDITIONS FOR RUBBER
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Appendix (Continued) Polymer Column
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Page 203 and 204:
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5. J West, E Rodriguez. Rubber Chem
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8 Size Exclusion Chromatography of
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associate. Girdler (67) and Speight
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Table 1 Fractions Obtained Using Co
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Figure 1 SEC analyses of an aged as
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Apparently more polar compounds are
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40% was fractionated into four frac
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Figure 7 SEC analyses of an unaged
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Figure 9 Comparison of percentage L
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Figure 11 Comparison of SEC chromat
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Figure 12 Comparisons of SEC chroma
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percentage LMS at the other locatio
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the total area into up to 12 sectio
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attempted to develop an SEC method
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parameterisbasedontheinternalpressu
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5 MODIFIED ASPHALTS The addition of
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Oxidation of the rubber and asphalt
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Figure 20 SEC chromatogram for an a
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Figure 21 Comparisons of apparent m
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© 2004 by Marcel Dekker, Inc. S/
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PS/10 4 þ 10 3 þ 500 þ 100 THF/1
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Nevertheless, SEC of asphalts is es
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56. NW Garrick, RR Biskur. Trans Re
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Asphalts 235 122. M-S Lin, JM Chaff
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Table 1 Applications of Acrylamide
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(AM/AA), and acrylamide/dimethyldia
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polymer, a large size filter of 5,
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Figure 1 Size exclusion chromatogra
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Table3 MWandMWDofaBroad-MWDPAMStand
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Another commercially available MW d
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Table 5 Weight-Average Molecular We
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Figure 6 (a) Size exclusion chromat
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compared to anormal product. By com
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StudyingtheKineticsofaChemicalReact
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this information, the higher MW pea
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46. CJ Kim, A Hamielec, A Bendek. J
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A relatively new technique utilizin
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where ais the exponent of the Mark-
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Figure 2 TDS chromatograms for full
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Figure 5 Comparison of molecular we
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Table 3 Summary of TDS Molecular We
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thepartiallyhydrolyzedPVAwiththecol
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Table 5 Summary of Conformation and
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a¼0.627andlog(K) ¼23.249.Theseare
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The limits of detection of the PVA
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Figure 12 PVAc broad molecular weig
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4 SUMMARY Advances in SEC character
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2.1 Molecular Weight Grades of PVP
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exclusion chromatography with low-a
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weightandmolecularweightdistributio
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Figure 4 PEOcalibrationofUltrahydro
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Figure 6 Overlay of GPC chromatogra
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plus Ultrahydrogel 120 A ˚ ,Shodex
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Figure 10 SEC traces of PVP/AA copo
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Figure 11 Molecular weight distribu
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2 CHEMICAL, MACROMOLECULAR AND MORP
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Table 2 The Relative Composition of
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considered to be 3. After the DS ha
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een extensively studied by methods
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The silylation was performed in LiC
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observed using column materials hav
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Table 6 (Continued) Packing materia
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4.5 Other Cellulose Derivatives Bes
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Table 8 SEC Conditions for Characte
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dextrans swell too much in cadoxen
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stirring at room temperature for an
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Figure 2 MMDofunbleached(HP)andblea
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Figure 4 MMDofbirchkraftpulpdegrade
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adequate when evaluating the influe
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differential refractive index (DRI)
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30. HA Krässig. Effects of structu
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67. E Sjöholm, K Gustafsson, A Col
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104. B Fleury, J Dubois, C Léonard
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136. D Miller, D Senior, R Sutcliff
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166. SS Cutié, CG Smith. Determina
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200. R Berggren, F Berthold, E Sjö
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13 Molar Mass and Size Distribution
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measurements, and vapor pressure os
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The calibration of SEC columns by c
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The division according to eluent ty
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Apolymer produced by UV irradiation
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Because DMAC/LiCl is also agood sol
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compoundsandwasexplainedbyadsorptio
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isolated lignins because they are e
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The Separon HEMA and Separon HEMA B
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Figure 4 GPC elution curves of the
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liquor is highest throughout the co
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topological anisotropy in the polym
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29. M Ristolainen, R Alen, J Knuuti
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eds. Proc Int Symp 1998. Canton, Pe
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92. L Jurasek. Towards a three dime
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Table 1 Selected Industries Connect
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into C3-metabolites, which then may
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Table 4 Key Enzymes in the Biosynth
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Table 5 Cloned Mutants of Starch En
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Figure 3 Modeled x-ray diffraction
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In the native environment (plant ce
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Figure 6 (a) Large starch granules
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number of branching points); crossl
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Both absolute approaches are extrao
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Table 7 (Continued) Approach Experi
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structures, excluded volumes, and t
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Figure 10 (a) SEC elution profile o
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Figure 12 Wheat glucans: DRI elutio
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Figure 13 Wheat glucans. Normalized
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Figure 16 Wheat glucan. Normalized
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Figure 18 Wheat glucan.Elution prof
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Figure 20 Wheat glucans. Absolute m
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Figure 22 Wheat glucan. (a) Intrins
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Figure 24 Wheat PA-glucan. Elution
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an Ubbelohde-viscometer for concent
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Rheological investigations of stabi
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shifts to applied laser light, whic
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Table 8 Characteristic Parameters f
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Table 8 (Continued) and H2O. A part
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10. SG Ball, MHBJ van de Wal, RGF V
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52. W Praznik, R Beck. J Chromatogr
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Page 455 and 456:
3 PROTEIN PARTITIONING IN SEC 3.1 G
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Figure 1 Plot of Kav vs. log M for
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yconsideringtheproteinsolutestobesp
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globular proteins and selected flex
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silanol groups (52-54); even capped
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most proteins to be maximally stabl
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Figure 4 Chromatograms of BSA and P
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concentrated) steps of protein puri
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Table 3 Characteristics of Dextran-
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preparative SEC. The capabilities o
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37. GR Noll, N Nagle, JO Baker, DJ
Page 477 and 478:
Page 479 and 480:
Figure 2 Separation of total E. col
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Figure 3 Separation of HaeIII-cleav
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The recovery of DNA fragments has b
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Endotoxin should also be removed fr
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Table 3 Best Columns for the Separa
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Figure 10 Dependence of HETP on flo
Page 491 and 492:
Appendix (Continued ) Polymer Colum
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REFERENCES 1. CT Wehr, SR Abbott. J
Page 495 and 496:
MALDI-MS has been applied to determ
Page 497 and 498:
Figure 1 Calibration curvesof SEC c
Page 499 and 500:
Figure 3 Chromatograms of epoxy res
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wherenandn0 aretheRIsofthesample an
Page 503 and 504:
Figure 5 SEC chromatogram of n-alka
Page 505 and 506:
Figure 7 Refractive indexes of comm
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Another detector recently applied i
Page 509 and 510:
Figure 11 Absolute MW calibration p
Page 511 and 512:
Figure 12 Chromatogram of Acrawax C
Page 513 and 514:
18 Two-Dimensional Liquid Chromatog
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largerispressuredropandresultingexp
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elations between molar masses and s
Page 519 and 520:
Figure 2 (Continued) chapter, one o
Page 521 and 522:
where Nis the column efficiency exp
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composition/architecture/molar mass
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solvent. Here again, solvent-solven
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or repulsive interactions between m
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macromolecules may strongly differ
Page 531 and 532:
temperature. The efficacy of an ads
Page 533 and 534:
however, aliphatic bonded groups ma
Page 535 and 536:
Figure 10 Schematic representation
Page 537 and 538:
packing materials for SEC of synthe
Page 539 and 540:
Quantitative relations between sila
Page 541 and 542:
Both strength and thermodynamic qua
Page 543 and 544:
where Cand Dare constants for apart
Page 545 and 546:
ThisisimportantwhenLCCCisappliedtoc
Page 547 and 548:
Page 549 and 550:
Page 551 and 552:
However, strong adsorption of macro
Page 553 and 554:
elution step may be sufficient for
Page 555 and 556:
Figure 16 Block scheme of a full ad
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processing of 2D-HPLC data. Knowled
Page 559 and 560:
Figure 20 Set of full retention-elu
Page 561 and 562:
distributions of complex polymers a
Page 563 and 564:
constituents were not discriminated
Page 565 and 566:
(Sec. 7) and therefore they can be
Page 567 and 568:
2. Identify sample solvents. First
Page 569 and 570:
1 Segmental interaction energy para
Page 571 and 572:
58. BG Belenkii. Pure Appl Chem 51:
Page 573 and 574:
19 Methods and Columns for High-Spe
Page 575 and 576:
Table 1 Summary of Methods for Incr
Page 577 and 578:
not savealot of time and solvent, d
Page 579 and 580:
Figure 3 Conventional SEC chromatog
Page 581 and 582:
chromatogram at 4mL/min, which is f
Page 583 and 584:
Sincethereductionoftheinternaldiame
Page 585 and 586:
Table 3 Summary of Column Performan
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Figure 11 Dependence of column perf
Page 589 and 590:
. Two-dimensional chromatography ru
Page 591 and 592:
The standard deviations for the mol
Page 593 and 594:
Figure 15 Comparison of time requir
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Figure 17 Accuracy and precision of
Page 597 and 598:
polymer analysis. Samples are “ru
Page 599 and 600:
just ignoring the fractionation of
Page 601 and 602:
20 Automatic Continuous Mixing Tech
Page 603 and 604:
out at low enough concentration tha
Page 605 and 606:
educed viscosity, h r, to be comput
Page 607 and 608:
Page 609 and 610:
Figure 2 Raw ACOMP signals from mul
Page 611 and 612:
Figure 4 Mw vs. monomer conversion,
Page 613 and 614:
decreases smoothly and monotonicall
Page 615 and 616:
Figure 7 Effects of fluctuating rea
Page 617 and 618:
Finally, the use of a light-scatter
Page 619 and 620:
Figure 8 Linear and cubic increases
Page 621 and 622:
where r(t) is now given by 2 6 r(t)
Page 623 and 624:
Figure 11 Light scattering from sol
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3.1 ASimple System: Equilibrium Cha
Page 627 and 628:
Figure 13 (a) ACM applied to the ch
Page 629 and 630:
Also of note in Fig. 13b is how hig
Page 631 and 632:
15. JM Starita, CL Rohn. Rheologica
Page 633 and 634:
52. M Hulden. Hydrophobically modif
Page 635 and 636:
21 Light Scattering and the Solutio
Page 637 and 638:
therefore, is to remove any lingeri
Page 639 and 640:
is often found in the literature wh
Page 641 and 642:
Figure 2 Configuration of an SEC se
Page 643 and 644:
5 THE IMPORTANCE OF SOFTWARE Like a
Page 645 and 646:
standard deviations of the measured
Page 647 and 648:
These include the differential weig
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Figure 8 Data of Fig. 7corrected fo
Page 651 and 652:
Figure 11 Data of Fig. 10 with spik
Page 653 and 654:
Figure 13 Fitstodatacollectedatasli
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Table 1 Errors (in %) Characteristi
Page 657 and 658:
homogeneous copolymer, that is, tak
Page 659 and 660:
process may be used to identify the
Page 661 and 662:
fractionated sample. They represent
Page 663 and 664:
Figure 16 An example of poor SEC ch
Page 665 and 666:
on) methods, whereby the average di
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23. WH Stockmayer, LD Moore Jr, M F
Page 669 and 670:
condition, as is explained in this
Page 671 and 672:
Figure 2 Partition coefficients KL
Page 673 and 674:
4 COLUMNS FOR HOPC Detailsaregiveni
Page 675 and 676:
and concomitant clogging of columns
Page 677 and 678:
Figure 5 Concentration dependence o
Page 679 and 680:
Table 1 Solution Volume, Polymer Ma
Page 681 and 682:
in Fig. 4a. The middle fractions (8
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Figure 10 SEC chromatograms for som
Page 685 and 686:
appropriate for the early fractions
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23 Size Exclusion/ Hydrodynamic Chr
Page 689 and 690:
Figure 2 Calibration curve for the
Page 691 and 692:
Figure 5 Elutionbehaviorofpolystyre
Page 693 and 694:
Table 1 Comparison Between SEC and
Page 695 and 696:
egular SEC column in which the pore
Page 697:
Such an ideal separation can be obt
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