Handbook of Size Exclusion Chromatography and Related ...

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where for species i, Kri ¼ refractometer constant, dn/dc ¼ specific refractive index increment, and c i ¼ concentration. The viscometer provides a signal proportional to the specific viscosity of the sample: 4DP hsp ¼ (Ip 2DP) where h sp is the specific viscosity, DP is the differential pressure across the middle of the capillary bridge of the viscometer, and Ip is the inlet pressure. Thus, at every elution increment, DPi ¼ 1 " # hspi 2 (2 þ hspi) At the very dilute concentrations used in SEC, the intrinsic viscosity at each increment, [h] i ¼ h spi=ci. Thus, the set of data points ci and [h]i are collected across the entire SEC chromatogram. These dilute concentrations also enable simplification of the basic Rayleigh light scattering equation to: kci R(Q) i ¼ 1 MiP(Q) where k is a constant dependent upon wavelength, refractive index, dn/dc, and R(Q) is the excess Rayleigh scattering factor (2). The P(Q) term approaches unity for molecules having sizes less than 1/20 of the wavelength of the incident light. In TDS, the hydrodynamic radius of the molecule, Rh is given by: Rh ¼ 3 [h]M p 4 0:025 The radius of gyration, Rg, can be determined from the Flory–Fox and Ptitsyn– Eizner equations (8,9): where, © 2004 by Marcel Dekker, Inc. Rg ¼ 1 6 1=2 [h]M F F ¼ 2:55 10 21 (1 2:631 þ 2:861 2 ) and 1 ¼ (2a 1)=3 Ip 1=3 1=3
where ais the exponent of the Mark–Houwink equation, [h] ¼KM a 2.2 Experimental TDS Work for PVA Figure 1 is a schematic of an experimental setup used by this author for aqueous SEC with aTDS interface. This system also employs athree-angle MALLSdetectorforthesimultaneouscaptureofdatafrombothTDSandMALLS detection. Table 1 summarizes the specific conditions used. The MALLS photometer (Mini-Dawn from Wyatt Technology, Santa Barbara, California, U.S.A.) is configured in series between the SEC instrument and aDRI detector (Waters Corporation Model 410, Milford, Massachusetts, U.S.A.). The TDS detector (Viscotek Model T60A, Houston, Texas, U.S.A.) is configured in a parallelarrangementwiththeDRIdetectorsothattheflowissplitevenlybetween the two detectors. The aqueous mobile phase of 0.05 M sodium nitrate was prefilteredthrougha0.45mmembrane(Gelman)toremoveanyparticulates.Data acquisition and processing were carried out using ASTRAversion 4.72 software for MALLS and Viscotek TriSEC Version 3.0 software for TDS. TheoffsetvolumebetweentheRIandTDSdetectorwasdeterminedusinga poly(ethylene glycol) standard of 22,800 molecular weight. The offset volume Figure 1 TDS/MALLS experimental setup. (Reprinted from American Laboratory, Vol. 35, 1, Copyright 2003 by International Scientific Communications, Inc.) © 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
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Table 7 Separation Ranges for Polym
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the decline in permeability is perm
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sample components can be varied by
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Figure 10 Diol bonding reactions. I
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ecause of the higher relative molec
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valuesfork1,k2,anda,theunknownmolec
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water-soluble and detergent-soluble
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the importance of secondary retenti
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discussed in Table 8(33). Based on
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individual dispersion processes ins
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The detector time constant can dist
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5.3 Mobile Phase A mobile phase is
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less steep and still linear at high
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35. P Bristow, J Knox. Chromatograp
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112. K Gooding, K Lu, G Vanecek, F
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for branched polymers or copolymers
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Figure 1 “Bridge design” flow-r
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Figure 3 A light-scattering photome
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Figure 5 SEC universal calibration
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where hn is the hydrodynamic volume
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It should be noted that dn=dc also
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sensitivity for many samples compar
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that is, log[h] vs. logM,generated
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Figure 8 Effect of band broadening
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Table 1 Measurement of Molecular We
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Figure 10 Differential refractomete
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Figure 11 (A) Mark-Houwink plot of
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Table 3 Measurement of Molecular We
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size information is derived from un
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Table 5 Molecular Weight Distributi
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By measuring the scattered intensit
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8 APPENDIX: INSTRUMENT COMPANIES 8.
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53. G Marot, J Lesec. J Liq Chromat
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125. D Slootmaekers, JAPP Van Dijk,
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200. JG Bindels, GJJ Bessems, BM De
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possibly with hydrodynamic volume (
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An insurmountable limitation of SEC
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to sDR(V) when either nPS ¼nPB ¼c
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1,4-trans;and8%1,2-vynil.TheglobalC
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The goal is to find the MWD and CCD
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As expected, pS is closer to the no
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Figure 3 Example 3: MWD and BD of a
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9. BH Zimm, WH Stockmayer. The dime
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45. RO Bielsa, GR Meira. Linear cop
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solubility properties. They are use
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determination of the absolute molec
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Figure 4 Result of the PBT analysis
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Figure 8 Result of natural spider s
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7 Size Exclusion Chromatography of
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As pointed out earlier, rubber must
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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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5. J West, E Rodriguez. Rubber Chem
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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
Page 235 and 236: 5 MODIFIED ASPHALTS The addition of
Page 237 and 238: Oxidation of the rubber and asphalt
Page 239 and 240: Figure 20 SEC chromatogram for an a
Page 241 and 242: Figure 21 Comparisons of apparent m
Page 243 and 244: © 2004 by Marcel Dekker, Inc. S/
Page 245 and 246: PS/10 4 þ 10 3 þ 500 þ 100 THF/1
Page 247 and 248: Nevertheless, SEC of asphalts is es
Page 249 and 250: 56. NW Garrick, RR Biskur. Trans Re
Page 251 and 252: Asphalts 235 122. M-S Lin, JM Chaff
Page 253 and 254: 9 Size Exclusion Chromatography of
Page 255 and 256: Table 1 Applications of Acrylamide
Page 257 and 258: (AM/AA), and acrylamide/dimethyldia
Page 259 and 260: polymer, a large size filter of 5,
Page 261 and 262: Figure 1 Size exclusion chromatogra
Page 263 and 264: Table3 MWandMWDofaBroad-MWDPAMStand
Page 265 and 266: Another commercially available MW d
Page 267 and 268: Table 5 Weight-Average Molecular We
Page 269 and 270: Figure 6 (a) Size exclusion chromat
Page 271 and 272: compared to anormal product. By com
Page 273 and 274: StudyingtheKineticsofaChemicalReact
Page 275 and 276: this information, the higher MW pea
Page 277 and 278: Appendix (Continued) Polymer Column
Page 279 and 280: Appendix (Continued) Polymer Column
Page 281 and 282: 46. CJ Kim, A Hamielec, A Bendek. J
Page 285: A relatively new technique utilizin
Page 289 and 290: Figure 2 TDS chromatograms for full
Page 291 and 292: Figure 5 Comparison of molecular we
Page 293 and 294: Table 3 Summary of TDS Molecular We
Page 295 and 296: thepartiallyhydrolyzedPVAwiththecol
Page 297 and 298: Table 5 Summary of Conformation and
Page 299 and 300: a¼0.627andlog(K) ¼23.249.Theseare
Page 301 and 302: The limits of detection of the PVA
Page 303 and 304: Figure 12 PVAc broad molecular weig
Page 305 and 306: 4 SUMMARY Advances in SEC character
Page 309 and 310: 2.1 Molecular Weight Grades of PVP
Page 311 and 312: exclusion chromatography with low-a
Page 313 and 314: weightandmolecularweightdistributio
Page 315 and 316: © 2004 by Marcel Dekker, Inc. Figu
Page 317 and 318: Figure 4 PEOcalibrationofUltrahydro
Page 319 and 320: Figure 6 Overlay of GPC chromatogra
Page 321 and 322: plus Ultrahydrogel 120 A ˚ ,Shodex
Page 323 and 324: Figure 10 SEC traces of PVP/AA copo
Page 325 and 326: Figure 11 Molecular weight distribu
Page 329 and 330: 2 CHEMICAL, MACROMOLECULAR AND MORP
Page 331 and 332: Table 2 The Relative Composition of
Page 333 and 334: considered to be 3. After the DS ha
Page 335 and 336: 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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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
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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
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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
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Figure 1 Calibration curvesof SEC c
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Figure 3 Chromatograms of epoxy res
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wherenandn0 aretheRIsofthesample an
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Figure 5 SEC chromatogram of n-alka
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Figure 7 Refractive indexes of comm
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Another detector recently applied i
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Figure 11 Absolute MW calibration p
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Figure 12 Chromatogram of Acrawax C
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18 Two-Dimensional Liquid Chromatog
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largerispressuredropandresultingexp
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elations between molar masses and s
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Figure 2 (Continued) chapter, one o
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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
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temperature. The efficacy of an ads
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however, aliphatic bonded groups ma
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Figure 10 Schematic representation
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packing materials for SEC of synthe
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Quantitative relations between sila
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Both strength and thermodynamic qua
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where Cand Dare constants for apart
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ThisisimportantwhenLCCCisappliedtoc
Page 547 and 548:
Page 549 and 550:
Page 551 and 552:
However, strong adsorption of macro
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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
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distributions of complex polymers a
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constituents were not discriminated
Page 565 and 566:
(Sec. 7) and therefore they can be
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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
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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
Page 587 and 588:
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
Page 595 and 596:
Figure 17 Accuracy and precision of
Page 597 and 598:
polymer analysis. Samples are “ru
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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:
© 2004 by Marcel Dekker, Inc. Figu
Page 609 and 610:
Figure 2 Raw ACOMP signals from mul
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Figure 4 Mw vs. monomer conversion,
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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
Page 655 and 656:
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
Page 667 and 668:
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
Page 683 and 684:
Figure 10 SEC chromatograms for som
Page 685 and 686:
appropriate for the early fractions
Page 687 and 688:
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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