Handbook of Size Exclusion Chromatography and Related ...

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increment for the copolymer at slice i is just dn ¼ dc pBi cpi (dn=dc) p þ cpi þ cBi cBi (dn=dc) B cpi þ cBi Returning to Eq. (1) and extrapolating to u ¼ 0, we have for slice i K ci Ri(0 8 ) ¼ 4p2 n 2 0 NAl 2 0 Ri(08) ¼ 1 Mp þ MBi cpi cpi þ cBi Since ci ¼ cpi þ cBi is measured by the DRI as ci ¼ cpi þ cBi ¼ (dn=dc) p þ cBi (dn=dc) B cpi þ cBi RI [cpi=(cpi þ cBi)](dn=dc) p þ [cBi=(cpi þ cBi)](dn=dc) B 2 (8) (9) (10) where RI is the calibrated RI detector response, Eq. (10) is easily solved for cBi (cpi having been determined from the UV detector). Since Mp is the known protein monomer, the measurement of Ri(u) extrapolated to u ¼ 08 combined with the determinations of cpi and cBi yields the conjugate mass Mbi from Eq. (9). Calculating the distributions of the amount of conjugate in the sample becomes a straightforward exercise. It should be noted, however, that the polarizabilities of the molecules have been assumed to be additive in Eq. (8). Stockmayer et al. (23) have shown that for the case of block copolymers, this assumption should be particularly true, but for random copolymers the hypothesis is more difficult to justify. As conjugated proteins are very similar to block copolymers, this assumption has been used. A far more difficult analysis is required if the protein exists in several aggregated states. Each of these states may be conjugated and a distribution of copolymers may be present in each slice. A given slice may contain a range of such protein aggregates whose varying conjugate coats have produced the same hydrodynamic size and, therefore, co-elution. The presence of such aggregates can be a major impediment to quantifying the stoichiometry. These slice-by-slice determinations become even more difficult because of band broadening which, if not suitably corrected, can seriously distort the results (22). In such cases, peak areas are used to obtain rather crude results relative to what one might have obtained with software correcting such band broadening. Fortunately, new software corrects for these band broadening distortions. Finally, a few comments about protein–protein interactions and their quantitation. The association of various nonchromophoric conjugates with proteins may be determined by similar techniques as long as each slice contains a single protein–protein associate. Wen et al. (21) have shown how an iterative © 2004 by Marcel Dekker, Inc.
process may be used to identify the correct association of the protein component. However,ifadistributionofassociatesispresent,themethoddescribedabovewell may yield misleading and quantitatively wrong results. 8 BRANCHING The characterization of branching by MALS has long been an objective beginning with the seminal paper on the subject by Zimm and Stockmayer (24). At that time SEC had not been invented. Indeed, the only means of fractionating asample was by precipitation fractionation, which yielded broad fractions and rendered attempts to measure distributions present futile. Nevertheless, by making aplot of log(M)vs. logkr2 gl,even of such crude fractions should reveal some quantitative elements of the presence of branching. Indeed, this approach was used later by Podzimek et al. (25) who plotted log(rg) vs. log(M)instead. Further details of Podzimek’sapproach are discussed in Sec. 10 and in Ref. 25. The quantitation of branching generally begins from calculation of the so-called branching ratio g ¼ 1=M Ð r 2 b dm 1=M Ð r 2 l dm ¼ kr2 gb l kr 2 gl l where the mean-square radii are calculated for the branched (b) and linear (l) molecules at the same molar mass. For the same molar mass, the branched molecules will be more compact than their linear counterparts and, therefore, the branching ratio will be less than unity. The ASTRA w software (Wyatt Technology Corporation, Santa Barbara, California, U.S.A.) provides means to calculate the average number of branch units per molecule, B, for both trifunctional (three units joined at one point) and tetrafunctional (four units) branching based on the corresponding relations (24) " p # 1 2 B 4B g3(B) ¼ 1 þ þ (12) 7 9p and g4(B) ¼ " p # 1 2 B 4B 1 þ þ 6 3p (11) (13) From these results one may calculate long-chain branching defined as the number of branches per 100 repeat units. Further details and examples, especially for the © 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
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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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© 2004 by Marcel Dekker, Inc. Figu
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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
Page 459 and 460:
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
Page 483 and 484:
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
Page 493 and 494:
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
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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
Page 515 and 516:
largerispressuredropandresultingexp
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elations between molar masses and s
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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
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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
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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: © 2004 by Marcel Dekker, Inc. Figu
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
Page 625 and 626: 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
Page 649 and 650: 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: homogeneous copolymer, that is, tak
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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