Handbook of Size Exclusion Chromatography and Related ...

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Figure 3 Data for a single slice plotted with error bars. where DRj(ui;cj) is the calculated standard deviation of the measured excess Rayleigh ratio at ui and Dcj is the standard deviation of the concentration cj. Similarcalculationsareperformedtoestablishtheerrorsassociatedwiththemean square radius values. The calculations discussed briefly above are both complex and essential for any MALS determinations of molecular and particle properties. With today’s armamentarium of high-speed and low-cost computing, all the benefits of MALS should be realized by all laboratories. Most important among such benefits is the ability to judge the precision of the results reported. Avariety of other quantities essential for the characterization of molecular and particle samples must also be reported with ameasure of their precision. Once again, only by performing detailed analyses based upon the well-proven application of error propagation can MALS measurements, or for that matter any measurements, be considered avalid and reproducible technique. OtherquantitiesdeterminedfromMALSdirectlywhoseprecisionisessential includethevariousmomentsofthemassandsizedistributionssocalculated.Typical among them are theweight, number, and z-average molar mass (see Sec. 9). In the case of fractionated proteins, for example, the monomeric masses must be presented as precisely as possible to provide the user continuing “cold comfort” for the MALS measurement. Protein masses are generally known aprioriin any event from calculations based on DNA sequencing. References to so-called standards used for empirical studies are always valuable. With precision insured by reporting of © 2004 by Marcel Dekker, Inc.
standard deviations of the measured quantities, systematic errors are more easily identified. Such might include selecting the wrong wavelength for the light source used, entering the wrong value of the refractive index increment, erroneous calibrationoftherefractiveindexorotherconcentrationsensitivedetectors,errorsin calibrating the MALS photometer, and so on. The importance of the Zimm plot procedure to yield the second virial coefficient, weight-average molar mass, and average mean-square radius for unfractionated samples requires that MALS software be capable of performing such determination, as well. This is easily implemented by preparing aset of aliquots spanning abroad range of unfractionated sample concentrations. Using a syringe pump or large injection loop plus chromatographic pump, individual aliquots are injected sequentially during a “collection” event. The resulting chromatograph at each scattering angle appears as aseries of plateaus such as shown in Fig. 4for the scattering at 908 from aliquots of starch sample in 90% DMSO. Apeak region is selected from each plateau as indicated by the vertical lines. The software then combines the corresponding data from all scattering anglesaveragedovereachpeakregionwiththeuser-enteredconcentrationofeach preparedaliquot toyieldaZimmplotsuchasthatshowninFig.5.Fromthisplot, the software calculates the molar mass (7:46 + 0:09) 10 6 , the r.m.s. radius 85:7 + 1:7 nm, and the second virial coefficient (1:46 + 0:19) 10 5 molmL/ g 2 . All software should be able to calculate and plot the important distributions of mass and r.m.s. radius (for MALS, the latter has a lower limit of about 8–10nm). Figure 4 Series of plateaus at 908, each corresponding to a different starch concentration injected into a flow cell using a syringe pump. © 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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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
Page 491 and 492:
Appendix (Continued ) Polymer Colum
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REFERENCES 1. CT Wehr, SR Abbott. J
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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
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
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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
Page 553 and 554:
elution step may be sufficient for
Page 555 and 556:
Figure 16 Block scheme of a full ad
Page 557 and 558:
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
Page 595 and 596: 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: 5 THE IMPORTANCE OF SOFTWARE Like a
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 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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