Handbook of Size Exclusion Chromatography and Related ...

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described the partitioning of hard-sphere solutes in a random pore system described as a “porous network.” Also unique to this study was an attempt to express SEC partitioning as a function of both complex pore and solute contributions. Furthermore, the authors treated the distribution of solutes of various shapes (spherical, thin rod, dumb-bell, and capsular shaped) in pores described as cylinders, slabs, spheres, and rectangular pockets. Giddings concluded that SEC partitioning may best be defined as ( sL=2) K ¼ e where K is the SEC equilibrium constant for a random plane pore model and sL is the product of the mean external molecular length, L, and the effective pore radius, s. The equilibrium partitioning of rigid solutes in a random-fiber pore model was also proposed by Giddings (32). Here the SEC equilibrium constant was defined as K ¼ e Ah where A is the projection of the molecular dimension, Ax, averaged over all directions in space and h is the fiber length per unit volume. The fiber diameter is assumed similar to the size of the solute molecule. Further contributions to SEC theory were made by Glandt (33) for the description of the spatial density distribution for “crowded pores.” This work contrasts earlier with studies based solely on dilute solutions of solutes where solute-wall effects are primarily considered. 3.2.2 Proteins as SEC Solutes It is noteworthy that the field of SEC elution theory turned largely to the description of partitioning of random-coil polymers during the late 1960s and throughout the following decade. Contributions from Cassassa and Tagami (34), based on Flory theory (35), served to further the understanding of high polymer SEC. This work focused on new descriptions of flexible solutes. When considering the elution of proteins as SEC solutes, the treatment of solution conformation becomes somewhat simplified when viewed from the perspective of the statistical mechanical arguments needed to describe high polymers. The hard shell or rigid sphere solute models described above are probably adequate for proteins. This approach was used by Squire (30) to extend Eq. (4) to © 2004 by Marcel Dekker, Inc. Ve V0 ¼ 1 þ g 1 M 1=3 C 1=3 3 (5) (6) (7)
yconsideringtheproteinsolutestobespherical.Thetermrisproportionaltothe cube root of the molecular weight. Equation (7) may then be rearranged in the manner described by Himmel and Squire (36), yielding two forms, one relating elution to the void volume of the column and the other to the total volume accessible to the mobile phase: F 0 v V1=3 e ¼ V 1=3 t Fv ¼ V1=3 e V 1=3 t V 1=3 0 V 1=3 0 V 1=3 0 V 1=3 0 ¼ C1=3 M 1=3 C 1=3 A 1=3 (8) ¼ C1=3 M 1=3 C 1=3 A 1=3 (9) whereCandAcorrespondtothemolecularweightsofsolutesjustlargeenoughto be rejected from the column pores, and solutes small enough to be included in all volumes of the column, respectively.Note that the right-hand quantity in Eqs (8) and (9) predicts alinear relationship between Fv and M 1=3 .The set of 37 proteins showninFig.1arereplottedaccordingtotheequationforF 0 v andareshowninFig.2. Figure 2 Plot of F 0 v the linear portion of the data is 0.992. © 2004 by Marcel Dekker, Inc. vs. M 1 = 3 for the data given in Fig. 1. The correlation coefficient for
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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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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
Page 407 and 408: Table 5 Cloned Mutants of Starch En
Page 409 and 410: Figure 3 Modeled x-ray diffraction
Page 411 and 412: In the native environment (plant ce
Page 413 and 414: Figure 6 (a) Large starch granules
Page 415 and 416: number of branching points); crossl
Page 417 and 418: Both absolute approaches are extrao
Page 419 and 420: Table 7 (Continued) Approach Experi
Page 421 and 422: structures, excluded volumes, and t
Page 423 and 424: Figure 10 (a) SEC elution profile o
Page 425 and 426: Figure 12 Wheat glucans: DRI elutio
Page 427 and 428: Figure 13 Wheat glucans. Normalized
Page 429 and 430: Figure 16 Wheat glucan. Normalized
Page 431 and 432: Figure 18 Wheat glucan.Elution prof
Page 433 and 434: Figure 20 Wheat glucans. Absolute m
Page 435 and 436: Figure 22 Wheat glucan. (a) Intrins
Page 437 and 438: Figure 24 Wheat PA-glucan. Elution
Page 439 and 440: an Ubbelohde-viscometer for concent
Page 441 and 442: Rheological investigations of stabi
Page 443 and 444: shifts to applied laser light, whic
Page 445 and 446: Table 8 Characteristic Parameters f
Page 447 and 448: Table 8 (Continued) and H2O. A part
Page 449 and 450: 10. SG Ball, MHBJ van de Wal, RGF V
Page 451 and 452: 52. W Praznik, R Beck. J Chromatogr
Page 453 and 454: 15 Size Exclusion Chromatography of
Page 455 and 456: 3 PROTEIN PARTITIONING IN SEC 3.1 G
Page 457: Figure 1 Plot of Kav vs. log M for
Page 461 and 462: globular proteins and selected flex
Page 463 and 464: silanol groups (52-54); even capped
Page 465 and 466: most proteins to be maximally stabl
Page 467 and 468: Figure 4 Chromatograms of BSA and P
Page 469 and 470: concentrated) steps of protein puri
Page 471 and 472: Table 3 Characteristics of Dextran-
Page 473 and 474: preparative SEC. The capabilities o
Page 475 and 476: 37. GR Noll, N Nagle, JO Baker, DJ
Page 477 and 478: 16 Size Exclusion Chromatography of
Page 479 and 480: Figure 2 Separation of total E. col
Page 481 and 482: Figure 3 Separation of HaeIII-cleav
Page 483 and 484: The recovery of DNA fragments has b
Page 485 and 486: Endotoxin should also be removed fr
Page 487 and 488: Table 3 Best Columns for the Separa
Page 489 and 490: 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
Page 499 and 500: Figure 3 Chromatograms of epoxy res
Page 501 and 502: wherenandn0 aretheRIsofthesample an
Page 503 and 504: Figure 5 SEC chromatogram of n-alka
Page 505 and 506: Figure 7 Refractive indexes of comm
Page 507 and 508: 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
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Page 549 and 550:
Page 551 and 552:
However, strong adsorption of macro
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elution step may be sufficient for
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Figure 16 Block scheme of a full ad
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processing of 2D-HPLC data. Knowled
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Figure 20 Set of full retention-elu
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distributions of complex polymers a
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constituents were not discriminated
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(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:
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19 Methods and Columns for High-Spe
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Table 1 Summary of Methods for Incr
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not savealot of time and solvent, d
Page 579 and 580:
Figure 3 Conventional SEC chromatog
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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
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The standard deviations for the mol
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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
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just ignoring the fractionation of
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20 Automatic Continuous Mixing Tech
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out at low enough concentration tha
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educed viscosity, h r, to be comput
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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
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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
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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