Handbook of Size Exclusion Chromatography and Related ...

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calibration constant for the detector k 0 that converts the signal into a change in refractive index, such that for each chromatogram slice, ci ¼ k0 dn=dc hi (23) This avoids the problems with the peak mass not corresponding to the injected mass and thus increases the measurement precision, but it means that dn=dc for the sample must be known. Because dn=dc must be known for the light-scattering calculation, this clearly does not require any additional work for SEC-light scattering. Furthermore, once the concentration detector is calibrated, dn=dc for unknown polymers can be determined using Eq. (23) if the injected mass is known. With this approach it is best to use a monochromatic light source for the refractometer having the same wavelength as the light source used for the lightscattering experiment. 3.4 Interdetector Delay Volume When a molecular weight sensitive detector is added as a second detector to an SEC system, it is essential that the dead volume in the connecting tubing between the measurement points of the two detector cells be known precisely. If this is not done, the calculated values contain significant errors. In particular, the measured polydispersity and Mark–Houwink coefficients are extremely sensitive to errors that may be incurred in the interdetector dead volume. A number of approaches can be used to determine the interdetector volume. The obvious procedure is to calculate the geometric offset volume from the connection volume between detectors. As discussed by Bruessau (31) and Lecacheux and Lesec (32), however, these calculated values are not correct because they do not take into account peak shape changes that can occur. The most commonly used approach for determining interdetector volume for either viscometers or light-scattering detectors is to measure peak maxima differences of a narrow molecular weight distribution polymer standard or a monodisperse solute, such as a protein. In a viscometer, a solute, such as methanol, can be employed for aqueous SEC. Measurement of peak onset difference, as well as the peak maxima difference of an excluded polymer peak, has been reported (33). A different procedure was used by Lecacheux and Lesec (32) for determining interdetector volume for both a viscometer and a light-scattering detector. In this approach, an excluded monodisperse polymer standard is injected. When the correct interdetector volume is selected, the calculated intrinsic viscosity, or molecular weight, is equal to the expected value and remains constant as a function of elution volume. To determine the interdetector delay volume for a viscometer, a broad molecular weight distribution standard can be injected and a Mark–Houwink plot, © 2004 by Marcel Dekker, Inc.
that is, log[h] vs. logM,generated using universal calibration. The interdetector volume is adjusted until the expected Mark–Houwink exponent is obtained (34). Anotherapproachtodeterminingtheinterdetectorvolumeofaviscometeris first to establish an [h] vs. elution volume calibration curve using aseries of narrow polymer standards of known intrinsic viscosities. A broad molecular weight standard is then injected and the interdetector volumeis adjusted to obtain superimposition of the intrinsic viscosity calibration curve (35). Withalight-scatteringdetector,alogMvs.elutionvolumecalibrationcurve is constructed from aseries of narrow molecular weight distribution polymer standards. Abroad molecular weight distribution standard is then injected, and an iterative procedure finds the interdetector volume that superimposes the broad MWD standard calibration curve onto the one established by the narrow standards (36). Finally,aspectrophotometric method has been proposed in which alowangle laser light-scattering (LALLS) detector isused as an absorption photometer (33). Interdetector volume is then determined by injecting asolute that absorbs radiation from the LALLS detector. Mourey and Miller (33) used copper cyclohexanebutyrate as the solute and determined interdetector volume using the peak onsets of the LALLS detector and refractometer. 3.5 Band Broadening SEC does not provide infinite resolution of species with different hydrodynamic volumes; as a result each slice has some residual polydispersity. This is primarily the result of the finite time required for agiven polymer to diffuse into and out of the stationary phase. The effect can be compounded by extra dead volume in the detectors or connecting tubing. In conventional SEC, band broadening leads to an overestimate of sample polydispersity. This is because the eluting peak is broadened so that it appears to cover awide molecular weight range. If alight-scattering detector is used as adetector, then the true molecular weight at each elution volume can be directly measured. If there is any band broadening, each elution volume is polydisperse in molecular weight, and the measured quantity is aweight average. The slope of the measured Mw against elution volume is flatter than the calibration curve for the molecular weight because of band broadening, and the sample appears less polydisperse. Although the weight-average molecular weight for the sample can still be measured correctly,the number-average molecular weight is overestimated because of the lack of resolution. As a result, polydispersity is underestimated. The error introduced to molecular weight parameters as afunction of band broadening is given in Fig. 7. These results are based on computer simulation studies (37). © 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
Page 9 and 10:
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
Page 37 and 38:
accurately for very large and very
Page 39 and 40:
4 GENERAL REFERENCES The interested
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46. TA Chamberlin, HE Tuinstra. US
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materials are commercially availabl
Page 45 and 46:
Table 1 Commercial Column Packing M
Page 47 and 48:
necessarily comparable. For this re
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adjusted such that the pore size di
Page 51 and 52:
narrowmolecular weight range, indiv
Page 53 and 54:
Figure 8 Effect of particle size on
Page 55 and 56:
Figure 9 SEC calibration using poly
Page 57 and 58:
Table 4 Typical Eluent Systems for
Page 59 and 60:
Figure 12 Analysis of poly-2-vinyl
Page 61 and 62:
24. E Meehan, S O’Donohue. The ro
Page 63 and 64:
into accepted laboratory techniques
Page 65 and 66:
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
Page 75 and 76:
Figure 3 Efficiency of amide-bonded
Page 77 and 78:
mechanically stable packing materia
Page 79 and 80: Figure 5 Pore size distributions of
Page 81 and 82: Figure 6 Separation of polystyrenes
Page 83 and 84: 60-120 A ˚ are large enough to be
Page 85 and 86: Table 6 Selected Silica-Based Colum
Page 87 and 88: Table 7 Separation Ranges for Polym
Page 89 and 90: the decline in permeability is perm
Page 91 and 92: sample components can be varied by
Page 93 and 94: Figure 10 Diol bonding reactions. I
Page 95 and 96: ecause of the higher relative molec
Page 97 and 98: valuesfork1,k2,anda,theunknownmolec
Page 99 and 100: water-soluble and detergent-soluble
Page 101 and 102: the importance of secondary retenti
Page 103 and 104: discussed in Table 8(33). Based on
Page 105 and 106: individual dispersion processes ins
Page 107 and 108: The detector time constant can dist
Page 109 and 110: 5.3 Mobile Phase A mobile phase is
Page 111 and 112: less steep and still linear at high
Page 113 and 114: 35. P Bristow, J Knox. Chromatograp
Page 115 and 116: 112. K Gooding, K Lu, G Vanecek, F
Page 117 and 118: for branched polymers or copolymers
Page 119 and 120: Figure 1 “Bridge design” flow-r
Page 121 and 122: Figure 3 A light-scattering photome
Page 123 and 124: Figure 5 SEC universal calibration
Page 125 and 126: where hn is the hydrodynamic volume
Page 127 and 128: It should be noted that dn=dc also
Page 129: sensitivity for many samples compar
Page 133 and 134: Figure 8 Effect of band broadening
Page 135 and 136: Table 1 Measurement of Molecular We
Page 137 and 138: Figure 10 Differential refractomete
Page 139 and 140: Figure 11 (A) Mark-Houwink plot of
Page 141 and 142: Table 3 Measurement of Molecular We
Page 143 and 144: size information is derived from un
Page 145 and 146: Table 5 Molecular Weight Distributi
Page 147 and 148: By measuring the scattered intensit
Page 149 and 150: 8 APPENDIX: INSTRUMENT COMPANIES 8.
Page 151 and 152: 53. G Marot, J Lesec. J Liq Chromat
Page 153 and 154: 125. D Slootmaekers, JAPP Van Dijk,
Page 155 and 156: 200. JG Bindels, GJJ Bessems, BM De
Page 157 and 158: possibly with hydrodynamic volume (
Page 159 and 160: An insurmountable limitation of SEC
Page 161 and 162: to sDR(V) when either nPS ¼nPB ¼c
Page 163 and 164: 1,4-trans;and8%1,2-vynil.TheglobalC
Page 165 and 166: The goal is to find the MWD and CCD
Page 167 and 168: As expected, pS is closer to the no
Page 169 and 170: Figure 3 Example 3: MWD and BD of a
Page 171 and 172: 9. BH Zimm, WH Stockmayer. The dime
Page 173 and 174: 45. RO Bielsa, GR Meira. Linear cop
Page 175 and 176: solubility properties. They are use
Page 177 and 178: determination of the absolute molec
Page 179 and 180: Figure 4 Result of the PBT analysis
Page 181 and 182:
Figure 8 Result of natural spider s
Page 183 and 184:
7 Size Exclusion Chromatography of
Page 185 and 186:
As pointed out earlier, rubber must
Page 187 and 188:
Table 2 Various Solvents and Operat
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Figure 2 Typical GPC calibrations w
Page 191 and 192:
© 2004 by Marcel Dekker, Inc. Figu
Page 193 and 194:
Natural and Synthetic Rubbe177 vari
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Another example, shown in Fig. 5 (3
Page 197 and 198:
APPENDIX: SEC CONDITIONS FOR RUBBER
Page 199 and 200:
Appendix (Continued) Polymer Column
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Page 203 and 204:
Page 205 and 206:
5. J West, E Rodriguez. Rubber Chem
Page 207 and 208:
Page 209 and 210:
associate. Girdler (67) and Speight
Page 211 and 212:
Table 1 Fractions Obtained Using Co
Page 213 and 214:
Figure 1 SEC analyses of an aged as
Page 215 and 216:
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
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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
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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
Page 247 and 248:
Nevertheless, SEC of asphalts is es
Page 249 and 250:
56. NW Garrick, RR Biskur. Trans Re
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Asphalts 235 122. M-S Lin, JM Chaff
Page 253 and 254:
Page 255 and 256:
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,
Page 261 and 262:
Figure 1 Size exclusion chromatogra
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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:
Page 279 and 280:
Page 281 and 282:
46. CJ Kim, A Hamielec, A Bendek. J
Page 283 and 284:
Page 285 and 286:
A relatively new technique utilizin
Page 287 and 288:
where ais the exponent of the Mark-
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
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thepartiallyhydrolyzedPVAwiththecol
Page 297 and 298:
Table 5 Summary of Conformation and
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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
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Page 309 and 310:
2.1 Molecular Weight Grades of PVP
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exclusion chromatography with low-a
Page 313 and 314:
weightandmolecularweightdistributio
Page 315 and 316:
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
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Figure 10 SEC traces of PVP/AA copo
Page 325 and 326:
Figure 11 Molecular weight distribu
Page 327 and 328:
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
Page 337 and 338:
The silylation was performed in LiC
Page 339 and 340:
observed using column materials hav
Page 341 and 342:
Table 6 (Continued) Packing materia
Page 343 and 344:
4.5 Other Cellulose Derivatives Bes
Page 345 and 346:
Table 8 SEC Conditions for Characte
Page 347 and 348:
dextrans swell too much in cadoxen
Page 349 and 350:
stirring at room temperature for an
Page 351 and 352:
Figure 2 MMDofunbleached(HP)andblea
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Figure 4 MMDofbirchkraftpulpdegrade
Page 355 and 356:
adequate when evaluating the influe
Page 357 and 358:
differential refractive index (DRI)
Page 359 and 360:
30. HA Krässig. Effects of structu
Page 361 and 362:
67. E Sjöholm, K Gustafsson, A Col
Page 363 and 364:
104. B Fleury, J Dubois, C Léonard
Page 365 and 366:
136. D Miller, D Senior, R Sutcliff
Page 367 and 368:
166. SS Cutié, CG Smith. Determina
Page 369 and 370:
200. R Berggren, F Berthold, E Sjö
Page 371 and 372:
13 Molar Mass and Size Distribution
Page 373 and 374:
measurements, and vapor pressure os
Page 375 and 376:
The calibration of SEC columns by c
Page 377 and 378:
The division according to eluent ty
Page 379 and 380:
Apolymer produced by UV irradiation
Page 381 and 382:
Because DMAC/LiCl is also agood sol
Page 383 and 384:
compoundsandwasexplainedbyadsorptio
Page 385 and 386:
isolated lignins because they are e
Page 387 and 388:
The Separon HEMA and Separon HEMA B
Page 389 and 390:
Figure 4 GPC elution curves of the
Page 391 and 392:
liquor is highest throughout the co
Page 393 and 394:
topological anisotropy in the polym
Page 395 and 396:
29. M Ristolainen, R Alen, J Knuuti
Page 397 and 398:
eds. Proc Int Symp 1998. Canton, Pe
Page 399 and 400:
92. L Jurasek. Towards a three dime
Page 401 and 402:
Table 1 Selected Industries Connect
Page 403 and 404:
into C3-metabolites, which then may
Page 405 and 406:
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:
Page 455 and 456:
3 PROTEIN PARTITIONING IN SEC 3.1 G
Page 457 and 458:
Figure 1 Plot of Kav vs. log M for
Page 459 and 460:
yconsideringtheproteinsolutestobesp
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:
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
Page 509 and 510:
Figure 11 Absolute MW calibration p
Page 511 and 512:
Figure 12 Chromatogram of Acrawax C
Page 513 and 514:
18 Two-Dimensional Liquid Chromatog
Page 515 and 516:
largerispressuredropandresultingexp
Page 517 and 518:
elations between molar masses and s
Page 519 and 520:
Figure 2 (Continued) chapter, one o
Page 521 and 522:
where Nis the column efficiency exp
Page 523 and 524:
composition/architecture/molar mass
Page 525 and 526:
solvent. Here again, solvent-solven
Page 527 and 528:
or repulsive interactions between m
Page 529 and 530:
macromolecules may strongly differ
Page 531 and 532:
temperature. The efficacy of an ads
Page 533 and 534:
however, aliphatic bonded groups ma
Page 535 and 536:
Figure 10 Schematic representation
Page 537 and 538:
packing materials for SEC of synthe
Page 539 and 540:
Quantitative relations between sila
Page 541 and 542:
Both strength and thermodynamic qua
Page 543 and 544:
where Cand Dare constants for apart
Page 545 and 546:
ThisisimportantwhenLCCCisappliedtoc
Page 547 and 548:
Page 549 and 550:
Page 551 and 552:
However, strong adsorption of macro
Page 553 and 554:
elution step may be sufficient for
Page 555 and 556:
Figure 16 Block scheme of a full ad
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
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
Page 599 and 600:
just ignoring the fractionation of
Page 601 and 602:
20 Automatic Continuous Mixing Tech
Page 603 and 604:
out at low enough concentration tha
Page 605 and 606:
educed viscosity, h r, to be comput
Page 607 and 608:
Page 609 and 610:
Figure 2 Raw ACOMP signals from mul
Page 611 and 612:
Figure 4 Mw vs. monomer conversion,
Page 613 and 614:
decreases smoothly and monotonicall
Page 615 and 616:
Figure 7 Effects of fluctuating rea
Page 617 and 618:
Finally, the use of a light-scatter
Page 619 and 620:
Figure 8 Linear and cubic increases
Page 621 and 622:
where r(t) is now given by 2 6 r(t)
Page 623 and 624:
Figure 11 Light scattering from sol
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 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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