656 BIOCHEMICAL AND SYNTHETIC POLYMER SEPARATIONS 13.10.3.5 Chemical Composition as a Function of Molecular Size A copolymer typically exhibits both molecular-weight and chemical-composition distributions. Depending on polymerization conditions, the chemical composition may or may not vary with polymer molecular weight. To investigate the presence of such chemical heterogeneity, we can couple SEC with a spectroscopic technique that yields chemical-composition information. Such a combined technique provides the average composition at each point in the SEC chromatogram, that is, for each molecular size. If only one of two monomers can be detected by UV, the combination of a UV detector and another concentration-sensitive detector (e.g., refractive index, RI) can in principle be used to follow the concentration of each monomer. Additional information can be obtained from combining SEC with either FTIR or NMR spectroscopy. Although information about chemical composition as a function of molecular size can be very valuable, even the smallest SEC fractions can contain a variety of molecules that vary in both chemical composition and molecular weight. That is, differences in chemical composition can result in molecules with different molecular weights having the same molecular ‘‘size’’ in solution, as illustrated in Figure 13.49. A fraction obtained from a high-resolution SEC separation (rectangular box in Fig. 13.49) will contain molecules with the same molecular size (gyration radius R g ) in solution, but with different molecular weights. It is often important to know the chemical-composition distribution, rather than just the average chemical com- position. Likewise the functionality-type distribution (FTD) may be more important than the average number of functional groups per molecule. This will be especially true if the chemical composition or the number of functional groups per molecule is known (or suspected) to vary. An example is reactive (pre-)polymers that are used in many formulations for sealants, adhesives, and coatings. Molecules without reactive (functional) groups will not react, molecules with one functional group will locally terminate the polymerization process, molecules with two functional groups will 0.025 0.020 0.015 0.010 0.005 0.000 Radius R g (μm) 0 50 100 150 200 250 300 Molecular wei g ht ( x10 −3 ) homopolymer A homopolymer B co-polymers of A and B fraction Figure 13.49 Schematic illustration of the relationship between molecular size and molecu- lar weight for (co-)polymers of different composition. Lines represent (from top to bottom) homopolymer A, copolymer AB (75:25), AB (50:50), AB (25:75), and homopolymer B. 13.10 SYNTHETIC POLYMERS 657 sustain the polymerization, and molecules with more than two functional groups promote the formation of resinous polymeric networks. Knowledge of only the average number of functional groups per molecule would be insufficient in this case. 13.10.4 Polymer Separations by Two-Dimensional Chromatography In comprehensive two-dimensional liquid chromatography (LC × LC; Sections 9.3.10, 13.4.5), the entire sample is subjected to two different successive separations, while the separation obtained in the first dimension is preserved. To simultaneously determine two mutually dependent distributions, such as the combination of MWD and CCD (MWD × CCD), a technique that separates according to molecular weight (e.g., SEC) must be combined with one that separates (largely) according to com- position, such as i-LC. Combination of the two separations (i-LC × SEC) then yields a two-dimensional chromatogram that represents an analysis of the sample according to both molecular weight and chemical composition; an example is shown in Figure 13.48. Corresponding one-dimensional separations are shown for SEC at the side, and for i-LC at the top of Figure 13.48. While neither of the latter one-dimensional separations provides an adequate separation of the total sample, the corresponding two-dimensional separation does. Another i-LC × SEC separa- tion is shown in Figure 13.50, for a more complex sample: chain-end-functionalized poly(methyl methacrylates). The horizontal time-axis for the i-LC separation is indicative of the chemical composition of the copolymer (note labels at top of figure for the number of functional groups in the molecule); while the vertical time-axis for the SEC separation is related to its molecular weight. Two-dimensional chromatograms such as those in Figures 13.48 and 13.50 can provide a useful qualitative picture of the composition of a copolymer. Different samples can be compared in great detail, and the results of such a comparison groups per molecule 1.2 1.1 1.0 0.9 0.8 0.7 SEC (min) i-LC (hr) 012 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Figure 13.50 Two-dimensional separation of chain-end-functionalized poly(methyl methacrylates). The dashed lines indicate areas in the 2D-chromatogram that correspond to molecules with zero, one or two functional groups, as indicated at the top of the figure. Adapted from [172]. 658 BIOCHEMICAL AND SYNTHETIC POLYMER SEPARATIONS can be used to better understand the properties of polymeric materials or related polymerization processes [173]. Unfortunately, it is much more difficult to obtain quantitative information from such figures, as a number of complications arise. 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CHAPTER FOUR TEEN ENANTIOMER SEPARATIONS with Michael L ¨ ammerhofer, Norbert M.Maier, and Wolfgang Lindner 14.1 INTRODUCTION, 666 14.2 BACKGROUND AND DEFINITIONS, 666 14.2.1 Isomerism and Chirality, 667 14.2.2 Chiral Recognition and Enantiomer Separation, 669 14.3 INDIRECT METHOD, 670 14.4 DIRECT METHOD, 675 14.4.1 Chiral Mobile-Phase-Additive Mode (CMPA), 675 14.4.2 Chiral Stationary-Phase Mode (CSP), 677 14.4.3 Principles of Chiral Recognition, 679 14.5 PEAK DISPERSION AND TAILING, 681 14.6 CHIRAL STATIONARY PHASES AND THEIR CHARACTERISTICS, 681 14.6.1 Polysaccharide-Based CSPs, 682 14.6.2 Synthetic-Polymer CSPs, 689 14.6.3 Protein Phases, 691 14.6.4 Cyclodextrin-Based CSPs, 697 14.6.5 Macrocyclic Antibiotic CSPs, 699 14.6.6 Chiral Crown-Ether CSPs, 706 14.6.7 Donor-Acceptor Phases, 707 14.6.8 Chiral Ion-Exchangers, 711 14.6.9 Chiral Ligand-Exchange CSPs (CLEC), 713 14.7 THERMODYNAMIC CONSIDERATIONS, 715 14.7.1 Thermodynamics of Solute-Selector Association, 715 Introduction to Modern Liquid Chromatography, Third Edition, by Lloyd R. Snyder, Joseph J. Kirkland, and John W. Dolan Copyright © 2010 John Wiley & Sons, Inc. 665 . CONSIDERATIONS, 715 14.7.1 Thermodynamics of Solute-Selector Association, 715 Introduction to Modern Liquid Chromatography, Third Edition, by Lloyd R. Snyder, Joseph J. Kirkland, and John W. Dolan Copyright. B. Gelotte, J. Chromatogr., 3 (1960) 330. 66. Y. Kato, T. Kitamura, and T. Hashimoto, J. Chromatogr., 266 (1983) 49. 67. Y. Kato, T. Kitamura, and T. Hashimoto, J. Chromatogr., 292 (1984) 418. 68 Reversed-Phase High Performance Liquid Chromatography,Aca- demic Press, New York, 1984. 169. A. M Striegel, W. W Yau, J. J Kirkland, and D. D Bly, Modern Size-Exclusion Liquid Chromatography, 2nd ed., Wiley-Interscience,