716 ENANTIOMER SEPARATIONS here R-orS-enantiomer); is the phase ratio (Section 2.3.1). Further manipulation of Equation (14.3) provides two additional relationships: ln K i =− 1 T · H ◦ i R + S ◦ i R (14.4) and G ◦ R,S = G ◦ R − G ◦ S =−R · T · ln K i,R K i,S =−R · T · ln α (14.5) That is, plots of ln K i against 1/T are predicted to be linear, with a slope that is proportional to H 0 i . Likewise the separation factor α for two enantiomers R and S can be related to the difference in their standard free energies of solute-selector association G 0 R,S , as well as related differences in enthalpy change H 0 R,S and entropy change S 0 R,S . 14.7.2 Thermodynamics of Direct Chromatographic Enantiomer Separation If a single type of (enantioselective) solute-selector interaction is solely considered and other adsorption mechanisms do not exist for the solute, K i in Equations (14.3) to (14.5) can be related to k and by k = K i (14.6) Values of G 0 R,S , H 0 R,S ,andS 0 R,S can be derived from values of α as a function of T, since the (usually unknown) phase ratio cancels in Equation (14.5) (but not in Eq. 14.4). Plots of ln k against 1/T are usually positive (k decreasing with T), implying a negative value of H 0 i or an enthalpically controlled retention pro- cess. That is, attractive (mostly electrostatic type) noncovalent interactions between solute and selector result in values of K i 1. The latter contributions to retention are usually opposed by entropic effects, since the solute-selector complex is more ordered compared with the solute in the mobile phase. That is, H ◦ > S ◦ and H ◦ > S ◦ , as observed for wide variety of different CSP-analyte mobile-phase systems. The usual result is a decrease in values of α for higher temperatures. The opposite behavior, an increase in enantioselectivity with T (called entropically con- trolled chiral recognition), has been observed in a few cases involving polysaccharide- and protein-type CSPs. The latter have been related to possible binding site-related (de)solvation phenomena [175] and/or conformational changes in backbones of the selector [176, 177]. Nonlinear plots of ln k against 1/T have also been observed occasionally [36]. Similar exceptions to a linear increase in ln k with 1/T have been observed for achiral separation as well (Section 2.3.2.2), possibly for similar reasons. Unusual temperature-induced behaviors of another kind have been observed for the separation of chiral dihydropyrimidinones on polysaccharide CSPs [178]. Plots of ln k against 1/T were obtained by (1) heating the column from 10 to 50 ◦ C and (2) cooling from 50 to 10 ◦ C; the resulting plots for an ethanol-solvated Chiralpak AD-H column were not superimposable. That is, the system exhibited significant hysteresis, which was not the result of conformational changes of the polysaccharide column but rather a slow equilibration of the stationary phase when T is changed. 14.7 THERMODYNAMIC CONSIDERATIONS 717 14.7.3 Site-Selective Thermodynamics The discussion above overlooks the fact that enantioselective retention does not necessarily involve a single retention site [179]. While this observation is true also for achiral retention, there is an important difference for enantiomeric separation. That is, other sites are likely to be non-enantioselective; the latter (referred to as type I in distinction to enantioselective type II sites [179]) might consist of the supporting matrix (e.g., silica), linker groups, spacer units, residues stemming from silanol end-capping, and even non-enantioselective binding sites that involve the selector. The presence of type-I sites is well known to compromise enantioselectivity. While the binding affinity of type-I sites is usually much lower than for type-II sites, the concentration of type-I sites may exceed that of type-II sites by orders of magnitude, especially for the case of macromolecular selectors such as proteins (Section 14.6.3). Consequently the contribution of type-I sites to overall retention is usually not negligible, and experimental retention data represent the sum of nonspecific (achiral) and specific (chiral) contributions to k: k R = k I,R + k II,R (14.7) and k S = k I,S + k II,S (14.7a) Values of k in Equations (14.7) and (14.7a) are for the injection of a small sample (nonoverloaded separation), and subscripts I and II refer to type-I and type-II sites, respectively; subscripts R and S refer to values for the R-andS-enantiomers, respectively. The experimental enantioselective separation factor is given by α = k R /k S (for k R > k S ), or α = k I,R + k II,R k I,S + k II,S (14.8) Retention at site I is the same for both enantiomers (i.e., it is non-enantioselective), so k I,R = k I,S = k I and α = k I + k II,R k I + k II,S (14.8a) If nonspecific retention is absent, k I = 0andα = k II,R /k II,S . We assume that the R-enantiomer is more retained so that k II,R /k II,S > 1. For k I > 0, the value of α in Equation (14.8a) decreases with increasing k I and approaches 1 (no enantioselectivity) for k I k II,R . It is obvious that a maximization of enantiomer selectivity can be achieved either by maximizing the selectivity of the enantioselective type-II sites (k II,R /k II,S ) or by minimizing the contribution to retention of the non-enantioselective type-I sites. When the goal is the interpretation of selector enantioselectivity (i.e., for type-II sites) as a function of the solute, selector, and experimental conditions, the intrinsic thermodynamic enantioselectivity (k II,R /k II,S ) is the appropriate quantity, 718 ENANTIOMER SEPARATIONS while the experimentally observed enantioselectivity (corresponding to α in Eq. 14.8a) can be misleading [179, 180]. From the preceding discussion it is clear that experimental values of α are only indirectly related to the various interactions that involve the solute and selector, as these values of α will reflect achiral as well as chiral interactions of solute with the stationary phase. The relative contributions of chiral and achiral sites to the observed enantioselectivity can be determined by fitting adsorption isotherm data for each enantiomers to a bi-Langmuir (two-site) model over a wide range in solute concentration. This procedure then provides values of k I,R , k II,R , k I,S , and k II,S for small samples (linear-isotherm values). If isotherms are acquired at different temperatures, values of H i can be obtained for each enantiomer at each site (I and II) [181, 182]. Values of G 0 R,S , H 0 R,S ,andS 0 R,S can be derived and used to interpret the basis of enantioselectivity for a given system. 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CHAPTER FIFTEEN PREPARATIVE SEPARATIONS with Geoff Cox 15.1 INTRODUCTION, 726 15.1.1 Column Overload and Its Consequences, 726 15.1.2 Separation Scale, 727 15.2 EQUIPMENT FOR PREP-LC SEPARATION, 730 15.2.1 Columns, 730 15.2.2 Sample Introduction, 731 15.2.3 Detectors, 733 15.2.4 Fraction Collection, 735 15.2.5 Product Recovery, 735 15.3 ISOCRATIC ELUTION, 737 15.3.1 Sample-Weight and Separation, 737 15.3.2 Touching-Peak Separation, 739 15.4 SEVERELY OVERLOADED SEPARATION, 748 15.4.1 Recovery versus Purity, 748 15.4.2 Method Development, 749 15.5 GRADIENT ELUTION, 751 15.5.1 Isocratic and Gradient Prep-LC Compared, 752 15.5.2 Method Development for Gradient Prep-LC, 753 15.6 PRODUCTION-SCALE SEPARATION, 754 Introduction to Modern Liquid Chromatography, Third Edition, by Lloyd R. Snyder, Joseph J. Kirkland, and John W. Dolan Copyright © 2010 John Wiley & Sons, Inc. 725 . Development for Gradient Prep-LC, 753 15.6 PRODUCTION-SCALE SEPARATION, 754 Introduction to Modern Liquid Chromatography, Third Edition, by Lloyd R. Snyder, Joseph J. Kirkland, and John W. Dolan Copyright. Approach to Chiral Separations by Liquid Chromatography, G. Subramanian, ed., VCH, Weinheim, 1994, p. 217. 77. T. Nakano, J. Chromatogr. A, 906 (2001) 205. 78. R. Cirilli, R. Costi, R. D. Santo, M Chromatogr. A, 906 (2001) 379. 62. P. Franco, A. Senso, L. Oliveros, and C. Minguill ´ on, J. Chromatogr. A, 906 (2001) 155. 63. T. Ikai, C. Yamamoto, M. Kamigaito, and Y. Okamoto, J. Chromatogr.