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
 (14.6)
Values of G
0
R,S
, H
0
R,S
,andS
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

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 =

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

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
,andS
0
R,S
can be
derived and used to interpret the basis of enantioselectivity for a given system. By
this methodology of adsorption isotherm measurements at variable temperatures,
Guiochon and coworkers investigated, for example, the thermodynamics of
2,2,2-trifluoro-1-(9-anthryl)-ethanol (TFAE) [182] and 3-chloro-1-phenylpropanol
(3CPP) [181] on O−9-tert-butylcarbamoylquinidine-modified silica under
normal-phase conditions site-selectively.
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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