Introduction to Modern Liquid Chromatography, Third Edition part 76 doc

706 ENANTIOMER SEPARATIONS
14.6.6 Chiral Crown-Ether CSPs
Stereoselective CSP-analyte complexation with chiral crown-ether CSPs and their
first application as CSPs were pioneered by Cram and coworkers [127]. In this
early work, two 1,1

-binaphthyl units were incorporated into a crown ether as
replacement elements of two ethylene groups of the well-known 18-crown-6.
Structural analogues of such 1,1

-binaphthyl-derived chiral crown-ether based
CSPs were later developed by Shinbo’s group using (3,3

-diphenyl-1,1

-binaphthyl)-
or (6,6

-dioctyl-3,3

-diphenyl-1,1

-binaphthyl)-20-crown-6 dynamically coated onto
octadecyl-silica [128]; a related CSP has been commercialized as Crownpak CR
by Daicel and Chiral Technologies (Fig. 14.24a). Since they are of synthetic ori-
gin, both enantiomeric forms, with opposite elution orders, are available—denoted
as Crownpak CR(+) and CR(−). Structural analogues are available, based on
(18-crown-6)-2,3,11,12-tetracarboxylic acid (i.e., tartaric acid incorporated into
crown ether) that is bivalently immobilized via two carboxylic functionalities
onto 3-aminopropylated-silica [129]. These are commercially available as Chi-
roSil RCA(+)andSCA(−) (from Regis, Morton Grove, IL) and ChiralHyun-CR-1

(from K-MAC, Korea) (Fig. 14.24b).
The applications of such chiral crown-ether-based CSPs are essentially
restricted to primary amines comprising mainly amino acids, amino acid esters,
amino alcohols, and chiral drugs with free primary amino functionality. Typically
aqueous mobile phases with pH between 1 and 3.5 are required to ensure full
protonation of the solute. The resulting chiral ammonium ions can bind to the
macrocyclic crown by inclusion complexation, driven by triple hydrogen-bond
formation between the ammonium ion and the three oxygens of the crown
(Fig. 14.25). Enantioselectivity may be governed by steric factors arising from the
substituents of the chiral ammonium ions and the residues attached to the chiral
moieties that are incorporated into the 18(20)-crown-6. Maintaining strongly acidic
conditions appears also important to suppress silanol interactions that can be
formed non-enantioselectively. This can be achieved by employing, for example,
5 mM perchloric acid in water or methanol-water mixtures (up to 15% methanol)
Crownpak CR
ChiroSil RCA
ChiroSil
(a) (b)
Silica
silica
O
O
O
O
O
O
Si
O
O
O

O
O
O
COO
H
C
O
N
H
O
SiO
O
O
O
O
O
HOOC
silica
N
H
Figure 14.24 Commercially available chiral crown-ether based CSPs (adapted from online
application notes provided by the suppliers).
14.6 CHIRAL STATIONARY PHASES AND THEIR CHARACTERISTICS 707
Si
NH
O
O
O
O
O

O
O
O
H
H
COOH
H
N
+
R
O
O
O
Si
HN
O
O
O
HOOC
Figure 14.25 Molecular-recognition mechanism for chiral crown-ether CSPs: Schematic rep-
resentation of solute-selector interaction driven by triple hydrogen bonding (adapted from the
Regis webpage).
as mobile phase. Such harsh conditions can prove harmful for both the equipment
and CSP, which has contributed to the limited popularity of these CSPs. Newer
work on crown-ether-based CSPs can be found in [130–133].
14.6.7 Donor-Acceptor Phases
The first silica-bound CSPs with entirely synthetic selectors were developed in the
late 1970s [134, 135]. Subsequent work by Pirkle and coworkers led in 1981 to the
first commercialized CSP with a DNB-phenylglycine derivative immobilized ionicly
onto silica. Later this synthetic chiral selector was grafted onto silica via a covalent

amide linkage; this chiral packing material is still commercially available from Regis,
Machery Nagel, and Merck as DNBPG (Fig. 14.26a). Such donor-acceptor-type CSPs
(Brush-type CSPs) are based on chiral, low-molecular-weight selectors that are neu-
tral, synthetic or semi-synthetic, and used in the NP mode. They are capable of gener-
ating enantioselectivity based on complementary, non-ionic attractive binding forces
[27]. Hydrogen bonding, face-to-face or face-to-edge π–π interaction (between
electron-rich and electron-poor aromatic groups), and dipole–dipole stacking play
important roles in stabilizing the selector-analyte complex and enantiorecognition.
Enantioselectivity is often supported by steric interactions of bulky groups, which
can represent effective steric barriers to a close selector-solute contact for one enan-
tiomer. Due to the relative importance of hydrogen-bonding and other non-ionic
electrostatic interactions, such CSPs are less effective in polar protic media, including
the RP and PO modes. Because of the important contribution of Pirkle’s group in this
field, such donor-acceptor-type CSPs are now often referred to as Pirkle-type CSPs.
A number of powerful CSPs evolved early on from Pirkle’s group as a result
of systematic chromatographic [136] and spectroscopic [137–139] studies of chiral
recognition phenomena, as well as the consistent exploitation of the reciprocity
principle of chiral recognition [140, 141]. This reciprocity recognizes that the roles
708 ENANTIOMER SEPARATIONS
N
H
HN
O
Si
O
2
N
NO
2
O

H
3
C
H
3
C
H
3
C
H
3
C
CH
3
CH
3
DNBPG
NH
Si
O
NO
2
NO
2
WHELK-O 1
N
H
HN
O
O

O
2
N
NO
2
Si
ULMO
(a)
(b)
(c)
Figure 14.26 Structures of popular Pirkle-type donor-acceptor phases. (a)DNBPG;(b)
WHELK-O 1; (c)ULMO.
of selector and analyte are interchangeable. Hence a single enantiomer of an analyte
that is well resolved by a CSP with a given chiral selector will (after its immobilization
at positions that are not involved in the chiral recognition process) be able to separate
the racemate of this selector. Such concepts and tools have been used for the rational
design of new advanced CSPs [136, 142].
As noted above, such donor-acceptor-type CSPs usually have been designed
to exploit π–π-stacking interactions between electron-rich and electron-deficient
aromatic systems as the primary attractions. Initially developed were either
CSPs with π-acidic groups (with electron-deficient aromatic moieties, usually
3,5-dinitrobenzoyl) for π-basic solutes (with electron-rich aromatic groups) or
CSPs with π-basic residues (e.g., naphthalene) for π-acidic solutes. The latter
CSPs (e.g., N-2-naphthylalanine undecylester-derived CSP) [143] seemed to have
less broad application and therefore disappeared form the market. Several of the
early-invented π-electron acceptor phases from the Pirkle group, in contrast, are
still available from Regis (e.g., DNBLeu, DNBPG, β-Gem 1, α-Burke 2, PIRKLE
1-J; see Table 14.3).
Eventually CSPs with both π-electron donor and acceptor moieties
incorporated into a single selector turned out to be more powerful in terms of

broader applicability. Along this line, the Whelk-O 1 phase was developed that has
pre-organized clefts for solute insertion and allows for simultaneous face-to-face
14.6 CHIRAL STATIONARY PHASES AND THEIR CHARACTERISTICS 709
Table
14.3
Commercially Available Donor-Acceptor (Pirkle-Type) CSPs
Chiral Selector Column Trade Name Supplier
π-electron acceptor/π-electron donor phases
3-[1-(3,5-dinitro
benzamido)-1,2,3,4-
tetrahydrophenanthrene-
2-yl]-propyl-silica
Whelk-O 1 Regis
11-[2-(3,5-dinitroben-
zamido)-1,2-
diphenylethylamino]-
11-oxoundecyl-silica
ULMO Regis
3-[N-(3,5-dinitrobenzoyl)-
(R) − 1-naphthyl-
glycine-amido]propyl-silica
Chirex 3005
(Sumichiral 2500)
Phenomenex
(Sumitomo)
π-electron acceptor phases
3-{3-{N-[2-(3,5-
dinitrobenzamido-1-cyclohexyl)]-
3,5-dinitrobenzamido}-
2-hydroxy-propoxy}-

propyl-silica
DACH-DNB Regis
3-[3-(3,5-dinitrobenzamido)-
2-oxo-4-phenyl-
azetidine-1-yl]-
propyl-silica
PIRKLE 1-J Regis
5-(3,5-dinitrobenzamido)-
4,4-dimethyl-5-dimethyl
phosphonyl-pentanyl-silica
α-Burke 2 Regis
11-[N-(3,5-dinitrobenzoyl)-3-
amino-3-phenyl-2-
(1,1-dimethylethyl)
propanoyl]-
undecyl-silica
β-Gem 1 Regis
3-[N-(3,5-dinitrobenzoyl)
leucine-amido]propyl-silica
Leucine (DNBLeu) Regis
3-[N-(3,5-dinitrobenzoyl)
phenylglycine-amido]
propyl-silica
Phenylglycine
(DNBPG)
Regis (Merck)
π-electron donor phases
3-{N-[(R)-(α-naphthyl)
ethylcarbamoyl]-(S)-
indoline-2-carboxamido}

propyl-silica (urea
linkage)
Chirex 3022
(Sumichiral OA
4900)
Phenomenex
(Sumitomo)
3-{N-[(R)-1-(α
-
naphthyl)
ethylcarbamoyl]-
(S)-tert-leucine-amido}
propyl-silica (urea
linkage)
Chirex 3020
(Sumichiral OA
4700)
Phenomenex
(Sumitomo)
710 ENANTIOMER SEPARATIONS
and face-to-edge π–π-interactions to facilitate chiral recognition [144, 145]
(Fig. 14.26b). Inspired by the work of Pirkle, several other research groups
followed this concept of CSPs based on synthetic, low-molecular-weight selectors.
Among others, Oi and coworkers developed amide-type and urea-type CSPs, now
commercialized as Sumichiral OA columns from Sumitomo or as Chirex columns
from Phenomenex. A number of structural variants have been made accessible; the
one denoted as Chirex 3005 (amide-type π-electron donor-acceptor phase) (see
Table 14.3) appears to have the broadest applicability, followed by the Chirex
3022 and to minor degree Chirex 3020 [urea-type π-electron donor-phases derived
from (S)-indoline-2-carboxylic acid and (R)-1-[α-naphthyl]ethylamine as well as

(S)-tert-leucine and (R)-1-[α-naphthyl]ethylamine, respectively] (Table 14.3).
Other powerful π-donor-acceptor-type CSPs utilized C
2
-symmetric
diamine scaffolds such as bis-N , N

-(3,5-dinitrobenzoyl)-1,2-diamino cyclo-
hexane from Gasparrini’s group [146, 147] (DNB-DACH
®
,Regis)and
N-3,5-dinitrobenzoyl-N

-undecanyl-1,2-diphenyl-1,2-diamine from Uray et al.
(ULMO
®
, Regis; Fig. 14.26c) [148]. The latter CSP allows, for instance,
the chromatographic separation of underivatized arylcarbinols as depicted in
Figure 14.27. The evolution of CSPs in the Pirkle laboratory, as well as some
design considerations and strategies that have lead to the modern donor-acceptor
phases, have been comprehensively reviewed by Welch [142]. More recently
some of the newer developments in this field were summarized and discussed by
Gasparrini [149].
Since donor-acceptor phases are almost always used in the NP mode, method
development is straightforward. It usually starts with a mixture of hexane or
heptane/2-propanol (1–10% polar solvent). For basic solutes, 0.1% of a basic
modifier such as diethylamine is added to the mobile phase; for acidic solutes,
0.1% of an acidic additive such as trifluoroacetic acid. After an initial separation,
the polar-solvent content is adjusted to achieve a reasonable retention factor (1<
k< 10). If no baseline separation results, 2-propanol can be substituted by other
polar solvents such as ethanol, dichloromethane, dioxane, methyl tert-butyl ether,

R
S
S
R
S
R
S
R
0 5 10 15
(
min
)
t
0
OH
OH
OH
OH
Figure 14.27 Separation of chiral alcohols on ULMO. Conditions: (R, R)-ULMO;
250 × 4-mm column; 99.5:0.5 n-heptane-isopropanol; 1 mL/min; 254 nm; 25
◦
C. Reprinted
with permission from [148].
14.6 CHIRAL STATIONARY PHASES AND THEIR CHARACTERISTICS 711
or ethyl acetate. If RP conditions are required, enantioselectivity values usually
drop significantly, since the retention- and selectivity-driving polar interactions are
effectively nullified (or at least extremely weakened) by such strong, protic solvents.
It should be noted that Regis offers a screening service for the Pirkle phases.
A number of characteristic benefits arise from the use of Pirkle-type CSPs. Since
the building blocks of the selectors are available in both enantiomeric forms, CSPs

can be developed in both configurations, allowing an opposite elution order for enan-
tiomers (Section 14.3). The low molecular weight of these selectors, with their limited
molecular dimensions, yields high surface concentrations of the CSP. As a result
the sample loading capacities are much higher than for protein phases, macrocylic
antibiotic CSPs, and cyclodextrin-based CSPs [61]. Synthetic donor-acceptor phases
have also proved to be valuable tools for SFC enantiomer separation [150, 151].
14.6.8 Chiral Ion-Exchangers
Chiral ion-exchangers utilize ionizable selectors to exploit ionic interactions between
oppositely charged selectors and analytes. Although a number of these CSPs are
based on large molecules (e.g., protein CSPs, glycopeptide CSPs), we refer here to
low-molecular-weight selectors that are similar to classical ion-exchangers yet have
a chiral backbone. These CSPs can also be regarded as a subset of Pirkle phases,
but carrying ionizable functional groups—thereby departing from the non-ionic
interaction mode of the Pirkle-type CSPs. Several chiral ion-exchangers have been
developed for the enantiomer separation of ionizable chiral compounds: chiral
anion-exchangers based on cinchona alkaloid derivatives for chiral acids [152],
chiral cation exchangers based on chiral amino sulfonic acids, and amino carboxylic
acids for the separation of chiral bases [153], and zwitterionic ion-exchangers for
the separation of both acids, bases, and zwitterionic solutes such as amino acids
and peptides [154]. Only the chiral anion-exchangers with cinchonan carbamate
selectors were commercially available at the time this book was published (under the
tradename Chiralpak QN-AX and Chiralpak QD-AX; from Chiral Technologies)
(Fig. 14.28a). The abbreviation AX refers to their anion-exchanger characteristics,
while QN and QD denote the type of cinchona alkaloid employed as backbone of
the selectors—quinine (QN) and quinidine (QD).
The selectors of these columns are highly enantioselective, as a result of
five stereogenic centers. While configurations in position N
1
,C
3

,C
4
are fixed as
1S,3R,4S, those of carbon C
8
and C
9
are opposite in quinine (8S,9R) and quini-
dine (8R,9S) as well as separation materials derived therefrom. The experimental
behavior of these cinchona-alkaloid derived CSPs is often under the stereocontrol
of the stereogenic center of C
9
; this gives them pseudoenantiomeric characteristics
as a result of an opposite configuration of the two alkaloids at this chiral center.
Aside from this peculiar configurational arrangement of the natural alkaloids, the
exceptional enantiorecognition capability of the cinchonan carbamate-based chiral
stationary phases arises also from several features: the bulky quinuclidine, the planar
quinoline ring, and the semi-flexible carbamate group with a bulky t-butyl residue.
These functionalities serve as potential binding sites, and they are structurally
assembled to form a semi-rigid scaffold with predefined binding clefts for analyte
insertion.
Much is known about the principal molecular recognition mechanisms of
these semi-synthetic CSPs from various chromatographic [156–158], FTIR and
712 ENANTIOMER SEPARATIONS
N
O
O
N
SH
H

N
O
silica
CH
3
H
9
8
1S
4S
3R
H
X
CHIRALPAK
®
CHIRALPAK
®
min0 4 8 12
(R)
(S)
min0 4 8 12
(S)
(R)
CH
3
N
COOH
O
H
CHIRALPAK

®
QD-AX
Quinidine-derived
CHIRALPAK
®
QN-AX
Quinine-derived
(a) (b)
QN-AX: (8S,9R)
QD-AX: (8R,9S)
Figure 14.28 Commercially available cinchona alkaloid-derived chiral anion-exchangers. (a)
Structure; (b) illustration of a reversal of elution order by change from the quinine-derived CSP
to the corresponding pseudoquinidine-derived CSP. Experimental conditions: Column dimen-
sion, 150 × 4-mm column; mobile phase, 1% acetic acid in methanol; temperature, 25
◦
C; flow
rate, 1 mL/min; UV detection at 230 nm. Adapted from [155].
NMR spectroscopic [159–163], thermodynamic [163, 164], molecular model-
ing [161, 163], and X-ray diffraction studies [161–163,165]. If complementary
H-donor-acceptor sites and aromatic moieties are incorporated into the guest
molecule, favorable intermolecular H-bonding and π–π-interactions may result
in stable complexes and exceptionally high enantioselectivities. Targeted optimiza-
tion based on knowledge from the mechanistic studies mentioned above has led to a
number of powerful CSPs [166], of which the commercially available ones provide
broad applicability.
The cinchona alkaloid-based, anion-exchange columns offer excellent chi-
ral resolving power for chiral carboxylic, sulfonic, phosphonic, and phosphoric
acids [166], preferably by way of the PO or RP mode. Their applicability covers
N-derivatized α-, β-, and γ -amino acids (Fig. 14.28b), their corresponding phospho-
nic, phosphinic, and sulfonic acid analogues, as well as many other pharmaceutically

relevant chiral acids (e.g., arylcarboxylic acids, aryloxycarboxylic acids, hydroxy
acids, pyrethroic acids, and a few underivatized amino acids).
If the cinchona-alkaloid based CSP is used with (weakly) acidic mobile phases,
the quinuclidine nitrogen becomes protonated and acts as the fixed charge of
the chiral anion-exchanger. Acidic analytes are then primarily retained by anion
exchange, and retention can be explained by a stoichiometric displacement model
[166]. Linear plots of log k versus the log of the counter-ion concentration [Z]
(i.e., of the buffer anion) then result (Section 7.5.1 and Eq. 7.13). As discussed
in Chapter 7, the slope of log k–log counter-ion concentration will, for a given
14.6 CHIRAL STATIONARY PHASES AND THEIR CHARACTERISTICS 713
column, vary with the charge on the analyte and the counter-ion, being steeper for
a larger analyte charge and less steep for a larger counter-ion charge. A change in
counter-ion concentration can be used to vary retention, often without much effect
on enantioselectivity. The eluotropic strength (competitor effectiveness) increases in
the order acetate ≤ formate < phosphate < citrate. A series of counter-ions (acid
additives) in the PO mode have been tested confirming these trends for nonaqueous
polar solvent-based mobile phases as well [167]. Other variables have a significant
effect on enantioselectivity and allow for flexible method development: pH (RP
mode), acid-base ratio (PO mode), and type and content of organic solvent(s) (RP
and PO modes).
Preferred mobile phases are composed of methanol plus 0.5–2% glacial acetic
acid, as well as 0.1–0.5% ammonium acetate (PO-mode), or methanol-ammonium
acetate buffer (total buffer concentration in the mobile phase between 10 and
100 mM, pH 5–6) (RP mode). Methanol may be replaced by acetonitrile or
methanol-acetonitrile mixtures, which are to some extent complementary (dif-
ferent enantioselectivities and elution orders) regarding their enantiorecognition
capabilities.
As noted above, quinine and quinidine CSPs are actually diastereomers, but
they behave like enantiomers. Therefore they usually (but not always) show opposite
elution orders, as illustrated in Figure 14.28b. This complementarity in their chiral

recognition profile can be systematically exploited in enantiomeric impurity-profiling
applications and preparative enantiomer separations—since it is desirable to have
the enantiomeric impurity elute first (Section 14.5). Cinchona carbamate-type CSPs
also show great promise for preparative enantiomer separations, by virtue of their
remarkable sample loadabilities. For example, adsorption isotherm measurements
for FMOC-α-allylglycine on the O−9-tert-butylcarbamoylquinidine-CSP revealed
a close to homogeneous adsorption mechanism with mass loading capacities of
20 mg/g CSP [168]. Although the primary application of these cinchonan carbamate
CSPs are for chiral acids, recent studies showed that they can be used for neutral
and basic compounds as well, via either RP [169] or NP mobile phases [170].
14.6.9 Chiral Ligand-Exchange CSPs (CLEC)
Chiral ligand-exchange CSPs allowed the first complete separation of a racemate by
chromatography in the late 1960s. Davankov immobilized proline onto a polystyrene
support and used this enantioselective matrix in combination with Cu(II)-ion con-
taining mobile phases for the enantiomer separation of amino acids [171]. The basic
principle of chiral ligand-exchange chromatography (CLEC) is the reversible coor-
dination of immobilized selectors and analytes within the metal-ion coordination
sphere that forms a mixed ternary metal-ion/selector/analyte complex (Fig. 14.29)
[172]. Depending on the steric and functional properties of the analytes, these
diastereomeric complexes result in enantioselectivity. During the chromatographic
process the coordinated ligands are reversibly replaced by other ligands from the
mobile phase such as ammonia and water. An important aspect of these separations
is that the exchange of ligands at the metal center is fast; otherwise, column efficiency
would be compromised.
An essential prerequisite for CLEC is the presence of metal-chelating function-
alities in both the selector and analyte [172]. Suitable structures feature bidentate
714 ENANTIOMER SEPARATIONS
N
X
O

Cu
N
(S)
(S)
O
O
H
2
O
O
(S)
(R)
N
X
O
Cu
N
O
O
H
2
O
O
Pol
y
st
y
rene-su
pp
ort Pol

y
st
y
rene-su
pp
ort
(S, S)(R, S)(a)(b)
Figure 14.29 Principle of chiral ligand-exchange chromatography. Ternary diastereomeric
Cu(II)-complexes of immobilized S-enantiomer of proline (X = H) (or hydroxyproline
X = OH) ligand with S-andR -proline analytes, (a)and(b), respectively. Adapted from [173].
OH
O
OH
OH
O
OH
H
3
C
OH
O
OH
H
3
C
OH
O
OH
H
3

C
CH
3
H
3
C
Time
(
min
)
02040
Figure 14.30 Enantiomer separation of hydroxy acids by chiral ligand-exchange chromatog-
raphy (CLEC). Experimental conditions: column, CHIRALPAK MA; mobile phase, 10%
ACN/H
2
Oplus2-mMCuSO
4
. Adapted from [8].
or tridentate ligands with two or three electron-donating functional groups, such
as hydroxyl, amino, and carboxylic functionalities. Such structural prerequisites are
typically found in α-amino acids, amino alcohols, and α-hydroxy acids (Fig. 14.30),
representative compounds that have been separated by CLEC. Cu(II) is the preferred
chelating metal ion, but Zn(II) and Ni(II) are suitable alternatives. As selectors for
14.7 THERMODYNAMIC CONSIDERATIONS 715
CLEC-type CSPs, rigid cyclic amino acids, such as proline and hydroxyproline, have
been shown to give the best results in combination with Cu(II). These chelating selec-
tors are either (1) covalently anchored onto the surface of silica and organic polymer
particles, respectively, or (2) dynamically coated onto reversed-phase materials (usu-
ally immobilized adsorptively by hydrophobic interactions based on the long alkyl
chain substituents of the selectors; only a low %-organic in the mobile phase is

tolerated). Because of the polar nature of the analytes for separation by CLEC, as
discussed above, the mobile phase is aqueous or aqueous based. The mobile phase
is usually doped with small quantities of metal ion, in order to compensate for loss
of metal from the column packing during chromatography, thereby rendering the
separation more stable.
The detection of nonchromophoric amino acids and hydroxy acids is possible
as a result of their enhanced UV absorbance in the presence of Cu
++
, while the
presence of metal ions in the mobile phase may hamper mass spectrometric detection.
Experimental conditions that can be varied in method development include mobile
phase pH, type and concentration of buffer salts, nature and content of organic
solvent, temperature, and the mobile-phase metal-ion concentration.
A number of covalently anchored and coated CSPs for CLEC are commercially
available, including Chiralpak MA+ (based on N, N-dioctyl-
L-alanine coated onto
RP18) from Chiral Technologies, Nucleosil Chiral-1 (based on
L-hydroxyproline
chemically bonded to silica) from Macherey-Nagel, and Chirex 3126 (based on
N, S-dioctyl-penicillamine coated onto RP18) from Phenomenex. In the past, CLEC
was the only procedure that enabled the direct enantiomer separation of amino acids
without derivatization. However, today the importance of chiral ligand-exchange
chromatography is reduced, as a result of more favorable alternatives. More details
can be found in a recent review [174].
14.7 THERMODYNAMIC CONSIDERATIONS
Analyte retention and enantioselectivity are, of course, based on the thermodynamics
of the retention process—similar to the separation of achiral solutes, as discussed in
preceding chapters. However, enantiomer separations are subject to some additional
thermodynamic considerations.
14.7.1 Thermodynamics of Solute-Selector Association

The equilibrium constant K
i
(see Fig. 14.9) of the solute-selector association can be
related to thermodynamic parameters
G
0
i
=−RT ln K
i
= H
0
i
− TS
i
0
(14.3)
Here G
0
i
, H
0
i
, and S
0
i
refer to the standard free energy, enthalpy, and entropy
changes upon the solute-selector complexation, R is the universal gas constant, T the
absolute temperature (in K), and subscript i denotes the corresponding species (i.e.,