Thermodynamic and nuclear magnetic resonance study of the reactions of α- and β-cyclodextrin with acids, aliphatic amines, and cyclic alcohols

Article abstract of DOI:10.1021/jp962715n

Titration calorimetry was used to determine equilibrium constants and standard molar enthalpy, Gibbs energy, and entropy changes for the reactions of a series of acids, amines, and cyclic alcohols with α- and β-cyclodextrin. The results have been examined in terms of structural features in the ligands such as the number of alkyl groups, the charge number, the presence of a double bond, branching, and the presence of methyl and methoxy groups. The values of thermodynamic quantities, in particular the standard molar Gibbs energy, correlate well with the structural features in the ligands. These structural correlations can be used for the estimation of thermodynamic quantities for related reactions. Enthalpy-entropy compensation is evident when the individual classes of substances studied herein are considered, but does not hold when these various classes of ligands are considered collectively. The NMR results indicate that the mode of accommodation of the acids and amines in the α-cyclodextrin cavity is very similar, but that the 1-methyl groups in 1-methylhexylamine and in 1-methylheptylamine and the N-methyl group in N-methylhexylamine lie outside the α-cyclodextrin cavity. This latter finding is consistent with the calorimetric results. Many of the thermodynamic and NMR results can be qualitatively understood in terms of van der Waals forces and hydrophobic effects.

Full text of DOI:10.1021/jp962715n

J. Phys. Chem. B 1997, 101, 87-100
87
Thermodynamic and Nuclear Magnetic Resonance Study of the Reactions of r- and
â-Cyclodextrin with Acids, Aliphatic Amines, and Cyclic Alcohols
†
Mikhail V. Rekharsky, Martin P. Mayhew, and Robert N. Goldberg*
Biotechnology DiVision, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Philip D. Ross
Laboratory of Molecular Biology, National Institutes of Health, Bethesda, Maryland 20892
Yuko Yamashoji and Yoshihisa Inoue
Department of Molecular Chemistry, Faculty of Engineering, Osaka UniVersity,
2
-1 Yamadaoka, Suita 565, Japan
X
ReceiVed: August 30, 1996; In Final Form: October 18, 1996
Titration calorimetry was used to determine equilibrium constants and standard molar enthalpy, Gibbs energy,
and entropy changes for the reactions of a series of acids, amines, and cyclic alcohols with R- and
â-cyclodextrin. The results have been examined in terms of structural features in the ligands such as the
number of alkyl groups, the charge number, the presence of a double bond, branching, and the presence of
methyl and methoxy groups. The values of thermodynamic quantities, in particular the standard molar Gibbs
energy, correlate well with the structural features in the ligands. These structural correlations can be used
for the estimation of thermodynamic quantities for related reactions. Enthalpy-entropy compensation is
evident when the individual classes of substances studied herein are considered, but does not hold when
these various classes of ligands are considered collectively. The NMR results indicate that the mode of
accommodation of the acids and amines in the R-cyclodextrin cavity is very similar, but that the 1-methyl
groups in 1-methylhexylamine and in 1-methylheptylamine and the N-methyl group in N-methylhexylamine
lie outside the R-cyclodextrin cavity. This latter finding is consistent with the calorimetric results. Many of
the thermodynamic and NMR results can be qualitatively understood in terms of van der Waals forces and
hydrophobic effects.
1. Introduction
reactions of a series of acids, aliphatic amines, and cyclic
alcohols (Figure 1) with R- and â-cyclodextrin. The results
obtained in this study together with some results from the
literature have been examined to obtain information about the
variation of thermodynamic quantities with structural features
in the ligand such as the number of alkyl groups, the charge
number, the presence of a double bond, branching, and the
addition of methyl and methoxy groups. This information can
be useful both for understanding the chemistry in these reactions
and for estimating thermodynamic quantities.
Reactions involving cyclodextrins are of importance to the
technology of drug delivery systems, separations, and foods.
1-6
These reactions also serve as excellent models for understanding
the basis of inclusion chemistry and as models of (enzyme +
substrate) interactions.7 The principal factors involved in the
binding are believed to be primarily van der Waals forces and
hydrophobic effects. Hydrogen bonding and steric effects can
also play a role. In the absence of a general model capable of
separating these effects, a practical approach toward understand-
ing these reactions is to perform thermodynamic studies in which
the chemical nature of the ligand is changed in a systematic
way. The trends in the results can then be examined and
correlated with structural features in the ligands. Such informa-
tion can provide a basis for the estimation of thermodynamic
quantities and could also prove useful for the validation and
calibration of computational models. Several classes of sub-
stances which react with cyclodextrins have been the subject
of systematic thermodynamic studies. These include hydro-
In contrast to comprehensive NMR studies on molecular
2,7
inclusion of aromatic compounds with cyclodextrins, the
complexation behavior of aliphatic ligands, such as acyclic
alcohols, amines, and carboxylic acids, has not been investigated
in detail by NMR. This is probably due to the fact that the
chemical shift changes found for complexation reactions involv-
ing aliphatic substances are much less than those for reactions
involving aromatic substances where a ring current exists. The
only related NMR investigations appear to be those of Casu et
8
,9
10-15
13,16
carbons,
nols,
aliphatic alcohols,
aliphatic-diols,
phe-
25
26
25
al. and Watanabe et al. Casu et al. used 300 MHz NMR
to study the complexation behavior of some alkyl glycosides
1
7,18
19
cyclohexane derivatives, naphthalene derivatives and
2
0-23
other aromatic compounds,
and phenethylamine and its
25
with R-cyclodextrin. They observed appreciable downfield
derivatives.24
shifts of the guest protons, but, due to the severe interference
of signals from the glycoside, they could only measure the
induced shifts of the R-cyclodextrin’s H1 and H2 protons.
In this study, we have used titration calorimetry to measure
equilibrium constants and standard molar enthalpies for the
†
26
Current address: Institute of Biomedical Chemistry, Russian Academy
Watanabe et al. studied the complexation behavior of R,ω-
of Medical Sciences, Pogodinskaya St., 10, Moscow 119832, Russia.
alkanedicarboxylates (7-12 methylene groups) with R-cyclo-
dextrin at pD ) 8 and pD ) 13. Due to the ionization of two
of the R-cyclodextrin’s hydroxyl groups at pD ) 13, the
*
Corresponding author. E-mail: goldber@tiber.nist.gov. Fax: +1-
3
01-330-3447.
X
Abstract published in AdVance ACS Abstracts, December 15, 1996.
S1089-5647(96)02715-0 CCC: $14.00 © 1997 American Chemical Society

88
J. Phys. Chem. B, Vol. 101, No. 1, 1997
Rekharsky et al.
Figure 1. Structures of the ligands used in this study. Atom-numbering schemes are shown for 1-methylheptylamine and for â-cyclodextrin.
exchange rate of the R,ω-alkanedicarboxylates is significantly
decreased by the electrostatic repulsion between the R-cyclo-
dextrin’s ionized hydroxyl groups and the acid’s carboxylate
groups. Thus, the protons of the free and complexed ligands
yield independent signals at different positions. Watanabe et
The NMR results obtained in this study provide additional
information on these complexation reactions and complement
the calorimetric findings.
2
. Experimental Section
26
al. also used NOESY to demonstrate through-ring inclusion
of the R,ω-alkanedicarboxylates. They also found that originally
equivalent methylene groups in the R,ω-alkanedicarboxylates
The principal substances used in this study, their respective
Chemical Abstracts Services registry numbers, empirical for-
mulas, molecular weights, mass fraction moisture contents, and
mole fraction purities are given in Table S1 contained in the
Supporting Information for this paper. In most cases, the mole
fraction purities of these substances are >0.99 and in all cases
are >0.95. The substances were used without further purifica-
tion. The characterization of the R- and â-cyclodextrin has been
(i.e. methylene groups located at the same distance from the
terminal carboxylate groups) appear at different positions
following through-ring inclusion. This is attributable to the fact
that the R-cyclodextrin cavity is asymmetric. However, their
study26 did not contain any additional information on the other
protons in the R-cyclodextrin upon complexation with the R,ω-
dicarboxylates of varying chain length. Thus, it seemed
desirable to use NMR to study the inclusion of some representa-
tive simple acids and amines, a fundamental host-guest system.
1
9
described previously. Moisture contents of the samples, as
determined by Karl Fischer analysis, were used in the calcula-
tions of the molalities of the substances in solution. Corrections
to these molalities were also made for the mole fractions of the

Reactions of R- and â-Cyclodextrin
J. Phys. Chem. B, Vol. 101, No. 1, 1997 89
H°, Standard Molar Gibbs Energies ∆ G°, and Standard
TABLE 1: Equilibrium Constants K, Standard Molar Enthalpies ∆
r
r
a
Molar Entropies ∆
r
S° for the Reaction r-Cyclodextrin(aq) + Ligand(aq) ) r-Cyclodextrin‚Ligand(aq) at T ) 298.15 K
ligand
m (mol kg-1)
N
K
∆
r
H° (kJ mol-1
)
∆
r
G° (kJ mol-1
)
∆
r
S° (J K-1 mol-1
)
acetate-
propanoate
0.48
2
2
2
2
2
2
2
1
1
2
1
2
2
2
2
2
6
2
2
2
2
2
2
2
2
2
b
-
0.224
0.295
0.148
0.275
0.148
0.155
0.126
0.122
0.090
0.102
0.043
0.313
0.280
0.311
0.111
0.084-0.190
0.178
0.095
0.200
0.066
0.050
0.227
0.209
0.044
0.012-0.024
b
-
c
2
-methylpropanoate
∼7
∼-3
-
butanoate
12.5 ( 1.5
23.5 ( 1.0
79.9 ( 1.1
300 ( 4
-10.6 ( 1.0
-12.5 ( 0.4
-6.3 ( 0.3
-7.83 ( 0.11
-14.4 ( 1.1
-15.7 ( 0.4
-2.2 ( 0.2
-0.3 ( 0.2
-10.9 ( 1.7
-4.9 ( 1.4
-2.8 ( 2.4
-12.4 ( 0.2
-3.8 ( 0.3
-8.4 ( 0.5
-12.4 ( 1.8
-12.8 ( 0.6
-7.9 ( 0.2
-9.3 ( 0.2
-9.6 ( 2.2
-7.3 ( 0.2
-9.5 ( 0.2
-8.0 ( 0.2
-12.0 ( 0.3
-10.2 ( 0.4
-8.6 ( 0.3
-6.7 ( 2.0
32 ( 10
-
(
()-2-methylbutanoate
-
pentanoate
-11.51 ( 0.12
-14.24 ( 0.14
-17.24 ( 0.50
-14.07 ( 0.40
-17.54 ( 0.72
-18.74 ( 0.19
-20.46 ( 0.27
-9.1 ( 0.4
-10.86 ( 0.04
-14.14 ( 0.04
-13.99 ( 0.08
-12.60 ( 0.08
-16.70 ( 0.11
-15.05 ( 0.03
-19.34 ( 0.14
-6.59 ( 0.16
-7.05 ( 0.15
-7.38 ( 0.17
-11.38 ( 0.03
-14.78 ( 0.03
-14.71 ( 0.10
-17.31 ( 0.03
-15.08 ( 0.03
-17.43 ( 0.03
-19.27 ( 0.06
-8.46 ( 0.13
-8.91 ( 0.13
-10.5 ( 0.5
-
hexanoate
trans-2-hexenoate
trans-3-hexenoate
-
-
282 ( 9
161 ( 5
-
heptanoate
843 ( 35
433 ( 5
-
6
-heptenoate
-
octanoate
-butylamine
N-methylbutylamine
2449 ( 130
14.3 ( 0.9
17.2 ( 1.0
19.6 ( 1.3
98.7 ( 1.0
389 ( 4
+
1
+
-10.74 ( 0.53
-11.2 ( 0.6
+
1
1
1
-methylbutylamine
-pentylamine
-hexylamine
+
-13.74 ( 0.14
-17.54 ( 0.18
-17.56 ( 0.66
-19.50 ( 0.20
-17.92 ( 0.18
-19.82 ( 0.20
-22.85 ( 0.23
-11.5 ( 0.4
+
+
N-methylhexylamine
378 ( 14
1080 ( 11
439 ( 5
+
1
1
1
1
-heptylamine
-methylhexylamine
-methylheptylamine
+
+
1130 ( 12
2376 ( 53
30.3 ( 1.5
36.4 ( 1.0
68 ( 12
+
-octylamine
0
cyclobutanol
cyclopentanol
cycloheptanol
0
0
-11.47 ( 0.19
-12.5 ( 1.9
-3.9 ( 2.7
0
cyclooctanol
235 ( 230
-13.5 ( 9.5
a
, 0.025 mol kg-1) + (Na , 0.025 mol kg-1), pH ) 6.90} was used for all reactions. The charge numbers of
Phosphate buffer {(NaH
2
PO
4
HPO
2 4
the ligands are those of the predominant species at pH ) 6.90. The molality m of the ligand for which the measurements were performed and N
the number of sets of titration experiments performed are given in columns 2 and 3, respectively. The molality of the R-cyclodextrin was in the
range 0.0008-0.0038 mol kg . The basis of the uncertainties is discussed in the text. b K and/or ∆
-1
r
H° for this reaction were too small to measure
c
with the titration calorimeter. Values designated as being approximate are uncertain by amounts that are comparable to the reported values.
impurities in the R- and â-cyclodextrin. All thermal titrations
with a charged ligand since the reaction is charge symmetric
and the activity coefficients in the numerator and denominator
of eq 2 should largely cancel at low and moderate ionic
strengths.
were performed with the OMEGA reaction cell of a MicroCal
2
7,28
MC-2 calorimeter.
The calorimetric procedures have been
described previously.1
9,29
Proton NMR spectra were measured at T ) 298 ( 1 K with
Calculations were also performed in which the cyclodextrin‚
a 600 MHz Bruker AM-600 instrument; D2O solutions buffered
(
1
ligand)2 complex was also assumed present in addition to the
-
3
at pD ) 7.0 with {D3PO4 (0.10 mol dm ) + NaOD} were
used for all experiments. All chemical shifts δ were relative
to the DOH signal at 4.75 ppm. The concentration of R-cy-
:1 complex. It was found that the additional parameters
obtained from these calculations had uncertainties that were
comparable to the parameters themselves and that the quality
of the overall fit was not improved. Also, the fits to the titration
curves with the 1:1 model showed no systematic deviations.
Thus, the use of the 1:1 complexation model and a single
binding site is justified and the data do not warrant more
complicated models. It was also found that the values of the
standard molar enthalpies of reaction ∆rH° and equilibrium
constants K obtained from the titration curves were not
significantly affected by the random deletion of up to ap-
proximately one-third of the data points in the titration curves.
This gives us additional confidence in the values of the
equilibrium constants and the standard molar enthalpies of
reaction.
-
3
clodextrin was fixed at 0.0050 mol dm for all experiments,
and an approximately equimolar amount of ligand was added
to the cyclodextrin solution. The ratio of the concentration of
the ligand to the concentration of the R-cyclodextrin in solution
was determined from the relative intensities of the signals of
the protons in the R-cyclodextrin and in the ligands.
3
. Results
.1. Calorimetry. The treatment of the data obtained with
3
1
9
the titration calorimeter has been described previously. All
equilibrium constants and standard molar enthalpies of reaction
reported in this paper are based on a 1:1 complexation model:
Thermodynamic quantities for the reactions of the various
ligands used in this study with R- and â-cyclodextrin in aqueous
phosphate buffer are presented in Tables 1 and 2, respectively.
The standard molar Gibbs energies of reaction and standard
molar entropies of reaction given in Tables 1 and 2 were
calculated from the measured equilibrium constants and standard
molar enthalpies of reaction. The results and uncertainties for
the equilibrium constants and standard molar enthalpies of
reaction in Tables 1 and 2 were obtained as weighted averages
of the results of the titration experiments done for each (ligand
+ cyclodextrin) pair. These uncertainties refer to two estimated
standard deviations of the mean. However, in some cases (see
below), these uncertainties were increased to allow either for a
cyclodextrin(aq) + ligand(aq) ) cyclodextrin‚ligand(aq)
(1)
The equilibrium constant for this reaction is
K ) a(cyclodextrin‚ligand)/{a(cyclodextrin)a(ligand)} (2)
where a is the activity of the indicated substance. The standard
state used for the solute is the hypothetical ideal solution of
-
1
unit molality (m° ) 1 mol kg ). Nonideality corrections are
assumed to be negligible for both the measured equilibrium
constants and the standard molar enthalpies of the reaction. This
approximation should hold reasonably well even when dealing

90
J. Phys. Chem. B, Vol. 101, No. 1, 1997
Rekharsky et al.
TABLE 2: Equilibrium Constants K, Standard Molar Enthalpies ∆
r
H°, Standard Molar Gibbs Energies ∆
r
G°, and Standard
a
Molar Entropies ∆ S° for the Reaction â-Cyclodextrin(aq) + Ligand(aq) ) â-Cyclodextrin‚Ligand(aq) at T ) 298.15 K
r
ligand
m (mol kg-1)
N
K
∆
r
H° (kJ mol-1
)
∆
r
G° (kJ mol-1
-5.3 ( 2.7
-9.54 ( 0.25
)
∆
r
S° (J K-1 mol-1
)
-
pentanoate
hexanoate
0.238
0.156
0.100
0.189
0.166
0.153
0.144
0.152
0.150
0.073-0.146
0.160
0.139
0.221
0.156
0.163
0.127
0.061
0.227
0.209
0.145
0.110
0.114
0.064
0.080
0.072
0.044
0.012-0.024
2
2
2
1
2
1
1
2
4
6
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
8.3 ( 5.5
46.9 ( 4.5
301 ( 134
15.9 ( 1.2
17.4 ( 2.4
379 ( 10
435 ( 26
b
11.9 ( 1.4
40.4 ( 1.7
38.0 ( 1.1
69.3 ( 1.6
7.9 ( 4.4
5.5 ( 0.3
1.75 ( 0.33
44.3 ( 5.2
50.4 ( 0.4
53.5 ( 1.5
-12.2 ( 0.8
-1.3 ( 1.0
17.8 ( 0.12
11.0 ( 0.19
-
-
heptanoate
-14.2 ( 1.5
-6.86 ( 0.20
-7.1 ( 0.4
-14.72 ( 0.06
-15.06 ( 0.15
-
benzoate
-10.5 ( 0.7
-7.5 ( 0.9
-9.41 ( 0.10
-11.78 ( 0.12
-
phenylacetate
-
3
4
2
3
4
3
4
1
1
1
1
1
-phenylbutanoate
-phenylbutanoate
-
-
-
-
-methylphenylacetate
-methylphenylacetate
-methylphenylacetate
-11.5 ( 1.1
-12.1 ( 0.4
-12.25 ( 0.23
-8.22 ( 0.11
∼5
-6.1 ( 0.3
-9.17 ( 0.11
-9.02 ( 0.08
-10.51 ( 0.06
-18.1 ( 1.2
-9.8 ( 0.4
-10.8 ( 0.3
7.7 ( 0.2
-
-
-methoxyphenylacetate
-methoxyphenylacetate
+
c
-pentylamine
-hexylamine
∼8
+
65 ( 16
76 ( 15
2.5 ( 0.4
-10.4 ( 0.7
-10.7 ( 0.55
43.3 ( 0.8
42.5 ( 0.6
+
-methylhexylamine
1.96 ( 0.22
∼0.2
+
-heptylamine
+
-octylamine
420 ( 137
14 ( 6
172 ( 5
-1.99 ( 0.26
3.7 ( 1.4
-15.0 ( 1.0
-6.5 ( 1.4
43.6 ( 1.0
34.2 ( 2.0
27.5 ( 0.1
26.5 ( 1.0
24.0 ( 0.6
25.9 ( 0.1
26.6 ( 0.1
28.7 ( 0.1
33.3 ( 0.6
22.5 ( 0.2
14.8 ( 0.6
0
cyclobutanol
cyclopentanol
0
-4.56 ( 0.05
-9.58 ( 0.29
-9.92 ( 0.15
-8.66 ( 0.09
-8.74 ( 0.09
-9.50 ( 0.10
-9.06 ( 0.17
-12.37 ( 0.12
-16.4 ( 0.5
-12.76 ( 0.08
-17.47 ( 0.08
-17.08 ( 0.06
-16.38 ( 0.04
-16.66 ( 0.05
-18.07 ( 0.05
-19.00 ( 0.07
-19.08 ( 0.09
-20.8 ( 0.3
0
1
(
(
3
-methylcyclohexanol
()-cis-2-methylcyclohexanol
()-trans-2-methylcyclohexanol
-methylcyclohexanol
cis-4-methylcyclohexanol
1150 ( 36
981 ( 22
741 ( 10
830 ( 16
1462 ( 26
2130 ( 61
2197 ( 73
4405 ( 484
0
0
0
d
0
0
trans-4-methylcyclohexanol
0
cycloheptanol
0
cyclooctanol
a
, 0.025 mol kg-1) + (Na , 0.025 mol kg-1), pH ) 6.90} was used for all reactions. The charge numbers of
Phosphate buffer {(NaH
2
PO
4
HPO
2 4
the ligands are those of the predominant species at pH ) 6.90. The molality m of the ligand for which the measurements were performed and N
the number of sets of titration experiments performed are given in columns 2 and 3, respectively. The molality of the R-cyclodextrin was in the
range 0.0010-0.0037 mol kg . The basis of the uncertainties is discussed in the text. b K and/or ∆
-1
r
H° for this reaction were too small to measure
c
d
with the titration calorimeter. Values designated as being approximate are uncertain by amounts that are comparable to the reported values. The
sample of 3-methylcyclohexanol was a mixture of the cis and trans isomers.
minimal error in the calorimetric measurements or for impurities
in the samples. The standard deviations of the mean are based
on the scatter of the data in a single titration experiment and
charge numbers of the ligands in Tables 1 and 2 are those of
the predominant species at pH ) 6.90.
3.3. Comparisons with Earlier Literature. The thermo-
dynamic results from the literature on the reactions of these
ligands with R- and â-cyclodextrin are summarized in Table 3.
2
9
were obtained from the computer program “Origin” used to
calculate the equilibrium constants and the standard molar
enthalpies of reaction. Clearly the sensitivity of the method is
reduced for reactions having small values of K (K < 10) and/
32
-
Siimer et al. reported K ) 10 ( 1 for the reaction of benzoate
with â-cyclodextrin at the temperature T ) 303.15 K. We adjust
this result to T ) 298.15 K with the value of ∆rH° for this
reaction determined in this study and obtain K ) 9 ( 1. This
value is not in agreement with the result K ) 15.9 ( 1.2 reported
-1
or small absolute values of ∆rH° (|∆rH°|< 3 kJ mol ). Also,
in some instances (e.g. cyclooctanol), the solubility of the ligand
is limited. These factors all place limitations on the size of the
measurable signal and can lead to larger uncertainties in the
thermodynamic quantities. Thus, in a few cases (see Tables 1
and 2), it was not possible to measure either K or ∆rH° for the
1
0
herein. Matsui and Mochida used a spectrophotometric
method to study the reaction of cyclobutanol, cyclopentanol,
cycloheptanol, and cyclooctanol with R- and â-cyclodextrin.
24
10
complexation reaction. For reasons stated previously, we have
adopted minimum uncertainties (0.01K and 0.01∆rH°) for the
results obtained from these experiments. Additionally, when
the mole fraction purity of a ligand x was less than 0.99, the
uncertainties in the equilibrium constants and standard molar
enthalpies of reaction were increased (in quadrature) by the
respective amounts (1 - x)K or (1 - x)∆rH°.
They reported that the standard error in their measured values
of log K was (0.04, but did not give estimates of total
uncertainties. We shall assume that a reasonable assignment
of random error in their results for log K is approximately two
standard errors ((0.08). On the basis of this assumption, their
results for the equilibrium constants for the reactions of all of
the cyclic alcohols with R-cyclodextrin and for the reaction of
cyclobutanol with â-cyclodextrin are in agreement with the
3
.2. Assignment of Charge Numbers of Ligands. We have
30,31
10
used two computerized databases
to locate pK’s for most
results of the present study. Their result for the equilibrium
of the acids and approximately one third of the amines studied
herein. The pK’s of these acids are in the range 4.0-4.9 and
the pK’s of the protonated amines are in the range 10.6-10.7.
On the basis of structural similarity, it is reasonable to assume
that the pK’s of the remaining acids and amines will fall either
into or very nearly into these ranges. Clearly, the alcohols will
not ionize unless placed in extremely alkaline solutions. Since
the pH of 6.9 used for the experiments was well removed (|pH
constant for the reaction of cyclooctanol with R-cyclodextrin
is more precise than our result. This is due to the reduced
sensitivity of the calorimetric method when studying a reaction
that has a small absolute value of ∆rH°. However, their results
for the equilibrium constants for the reactions of cyclopentanol,
cycloheptanol, and cyclooctanol are systematically lower than
the results obtained in this study. Matsui and Mochida10 used
a (H2SO4 + Na2SO4) buffer in their studies involving R-cyclo-
dextrin and a (citrate + phosphate) buffer in their studies
involving â-cyclodextrin. Citrate, however, is known to bind
-
pK| g2) from the pK’s at which ionizations occur, the
complication of having more than one species present in these
solutions in any significant amount (>1%) is avoided. The
3
3
to â-cyclodextrin. Therefore, one expects systematic differ-

Reactions of R- and â-Cyclodextrin
J. Phys. Chem. B, Vol. 101, No. 1, 1997 91
TABLE 3: Literature Values of the Equilibrium Constants K and Standard Molar Enthalpies ∆
â-Cyclodextrin with Organic Ligands
r
H° for the Reactions of r- and
ligand
K
∆
r
H° (kJ mol-1)
T (K)
buffer
pH
method
ref
R-cyclodextrin(aq) + Ligand(aq) ) R-Cyclodextrin‚Ligand(aq)
cyclobutanol0
cyclopentanol
cycloheptanol
39 ( 7
46 ( 8
79 ( 13
178 ( 30
298.15
298.15
298.15
298.15
H
H
H
H
+ Na
+ Na
+ Na
+ Na
SO
SO
SO
SO
1.2
1.2
1.2
1.2
spectrophtometry
spectrophotometry
spectrophotometry
spectrophotometry
10
10
10
10
2
SO
2
SO
2
SO
2
SO
4
4
4
4
2
2
2
2
4
4
4
4
0
0
0
cyclooctanol
â-Cyclodextrin(aq) + Ligand(aq) ) â-Cyclodextrin‚Ligand(aq)
benzoate-
cyclobutanol
cyclopentanol
cycloheptanol
cyclooctanol
10 ( 1
15 ( 3
120 ( 11
1700 ( 290
2000 ( 340
-19.0 ( 1.4
a
303.15
298.15
298.15
298.15
298.15
none
?
calorimetry
32
10
10
10
10
0
citrate + phosphate
citrate + phosphate
citrate + phosphate
citrate + phosphate
6.4
6.4
6.4
6.4
spectrophotometry
spectrophotometry
spectrophotometry
spectrophotometry
0
0
0
a
Siimer et al.32 reported a negative value of ∆
-
r
H° for the dissociation reaction of the complex â-cyclodextrin‚benzoate (aq). This corresponds
to a positive value for ∆
r
H° for the complexation reaction as written above. We have assumed that the sign of their32 reported enthalpy is in error
and have reversed it in this table.
ences between results obtained with the interacting citrate buffer
4. Discussion
24
and with a noninteracting phosphate buffer. This was also
found to be the case when acetate was used instead of phosphate
4
.1. General Ideas and Approach. The most likely mode
of complexation of ligands to cyclodextrins consists of insertion
of the hydrophobic portion of the ligand into the cyclodextrin
cavity with the polar group of the ligand remaining solvent
2
4
buffer in the study of cyclodextrin complexation reactions.
Specifically, the equilibrium constants obtained with acetate
buffer were, in nearly all cases, 10-50% lower than those
obtained with phosphate buffer.24
2
exposed at the wide top end of the cavity. In general, the
complexation is noncovalent. A combination of hydrophobic
effects and van der Waals forces and, in some cases, hydrogen
bonding between the ligand and the cyclodextrin is involved.
The resultant of all these interactions is described by the
thermodynamic quantities. Although, at present, it does not
appear possible to obtain a rigorous, quantitative breakdown of
the relative contributions of these various interactions for any
specific (ligand + cyclodextrin) reaction, we believe that the
following qualitatiVe picture is useful for understanding these
complexation reactions. Namely, hydrophobic effects should
be typified by negative values of the standard molar heat-
capacity change ∆rC°p and, at or near T ) 298.15 K, small
Ross and Rekharsky34 have recently carried out a thermo-
dynamic investigation using model compounds to obtain a set
of thermodynamic parameters that are characteristic of hydrogen
bonding and hydrophobic effects. In their investigation, they
+
studied the reactions of four n-amines, N-methylhexylamine ,
+
-
-
1
-methylhexylamine , 1-hexanoate , and 1-heptanoate with
-
R-cyclodextrin and the reactions of 3-phenylbutanoate and cis-
-methylcyclohexanol with â-cyclodextrin. The thermodynamic
4
quantity of principal interest in their study was the standard
molar heat-capacity change ∆rC°p, which was obtained from
the dependence of ∆rH° on temperature. The measurements
-
1
done by Ross and Rekharsky34 were done independently of the
positive values of ∆ H° (<∼10 kJ mol ) and positive values
r
35-38
of ∆rS°.
Also, when the ligand is in the cyclodextrin cavity,
results of the present study and are based on the results of a
single titration experiment performed at each temperature. The
results of the current study for the aforementioned reactions
are either in complete agreement or near agreement with the
there is the possibility of attractive van der Waals interactions
as well as hydrogen bonding.
2
4,34
These attractive interactions
are characterized by negative ∆rH°’s. Using the simple qualita-
tive argument that a ligand that is strongly bound within the
cyclodextrin cavity has lost some freedom of motion, one
expects it to have a lower entropy than if it were weakly bound
within the cavity. Thus, one should expect some “enthalpy-
entropy compensation” for these complexation reactions. Also,
since the R-cyclodextrin cavity (approximate internal dimensions
results obtained by Ross and Rekharsky.3
4
3.4. NMR. The results of the NMR measurements are given
in Tables 4 and 5. As is the case with the calorimetric results,
+
the predominant species in solution are the alkylammonium
-
and alkanoate ions. The ligand (guest) protons Gn are
numbered sequentially from the methylene adjacent to the
ammonium or carboxylate group. The cyclodextrin (host)
protons Hn are numbered as usual (see Figure 1). Due to the
4
.9 Å × 7.9 Å) is smaller than the â-cyclodextrin cavity
1
(approximate internal dimensions 6.2 Å × 7.9 Å) and since
van der Waals forces are critically dependent on distance of
separation, one expects that these forces will be larger (∆rH°
more negative) for the complexation of a given ligand to
R-cyclodextrin than to â-cyclodextrin. This assumes the same
mode of inclusion of that ligand into both R- and â-cyclodextrin.
Accordingly, the van der Waals interactions will be highly
dependent on the size and possibly the shape of the ligand.
Clearly, if a ligand cannot be accommodated within the
+
presence of chiral centers in 1-methylhexylamine and 1-me-
+
thylheptylamine , the values of the chemical shifts for the G2
protons are different and are distinguished as G2a and G2b.
Similarly, it is necessary to distinguish the H6 protons of
R-cyclodextrin. As exemplified in Figure 2 for the complexation
+
of octylamine with R-cyclodextrin, all of the ligand protons
(G1 to G8) show significant downfield shifts upon complexation,
while the complexation-induced chemical shift changes ∆δ of
the cyclodextrin protons (H1 to H6) are much smaller in scale
and more scattered in direction. Except for relatively small
deviations (δ < 0.02), the chemical shifts of the G1, G2, G3,
and Gn protons of the amines appear at 2.91, 1.58, 1.29, and
cyclodextrin cavity, steric effects play a dominant role. While
18,35,39-43
these concepts are not new,
it will be seen in the
following discussion that these rather straightforward ideas
provide a useful qualitative framework with which to account
for much of the thermodynamic data.
0
.80, respectively, while the chemical shifts of the G1, G2, G3,
and Gn protons of the acids appear, respectively, at 2.10, 1.47,
.22, and 0.80. This constancy in these chemical shifts is
consistent with the absence of any micelle formation.
The ligands used in this study were selected so as to allow
for the examination of how several structural features affect the
thermodynamics of complexation reactions of cyclodextrins. The
features examined are (1) the number of alkyl groups in the
1

92
J. Phys. Chem. B, Vol. 101, No. 1, 1997
Rekharsky et al.
TABLE 4: Chemical Shifts δ of Ligand Protons and Chemical Shift Changes ∆δ upon Complexation of Ligands with
a,b
r-Cyclodextrin in Aqueous Phosphate Buffer at pD ) 7.0 and T ) 298 ( 1 K
δ or ∆δ
ligand
-pentylamine+
[H]/[G]c
0
G1
G2a
G2b
G3
G4
G5
G6
G7
G8
1-Me
N-Me
1
1
1
2.91
2.94
-0.03
2.92
2.96
-0.04
3.28
3.31
-0.03
2.94
2.99
-0.05
2.92
2.96
-0.04
3.28
3.32
-0.04
2.90
2.95
-0.05
2.11
2.13
-0.02
2.10
1.58
1.63
1.27
1.33
-0.06
1.30
1.39
-0.09
1.30
1.38
-0.08
1.30
1.38
-0.08
1.30
1.38
-0.08
1.28
1.37
-0.09
1.29
1.36
-0.07
1.23
1.27
-0.04
1.23
1.27
1.33
-0.06
1.25
1.36
-0.11
1.25
1.34
-0.09
1.25
1.35
-0.10
1.28
1.38
-0.10
1.28
1.37
-0.09
1.24
1.36
-0.12
0.81
0.84
-0.03
1.19
0.82
0.86
-0.04
1.24
1.35
-0.11
1.24
1.34
-0.10
1.24
1.35
-0.11
1.22
1.35
-0.13
1.22
1.34
-0.12
1.22
1
δ:
0
.04
.04
.93
.96
.00
.08
.00
.92
.02
.92
.02
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
-0.05
-hexylamine+
1.59
1.65
0.80
0.87
-0.07
0.81
0.85
-0.04
0.80
0.86
-0.06
1.22
1.35
-0.13
1.22
1
δ:
0
-0.06
1.57,
1.64,
-0.07,
-methylhexylamine+
1.50
1.54
-0.04
1.22
1.25
-0.03
0
δ:
0
N-methylhexylamine+
1.60
1.66
2.63
2.65
-0.02
0
δ:
0
-0.06
1
1
1
-heptylamine+
1.59
1.65
0.80
0.85
-0.05
0.80
0.85
-0.05
1.20
1
δ:
0
-0.06
1.57,
1.66,
-0.09,
-methylheptylamine+
-octylamine+
1.50
1.54
-0.04
1
δ:
0
1.34
-0.12
1.20
1.31
-0.11
1.57
1.64
0.78
0.83
-0.05
1
δ:
0
1.36
-0.14
1.31
-0.11
-0.07
pentanoate-
hexanoate-
heptanoate-
octanoate-
1.45
1.50
0
δ:
0
-0.05
1.47
1.55
0.80
0.85
-0.05
1.21
1.33
-0.12
1.21
1
δ:
0
2.14
-0.04
2.10
2.14
-0.04
2.10
1.32
-0.09
1.21
1.33
-0.12
1.21
1.30
-0.11
1.21
1.33
-0.12
1.21
-0.08
1.47
1.55
0.79
0.86
-0.07
1.21
1.31
-0.10
0
δ:
0
1
δ:
-0.08
1.47
1.53
0.79
0.84
-0.05
2.13
-0.03
1.31
-0.10
1.31
-0.10
1.31
-0.10
-0.06
a
The atom-numbering scheme is discussed in the text and in Figure 1. b The pooled standard deviation of the δ values is 0.011. c The quantity
[
H]/[G] is the ratio of the concentration of the R-cyclodextrin (the host) to the concentration of the ligand (the guest). The concentration of
-
3
R-cyclodextrin was 0.0050 mol dm . Under these conditions, the complexation of ligand and R-cyclodextrin is not complete; the values of the
fractions R of ligand and R-cyclodextrin that are complexed are given in the Discussion section.
ligand, (2) branching (i.e. comparison of results for primary and
secondary ligands), (3) the charge number on the ligand, (4)
the presence of a double bond, and (5) the addition of methyl
groups and methoxy groups to a central moiety. The matter of
enthalpy-entropy compensation is also discussed.
The ∆rG° results for the aliphatic sec-amines, alkane-1,2-
diols, and neutral aliphatic n-acids can be adequately represented
by straight lines in Figure 3. The data for the remaining classes
of ligands in Figure 3 and all of the results in Figure 6 can be
represented by quadratic equations of the form ∆ G° ) a +
r
1
2
a2NC + a3(NC) , where a1, a2, and a3 are adjustable parameters.
A quantity of particular interest in Figures 3 and 6 is the
increment in ∆rG° per alkyl group. We have calculated d∆rG°/
dNC, the slope of the linear fits of ∆rG° against NC, for each
class of ligand. The values of d∆rG°/dNC range from -2.6 kJ
4
.2. General Trends. The values of ∆rS° for all but one of
the reactions (R-cyclodextrin + cyclooctanol) involving R-cy-
clodextrin are negative (see Table 1); these reactions are
“
∆
enthalpy driven” at T ) 298.15 K. In contrast, the values of
rS° are positive for most of the reactions of â-cyclodextrin
-
1
with the various ligands reported in Table 2. Thus, for the
reactions with â-cyclodextrin, there is a substantial entropic
contribution to ∆rG°. Additionally, the values of ∆rH° for
nearly all of the reactions involving R-cyclodextrin are more
exothermic than the values of ∆rH° for the corresponding
reactions involving â-cyclodextrin. Cycloheptanol and, again,
cyclooctanol are the exceptions.
mol (the reactions of the sec-alkanols with R-cyclodextrin)
-
1
to -3.8 kJ mol (reactions of the alkane-1,2-diols with
-
1
R-cyclodextrin) and -4.5 kJ mol (reactions of the ionized
aliphatic n-acids with â-cyclodextrin). The values of d∆rG°/
dNC for the remaining classes of ligands are in a remarkably
-
1
narrow range of -3.5 to -2.5 kJ mol . The average values
of d∆rG°/dNC (all classes of ligands included) are -3.1 and
-
1
-
3.3 kJ mol for the reactions of these ligands with R- and
4.3. The CH2 Increment. Plots of the standard molar Gibbs
â-cyclodextrin, respectively. The standard deviations in these
quantities are small: 0.12 and 0.25 kJ mol , respectively.
energies, enthalpies, and entropies for the reactions of various
classes of ligands with both R- and â-cyclodextrin as a function
of NC, the number of hydrocarbon carbon atoms (i.e. CH, CH2,
and CH3 groups) in the chemical formula of the ligands, are
shown in Figures 3-8. According to this convention, the carbon
in the carboxylate group is not counted in the calculation of
NC. The most striking features in these plots (see Figures 3, 4,
-
1
Some regularity is also seen in the standard molar enthalpies
of the reactions involving R-cyclodextrin. Here, the range of
values of d∆rH°/dNC obtained from linear fits of ∆rH° against
-
1
NC is -4.8 to -1.9 kJ mol . The average value of d∆rH°/
-
1
-1
dNC is -3.4 kJ mol (standard deviation s ) 0.3 kJ mol ).
Somewhat less regularity is seen (Figure 7) for the standard
molar enthalpies of reaction with â-cyclodextrin. Here, the
6, and 7) is the regular dependence of ∆rG° and ∆rH° on NC.
It is also seen that there are characteristic differences between
the various classes of ligands.
-
1
range of values of d∆rH°/dNC is -4.8 to -0.6 kJ mol . The

Reactions of R- and â-Cyclodextrin
J. Phys. Chem. B, Vol. 101, No. 1, 1997 93
TABLE 5: Chemical Shifts δ of r-Cyclodextrin Protons and Chemical Shift Changes ∆δ upon Complexation with Aliphatic
a,b
Acids and Amines in Aqueous Phosphate Buffer at pD ) 7.0 and T ) 298 ( 1 K
δ or ∆δ
ligand
[H]/[G]c
H1
H2
H3
H4
H5
H6a
H6b
none
4.99
4.99
0.00
5.01
-0.02
5.00
-0.01
5.01
-0.02
5.01
-0.02
5.01
-0.02
4.99
0.00
5.00
-0.01
5.00
-0.01
5.00
-0.01
5.01
3.57
3.58
-0.01
3.60
-0.03
3.60
-0.03
3.60
-0.03
3.60
-0.03
3.60
-0.03
3.60
-0.03
3.56
0.01
3.56
-0.01
3.56
0.01
3.56
0.01
3.92
3.89
0.03
3.90
0.02
3.89
0.03
3.89
0.03
3.89
0.03
3.89
0.03
3.89
0.03
3.91
0.01
3.91
0.01
3.91
0.01
3.90
0.02
3.53
3.53
0.00
3.54
-0.01
3.54
-0.01
3.54
-0.01
3.55
-0.02
3.55
-0.02
3.57
-0.04
3.52
0.01
3.53
0.00
3.54
-0.01
3.57
3.78
3.76
0.02
3.77
0.01
3.76
0.02
3.76
0.02
3.77
0.01
3.77
0.01
3.78
0.00
3.76
0.02
3.77
0.01
3.78
0.00
3.78
0.00
3.80
3.78
0.02
3.80
0.00
3.79
0.01
3.79
0.01
3.79
0.01
3.79
0.01
3.80
0.00
3.79
0.01
3.79
0.01
3.79
0.01
3.79
0.01
3.85
3.83
0.02
3.85
0.00
3.84
0.01
3.84
0.01
3.84
0.01
3.84
0.01
3.84
0.01
3.84
0.01
3.85
0.00
3.85
0.00
3.84
0.01
1
1
1
-pentylamine+
1.04
∆
δ:
1.04
δ:
0.93
δ:
0.96
δ:
1.00
δ:
1.08
δ:
0.83
δ:
0.92
δ:
1.02
δ:
0.92
δ:
1.02
δ:
-hexylamine+
∆
-methylhexylamine+
∆
N-methylhexylamine+
∆
1
1
1
-heptylamine+
∆
-methylheptylamine+
-octylamine+
∆
∆
pentanoate-
hexanoate-
heptanoate-
octanoate-
∆
∆
∆
∆
-0.02
-0.04
a
The atom-numbering scheme for R-cyclodextrin is described in Figure 1. b The pooled standard deviation of the δ values is 0.011. c The quantity
[
H]/[G] is the ratio of the concentration of the R-cyclodextrin (the host) to the concentration of the ligand (the guest). The concentration of
-
3
R-cyclodextrin was 0.0050 mol dm . Under these conditions, the complexation of ligand and R-cyclodextrin is not complete; the values of the
fractions R of ligand and R-cyclodextrin that are complexed are given in the Discussion section.
Figure 2. Proton NMR spectra of (a) free octylamine and R-cyclodextrin measured separately and (b) their equimolar mixture. The conditions of
measurement are described in the Experimental Section.
-
1
It has been noted14-16,46 that a value of d∆rG°/dNC (i.e. a
average value of d∆rH°/dNC is -2.5 kJ mol (s ) 0.6 kJ
-
1
-1
mol ). The standard molar entropies of reaction (Figures 5
and 8) are even less regular: the average values of d∆rS°/dNC
are 0.46 J K mol (s ) 0.9 J K mol ) and 2.6 J K
mol (s ) 1.9 J K mol ) for the reactions involving R- and
â-cyclodextrin, respectively.
CH2 increment) of ∼ -3 kJ mol at T ) 298.15 K is typical
for the transfer of an alkyl group in a hydrocarbon chain from
water to the interior of a micelle and not too far from the CH2
increment for the transfer of an alkane from water to a liquid
hydrocarbon phase. Thus, the pooled value of d∆rG°/dNC )
-
1
-1
-1
-1
-1
-
1
-1
-1

94
J. Phys. Chem. B, Vol. 101, No. 1, 1997
Rekharsky et al.
Figure 3. Standard molar Gibbs energies ∆
r
G° for the reactions of
, the
Figure 4. Standard molar enthalpies ∆
r
H° for the reactions of various
classes of ligands with R-cyclodextrin as a function of N , the number
C
various classes of ligands with R-cyclodextrin as a function of N
C
number of hydrocarbon carbon atoms in the chemical formula of the
ligand; that is, the carbon in the carboxylate group is not counted. The
symbols and their significance are as follows: (O connected with s)
n-alkanols; (4 connected with ‚‚‚) aliphatic n-amines; (+ connected
of hydrocarbon carbon atoms in the chemical formula of the ligand;
that is, the carbon in the carboxylate group is not counted. The symbols
and their significance are as follows: (O connected with s), n-alkanols;
4 connected with ‚‚‚), aliphatic n-amines; (+ connected with ---) ionized
aliphatic n-acids; (× connected with - ‚ -) alkane-1,ω-diols; (]
with ---) ionized aliphatic n-acids; (× connected with - ‚ -), alkane-
+
+
+
1
,ω-diols; (] connected with - - -) N-methylbutylamine and N-
connected with ---) N-methylbutylamine and N-methylhexylamine ;
(3 connected with s) aliphatic sec-amines; (0 connected with ‚‚‚) sec-
alkanols; (* connected with ----) alkane-1,2-diols. The sources of the
+
methylhexylamine ; (3 connected with s) aliphatic sec-amines; (0
connected with ...) sec-alkanols; (* connected with ---) alkane-1,2-diols;
1
3
(
[ connected with - ‚ -) ionized aliphatic sec-acids; (X connected
data are as follows: n-alkanols, Andini et al. (N
C
) 2), Rekharsky et
15
14
with - - -) neutral aliphatic n-acids. The sources of the data are as
follows: n-alkanols, Matsui and Mochida (N
Hall e´ n et al. (N
alkanols, Matsui and Mochida (N
Rekharsky et al.; alkane-1,2-diols, Andini et al.; neutral aliphatic
n-acids, Gelb et al.;
aliphatic n-acids, N-methylbutylamine , and N-methylhexylamine , this
al. (N
C
) 4), and Hall e´ n et al. (N
C
) 3, 5, 6, and 7); alkane-1,ω-
diols, Bastos et al.; sec-alkanols, Rekharsky et al.; alkane-1,2-diols,
Andini et al.; aliphatic n-amines, aliphatic sec-amines, ionized aliphatic
n-acids, N-methylbutylamine , and N-methylhexylamine , this study.
1
0
16
15
C
) 1, 2, 7, and 8) and
1
4
16
13
C
) 3-6); alkane-1,ω-diols, Bastos et al.; sec-
10
+
+
C
) 8) with the remaining data from
1
5
13
44,45
aliphatic n-amines, aliphatic sec-amines, ionized
These quantities were obtained by combination of the appropri-
ate thermodynamic quantities for the reactions of the various
ligands with R- and â-cyclodextrin. Thus, a slope of 485 (
+
+
study.
1
36 K was obtained from a plot of ∆rH° vs ∆rS° for these
1
-
3.2 kJ mol- found herein is both indicative of and consistent
exchange reactions. This latter, somewhat uncertain, slope is
with the presence of hydrophobic effects. Also, the somewhat
more negative value of d∆rH°/dNC for the reactions of the
ligands with R-cyclodextrin than with â-cyclodextrin is con-
sistent with the presence of increased van der Waals interactions
for the alkyl groups in the R-cyclodextrin cavity in comparison
to that in the â-cyclodextrin cavity.
greater than the slopes (range of 239-360 K) obtained in
15,18,19,24
previous studies.
However, some enthalpy-entropy compensation is evident
when individual classes of substances are considered. This is
demonstrated in plots of ∆rH° vs ∆rS° (Figures 9 and 10) for
the reactions of the various classes of ligands considered herein.
Note, however, that two points (one for the reaction of
4.4. Enthalpy-Entropy Compensation. To examine en-
-
thalpy-entropy compensation in these complexation reactions,
we have constructed plots of the standard molar enthalpies as
a function of the standard molar entropies. A slope of 236 (
butanoate with R-cyclodextrin and the other for the reaction
of 2-propanol with â-cyclodextrin) were not included in the
least-squares fits used to obtain the straight lines in Figures 9
and 10. It is also seen in these figures that the slopes of the
linear fits for the various classes of ligands vary by substantial
amounts. Thus, no meaningful slope or compensation temper-
ature can be obtained.
9
3 K was obtained from a plot that used all of the results for
the reactions with â-cyclodextrin discussed herein. This value
is in agreement with a typical compensation temperature of
∼
300 K, which is obtained if the enthalpy-entropy compensa-
16
tion is essentially complete. However, for the reactions with
R-cyclodextrin, the ∆rH°’s were found to be poorly correlated
with the ∆rS°’s and a meaningful slope could not be obtained
The alkane-1,ω-diols present a particularly interesting case.
They display a zigzag pattern in the plots of ∆rH° and ∆rS°
against NC (Figures 4 and 5). Also, their slopes in Figure 5
and in the enthalpy-entropy plot (Figure 9) are opposite in sign
to those seen for the other classes of substances. Interestingly,
even though they cannot be represented properly by a straight
line in Figure 9, they are well represented by a smooth curve
in the plot of ∆rG° against NC (Figure 3). Thus, as pointed out
1
8
using all of the results. Following Bertrand et al. and our
earlier practice,
1
5,19,24
we also examined the differences in
thermodynamic quantities for the exchange reaction
R-cyclodextrin‚ligand(aq) + â-cyclodextrin(aq) ) (3)
R-cyclodextrin(aq) + â-cyclodextrin‚ligand(aq)
1
6
by Bastos et al., there is a strong “enthalpy-entropy com-
pensation” for this class of ligand.

Reactions of R- and â-Cyclodextrin
J. Phys. Chem. B, Vol. 101, No. 1, 1997 95
Figure 5. Standard molar entropies ∆
r
S° for the reactions of various
, the number
Figure 6. Standard molar Gibbs energies ∆
r
G° for the reactions of
, the
classes of ligands with R-cyclodextrin as a function of N
C
various classes of ligands with â-cyclodextrin as a function of N
C
of hydrocarbon carbon atoms in the chemical formula of the ligand;
that is, the carbon in the carboxylate group is not counted. The symbols
and their significance are as follows: (O connected with s), n-alkanols;
number of hydrocarbon carbon atoms in the chemical formula of the
ligand; that is, the carbon in the carboxylate group is not counted. The
symbols and their significance are as follows: (O connected with s)
n-alkanols; (4 connected with ‚‚‚) aliphatic n-amines; (+ connected
(
4 connected with ‚‚‚) aliphatic n-amines; (+ connected with ---)
-
ionized aliphatic n-acids; (× connected with - ‚ -) alkane-1,ω-diols;
with ---) ionized aliphatic n-acids; (× connected with - ‚ -) benzoate ,
+
phenylacetate
-
, 3-phenylpropanoate
-
, and 4-phenylbutanoate ; (0
-
(
] connected with - - -) N-methylbutylamine and N-methylhexyl-
+
connected with ‚‚‚) sec-alkanols; (] connected with - - -) cyclic
amine ; (3 connected with s) aliphatic sec-amines; (0 connected with
‚‚) sec-alkanols; (* connected with (---) alkane-1,2-diols. The values
of ∆ S° were calculated from the values of ∆ G° and ∆ H° used,
respectively, in Figures 3 and 4.
‚
alcohols. The sources of the data are as follows: cyclic alcohols,
Rekharsky et al.19 (N
) 6) with the remaining data from this study;
C
15
r
r
r
n-alkanols, Rekharsky et al. (N
C
) 3 and 4) with the remaining data
10
from Matsui and Mochida;10 sec-alkanols, Matsui and Mochida (N
C
1
5
)
8) with the remaining data from Rekharsky et al.; aliphatic
4
.5. Branching. The differences in the ∆rG°, ∆rH°, and
-
-
n-amines, ionized aliphatic n-acids, benzoate , phenylacetate , and
∆
rS° for the reactions of n- and sec-aliphatic alcohols, acids,
-
-
24
4-phenylbutanoate , this study; 3-phenylpropanoate , Rekharsky et al.
and amines with R- and â-cyclodextrin are conveniently
represented in terms of the exchange reaction
+
thylhexylamine } with â-cyclodextrin. Within each set of
reactions, the values of the respective thermodynamic quantities
K, ∆rG°, ∆rH°, and ∆rS° are nearly the same. From this result
and on the basis of the concepts and results previously presented,
it is likely that the methyl groups attached either to the C1
sec-ligand(aq) + cyclodextrin‚n-ligand(aq) )
n-ligand(aq) + cyclodextrin‚sec-ligand(aq)
(4)
+
+
Thermodynamic quantities for reaction 4 are obtained by
combination of the appropriate thermodynamic quantities for
the reactions of the primary and secondary ligands with the
pertinent cyclodextrin. These quantities are summarized in
Table 6. The averages and respective standard deviations of
these quantities for the reactions involving R-cyclodextrin are
carbon (e.g. in 1-methylbutylamine , 1-methylhexylamine , and
+
1-methylheptylamine ) or to the nitrogen in N-methylbutyl-
+
+
amine and in N-methylhexylamine are located outside the
cyclodextrin cavity.
4.6. Charge on the Ligand. The equilibrium constants for
the complexation reactions of the ionized aliphatic acids are
significantly smaller than the equilibrium constants for the
-
1
-1
〈
∆rG°〉 ) 2.6 kJ mol , s ) 0.26 kJ mol ; 〈∆rH°〉 ) 1.6 kJ
-
1
-1
-1
-1
44,45
mol , s ) 0.65 kJ mol ; and 〈∆rS°〉 ) -2.9 J K mol , s
corresponding reactions of the aliphatic neutral acids.
-
1
-1
21,47
)
2.4 J K mol . The averages and respective standard
Examination of results
for the respective complexation
-
deviations of these quantities for the reactions involving
reactions of benzoate and the neutral benzoic acid species with
R- and â-cyclodextrin shows that this same situation holds for
these reactions. These observations are consistent with the
-
1
-1
â-cyclodextrin are 〈∆rG°〉 ) 1.0 kJ mol , s ) 0.31 kJ mol ;
-
1
-1
〈
K
∆rH°〉 ) 1.3 kJ mol , s ) 1.4 kJ mol ; and 〈∆rS°〉 ) 1.0 J
-
1
-1
-1
-1
20
mol , s ) 4.0 J K mol . Thus, it is seen that the
general rule seen in the literature (see Inoue et al’s Table 2)
differences in thermodynamic quantities associated with chain
branching are reasonably constant, particularly for the ∆rG°’s.
It is interesting to examine the thermodynamic effects of
substitution of a methyl group near the charged amino group.
This was done by comparing the thermodynamic results for the
that the presence of a charge on a ligand correlates with a smaller
equilibrium constant for the reaction of that ligand with R- and
â-cyclodextrin than for the corresponding reaction of the
uncharged ligand. A likely rationale for this phenomenon is
that the polar, charged portion of the ligand is solvent exposed
+
2
following sets of reactions: {1-butylamine , 1-methylbutyl-
at the wide top end of the cyclodextrin cavity. Thus, in this
+
+
amine , and N-methylbutylamine } with R-cyclodextrin; {1-
situation, there will be an attractive interaction between the polar
charged portion of the ligand and the (polar) bulk water
molecules existing just outside the cyclodextrin cavity. This
attractive interaction should lead to a lower value of the
+
+
+
hexylamine , 1-methylhexylamine , and N-methylhexylamine }
+
with R-cyclodextrin; {1-heptylamine and 1-methylheptyl-
+
+
amine } with R-cyclodextrin; and {1-hexylamine and 1-me-

96
J. Phys. Chem. B, Vol. 101, No. 1, 1997
Rekharsky et al.
Figure 7. Standard molar enthalpies ∆
r
H° for the reactions of various
, the number
Figure 8. Standard molar entropies ∆ S° for the reactions of various
r
classes of ligands with â-cyclodextrin as a function of N
C
classes of ligands with â-cyclodextrin as a function of N , the number
C
of hydrocarbon carbon atoms in the chemical formula of the ligand;
that is, the carbon in the carboxylate group is not counted. The symbols
and their significance are as follows: (O connected with s) n-alkanols;
of hydrocarbon carbon atoms in the chemical formula of the ligand;
that is, the carbon in the carboxylate group is not counted. The symbols
and their significance are as follows: (O connected with s) n-alkanols;
(4 connected with ‚‚‚), aliphatic n-amines; (+ connected with ---)
(
4 connected with ‚‚‚), aliphatic n-amines; (+ connected with ---)
-
-
ionized aliphatic n-acids; (× connected with - ‚ -) benzoate ,
ionized aliphatic n-acids; (× connected with - ‚ -) benzoate ,
-
-
-
-
-
-
phenylacetate , 3-phenylpropanoate , and 4-phenylbutanoate ; (0
connected with ‚‚‚) sec-alkanols; (] connected with - - -) cyclic
alcohols. The sources of the data are as follows: cyclic alcohols,
phenylacetate , 3-phenylpropanoate , and 4-phenylbutanoate ; (0
connected with ‚‚‚), sec-alkanols; (] connected with - - -) cyclic
alcohols. The values of ∆ S° were calculated from the values of ∆ G°
r
r
1
9
Rekharsky et al. (N
n-alkanols, Rekharsky et al. (N
) 5 and 6); sec-alkanols, Rekharsky et al.; aliphatic n-amines,
C
) 6) with the remaining data from this study;
and ∆ H° used, respectively, in Figures 6 and 7.
r
15
10
C
) 3 and 4) and Matsui and Mochida
15
(N
C
are being more snugly accommodated within the cyclodextrin
cavity. This could lead to increased van der Waals interactions
and an increase in the exothermicity of the reaction.
-
-
ionized aliphatic n-acids, benzoate , phenylacetate , and
4
-
-
24
-phenylbutanoate , this study; 3-phenylpropanoate , Rekharsky et al.
equilibrium constant for the complexation of the charged ligand
and the cyclodextrin. A ligand having less charge would bind
more strongly to the cyclodextrin.
There is no similar decrease in the values of ∆rH° for the
reactions of the cyclic alcohols with R-cyclodextrin. Instead,
the values of the corresponding thermodynamic quantities in
the range NC ) 4 to NC ) 7 show no drastic changes and they
are not too different from each other. However, there is a
4
.7. Unsaturated Compounds. The equilibrium constants
-
-
for the reactions of trans-3-hexenoate and of 6-heptenoate
with R-cyclodextrin are approximately half those for the
-
1
remarkable increase in the values of both ∆rH° (8.6 kJ mol )
-
-
-1
-1
respective reactions of hexanoate and heptanoate . Compari-
son of the respective values of ∆rH° and ∆rS° for these reactions
shows that this is an entropic effect. It is possible that when
these substances are bound in the cyclodextrin cavity, the
unsaturated acid has a greater loss of freedom of motion than
the saturated acid. A possible explanation for the anomalous
and ∆rS° (38.7 J K mol ) in going from cycloheptanol to
cyclooctanol. Thus, it is likely that the nature of the complex-
ation of cyclooctanol with R-cyclodextrin is quite different than
for the cyclic alcohols containing fewer carbons.
4.9. Methyl and Methoxy Groups. In this study, a series
of ligands were systematically selected (see Figure 1 and Table
2) so as to allow for the examination of differences in
thermodynamic quantities attributable to the addition of a methyl
group to cyclohexanol. These systematic variations involved
the reactions of these ligands with â-cyclodextrin. The ther-
modynamic quantities for the reaction of cyclohexanol with
â-cyclodextrin were taken from the study of Rekharsky et al.19
In this series, one expects the effective radius of the cyclohexane
part of the ligand in the â-cyclodextrin cavity to be unchanged
by the addition of a methyl group in either the 1 or 4 position.
However, this effective radius will be changed by the addition
of a methyl group in either the 2 or 3 position. Thus, changes
in the position of the methyl group could involve a subtle
combination of both steric effects and van der Waals interac-
tions, and a simple picture was not anticipated. Interestingly,
however, the average value of the quantity {∆rH°(meth-
ylcyclohexanol derivative) - ∆rH°(cyclohexanol)} is very
-
behavior of the trans-2-hexenoate could be delocalization of
the charge on this ligand due to conjugation. This delocalization
could result in enhanced van der Waals interactions as well as
a lowering of the charge density on the carboxyl group. As
pointed out above, a lower charge would probably lead to a
larger value of the binding constant.
4.8. Cyclic Alcohols. The thermodynamics of the reactions
of the cyclic alcohols with R- and â-cyclodextrin exhibit some
interesting patterns. We first consider the reactions involving
â-cyclodextrin and note that the corresponding thermodynamic
quantities for the reactions of cyclobutanol and 1-butanol are
comparable. However, as the number of carbon atoms NC in
the cyclic alcohol increases, there is a rapid decrease in the
values of ∆rH° as well as some decrease in the values of ∆rS°.
In contrast, this behavior is not found for the reactions of the
n-alkanols with â-cyclodextrin. These observations are con-
sistent with the view that, as NC increases, the cyclic alcohols
-
1
-1
constant; it is -2.6 kJ mol (s ) 0.2 kJ mol ). Also, the

Reactions of R- and â-Cyclodextrin
J. Phys. Chem. B, Vol. 101, No. 1, 1997 97
TABLE 6: Standard Molar Gibbs Energies ∆ G°,
r
r r
Enthalpies ∆ H°, and Entropies ∆ S° for the Exchange
Reaction sec-Ligand(aq) + Cyclodextrin‚n-Ligand(aq) )
n-Ligand(aq) + Cyclodextrin‚sec-ligand(aq)a
b
G° (kJ mol-1
H° (kJ mol-1
r
∆ )
S° (J K-1 mol-1
N
C
∆
r
)
∆
r
)
Aliphatic Alcohols + R-Cyclodextrin
3
2.12
5.6
1.1
11.7
-5.8
-6.6
-2.0
-6.5
4
5
6
7
8
2.92
1.70
1.78
2.74
3.71
-0.3
1.2
0.8
Aliphatic Amines + R-Cyclodextrin
5
7
8
4.00
2.5
1.6
3.0
-4.9
-2.2
4.0
2.31
1.84
Aliphatic Acids + R-Cyclodextrin
-1.0
3
3.1
-13.5
Aliphatic Alcohols + â-Cyclodextrin
3
4
5
6
8
1.36
5.1
-0.5
-0.75
1.5
12
0.31
1.67
1.49
0.22
-0.5
-7.5
0
a
Figure 9. Standard molar enthalpies ∆
r
H° as a function of the standard
molar entropies ∆ S° for the reactions of various ligands with
r
The values of ∆ G° for the reactions involving the alcohols are
from Rekharsky et al.15 and the references cited therein. The data for
the reactions involving the aliphatic acids and amines are from this
r
R-cyclodextrin. The symbols and their significance are as follows: (O
and s) n-alkanols; (4 and ‚‚‚) aliphatic n-amines; (+ and ---) ionized
aliphatic n-acids; (× and - ‚ -) alkane-1,ω-diols; (] and - - -)
N-methylbutylamine+ and N-methylhexylamine ; (3 and s) aliphatic
sec-amines; (0 and ‚‚‚), sec-alkanols; (* and ---) alkane-1,2-diols. The
straight lines are least-squares fits to the data.
study. b
CH
N
is the number of hydrocarbon carbon atoms (CH, CH
C
2
, and
3
groups) in the chemical formula of the ligand; that is, the carbon
+
in the carboxylate group is not counted.
-1
value of d∆rH°/dNC (-2.5 kJ mol ) found for the reactions of
the various classes of ligands with â-cyclodextrin, the difference
in the ∆rS°’s is not close to the corresponding average value of
d∆rS°/dNC. It is also noted that small structural changes in a
ligand can cause substantive changes in thermodynamic quanti-
ties. For example the equilibrium constant for the reaction of
trans-4-methylcyclohexanol with â-cyclodextrin is almost twice
as large as that of cis-4-methylcyclohexanol.
A similar systematic variation involving the reactions of these
ligands with â-cyclodextrin was also performed for the addition
-
of methyl and methoxy groups to phenylacetate . The most
striking result obtained from these variations is that the addition
of a methyl or methoxy groups in the 2 position on these
substances correlates with a significantly lower value of the
equilibrium constant for the formation of the â-cyclodextrin‚-
2
4
ligand complex. A similar destabilization has been observed
+
for methoxy derivatives of phenethylamine . It is very likely
that these destabilizations are due to steric effects. It was also
found that addition of a methyl group in either the 3 or 4 position
-
of phenylacetate or of a methoxy group in the 3 position of
-
-1
phenylacetate lowers ∆rH° by ∼4.5 kJ mol . However,
-
addition of a methoxy group in the 4 position of phenylacetate
-
1
lowers ∆rH° by only 0.7 kJ mol . A possible explanation for
this anomalous result is that the methoxy group in
-
4
-methoxyphenylacetate is not contained in the â-cyclodextrin
Figure 10. Standard molar enthalpies ∆
molar entropies ∆ S° for the reactions of various ligands with
â-cyclodextrin. The symbols and their significance are as follows: (O
r
H° as a function of the standard
cavity.
r
The effects of methyl and methoxy groups can be further
explored by a comparison of the values of the thermodynamic
quantities for the exchange reactions
-
-
-
and s) benzoate , phenylacetate , 3-phenylpropanoate , and
-
4
(
-phenylbutanoate ; (4 and ‚‚‚) cyclic alcohols; (+ and ---) n-alkanols;
× and - ‚ -) sec-alkanols; (] and - - -) aliphatic n-amines; (3 and
s) ionized aliphatic n-acids. The straight lines are least-squares fits to
+
the data.
R-phenethylamine (aq) +
-
R-phenylacetate ‚â-cyclodextrin(aq) ) (5)
average value of the quantity {∆rS°(methylcyclohexanol deriva-
tive) - ∆rS°(cyclohexanol)} is also very constant; it is -5.5 J
+
-
1
-1
-1
-1
R-phenethylamine ‚â-cyclodextrin(aq) +
K
mol (s ) 1.3 J K mol ). While the value of -2.6 kJ
-
-
1
mol for the enthalpy difference is very close to the average
R-phenylacetate (aq)

98
J. Phys. Chem. B, Vol. 101, No. 1, 1997
Rekharsky et al.
Here, “R-” is a methyl or methoxy group (and its position) in
+
-
either phenethylamine or in phenylacetate . If there is no
substituent group, reaction 5 pertains to the exchange reaction
+
-
involving phenethylamine and phenylacetate . Values of the
thermodynamic quantities for reaction 5 were calculated with
the results obtained in this study together with the results
previously reported by Rekharsky et al.24 It was found that the
values of ∆rG° for reaction 5 fall in a narrow range (0.7-1.9
-
1
kJ mol ). However, the values of ∆rH° and ∆rS° are less
-1
constant and their respective ranges are (-5.3 to -0.1 kJ mol )
-
1
-1
and (-24 to -3 J K mol ).
4.10. Estimation of Thermodynamic Quantities. Empiri-
cal observations such as those discussed above can be very
useful for the estimation of thermodynamic quantities. For
example, the equilibrium constant for the complexation reaction
+
of 1-heptylamine with â-cyclodextrin could not be measured
with titration calorimetry because the standard molar enthalpy
of this reaction was near zero. However, we can estimate ∆rG°
-
1
)
-12.7 kJ mol , corresponding to K ≈ 168, for this reaction
+
from the â-cyclodextrin results for 1-hexylamine and 1-octyl-
amine . Combined with our measured value of ∆rH°, this leads
+
-1
-1
to ∆rS° ≈ 43 J K mol . The interpolated value of ∆rH°
-1
(
0.3 kJ mol ) from Table 2 is close to the measured value (∼0.2
-1
kJ mol ). As a second example, the literature does not contain
a result for the equilibrium constant for the complexation of
neutral 2-methylpropanoic acid with R-cyclodextrin. However,
extrapolation of the data for the neutral aliphatic n-acids (see
Figure 11. Profiles of complexation induced changes in chemical shifts
+
+
∆δ in protons of pentylamine
(O connected with s); hexylamine
+
(4 connected with ‚‚‚); 1-methylhexylamine (+ connected with ---);
+
+
N-methylhexylamine (× connected with - ‚ -); heptylamine (]
+
-
1
connected with - - -); 1-methylheptylamine (3 connected with s);
Figure 3) leads to ∆rG° ) -12.2 kJ mol for the reaction of
neutral 1-butanoic acid (NC ) 3) with R-cyclodextrin. We then
use 〈∆rG°〉 ) 2.6 kJ mol for the exchange reaction (4)
involving the branched and unbranched ligands to obtain an
+
and octylamine (0 connected with ...).
-
1
-
1
estimated ∆rG° ≈ -9.6 kJ mol
and K ≈ 48 for the
complexation of neutral 2-methylpropanoic acid with R-cyclo-
dextrin. Clearly, many additional estimates for substances can
be made using the results obtained in this study.
4
.11. NMR. Several interesting features are seen in an
examination of the profiles of the changes in chemical shifts
see Figures 11-14) determined in this study. Most signifi-
(
cantly, it is seen that all of the normal and branched hexylamines
and heptylamines have very similar profiles, independent of the
presence of an extra 1-methyl or N-methyl group. Furthermore,
the values of ∆δ for the 1-methyl and N-methyl protons are
relatively small (-0.02 to -0.05). On this basis, it is concluded
that these 1-methyl and N-methyl groups lie outside the
R-cyclodextrin cavity and make no significant contribution to
the stabilization of the cyclodextrin‚ligand complex. This
finding is consistent with the calorimetric results.
The concentrations c of R-cyclodextrin and ligand were kept
-
3
approximately equal (c ) 0.005 mol dm ) in the NMR
experiments. Under these conditions, the fractions R of ligand
and R-cyclodextrin that are complexed will not be unity. Using
the equilibrium constants given in Table 1, the following values
+
+
of R are calculated: 1-pentylamine , 0.27; 1-hexylamine , 0.50;
Figure 12. Profiles of complexation-induced changes in chemical shifts
∆δ in R-cyclodextrin protons upon inclusion of amines. The symbols
and connecting lines correspond to the same amines as in Figure 11.
+
+
1
-methylhexylamine , 0.52; N-methylhexylamine , 0.49; 1-hep-
tylamine , 0.65; 1-methylheptylamine , 0.66; 1-octylamine ,
.75; pentanoate , 0.23; hexanoate , 0.45; heptanoate , 0.62;
and octanoate , 0.75. It was found that the quantity ΣNH(∆δ),
defined as the sum of the ∆δ’s for a given ligand weighted by
the number of hydrogens NH in a given position (see Table 4),
was found to correlate well with the R values. This correlation
is in accord with expectations.
+
+
+
-
-
-
0
-
for the terminal methyl group. While the maximum values of
|
∆δ| are comparable for the amines and acids, the |∆δ| plateau
appears earlier for the acids. This indicates that the mode of
accommodation of the acids and amines is similar and suggests
that the alkyl chain of the n-alkanoates is embedded slightly
deeper in the cyclodextrin cavity than the corresponding
n-amines. This would be consistent with the finding from the
calorimetry that, for the same value of NC, the acids bind more
As can be seen from Figures 11 and 13, the |∆δ| values of
the ligands increase constantly up to four methylene groups and
reach a plateau in the region G4 to G6 for the amines and G3
to G6 for the acids. These |∆δ| values then decrease rapidly

Reactions of R- and â-Cyclodextrin
J. Phys. Chem. B, Vol. 101, No. 1, 1997 99
the depth of ligand penetration. Also, the |∆δ|’s of the H1,
H2, and H4 cyclodextrin protons located outside the cavity were
2
4
found to be negligible (e0.02). In this context, the small but
steady downfield shifts of the H1, H2, and H4 protons found
in this study, particularly upon inclusion of the amines, are
unusual. These H1, H2, and H4 protons are located outside
the cavity and cannot interact directly with that part of the ligand
molecule located in the cyclodextrin cavity. Therefore, the
downfield shifts of these outside protons can be attributed to
hydrogen bonding of the amine’s ammonium protons to the
cyclodextrin’s ethereal and alcoholic oxygens connected, re-
spectively, to [C1/C4′] and C2. This, in turn, indirectly reduces
the electron density of the H1, H2, and H4 protons and leads
to the small but steady downfield shifts that are observed.
5
. Conclusions
The interactions of the acids, amines, and alcohols and the
related substances studied herein with R- and â-cyclodextrin
can be qualitatively understood in terms of van der Waals forces
and hydrophobic effects. Hydrogen bonding and steric effects
also play a role in selected instances. Enthalpy-entropy
compensation is evident when individual classes of substances
are considered, but does not hold when these various classes of
ligands are considered collectively. The values of the CH2
increment d∆rG°/dNC for the reactions of a variety of ligands
with both R- and â-cyclodextrin are remarkably constant
Figure 13. Profiles of complexation-induced changes in chemical shifts
-
-
∆
δ in protons of pentanoate (O connected with s); hexanoate (4
connected with ...); heptanoate (+ connected with ---); and octanoate
× connected with - ‚ -).
-
-
(
-
1
(
average value ) -3.2 kJ mol ) and are consistent with the
presence of hydrophobic effects. However, the corresponding
increments for the enthalpy and entropy show less regularity.
In general, the values of thermodynamic quantities, ∆rG° in
particular, correlate well with structural features (branching,
charge number, double bonds, and methyl and methoxy groups)
in the ligands. Thermodynamic quantities for appropriately
formulated exchange reactions are useful in summarizing the
differences characteristic of these structural features and can
be very useful for the estimation of thermodynamic quantities.
The NMR results indicate that the mode of accommodation of
the acids and amines in the R-cyclodextrin cavity is very similar,
but that the 1-methyl groups in 1-methylhexylamine and in
1-methylheptylamine and the N-methyl group in N-methylhexy-
lamine lie outside the cavity. These findings are consistent with
the calorimetric results. The downfield shifts of the R-cyclo-
dextrin’s protons that are located outside the cavity can be
attributed to hydrogen bonding of the amine’s ammonium
protons to the cyclodextrin’s ethereal and alcoholic oxygens
connected, respectively, to [C1/C4′] and C2.
Acknowledgment. We thank Dr. David Vanderah for his
careful reading of this paper.
Supporting Information Available: One table (3 pages)
containing information on the principal substances used in this
study. Ordering information is given on any current masthead
page.
Figure 14. Profiles of complexation-induced changes in chemical shifts
∆
δ in R-cyclodextrin protons upon inclusion of acids. The symbols
and connecting lines correspond to the same acids as in Figure 13.
tightly than the amines. This difference in depth of penetration
could be attributable to charge delocalization at the carboxylate
group.
References and Notes
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(
(
1
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(