Complexation equilibria involving salts in non-aqueous solvents: Ion pairing and activity considerations

Article abstract of DOI:10.1002/chem.201002522

Complexation of anions, cations and even ion pairs is now an active area of investigation in supramolecular chemistry; unfortunately it is an area fraught with complications when these processes are examined in low polarity organic media. Using a pseudorotaxane complex as an example, apparent K_a2 values (=[complex]/{[salt]_o-[complex]}{[host]_o-[complex]}) for pseudorotaxane formation from dibenzylammonium salts (2-X) and dibenzo-[24]crown-8 (1, DB24C8) in CDCl₃/CD₃CN 3:2 vary with concentration. This is attributable to the fact that the salt is ion paired, but the complex is not. We report an equilibrium model that explicitly includes ion pair dissociation and is based upon activities rather than molar concentrations for study of such processes in non-aqueous media. Proper analysis requires both a dissociation constant, K_ipd, for the salt and a binding constant for interaction of the free cation 2⁺ with the host, K_a5; K_a5 for pseudorotaxane complexation is independent of the counterion (500M^-1), a result of the complex existing in solution as a free cation, but K_ipd values for the salts vary by nearly two orders of magnitude from trifluoroacetate to tosylate to tetrafluoroborate to hexafluorophosphate anions. The activity coefficients depend on the nature of the predominant ions present, whether the pseudorotaxane or the ions from the salt, and also strongly on the molar concentrations; activity coefficients as low as 0.2 are observed, emphasizing the magnitude of their effect. Based on this type of analysis, a method for precise determination of relative binding constants, K_a5, for multiple hosts with a given guest is described. However, while the incorporation of activity coefficients is clearly necessary, it removes the ability to predict from the equilibrium constants the effects of concentration on the extent of binding, which can only be determined experimentally. This has serious implications for study of all such complexation processes in low polarity media.

Full text of DOI:10.1002/chem.201002522

DOI: 10.1002/chem.201002522
Complexation Equilibria Involving Salts in Non-Aqueous Solvents:
Ion Pairing and Activity Considerations
[
a]
[a, b]
[c, d]
Harry W. Gibson,* Jason W. Jones,
Lev N. Zakharov,
[a]
[
c, e]
Arnold L. Rheingold,
and Carla Slebodnick
Abstract: Complexation of anions, cat-
ions and even ion pairs is now an
active area of investigation in supra-
molecular chemistry; unfortunately it is
an area fraught with complications
when these processes are examined in
low polarity organic media. Using a
pseudorotaxane complex as an exam-
molar concentrations for study of such
processes in non-aqueous media.
Proper analysis requires both a dissoci-
ation constant, Kipd, for the salt and a
binding constant for interaction of the
the predominant ions present, whether
the pseudorotaxane or the ions from
the salt, and also strongly on the molar
concentrations; activity coefficients as
low as 0.2 are observed, emphasizing
the magnitude of their effect. Based on
this type of analysis, a method for pre-
cise determination of relative binding
+
free cation 2 with the host, K ; K
a5
a5
for pseudorotaxane complexation is in-
ꢁ
1
dependent of the counterion (500m ),
a result of the complex existing in solu-
tion as a free cation, but Kipd values for
the salts vary by nearly two orders of
magnitude from trifluoroacetate to to-
sylate to tetrafluoroborate to hexa-
fluorophosphate anions. The activity
coefficients depend on the nature of
ple,
=[complex]/
[complex]}) for pseudorotax-
apparent
Ka2
values
constants, K , for multiple hosts with a
a5
(
A
C
H
T
U
N
G
T
R
E
N
N
U
N
G
{[salt] ꢁ
A
H
U
G
R
N
N
given guest is described. However,
while the incorporation of activity coef-
ficients is clearly necessary, it removes
the ability to predict from the equilibri-
um constants the effects of concentra-
tion on the extent of binding, which
can only be determined experimentally.
This has serious implications for study
of all such complexation processes in
low polarity media.
o
A{ [host] ꢁ
C
H
T
U
N
G
T
R
E
N
N
U
N
G
ACHTUNGTRENNUNG
o
ane formation from dibenzylammoni-
um salts (2-X) and dibenzo-[24]crown-
8
(1, DB24C8) in CDCl /CD CN 3:2
3 3
vary with concentration. This is attrib-
utable to the fact that the salt is ion
paired, but the complex is not. We
report an equilibrium model that ex-
plicitly includes ion pair dissociation
and is based upon activities rather than
Keywords: crown compounds · in-
clusion compounds · ion pairs ·
supramolecular chemistry
Introduction
nant role in modern supramolecular chemistry, dating to
Pedersenꢀs discovery of the alkalai metal templated forma-
[3]
[4]
The field of supramolecular chemistry has experienced an
tion of crown ethers. Indeed the study of “anion binding”
[1]
[5]
explosive growth over the past few decades, and the past
decade has seen the application of non-covalent chemistry
to such diverse areas as sensors, molecular electronics, and
and “cation binding”, the latter mainly focused on ammo-
nium salts because of their biological importance and pH
sensitivity, continues unabated.
[2]
molecular machines. Charged species have played a domi-
To tune potential applications, there exists a strong need
to predict and control the reversible interactions that are
the basis of supramolecular chemistry. As a result, a number
of experimental methods have been reported to measure as-
sociation constants, including calorimetry and various spec-
[
a] Prof. Dr. H. W. Gibson, Dr. J. W. Jones, Dr. C. Slebodnick
Department of Chemistry, Virginia Polytechnic Institute
and State University, Blacksburg, VA 24061-0212 (USA)
E-mail: hwgibson@vt.edu
[6]
[
[
b] Dr. J. W. Jones
troscopic measurements. Many of these techniques are
cross-over technologies from the biological sciences and ba-
sically employ Equation (1).
Present address:
E.I. duPont de Nemours and Company
Wilmington, DE 19880-0402 (USA)
[
c] Dr. L. N. Zakharov, Prof. Dr. A. L. Rheingold
Department of Chemistry, University of Delaware
Newark, DE 19716 (USA)
Ka1
ƒ
!
H þG ƒ HG
d] Dr. L. N. Zakharov
Ka1 ¼½HGꢀ=½Hꢀ½Gꢀ¼½HGꢀ=ð½Hꢀꢁ½HGꢀÞð½Gꢀꢁ½HGꢀÞ
o
o
ð1Þ
Present address:
X-ray Crystallography Facility
University of Oregon, Eugene, Oregon 97403 (USA)
However, the biological models and Equation (1) are in-
tended for use with aqueous solutions, whereas many syn-
thetic complexes are studied in low dielectric constant or-
ganic media in order to avoid H-bonding competition.
While solvent/complex interactions are minimized in low di-
[
e] Prof. Dr. A. L. Rheingold
Present address:
Department of Chemistry and Biochemistry
University of California, San Diego, La Jolla, CA 92093 (USA)
3192
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 3192 – 3206

FULL PAPER
[
9]
electric solvents, so too are solvent/ion interactions: as a
The well studied pseudorotaxane formed from dibenzo-
[7]
result, ion pair formation is known to occur. This has often
[24]crown-8 (1) and dibenzylammonium salts (2-X)
(Scheme 1) is an ideal candidate for complexation studies
because exchange is slow on the NMR time scale: in addi-
tion to peaks associated with the starting compounds, new
signals corresponding to complex formation (1·2-X) are
readily discerned; by integration, the complex stoichiometry
[8]
[10]
been ignored in host/guest studies of salts in low dielectric
constant media.
In such cases there are at least four extreme situations
that may occur, as outlined below. First, both the guest salt
and the complex may be ion paired:
(
1:1) and concentration may be readily determined.
Ka2
þ
ꢁ
þ
ꢁ
ƒ
!
H þG X
ƒ HG X
þ
ꢁ
þ
ꢁ
Ka2 ¼½HG X ꢀ=½Hꢀ½G X ꢀ
ð2Þ
þ
ꢁ
þ
ꢁ
þ
ꢁ
þ
ꢁ
¼
½HG X ꢀ=ð½Hꢀꢁ½HG X ꢀÞð½G X ꢀꢁ½HG X ꢀÞ
o
o
Second, the guest salt and the complex may be completely
ionized, that is, not ion paired:
Scheme 1. Formation of pseudorotaxane complex from dibenzo-
[
24]crown-8 (1) and dibenzylammonium salts (2-X).
G X ! Gþ þXꢁ
þ
ꢁ
Ka3
H þGþ
þ
Considering the process in Equation (2) [or equivalently
ƒ
!
ƒ HG
Eq. (3)] by the procedure used generally in the literature,
the concentration of the complex, [HG ], can be measured
and the concentration of the uncomplexed salt, [G X ], is
+
þ
þ
þ
þ
þ
ꢁ
þ
Ka3 ¼½HG ꢀ=½Hꢀ½G ꢀ¼½HG ꢀ=ð½Hꢀꢁ½HG ꢀÞð½G X ꢀꢁ½HG ꢀÞ
o
o
+
ꢁ
ð3Þ
+
ꢁ
+ꢁ
+
assumed to be [G X ] ꢁ
A
H
U
G
E
N
N
ACHTUNGTRNENUNG[ HG ]. We
0
0
examined the formation of pseudorotaxane 1·2-X by
1
Third, the guest salt could be completely ionized and the
complex ion paired:
H NMR spectroscopy over a range of starting host and
guest concentrations at 295 K in CDCl /CD CN 3:2 (by
volume).
3
3
[11]
Several important facts were revealed: 1) the
þ
G X ! Gþ þXꢁ
ꢁ
concentration based Ka2 values according to Equation (2)
[or Ka3 via Eq. (3)] varied strongly with a) host concentra-
tion and b) salt concentration; 2) the chemical shifts attrib-
uted to the pseudorotaxane were invariant with concentra-
tion and anion (Figure 1), whereas the chemical shifts attrib-
uted to uncomplexed guest salt 2-X changed with concentra-
Ka4
H þGþ þXꢁ ƒ HG X
þ
ꢁ
ƒ!
þ
ꢁ
þ
ꢁ
Ka4 ¼½HG X ꢀ=½Hꢀ½G ꢀ½X ꢀ
ð4Þ
þ
ꢁ
þ
ꢁ
þ
ꢁ
þ
ꢁ
2
¼
½HG X ꢀ=ð½Hꢀꢁ½HG X ꢀÞð½G X ꢀꢁ½HG X ꢀÞ
o
o
[11,12]
tion and were dependent on the anion.
Fourth, the guest salt could be ion paired and the complex
fully ionized:
Kipd
þ
ꢁ
ƒ G þXꢁ
þ
ƒ
!
G X
Ka5
þ
þ
þ
ƒ
!
H þG
ƒ HG
Ko5
ꢁ
ƒ HG þXꢁ
þ
ƒ
!
H þG X
þ
ꢁ
þ
ꢁ
Ko5 ¼KipdKa5 ¼½HG ꢀ½X ꢀ=½Hꢀ½G X ꢀ
ð5Þ
þ
ꢁ
þ
þ
ꢁ
¼
½HG ꢀ½X ꢀ=ð½Hꢀꢁ½HG ꢀÞ½G X ꢀ
o
Note that in all cases except the latter, the equilibria can
be evaluated simply by NMR spectroscopy because all of
the concentrations can be directly determined. However, in
the last case, note that in Equation (5) there is no direct way
to determine the concentration of either the free counterion
ꢁ
+
ꢁ
1
X or the ion paired salt G X under ordinary circumstances,
that is, in the absence of knowledge of Kipd. Because of the
ion pair dissociation equilibrium the concentrations of three
Figure 1. Partial 400 MHz H NMR spectra of DB24C8 (1, 4.00 mm) and
dibenzylammonium salts (2-X, 4.00 mm) with various counterions
inCD
3
CN/CDCl
3
2:3 at 22ꢂ18C. The signals of protons in the pseudoro-
taxane are indicated by subscript “c”. OTs=tosylate anion. TFA=tri-
fluoroacetate anion. The same chemical shifts for the pseudorotaxane
complex were observed with 1 and 2-OTf (triflate=trifluoromethanesul-
fonate); see Supporting Information.
+
ꢁ
+
ꢁ
species, G , X and G X , are not simply related to the
original concentration of guest salt and the concentration of
complex.
Chem. Eur. J. 2011, 17, 3192 – 3206
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www.chemeurj.org
3193

H. W. Gibson et al.
We, therefore, concluded that Equation (2) (or 3) does
not obtain in the formation of these pseudorotaxanes from
dibenzo-[24]crown-8 in low polarity solvents at concentra-
tions used in NMR analyses, typically 1 to 10 mm; in these
cases the guest is entrapped in the small cavity of the host
in such a way that ion pairing of the complex does not
points) for extents of complexation between 10 and 90%
[14]
(near the Weber rule range of 20–80% complexation );
ꢁ1
Stoddart et al. reported K=360m in this solvent by a
[15]
single measurement at unspecified concentrations.
The
apparent lack of concentration dependence is attributed to
the higher polarity of acetone (e = 20.7) vs. 2:3 (v/v)
CD CN/CDCl (e estimated to be 17.5 by volume averag-
[13]
occur.
To evaluate these equilibria, we proposed data
3
3
treatments that used Equation (5) with approximations of
ing), thus allowing most of the guest 2-PF to be predomi-
6
ꢁ
+
the concentrations of the counterion X and guest salt G
nantly ionized and the ammonium cation to be captured by
the crown ether guest as a non-ion paired complex, making
Equation (3) a good approximation. Indeed there is evi-
dence that in mixed solvents selective solvation influences
ꢁ
X . Here we describe a more rigorous approach to analysis
of such systems and introduce guidelines for detection of
this situation, which we believe occurs more widely than
presumed.
[16]
ion pairing in a non-linear manner; this may explain the
large effect observed for a relatively small change in bulk di-
electric constant from acetone to CD CN/CDCl 2:3. (Note:
3
3
these results were derived from spectra recorded immediate-
ly after solution preparation, thus avoiding the complication
that results when the ammonium salt reacts with the sol-
Results and Discussion
Effect of solvent: In our prior work we used the 2:3 (v/v)
CD CN/CDCl solvent system and showed that 2-TFA had a
[17]
vent.
)
3
3
[11]
low ion-pair dissociation constant therein.
Figure 2 dis-
plays spectra of 1 and 2-TFA taken in CDCl . Note that no
Effect of concentrations: In continuation of our previous
3
new signals appear; the crown ether protons remain essen-
tially unchanged, as do the guest signals, with up to a 21-
work in CD CN/CDCl 2:3, we varied the equimolar con-
3
3
centrations of 1 and 2-PF from 1 to 50 mm. A plot of K
6
a2
fold excess of the latter. We conclude that in CDCl the
(or equivalently K ) versus concentration resulted in a
3
a3
guest salt is essentially totally ion paired and hence does not
interact with the crown ether.
curve that approached an asymptotic limit of K =4.5ꢂ
a2
2
ꢁ1
10 m (Figure 3). The same asymptotic behavior was found
3
ꢁ1
On the other hand in CD CN/CDCl 2:3, complex 2-PF
possesses a relatively high ion-pair dissociation constant.
In the present work we examined
with 1 and 2-BF , but with a limit of K =1.3ꢂ10 m (see
3
3
6
11]
4
a
2
[
Supporting Information). And with 1 and 2-TFA the limit-
ꢁ
1
1
and 2-PF6 in
ing value was ~20m (see Supporting Information).
[
D ]acetone. Indeed, over a range of concentrations (2 to
6
1
6 mm in 1 and 2 to 16 mm in 2-PF , see Supporting Informa-
Effect of added counterions: At constant equimolar concen-
trations (3.00 mm) of DB24C8 and 2-PF in CD CN/CDCl
3
6
tion) in this solvent the complexation of guest 2-PF by di-
6
6
3
benzo-[24]crown-8 (1) seems to follow the scenario de-
scribed by Equation (3) above. That is, Ka3 is constant
2:3 tetrabutylammonium TFA (TBA-TFA) was added in
increasing concentrations; at TBA-TFA concentrations
ꢃ~15 mm no detectable complexation occurred. This is the
result of the strong ion pairing
ꢁ1
within experimental error: K =418ꢂ41m
(10 data
a3
of 2-TFA. (We demonstrated by
1
H NMR that TBA-TFA does
not interact with the crown
ether; see Supporting Informa-
tion). In the X-ray crystal struc-
ture of the DBA-TFA salt
(
Figure 4) each carboxylate hy-
drogen bonds with an N-H
proton on two proximal cations.
The tosylate salt in the crystal-
line phase also forms a hydro-
gen bonded linear structure
(
Figure 5), while the triflate
exists as a tetramer composed
of two cations and two anions
(
Figure 6). In solution similar
interactions presumably take
place.
In a related study, [1] and [2-
1
PF ] were both held constant at
Figure 2. H NMR spectra (400 MHz, 22.18C, CDCl
3
) of solutions of DB24C8 (1, 3.5 mm) with (from top to
6
bottom) 0, 1, 3, 12 and 21 equivalents of 2-TFA. Solvent/guest impurities are labeled with *.
1.67 mm and tetrabutylammoni-
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Ion Pairing
FULL PAPER
Figure 3. Variation of Ka2 with equimolar concentrations of DB24C8 and
2
6 3 3
-PF in CD CN/CDCl 2:3 at 228C.
Figure 5. Single crystal X-ray structure of 2-OTs. Hydrogen bonds are in-
dicated by the dashed lines. The sulfonate oxygen atoms are hydrogen
bonded to the N-H protons on the two adjacent cations, forming a non-
covalent polymeric structure.
+
ꢁ
found when nBu N BF
A
H
U
G
R
N
U
G
4
4
4
lution of 1 (0.657 mm) and 2-BF (1.27 mm) (see Supporting
4
Information). Furthermore when an equimolar solution
+
2
.50 mm in both 1 and 2-TFA reached 50.2 mm in Et N
4
ꢁ
TFA
A
H
U
G
R
N
U
G
was found to interact with the crown ether, producing small
chemical shifts, attributed to formation of a perching com-
plex (see Supporting Information). The same result was
noted with an equimolar solution 1.67 mm in 1 and 2-OTs
upon addition of 50.0 mm TBA-OTs, that is, complexation
was essentially prevented.
Figure 4. Single crystal X-ray structure of 2-TFA. Hydrogen bonds are in-
dicated by the dashed lines. The carboxylate oxygen atoms are hydrogen
bonded to the N-H protons on the two adjacent cations, forming a non-
covalent polymeric structure.
Interestingly, when the concentration of TBA-PF6 was
held constant at 102 mm, the K values were constant (2.7ꢂ
a2
3
ꢁ1
10 m ) irrespective of the equimolar concentrations of
DB24C8 and 2-PF (Figure 8), in contrast to the results in
6
Figure 3, but in accord with those of Figure 7.
um hexafluorophosphate (TBA-PF ) was titrated into the
The report of Montalti and Prodi that addition of TBA-Cl
to a solution of 1 and 9-anthrylmethylmethylammonium–
PF6 in CD Cl effectively resulted in dethreading of the
6
solution. As shown in Figure 7, the value of K decreased
a2
3
ꢁ1
from 3.37ꢂ10 m at 1.68 mm TBA-PF to a constant value
of 2.8ꢂ10 m above ~15 mm of the TBA salt. Note that this
6
2
2
3
ꢁ1
known pseudorotaxane, a phenomenon attributed to the for-
mation of a tight secondary ammonium chloride ion pair
asymptotic limit was quite different from that of Figure 3
2
ꢁ1
3
ꢁ1
[18]
(
4.5ꢂ10 m ). An asymptotic limit of K =1.6ꢂ10 m was
analogous to 2-Cl, is consistent with the results reported
a2
Chem. Eur. J. 2011, 17, 3192 – 3206
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3195

H. W. Gibson et al.
Figure 8. Variation of Ka2 with equimolar concentration of for DB24C8
and 2-PF
TBA-PF
6 3 3
(in CD CN/CDCl 2:3, 21.78C) in the presence of 103 mm
.
6
asymptotic limits in Figure 3 and 7 clearly indicate that an-
other factor is involved; in addition to ion pairing, activity
coefficients need be considered.
Theory
Figure 6. Single crystal X-ray structure of 2-OTf. Hydrogen bonds are in-
dicated by the dashed lines. The sulfonate oxygen atoms are hydrogen
bonded to the N-H protons on the two adjacent cations, forming a non-
covalent tetrameric structure.
As shown in Equation (5), we consider ion pair dissociation
[19]
as a pre-equilibrium step in the complexation process and
assume that a) the electrolyte exists in solution as a mono-
mer in equilibrium with its component ions, b) it is the free
ammonium ion that forms the complex, the latter being
fully dissociated, and c) there are no other species present.
In such systems activity coefficients are an important con-
sideration. The activity coefficient is exponentially related
to the inverse 3/2 power of the permittivity; as a result it is
extremely sensitive to ionic strength in solvents with low di-
[
20]
electric constants.
Debye–Hꢃckel treatment at 298 K in chloroform (e=
For example, use of the limiting
[21]
4
ꢁ
.81)
for salts composed of monovalent ions yields
1
/2
logg =33.6m , in which g is the activity coefficient and
ꢂ
ꢂ
m is the ionic strength. Thus, the activity coefficient of a
chloroform solution with an ionic strength of 1.00 mm is esti-
mated to be 0.09 (see Figure 9). Restated, this means that in
order for g to be ꢃ0.90 and simulate ideal bahavior (g =
ꢂ
ꢂ
Figure 7. Variation of
6
Ka2 for DB24C8 and 2-PF (1.2 mm each in
ꢁ
6
1
) in CHCl , m must be less than 1.85ꢂ10 m! Taking the
3
CD CN/CDCl 2:3, 21.78C) in the presence of added TBA-PF .
3
3
6
volume average dielectric constant (e=17.5) for 3:2 (v:v)
1
/2
CHCl /CH CN, ꢁlogg =4.84m ; for an ionic strength of
3
3
ꢂ
above; for the crystal structure of 2-Cl, see the Supporting
Information. The loss of the complex signal for 1 and 2-OTs
and 1 and 2-TFA upon the addition of a large excess of
1.00 mm, g =0.703. And, for g >0.90, m must be less than
ꢂ ꢂ
ꢁ
4
[21]
8.9ꢂ10 m. With acetonitrile as solvent (e=38.8 ) ꢁlogg
ꢂ
1
/2
=1.47m ; for an ionic strength of 1.00 mm, g =0.898. With
ꢂ
+
ꢁ
[21]
1/2
R N X (X=OTs or TFA) reflects the fact that quaternary
acetone as solvent (e=20.7 ) ꢁlogg =3.76m ; for an
4
ꢂ
ammonium salts generally dissociate more completely than
secondary ammonium salts, because the quaternary cations
are more readily solvated than secondary ammonium ions,
ionic strength of 1.00 mm, g =0.760. It is clear from these
ꢂ
examples that concentration does not approximate activity
in these systems, and, therefore, “constants” calculated from
concentration-based methods in these low dielectric media
are a priori questionable.
Inclusion of activity coefficients in Equation (5) yields
Equation (5a):
ꢁ
and the resultant higher concentration of free X from the
quaternary salt causes increased ion pairing of the dibenzyl-
ammonium cation (le Chatelierꢀs principle), resulting in less
+
free 2 available for complexation. However, the differing
3196
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Chem. Eur. J. 2011, 17, 3192 – 3206

Ion Pairing
FULL PAPER
þ
1=2
þ
ꢁ
1=2
Ko5 ¼g ½HG ꢀfK K ½Hꢀg =½Hꢀ½G X ꢀ
ꢂ
ipd a5
þ
1=2
þ
ꢁ
1=2
¼
g ½HG ꢀfK ½Hꢀg =½Hꢀ½G X ꢀ
ꢂ
o5
1=2
þ
1=2
þ
ꢁ
1=2
Ko5 =g ¼½HG ꢀ=½Hꢀ ½G X ꢀ
ð5cÞ
ꢂ
Under this condition, that is, when [H] is high, all of the
ꢁ
free counterion X essentially results from complex forma-
+
ꢁ
tion, and [HG ] ꢄ[X ]. Since at infinite dilution g =1, a
ꢂ
+
ꢁ
0
plot of the right hand side of Equation (5c) versus [G X ]
extrapolated to zero concentration will yield Ko5 as the y in-
tercept. In other words the data are extrapolated to a condi-
tion at which the concentrations reflect the activities.
+
ꢁ
Figure 9. g
ꢂ
vs m for a monovalent salt, G X , in CHCl
3
at 298 K, as cal-
culated by the limiting Debye–Hꢃckel equation.
At the other extreme when K [H] !1 from Equa-
tion (5b)
a5
2
þ
ꢁ
þ
ꢁ
Ko5 ¼gꢂ ½HG ꢀ½X ꢀ=½Hꢀ½G X ꢀ
ð5aÞ
Expressing the overall equilibrium as individual steps in
terms of activities:
þ
1=2
þ
ꢁ
1=2
Ko5 ¼g ½HG ꢀK
=½Hꢀ½G X ꢀ
ꢂ
ipd
1
=2
1=2
þ
þ
ꢁ
1=2
K =g K
¼K K
=g ¼½HG ꢀ=½Hꢀ½G X ꢀ
ð5dÞ
o5
ꢂ
ipd
a5 ipd
ꢂ
2
þ
ꢁ
þ
ꢁ
Kipd ¼gꢂ ½G ꢀ½X ꢀ=½G X ꢀ
ð6Þ
Under this condition, that is, when [H] is low, the free coun-
terion is essentially all generated as a result of ion pair dis-
+
Solving for [G ]:
+
ꢁ
sociation of G X . A plot of the right hand side of Equa-
+
ꢁ
þ
þ
ꢁ
2
ꢁ
tion (5d) versus [G X ] extrapolated to zero concentration
0
½
G ꢀ¼K ½G X ꢀ=g ½X ꢀ
ð6aÞ
ð7Þ
ipd
ꢂ
1
/2
will yield K K
as the y intercept. Again the data are ex-
a5 ipd
trapolated to a condition at which the concentrations reflect
and
the activities, that is, g =1. Provided both binding regions
ꢂ
are experimentally observable, the individual constants may
then be determined from the ratio of the intercepts of plots
of Equation (5c) and (5d).
þ
þ
Ka5 ¼½HG ꢀ=½Hꢀ½G ꢀ
+
Solving for [HG ]:
þ
½
HG ꢀ¼K ½Hꢀ½Gþꢀ
ð7aÞ
ð7bÞ
ð8aÞ
a5
Application of the Pre-equilibrium Model
Substituting Equation (6a) into (7a):
1
We have applied these treatments to our H NMR data for
+
þ
þ
ꢁ
2
ꢁ
pseudorotaxane 1·2
formation. Provisionally assuming
½
HG ꢀ¼K ½HꢀKipd½G X ꢀ=g ½X ꢀ
a5
ꢂ
ꢁ
1
K =500m , we studied host–guest solutions in which [1]
a5
0
ꢃ15.0 mm (K [H] ꢃ7.5@1.0, error 1/8.5 ꢅ12%) and at
a5
Conservation of charge requires that
the other extreme, K [H] !1, we studied host/guest solu-
a5
tions in which [1] ꢅ0.500 mm (K [H] ꢅ0.25 ! 1.0, error
ꢁ
þ
þ
0
a5
½
X ꢀ¼½G ꢀþ½HG ꢀ
0
.25/1.25 ꢅ20%). Plots of Equation (5c) for four counter-
ions are shown in Figure 10. Plots of Equation (5d) are
shown in Figure 11. In both plots we used [G X ]=
Substitution of Equations (6a) and (7b) into Equation (8a)
leads to
+
ꢁ
+
ꢁ
+
[
G X ] ꢁ
ACHTUNGTRENNGNU[ HG ]; see Supporting Information for a discus-
o
sion of the errors introduced by this approximation, which
ꢁ
þ
ꢁ
2
1=2
½
X ꢀ¼fðK ½G X ꢀ=g Þð1 þK ½HꢀÞg
ð8bÞ
decrease in the order PF >BF >OTs>TFA and approach
zero at low salt concentration.
ipd
ꢂ
a5
6
4
Substituting Equation (8b) into Equation (5a):
It is interesting to compare the intercepts of these plots.
1
/2
From Figure 10 the values of Ko5 are 1.88, 1.40, 0.489 and
0.304, respectively, for X=PF , BF , OTs and TFA. Note
Ko5 ¼g ½HG ꢀfðK ½G X ꢀ=g Þð1 þK ½HꢀÞg1=2=
2
þ
þ
ꢁ
2
6
4
ꢂ
ipd
ꢂ
a5
1
/2
0.5
that Ko5 =[KipdK ] . Since K is identical for all of the
a5
a5
þ
ꢁ
þ
1=2
þ
ꢁ
1=2
½
Hꢀ½G X ꢀ¼g ½HG ꢀfK ð1 þK ½HꢀÞg =½Hꢀ½G X ꢀ
ꢂ
ipd
a5
counterions, the intercepts yield the following ratios: KipdPF6
/
ð5bÞ
KipdBF4 =1.80, KipdPF6/KipdOTs 14.7, KipdPF6/KipdTFA =38.2.
=
1
/2
From Figure 11 the values of Ka5 Kipd are 42.4, 31.3, 10.9
and 6.76, respectively, for X=PF , BF , OTs and TFA. From
Equation (5b) may be evaluated under two extremes. When
6
4
K [H]@1 Equation (5b) reduces to
a5
the values from these plots we can calculate the following
Chem. Eur. J. 2011, 17, 3192 – 3206
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
3197

H. W. Gibson et al.
ratios:
KipdPF6/KipdBF4 =1.83,
KipdPF6/KipdOTs =15.1,
KipdPF6/
KipdTFA =39.2. The latter values
from Equation (5d) are in ex-
cellent agreement (ꢂ3% rela-
tive) with the values calculated
using Equation (5c); this self-
consistency provides corrobora-
tion of the validity of the ap-
proach, since the two sets of
measurements are basically in-
dependent of each other.
Table 1 summarizes the individ-
ual constants.
The values of Kipd in Table 1
are roughly in accord with re-
ported activity-based values for
[22]
tetraalkylammonium
salts
and concur with the observa-
tion that PF salts are generally
6
[23]
the most dissociated.
To ap-
preciate the effect of the differ-
ences in Kipd, consider the fol-
lowing extents of ionization cal-
culated for solutions of the
DBA salts alone at 1.00 (10.0)
mm: PF : 90% (55%); BF :
Figure 10. Plots of Equation (5c) (Ka5[H]@1) for solutions of 1 and a) 2-PF
in CDCl /CD CN 3:2, 295 K.
6 4
, b) 2-BF , c) 2-OTs, and d) 2-TFA
3
3
6
4
82% (46%); OTs: 49%
(
19%); TFA: 35% (12%).
Moreover, the values of Ka5 for
all the salts are identical within
experimental error, as mandat-
ed by this equilibrium treat-
ment. Because Table 1 includes
analysis based on activity coef-
ficients, whereas all other previ-
ously published values assume
g =1, we believe these to be
ꢂ
the most accurate Ka5 values re-
ported to date for pseudorotax-
+
ane 1·2 formation.
With Ka5 and Kipd in hand, g
ꢂ
may be calculated for each data
point according to Equa-
tions (5c) and (5d). Figure 12
displays these results for all 1
and 2-X solutions and demon-
strates the large variation in ex-
+
ꢁ
perimental g with [G X ] .
ꢂ
0
The existence of two families of
activity curves is not unexpect-
ed: when K [H]@1 (Figure 12,
a5
top dotted curves), complex
+
cations 1·2 dominate; at the
other
extreme
(Figure 12,
K [H] !1, bottom solid
curves), guest cations 2 domi-
Figure 11. Plots of Equation (5d) (Ka5[H]!1) for solutions of 1 and a) 2-PF
TFA in CDCl /CD CN 3:2, 295 K.
6
, b) 2-BF
4
, c) 2-OTs, and d) 2-
a5
+
3
3
3198
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ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 3192 – 3206

Ion Pairing
FULL PAPER
Table 1. Equilibrium constants for 2-X salts with 1 calculated from Equation (5c) and (5d) [CDCl
3
/CD
3
CN ally, that is, g ~1. The decrease
ꢂ
3
:2, 295 K].
in activity coefficient follows
2
ꢁ1 [a]
[b]
X
Intercept (A)
of Figure 10
Equation (5c)
Intercept (B)
of Figure 11,
Equation (5d)
Ko5 =A
K
a5 [m
]
Kipd [m]
the order OTs>TFA>PF >
6
BF4 for K [H] !1 and OTs>
a5
TFA>BF ꢃPF for K [H]@
4
6
a5
6.94 (ꢂ3.40) ꢂ 10ꢁ
3
3
4
4
PF
BF
OTs
TFA
ave
6
1.88ꢂ0.08
1.40ꢂ0.10
0.489ꢂ0.001
0.304ꢂ0.002
–
42.4ꢂ1.4
31.3ꢂ1.0
10.9ꢂ0.3
6.76ꢂ0.11
–
3.53ꢂ0.33
509ꢂ80
500ꢂ110
497ꢂ30
495ꢂ30
500ꢂ63
1
. Note the fact that BF and
4
ꢁ
4
1.96ꢂ0.28
3.92 (ꢂ3.00) ꢂ 10
ꢁ
PF switch positions in the two
0.239ꢂ0.001
0.0924ꢂ0.0012
4.80 (ꢂ0.80) ꢂ 10
6
ꢁ
1.85 (ꢂ0.30) ꢂ 10
different regimes.
–
Looking back to Figures 3, 7
and 8, we can now rationalize
the results. In Figure 3 in the
2
2
[
a] Ka5 =(B/A) . [b] Kipd =(B/Ka5) .
plateau region K [1]@1. In
a5
Figure 7 K [1] <1 and ions
a5
from TBA-PF predominate; in
6
this case the pseudorotaxane
cation and the dibenzylammo-
nium cation are at relatively
low concentrations. The results
shown in Figure 8 indicate that
even when the concentrations
of the host and guest are in-
creased the effect of the added
quaternary salt is dominant and
thus the ultimate value of Ka2 is
the same in Figures 7 and 8.
The plateau in Figure 3 corre-
sponds to the situation in which
2
ꢁ
the value of K /g [X ] is con-
o5
ꢂ
stant, meaning that the product
2
ꢁ
g
[X ] is constant; in other
ꢂ
words, in this regime the in-
creasing anion concentration is
offset by the change in activity
coefficient. The reasons that
the plateau values of Figures 3,
7 and 8 are different are two-
fold: 1) because of the higher
Figure 12. g
ꢂ
as calculated according to Equation (5c) (Ka5[H]@1, top dotted curves) and Equation (5d)
+
ꢁ
0
(
K
a5[H] !1, bottom solid curves) vs. [G X ]
6 4
for solutions of 1 and a) 2-PF , b) 2-BF , c) 2-OTs, and d) 2-
TFA in CDCl /CD CN 3:2, 295 K. The lines have been added to guide the eye.
3
3
Kipd value for TBA-PF relative
6
to 2-PF6 the ionic strength is
nate. Interestingly, in the K [H]@1 regime, g changes less
higher in the latter cases, caus-
a5
ꢂ
than is the case when K [H] !1. This is most likely a conse-
ing a smaller g and, 2) in the latter two cases (Figures 7
a5
ꢂ
quence of the lower solvation energy of the larger pseudoro-
and 8) the presence of the tetrabutylammonium cation
+
+
taxane cation 1·2 relative to 2 , as described to a first ap-
likely alters the average value of g .
ꢂ
[24]
proximation by the Born model. We speculate that this is
due to delocalization of charge in the pseudorotaxane
cation, which would effectively impart more “ideal” charac-
Direct Determination of Kipd Values
+
ter to the complex ion, 1·2 , than is the case for the
+
“
naked” 28 ammonium ion, 2 .
In our early work, we attributed changes in the chemical
shifts of the uncomplexed dibenzylammonium species, par-
ticularly the benzylic protons, to time-averaged exo or
The activity coefficients vary significantly with the anion.
The logarithms of the activity coefficients are linear with the
salt concentrations as described in Figures 13 and 14 for the
two extreme cases; this is in accord with Debye–Hꢃckel
theory.
[12a]
perching type complexation with the crown ether;
how-
ever, it now clear that the major cause of these chemical
shift changes is time averaging caused by the dynamic ion
ꢁ
It is interesting to compare the effects of different anions
on the activity coefficients. As seen in Table 2 there is a
wide variation both when K [H] !1 and when K [H]@1.
pair equilibrium of the salt as it responds to the free X gen-
erated by formation of the pseudorotaxane complex. Other
authors have used chemical shift data to estimate K values
a5
a5
ipd
[25]
Under most conditions the tosylate salt behaves nearly ide-
for various salts in organic solvents; however, they ignor-
Chem. Eur. J. 2011, 17, 3192 – 3206
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
3199

H. W. Gibson et al.
determine the chemical shifts of
the free cation and the fully
ion-paired cation. We examined
a number of the salts 2-X as
functions of their concentra-
tions; all displayed concentra-
tion dependent chemical shifts,
particularly for the benzylic
protons. For 2-PF6 and 2-TFA
we observed anomalous behav-
ior in terms of chemical shifts
at both very high and very low
concentrations (see Supporting
Information), thus making esti-
mation of the chemical shifts of
the free and fully ion paired
cation precarious. In view of
the possibility of formation of
more complicated species, such
[25e,26]
as triple ions,
at the ex-
tremes, we consider estimation
of K
values for these salts
ipd
1
using H NMR data to be ques-
tionable.
+
Figure 13. Plots of ꢁlogg
ꢂ 6 4
versus [1·2 ] for solutions of 1 and a) 2-PF , b) 2-BF , c) 2-OTs, and d) 2-TFA in
CDCl /CD CN 3:2, 295 K, Ka5[H]@1.
3
3
Utilization of the Model as
a Predictive Tool
Due to the fact that the activity
coefficients vary significantly
with concentration, prediction
of extents of complexation
using the derived Kipd and Ka5
values becomes a daunting task.
To illustrate, in Figure 15
+
+
ꢁ
1/2
[
H·G ]/
A
H
U
G
R
N
N
[G X ]
(determined
is plotted
experimentally)
versus [H·G ]/
+
+
ꢁ
1/2
ACHTUNGTRENNUNG[ G X ] calcu-
lated according to rearranged
Equation (5b) assuming g =1,
ꢂ
2
ꢁ1
K =5.1ꢂ10 m
6
and Kipd =
.9ꢂ10 m; the line corre-
a5
ꢁ
3
sponds to a perfect relationship.
There is a clear lack of agree-
ment between predicted and
experimental values. These re-
sults reflect the fact that the ac-
tivity coefficient is lower at
Figure 14. Plots of ꢁlogg
ꢂ 0 6 4
versus [2-X] for solutions of 1 and a) 2-PF , b) 2-BF
, c) 2-OTs, and d) 2-TFA in higher ionic strength, leading to
CDCl /CD CN 3:2, 295 K, Ka5[H]!1.
3
3
relatively greater extents of
complexation on a molar basis
relative to the low ionic
ed changes in activity coefficients, which will affect different
points along the curve differently. In principle the same ap-
proach described above could be employed, except that the
ion pairing equilibria are fast exchange and thus one must
strength situation, as can be seen from Equation (7b). These
results also reflect the dependence of the activity coefficient
on the nature of the predominant cation, whether the free
+
sec-ammonium cation (2 ) or the pseudorotaxane complex
3200
www.chemeurj.org
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 3192 – 3206

Ion Pairing
FULL PAPER
+
ꢁ
Table 2. Variation of experimental activity coefficients (g
ꢂ
) with concentration and anion in CDCl
3
/CD
3
CN a large excess of salt (N X )
such that essentially all of the
free anion results from ion pair
3
:2.
K
a5[H] !1
Ka5[H]@1
[
!
X=OTs
X=TFA
X=BF
X=PF
1]/[2-X]/mmmm
A
C
H
T
U
N
G
T
R
E
N
N
U
N
G
0.50/0.50
0.50/1.00
0.50/2.00
0.75
20.0/15.0
20.0/10.0
16.0/16.0
dissociation of this salt alone
Kipd,NX) affords a quantitative
means of evaluating relative
(
0.93
0.91
0.85
0.62
0.84
–
0.44
–
0.98
0.84
0.38
0.34
0.99
0.87
0.45
0.42
0.98
0.82
0.38
0.32
cation binding constants, K , as
4
0.29
0.60
a5
follows:
6
2
þ
ꢁ
þ
ꢁ
Kipd,NX ¼gꢂ ½N ꢀ½X ꢀ=½N X ꢀ
ð9Þ
ꢁ
Solving for [X ]:
ꢁ
þ
ꢁ
2 1=2
½
X ꢀ¼fK
½N X ꢀ=g
g
ð9aÞ
ipd,NX
ꢂ
Substitution of Equation (9a) into Equation (5a) leads to
þ
þ
ꢁ
1=2
þ
ꢁ
Ko5 ¼Kipd, 2-XKa5 ¼g ½HG ꢀfK
½N X ꢀg =½Hꢀ½G X ꢀ
ꢂ
ipd,NX
ð10Þ
þ
ꢁ
1=2
þ
þ
ꢁ
Ka5 ¼ðg fK
½N X ꢀg =Kipd, 2 XÞ½HG ꢀ=½Hꢀ½G X ꢀ
ꢂ
ipd,NX
-
+
+
ꢁ1/2
Figure 15. Plot of [H·G ]/
ACHTUNGTNERNUNG[ G X ] calculated according to Equation (5b)
+ +
þ
þ
ꢁ
ꢁ
1/2
¼ðconstantÞ½HG ꢀ=½Hꢀ½G X ꢀ
(
solid line, g =1) versus [H·G ]/ACHTNUGTRENNUNG
for solutions of 1 and 2-PF
ꢂ
6
3
3
ð10aÞ
Equation (10a) provides a means of evaluating the relative
+
(
1·2 ). Disregard of g in estimation of equilibrium con-
ꢂ
values of Ka5 for two or more hosts and any given guest in
stants amounts to the assumption that g =1 and mirrors
the widespread use of invalid Equation (2) [or Eq. (3)] in
the literature.
+
ꢁ
ꢂ
the presence of excess N X . Thus, from Equation (10a) the
+
ratio
H ]
K
/Ka5,B is equivalent to the ratio ([H G ]/
a5,A
ꢁ
A
+
+
+
ꢁ
[
A
H
U
G
R
N
U
[G X ])/
A
H
U
G
R
N
U
([H G ]/[H ]
ACHTUNGERTNNUGN[ G X ]), providing
a
rigorous
A
B
B
To utilize the binding constants for their intended purpose
as predictive tools, activity coefficients must therefore be
known (or be capable of being estimated) a priori. While
the activity coefficients are well-behaved in each binding
regime (Figures 13 and 14), they are dependent on the
nature of the anion and the concentrations. Based on these
considerations, we conclude that it is difficult, if not impossi-
ble, to use the two equilibrium constants involved in these
processes to predict extents of complexation.
quantitative comparison of binding efficiencies of the two
hosts A and B. In fact we have applied this method in two
published cases. We showed that the dibenzylammonium
pseudorotaxane complexes of the syn- and anti-isomers of
bis(carbomethoxy)dibenzo-[30]crown-10 were not ion-
paired in CDCl /CD CN 3:2, thereby displaying the same
3
3
concentration dependent Ka2 behavior described here; how-
ever, application of the above treatment allowed us to deter-
mine the Ka5 value for these two hosts based on the now
[13f]
known Ka5 for DB24C8 (1) under the same conditions.
Likewise Ka5 for a polystyryl DB24C8 with the dibenzylam-
monium cation was also determined.
Comparisons between Hosts for Any Given Guest
[28]
On a more positive note, however, results from these studies
suggest an experimental method to compare the binding ef-
ficiencies of two or more hosts for any given guest in a pre-
cise manner. Such a comparison is of great practical interest:
the ultimate goal in many host/guest studies is the develop-
ment of a host moiety that selectively and strongly binds a
specific guest species; for example, the formation of high
molecular weight supramolecular polymers from small mole-
cule building blocks requires very high association constants
Final Comments
It should be noted that the more soluble the salt in low po-
larity organic solvents, the greater the ionization constant,
Kipd, and consequently the higher the ionic strength and thus
the lower the activity coefficient. This can be seen by inspec-
tion of Table 2; the more soluble BF and PF salts display
4
6
4
ꢁ1 [27]
(
>10 m ).
As shown in Figures 7 and 8 the extent of
lower activity coefficients relative to the less soluble OTs
and TFA salts. Therefore, the choice of the more soluble
salts actually complicates the analysis, while at the same
time it increases the extent of complexation as a result of a
complexation approaches an asymptotic limit upon addition
of a salt whose cation does not interact with the host and
whose anion is identical to that of the guest. The addition of
Chem. Eur. J. 2011, 17, 3192 – 3206
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
3201

H. W. Gibson et al.
ꢁ
higher cation concentration and the lower activity coeffi-
cient [see Eq. (5e)].
ammonium salt with the same anion (X ) as the guest salt
(2-X).
Furthermore, as we observed earlier, complexation of the
counterion X in these situations will lead to a higher per-
þ
þ
ꢁ
2
ꢁ
ꢁ
½
HG ꢀ¼K ½Hꢀ½G X ꢀ=g ½X ꢀ
ð5eÞ
o5
ꢂ
centage of complexation of the cations because the dissocia-
tion to the free cations will be encouraged (le Chatelierꢀs
[11]
Conclusion
principle). Indeed this realization has resulted in the syn-
thesis of ditopic hosts capable of binding both the anionic
[31]
These studies reveal the importance of correctly defining
equilibria when deriving quantitative descriptions of host–
guest interactions. When salts are involved, particularly in
low dielectric constant solvents, ion pairing must be consid-
ered. This may be easily done by comparing Ka2 or Ka3
values for a given system at various starting component con-
centrations. If Ka2 or Ka3 values do not vary with [host] or
and cationic species with greater affinity.
Experimental Section
General experimental procedures: Dibenzo-[24]crown-8 (1) was pur-
chased commercially and used without further purification. All solvents
were used as received from the vendor. Melting points were determined
in a Mel-temp II melting point apparatus and are corrected. All proton
NMR spectra were recorded on Varian Unity or Inova 400 MHz instru-
ments using tetramethylsilane as an internal standard; the following ab-
breviations are used: b (broad), s (singlet), d (doublet), m (multiplet), t
(triplet), ArH (aromatic hydrogen). Elemental analyses were performed
by Atlantic Microlab, Inc., Norcoss, GA.
[
guest], then either the salt and the complex are both ion-
paired [Eq. (2)] or the salt and the complex are both essen-
tially not ion paired [Eq. 3)]. In these circumstances, provid-
ed activities may be estimated in the second case, a single
point determination of K at any given temperature may be
adequate.
a
On the other hand, if Ka2 or Ka3 values fluctuate with con-
centration, it indicates that the situation described by Equa-
tion (5) obtains and a broad range of host and guest concen-
trations must be examined to properly quantify binding.
Moreover, because activity varies with temperature, exten-
sive studies would have to be run at all temperatures to
derive meaningful thermodynamic parameters DH and DS .
Failure to consider the low activity coefficients of salts at
NMR concentrations (>1 mm) in low dielectric media can
lead to erroneous analyses of such systems. For example, it
may lead to use of curve fitting-based (“black-box”) rou-
tines that employ undetected or hypothesized species to ac-
count for the resultant deviations from simpler theories.
[
13c]
Dibenzylammonium chloride (2-Cl): A described by Stoddart et al.
a
1
2.2m stock HCl solution (42 mL) was transferred to a 250 mL round-
bottom flask and diluted with dionized water to yield a 2.0m HCl solu-
tion. To this solution, dibenzylamine (4.9416 g, 25.05 mmol) was slowly
added, whereupon the white precipitate of dibenzylammonium chloride
was immediately observed. The mixture was allowed to stir for 6 h before
the chloride salt was collected via vacuum filtration, recrystallized from
O (3ꢂ) and dried (4.60 g, 80%). M.p. 275–2778C (lit., not reported);
H NMR (DMSO, 400 MHz): d = 9.89 (brs, 2H), 7.57 (d, J=7 Hz, 4H),
.43–7.37 (m, 6H), 4.10 ppm (s, 4H); elemental analysis calcd (%) for
0
0
H
2
1
7
C H NCl: C 71.94, H 6.90, N 5.99; found: C 71.91, H 6.83, N 5.96.
1
4
16
Dibenzylammonium hexafluorophosphate (2-PF ): Also described by
6
[
13c]
Stoddart et al.,
warm, deionized water (100 mL) was added to diben-
zylammonium chloride (4.6 g, 20 mmol). Heating resulted in complete
solvation of the chloride salt, whereupon slow addition of saturated aque-
ous ammonium hexafluorophosphate yielded a thick, white precipitate
that was collected via vacuum filtration, washed excessively with warm
[29]
Note that use of UV/Vis or fluorescence
spectroscopic
measurements allows lower concentrations to be employed,
relative to NMR, and salts may be completely ionized or
nearly so and the situation is described by Equation (3) with
appropriate account of activity coefficients; however, the re-
sults from such measurements cannot be extended to higher
concentrations without due consideration of the issues
raised here. Similar reservations apply to use of titration mi-
crocalorimetry to study such systems; great care must be
taken, since normally the software does not take account of
situations described by Equation (5). Unfortunately even
a rigorous analysis suffers the same end result; the resultant
association constants cannot predict concentrations of all
species at all concentrations, because the activity coefficients
cannot be predicted with confidence. These findings are in
accord with a former colleagueꢀs [Charles B. (“Charlie”)
Duke] conclusions that: “…1) All theories are wrong; itꢀs
just a matter of degree. 2) All experiments measure some-
thing. Itꢀs probably not what you think they measure, and if
[
13c]
water and dried (4.30 g, 64%). M.p. 208–2108C (lit.: 192–1938C,
207–
[
32]
1
2
4
4
098C ); H NMR (CD CN, 400 MHz): d = 7.49 (s, 10H), 4.25 ppm (s,
3
H); elemental analysis calcd (%) for C14
.08; found: C 48.97, H 4.62, N 3.99.
6
H16NPF : C 48.99, H 4.70, N
Dibenzylammonium methanesulfonate (2-OMs): Methanesulfonic acid
1.00019 g, 10.41 mmol) was added to diethyl ether (100 mL) at room
(
temperature and dibenzylamine (2.00 mL, 10.4 mmol, via a 2 mL TD
volumetric pipette) were added dropwise to the stirred acid solution, re-
sulting in an immediate white precipitate. The precipitate was collected
via vacuum filtration, washed with copious amounts of diethyl ether, and
[
8j]
1
dried (3.05 g, 95%). M.p. 135–1378C (lit., not reported); H NMR
(
CDCl
(m, 6H), 3.94 (t, J=5 Hz, 4H), 2.60 ppm (s, 3H); elemental analysis
calcd (%) for C15 S: C 61.41, H 6.53, N 4.77; found: C 61.21, H
.49, N 4.70.
Dibenzylammonium p-toluenesulfonate (2-OTs): p-Toluenesulfonic acid
2.8533 g, 15.13 mmol) was dissolved in methanol (25 mL) at room tem-
3
, 400 MHz): d = 9.24 (brs, 2H), 7.45 (d, J=8 Hz, 4H), 7.39–7.30
H
19NO
3
6
(
perature. Dibenzylamine (2.9660 g, 15.03 mmol) was added dropwise to
the stirred acid solution, resulting in a white precipitate. The precipitate
was collected via vacuum filtration, washed with cold methanol, and
1
[
30]
dried (5.35 g, 92%). M.p. 166–1688C (lit., not reported); H NMR
it is, not to the precision needed.”…
(
4
2
CDCl
3
, 400 MHz): d = 9.27 (brs, 2H), 7.59 (d, J=8 Hz, 2H), 7.38 (m,
H), 7.27 (m, 6H), 7.13 (d, J=8 Hz, 2H), 3.91 (t, J=5 Hz, 4H),
.38 ppm (s, 3H); elemental analysis calcd (%) for C21 S: C 68.27,
However, this research did result in the development of a
method to determine the relative binding constants for vari-
ous hosts with a given guest by the addition of a tetrabutyl-
H
23NO
3
H 6.27, N 3.79; found: C 68.09, H 6.23, N 3.80.
3202
www.chemeurj.org
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 3192 – 3206

Ion Pairing
FULL PAPER
Dibenzylammonium tetrafluoroborate (2-BF
4
): Tetrafluoroboric acid,
try and systematic absences were consistent with the monoclinic space
5
4% by weight in diethyl ether (1.55 g, 18 mmol), was added to diethyl
ether (100 mL) at room temperature. Dibenzylamine (2.00 mL,
0.4 mmol, via a 2 mL TD volumetric pipette) was added dropwise to the
groups P2
1
/n. The structure was solved by direct methods and refined
[
35]
using the SHELXTL 97 program package.
volved an anisotropic model for all non-hydrogen atoms. Hydrogen atom
positions and isotropic thermal parameters were refined independently.
The final refinement in-
1
stirred acid solution. A white precipitate was observed immediately, col-
lected via vacuum filtration, washed with diethyl ether and dried (2.00 g,
6
7
C
1
Preparation of solutions and H NMR analyses: To minimize experimen-
tal error in these studies, solutions were prepared by precisely weighing a
[
33]
1
8%). M.p. 196–1988C (lit. 1868C ); H NMR (CDCl
.37 (s, 10H), 4.03 ppm (s, 4H); elemental analysis calcd (%) for
: C 58.98, H 5.66, N 4.91; found: C 59.10; H 5.61; N 4.97.
3
, 400 MHz): d =
ꢁ2
ꢁ5
minimum of 1.0ꢂ10 (ꢂ5ꢂ10 ) g each host and guest component by
14
H
16NBF
4
ꢁ4
means of an analytical balance which read to 1.0ꢂ10 g into a 5.00
Dibenzylammonium trifluoromethanesulfonate (2-OTf): Trifluorometha-
nesulfonic acid (1.64494 g, 10.96 mmol) was added to diethyl ether
(ꢂ0.02) or 10.00 (ꢂ0.02) mL volumetric flask equipped with a ground
glass stopper to make a moderately concentrated (nominally 16.0 mm)
master solution. A CD CN/CDCl 2:3 (by volume) solvent mixture was
(
~100 mL) at room temperature. Dibenzylamine (2.00 mL, 10.40 mmol,
3
3
via a 2 mL TD volumetric pipette) was added dropwise to the stirred acid
chosen because the 2-X salts investigated displayed a wide range of solu-
solution. A white precipitate was observed and collected via vacuum fil-
bility behaviors in the lower dielectric constant solvent, whereas they
tration, washed with diethyl ether and dried (2.60 g, 72%). M.p. 115–1178C
were all well-solvated by CH CN. This solution was then sequentially di-
luted (no more than four sequential dilutions per master solution) by
3
1
(
(
C
lit., no report); H NMR (CDCl
3
, 400 MHz): d = 8.18 (brs, 2H), 7.39
m, 10H), 3.97 ppm (t, J=5 Hz, 4H); elemental analysis calcd (%) for
SO : C 51.87, H 4.84, N 4.03; found: C 51.90, H 4.64, N 3.99.
Dibenzylammonium trifluoroacetate (2-TFA): Trifluoroacetic acid
15.4 mL, 200 mmol) was added to a 100 mL volumetric flask and diluted
with dionized water, to yield a 2.00m solution. Dibenzylamine (1.98254 g,
0.24 mmol) was added to a round bottom flask, to which the TFA solu-
transferring specific volumes of the higher concentration solution to a
clean volumetric flask via a to-deliver volumetric pipette (ꢂ0.006 mL)
and diluting to the mark. The fresh solutions were filtered through a
cotton-filled disposable pipette before 0.500 (ꢂ0.006) mL of each solu-
tion component (both host and guest) at a specified concentration was
transferred via a to-deliver pipette to a 5.0 mm NMR tube. NMR spec-
troscopic data were collected on a temperature controlled 400 MHz spec-
trometer within 1 hour of mixing the solutions. Table 3 displays results
for the full data sets utilized in these studies. When Kap[H]@1, the frac-
tion of total crown moieties occupied by guest was determined by inte-
15
H
16NF
3
3
(
1
tion was slowly added. A white precipitate was immediately observed
and collected via vacuum filtration, washed with water, and dried (2.23 g,
1
7
1%). M.p. 147–1498C (lit. no report); H NMR (CDCl
3
, 400 MHz): d =
9
.90 (brs, 2H), 7.21–7.31 (m, 10H), 3.81 ppm (t, J=5 Hz, 4H); elemental
analysis calcd (%) for C16
1.63, H 5.28, N 4.42.
H
16NO
2
F
3
: C 61.73, H 5.18, N 4.50; found: C
gration of the complexed and uncomplexed crown signals H
ar,H; the same signals were followed when Kap[H] !1 and [H]
g
and/or
ꢃ[G
+
6
H
0
ꢁ
+
ꢁ
3
0 ap 0
X ] . When K [H] !1, and [H] <[G X ] , the fraction of host occu-
Crystallography: Long thin needles (~1.0ꢂ0.2ꢂ0.01 mm ) of 2-OTs, 2-
TFA, and 2-OTf were crystallized by vapor diffusion of pentane into
0
pied (represented by q) was determined by integration of the complexed
and uncomplexed guest signals H
1
and/or Har,G.
chloroform solution at room temperature. A needle was cut (~0.2ꢂ0.1ꢂ
3
0
.02 mm ), mounted on a nylon CryoLoop (Hampton Research) with
Maximum possible concentration errors were calculated by accumulation
(summing) of weighing and dilution errors. For example, the error in pre-
Krytox Oil (DuPont) and centered on the goniometer of a Oxford Dif-
fraction XCalibur2 diffractometer equipped with a Sapphire 2CCD de-
tector. The data collection routine, unit cell refinement, and data process-
ꢁ
2
paring [1]=0.985 mm was calculated as follows: 1.1104ꢂ10 g of 1 (error
ꢁ
5
in weighing=5.0ꢂ10 g/0.01104 g=0.45%) was added to a 5.00 mL
[
34]
ꢁ5
ing were all carried out with the program CrysAlis. The Laue symme-
volumetric flask and diluted to the mark (dilution error=2.0ꢂ10 L/
Table 3. Fraction of crown ether complexed (q) as a function of [1]
0
and [2-X]
0
, CDCl
[1]
3
/CD
3
CN (3:2), 228C.
[
[
1]
mm]
0
A
C
H
T
U
N
G
T
R
E
N
N
U
N
G
[2-PF
6
]
0
q
[1]
[mm]
0
A
U
T
E
N
N
[2-BF
4
]
0
q
0
A
H
U
G
R
N
U
G
0
q
[1]
0
A
H
U
G
R
N
U
G
0
q
[mm]
[mm]
[mm]
[mm]
[mm]
[mm]
2
2
2
2
2
2
1
1
7
5
4
3
3
3
3
3
3
2
1
1
1
0
0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
4.9
0.0
.45
.00
.00
.73
.73
.73
.73
.73
.73
.00
.89
.00
.00
.492
.492
.492
.492
.492
4.99
20.0
15.0
9.99
7.50
4.99
3.73
3.73
3.73
3.73
4.00
3.80
3.73
1.93
1.19
0.918
5.00
2.00
3.73
1.00
0.998
3.75
2.50
2.00
0.999
0.500
0.241
0.872
0.698
0.478
0.361
0.241
0.241
0.343
0.446
0.636
0.716
0.646
0.771
0.437
0.285
0.231
0.85
0.668
0.710
0.588
0.575
0.802
0.792
0.742
0.672
0.454
20.0
20.0
20.0
20.0
20.0
16.0
8.00
8.00
4.00
4.00
3.82
3.73
3.72
2.00
2.00
1.00
1.00
0.492
0.492
0.492
0.492
0.492
15.0
10.0
6.01
4.99
2.49
16.0
8.00
8.00
4.00
4.00
3.74
3.81
3.83
2.00
2.00
1.00
1.00
2.00
1.50
1.00
0.751
0.500
0.659
0.458
0.28
20.0
20.0
20.0
20.0
16.0
8.00
8.00
4.00
4.00
3.82
2.00
2.00
1.89
1.20
1.00
1.00
0.95
0.492
0.492
30.0
19.9
15.0
9.93
16.0
8.00
8.00
4.00
4.00
3.75
2.00
2.00
3.75
3.75
1.00
1.00
3.75
1.99
0.997
0.410
0.334
0.287
0.227
0.350
0.336
0.329
0.325
0.304
0.306
0.294
0.279
0.365
0.418
0.240
0.241
0.444
0.382
0.275
20.0
16.0
16.0
8.00
8.00
4.00
4.00
3.82
3.82
3.82
3.82
3.82
3.82
3.82
3.82
2.00
2.00
1.20
1.00
0.75
0.502
0.502
0.502
0.34
20.0
16.0
16.0
8.00
8.00
4.00
4.00
20.0
15.4
10.0
7.71
5.00
3.85
3.77
3.76
2.00
2.00
3.77
1.00
3.77
5.02
2.51
1.26
3.77
0.275
0.271
0.290
0.269
0.258
0.224
0.241
0.501
0.442
0.373
0.324
0.272
0.237
0.269
0.232
0.207
0.225
0.408
0.219
0.405
0.489
0.339
0.236
0.424
0.234
0.119
0.790
0.759
0.761
0.707
0.709
0.688
0.679
0.723
0.620
0.662
0.562
0.565
0.8
0.728
0.663
0.567
0.443
Chem. Eur. J. 2011, 17, 3192 – 3206
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
3203

H. W. Gibson et al.
ꢁ
3
5
.00ꢂ10 L=0.4%). 2.00 mL of this 4.92 mm solution of 1 was then
transferred by means of volumetric pipette (pipette error=6.0ꢂ
mL/2.00ꢂ10 mL=0.3%) to a 10 mL volumetric flask and diluted
We factored into our calculations errors from solution preparation and
NMR integration. For integration errors, we allowed a standard deviation
of ꢂ2% in the calculated percentage of complexed 1, which overesti-
mates the true errors as determined from Tables 3 and 4. These errors
were then followed through all calculations. For analysis, data points
above 90% and below 10% complexed were ignored. Linear regres-
sions were performed using the entire error range (abscissa and ordinate)
at each data point; standard errors in both the intercept and slopes based
on regression were used to determine errors in Ka5 and Kipd, as shown in
Table 1.
a
ꢁ
6
ꢁ3
1
0
ꢁ
5
ꢁ3
to the mark (dilution error=2.0ꢂ10 L/10.00ꢂ10 L=0.2%) to yield
1]=0.985 mm. The cumulative error is thus 1.35%, while the random
error (the square root of the sum of the squares of the individual errors)
is 0.70%. When equal volumes of host and guest of the same concentra-
tion are mixed, for this step the cumulative error in both components is
[
[
14]
ꢁ
6
ꢁ3
1
.2% (6.0ꢂ10 mL/5.0ꢂ10 L), while the random error is 0.63%.
Spectrometer-based errors were determined by preparing seven inde-
pendent master solutions 8.00mm in 1 and seven independent master sol-
utions 8.00mm in 2-TFA. A total of twelve independent 1/2-TFA mix-
tures at 4.00 mm in each component were then investigated by following
H
g
, chosen because the pseudorotaxane resonance is well resolved from
that of the free host. The average percentage of complexed crown was
3.9%, with a standard deviation of 0.3% (Table 4). Nearly identical per-
2
Acknowledgements
The authors are grateful to the NSF (grants DMR-0097126 and DMR-
Table 4. Fraction of host occupied by guest (q) for twelve independently
prepared solutions initially 4.00 mm in both 1 and 2-TFA, CDCl /CD CN
3:2), 295 K.
0
704076) for support of this work. J.W.J. acknowledges support from the
3
3
Environmental Management Science Program, Office of Science, US De-
partment of Energy, through the Higher Education Research Experience
(HERE) at Oak Ridge National Laboratory. We are grateful to the Na-
tional Science Foundation for funds to purchase the Varian Unity Plus
NMR (DMR-8809714) and the Varian Inova NMR (CHE-0131124) in-
struments, and the single-crystal X-ray diffractometer (CHE-0131128).
(
Trial
q[a]
q[b]
q[c]
q[d]
1
2
3
4
5
6
7
8
9
0.240
0.237
0.238
0.248
0.245
0.243
0.245
0.242
0.239
0.242
0.244
0.241
0.242
0.003
0.250
0.260
0.250
0.251
0.248
0.250
0.246
0.245
0.245
0.245
0.250
0.251
0.249
0.004
0.238
0.232
0.232
0.231
0.238
0.239
0.238
0.232
0.226
0.239
0.239
0.237
0.235
0.004
0.230
0.241
0.239
0.239
0.238
0.242
0.239
0.237
0.239
0.239
0.238
0.241
0.239
0.003
[
1] a) D. J. Cram, J. M. Cram, Container Molecules and Their Guests
Ed.: J. F. Stoddart), RSC, Cambridge, 1994; b) J.-M. Lehn, Supra-
(
molecular Chemistry, VCH, Weinheim, 1995; c) P. D. Beer, P. A.
Gale, D. K. Smith, Supramolecular Chemistry, Oxford University
Press, Oxford, 1999; d) J. W. Steed, J. L. Atwood, Supramolecular
Chemistry, Wiley, New York, 2000; e) L. F. Lindoy, I. M. Atkinson,
Self-Assembly in Supramolecular Systems (Ed.: J. F. Stoddart), RSC,
Cambridge, 2000; f) Core Concepts in Supramolecular Chemistry
and Nanochemistry (Eds.: J. W. Steed, D. R. Turner, K. J. Wallace),
Wiley, New York, 2007; g) P. A. Gale, Royal Soc. Ser. Adv. Sci. 2007,
1
1
1
0
1
2
Average
std. dev.
[
[
a] Via analysis of HAr,G. [b] Via analysis of HAr,H. [c] Via analysis of H
d] Via analysis of H
1
.
3
, 105–125; h) Supramolecular Chemistry, 2nd ed. (Eds.: J. W. Steed,
g
.
J. L. Atwood), Wiley, New York, 2009.
[
2] See, for example: a) B. C. Bunker, D. L. Huber, J. G. Kushmerick, T.
Dunbar, M. Kelly, C. Matzke, J. Cao, J. O. Jeppesen, J. Perkins,
A. H. Flood, J. F. Stoddart, Langmuir 2007, 23, 31–34; b) Y. Liang,
H. Wang, S. Yuan, Y. Lee, L. Gan, L. Yu, J. Mater. Chem. 2007, 17,
cent binding and standard deviations were found for the aromatic
24.2%, ꢂ0.3%) and benzylic (23.5%, ꢂ0.4%) protons of 2-TFA. Be-
(
2
183–2194; c) M. A. Palacios, R. Nishiyabu, M. Marquez, P. Anzen-
cause integration limits were manually set in these studies, and thus error
introduced, a randomly chosen sample from the above twelve 1/2-TFA
mixtures was further examined. Five independent Fourier transforma-
tions yielded a standard deviation in percent binding of 0.1%, signifying
the high reproducibility of manual transformations (Table 5). Of note,
these studies were performed over the course of a full year: although rel-
ative humidity fluctuated greatly over this time frame, percent complexa-
tion did not. We conclude that atmospheric water has little influence on
binding properties of samples prepared and exmined in this manner.
bacher, Jr., J. Am. Chem. Soc. 2007, 129, 7538–7544; d) E. R. Kay,
D. A. Leigh, F. Zerbetto, Angew. Chem. 2007, 119, 72–196; Angew.
Chem. Int. Ed. 2007, 46, 72–191; e) T. Ogoshi, A. Harada, Sensors
2
008, 8, 4961–4982; f) X. Y. Ling, D. N. Reinhoudt, J. Huskens, Pure
Appl. Chem. 2009, 81, 2225–2233; g) D. Li, W. F. Paxton, R. H.
Baughman, T. J. Huang, J. F. Stoddart, P. S. Weiss, Mater. Res. Soc.
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Chem. Res. 2009, 42, 1489–1500; i) V. Balzani, A. Credi, M. Venturi,
Chem. Soc. Rev. 2009, 38, 1542–1550; j) M. A. Olson, A. B.
Braunschweig, L. Fang, T. Ikeda, R. Klajn, A. Trabolsi, P. J. Wesson,
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Chem. 2009, 121, 1824–1829; Angew. Chem. Int. Ed. 2009, 48, 1792–
Table 5. Fraction of host occupied by guest (q) for five independent
Fourier transformations [1]
95 K.
0
=[2-TFA]
0
=4.00 mm, CDCl
3
/CD
3
CN (3:2),
1
797; k) J. R. Kumpfer, J. Jin, S. J. Rowan, J. Mater. Chem. 2010, 20,
2
1
45–151; l) V. Palermo, E. Schwartz, C. E. Finlayson, A. Liscio,
q[a]
q[b]
q[c]
q[d]
M. B. J. Otten, S. Trapani, K. Muellen, D. Beljonne, R. H. Friend,
R. J. M. Nolte, A. E. Rowan, P. Samori, Adv. Mater. 2010, 22, E81–
E88; m) L. A. Baumes, M. Buaki Sogo, P. Montes-Navajas, A.
Corma, H. Garcia, Chem. Eur. J. 2010, 16, 4489–4495; n) Q. Zhang,
Y. Tu, H. Tian, Y.-L. Zhao, J. F. Stoddart, H. Agren, J. Phys. Chem.
B 2010, 114, 6561–6566.
3] C. J. Pedersen, J. Am. Chem. Soc. 1967, 89, 7017–7036.
4] E. A. Katayev, P. J. Melfi, J. L. Sessler in Modern Supramolecular
Chemistry (Eds.: F. Diederich, P. J. Stang, R. R. Tykwinski), Wiley-
VCH, Weinheim, 2008, pp. 315–347.
Trial
1
2
3
4
0.241
0.244
0.242
0.244
0.243
0.243
0.001
0.251
0.252
0.253
0.251
0.252
0.252
0.001
0.237
0.235
0.236
0.239
0.236
0.237
0.001
0.241
0.242
0.243
0.242
0.242
0.242
0.001
5
[
[
average
std. dev.
[
[
a] Via analysis of HAr,G. [b] Via analysis of HAr,H. [c] Via analysis of H
d] Via analysis of H
1
.
g
.
[5] A. Spaeth, B. Koenig, Beilstein J. Org. Chem. 2010, 6, No. 32.
3204
www.chemeurj.org
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 3192 – 3206

Ion Pairing
FULL PAPER
[
6] a) R. H. Griffey, Chem. Biol. 2002, 9, 958–959; b) K. Hirose, J. In-
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, B
A
H
U
G
R
N
U
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H
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[
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[
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[29] We recognize the advantage to be gained in studying complexation
in the low concentration regime by fluorescence spectroscopy, but
found that the emission spectra for 1 and 2-X overlap, 1 yielding
l
emmax =410 nm, and 2-PF
6
yielding a broad emission band from 370
6 6
PF and bis(m-nitrobenzyl)ammonium PF [d) P. R. Ashton, M. C. T.
to >500 nm, with lemmax =425 nm. The excitation spectra also over-
Chem. Eur. J. 2011, 17, 3192 – 3206
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
3205

H. W. Gibson et al.
lap, 1 displaying lexmax =277 nm, and 2-PF
tion band from 260 to 400 nm.
6
yielding a broad excita-
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[
32] W. S. Bryant, PhD Thesis, Virginia Polytechnic Institute and State
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Received: September 1, 2010
Published online: February 9, 2011
3206
www.chemeurj.org
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 3192 – 3206