Host-guest complexes of cucurbituril with 4-amino-4′-nitroazobenzene and 4,4′-diaminoazobenzene in acidic aqueous solutions

Article abstract of DOI:10.1039/a708015h

The thermodynamics and kinetics of the reaction of cucurbituril (Cuc) with 4-amino-4′-nitroazobenzene (DO3) and 4,4′-diaminoazobenzene (Diam) have been studied in aqueous HCl, and it is shown that DO3 is well suited as an indicator for uncomplexed Cuc (actual concentration of Cuc) and Diam is well suited as an indicator for the total concentration of Cuc (sequestering agent) in aqueous solutions. The formation of 1:1 guest-host complexes is observed. For proton concentrations up to 1 mol dm^-3, DO3 reacts according to eqn. (a), with the values for the dissociation constant of DO3H⁺ log(K_a/dm³ mol^-1) = CucH⁺ + DO3H₂²⁺ ? CucH⁺ + DO3H⁺ + H⁺ ? CucH⁺ + DO3 + 2H⁺ ? CucDO3H⁺ + 2H⁺ (a) -2.42, DO3H₂²⁺ log(K_b/dm³ mol^-1) = 0.53, for the stability constant of CucDO3H⁺ log (K_c/mol dm³) = 8.05 and for the rate constant of complex formation log (k_f/dm³ mol^-1 s^-1) = 5.25. Reaction enthalpies and activation energies have also been determined. The complexation of Cuc with Diam has been studied in 0.1-1 mol dm^-3 HCl where a very strong complexation has been observed.

Full text of DOI:10.1039/a708015h

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Host–guest complexes of cucurbituril with 4-amino-4Ј-nitroazo-
benzene and 4,4Ј-diaminoazobenzene in acidic aqueous
solutions
Roland Neugebauer and Wilhelm Knoche
Fakultät für Chemie, Universität Bielefeld, D-33501 Bielefeld, Germany
The thermodynamics and kinetics of the reaction of cucurbituril (Cuc) with 4-amino-4Ј-nitroazobenzene
(DO3) and 4,4Ј-diaminoazobenzene (Diam) have been studied in aqueous HCl, and it is shown that DO3
is well suited as an indicator for uncomplexed Cuc (actual concentration of Cuc) and Diam is well suited
as an indicator for the total concentration of Cuc (sequestering agent) in aqueous solutions. The
formation of 1:1 guest–host complexes is observed. For proton concentrations up to 1 mol dm؊3, DO3
reacts according to eqn. (a), with the values for the dissociation constant of DO3H؉ log(Ka/dm3 mol؊1) ؍
CucH؉ ؉ DO3H22؉
CucH؉ ؉ DO3H؉ ؉ Hϩ
CucH؉ ؉ DO3 ؉ 2H؉
CucDO3H؉ ؉ 2H؉ (a)
؊2.42, DO3H22؉ log(Kb/dm3 mol؊1) ؍ 0.53, for the stability constant of CucDO3H؉ log (Kc/mol dm3) ؍
8.05 and for the rate constant of complex formation log (kf /dm3 mol؊1 s؊1) ؍ 5.25. Reaction enthalpies
and activation energies have also been determined. The complexation of Cuc with Diam has been
studied in 0.1–1 mol dm؊3 HCl where a very strong complexation has been observed.
Host–guest complexes of cucurbituril 1 with substituted amines
O
and alkali metal ions have been studied by several authors using
O
O
48% aqueous formic acid as solvent,1,2 and most of the results
have been reviewed recently.1,3 But it is known that cucurbituril
is also sparingly soluble in dilute aqueous solutions of HCl, and
a study of its complexation at different proton concentrations
should give further insight into the mechanism of complex
formation, especially concerning the degree of protonation of
reactants and complex. Thus we report in this contribution
results on the thermodynamics and kinetics of the binding of
some ligands to cucurbituril in aqueous solutions of 0.05–5 mol
dmϪ3 hydrochloric acid. Complexation is monitored by optical
absorbance, and therefore the guest molecules should absorb
light in the visible region where cucurbituril does not absorb
light, and complexation should be accompanied by a large
change in absorbance. Furthermore, ligands have been chosen
which are suitable as indicators for the investigation of the
binding of optically non-absorbing guests.
N
N
N
N
N
N
N
O
N
N
N
N
N
O
N
O
O
N
N
O
O
N
N
N
N
N
N
N
N
N
O
O
O
1
NH2
NH2
NH2
N
N
N
The following guests have been chosen: (i) 4-amino-4Ј-
nitroazobenzene 2 forming relatively strong complexes with
cucurbituril, so it may be used as an indicator for competing
complex formation with non-absorbing guests, e.g. alkali metal
ions, (ii) 4,4Ј-diaminoazobenzene 3 forming very strong com-
plexes with cucurbituril, so it may be used as an indicator for
the titration of total concentration of cucurbituril, (iii) 4-
methylbenzylamine 4, in order to be able to compare our results
with those obtained previously in 48% formic acid.1,2 The two
carbonyl-fringed portals at the upper and lower side of the
cucurbituril molecule have a diameter of 4 Å. The internal
cavity has a diameter of ca. 5.5 Å, and the separation of the
portals is 6 Å.1
N
NO2
NH2
2
4
3
Cucurbituril 1 was obtained from Merck. When it was sus-
pended in water, an acidic suspension was obtained. Therefore
cucurbituril was washed by suspending it several times in twice
distilled water, until the pH of the suspension remained higher
than 5.6. All other chemicals were commercially available with
grade p.a., and thrice distilled water was used for preparing the
solutions.
At equilibrium absorbances were determined spectrophoto-
metrically with an accuracy of δA = 0.001 for A < 1.5. Kinetic
measurements were started by mixing equal volumes of solu-
tions of cucurbituril and of guest, both containing the same
concentration of HCl. The experiments were performed under
pseudo-first-order conditions, i.e. (i) the concentration of HCl
was large compared to those of cucurbituril and guest and (ii)
Experimental
4-Methylbenzylamine 4 was obtained from Aldrich (97%) and
used without further purification. 4-Amino-4Ј-nitroazobenzene
2 was obtained from Aldrich. Chromatography showed that the
sample consisted of three major substances, which could be
separated into ca. 90% 4-amino-4Ј-nitroazobenzene, 10% 4,4Ј-
diaminoazobenzene and <1% insoluble white substance.
J. Chem. Soc., Perkin Trans. 2, 1998
529

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Table 1 Dissociation constants, absorption coefficients (λ = 526 nm),
rate constants, and thermodynamic constants relating to species in
eqns. (19)–(21), at T = 25 ЊC
εDO3/Ϫ1 cmϪ1
5 100 200
14 200 200
39 750 200
54 500 1000
2.42 0.02
εDO3H /Ϫ1 cmϪ1
ϩ
εDO3H2 /Ϫ1 cmϪ1
2ϩ
εCucDO3H /Ϫ1 cmϪ1
ϩ
pKDO3H,1
pKDO3H,2
pKCucDO3
Ϫ0.53 0.05
8.05 0.05
pKCucH,2
Ϫ0.25 0.08
∆rHЊDO3H,1/kJ molϪ1
∆rHЊDO3H,2/kJ molϪ1
∆rHЊCucDO3/kJ molϪ1
∆rSЊDO3H,1/J molϪ1 KϪ1
∆rSЊDO2H,2/J molϪ1 KϪ1
∆rSЊCucDO3/J molϪ1 KϪ1
20
12
79
21
51
2
2
4
4
5
112 10
5.25 0.05
Ϫ2.8 0.1
log(kf /sϪ1 Ϫ1
)
Fig. 1 εexp vs. pH for solutions of DO3 at different wavelengths,
T = 25 ЊC: (᭹) λ = 328 nm; (ϩ) λ = 422 nm; (᭺) λ = 498 nm. The curves
log(kb/sϪ1
)
Ea,f /kJ molϪ1
Ea,b/kJ molϪ1
18
97
2
4
are calculated with the dissociation constants given in Table 1. Insert:
2ϩ
spectra of 1 DO3, 2 DO3Hϩ and 3 DO3H2
.
Figs. 1 and 2, εexp, the absorption per pathlength and per concen-
tration [see eqn. (2)], is plotted. A, d and Do are absorbance,
A
(2)
εexp
=
d Do
optical pathlength and total concentration of ligand, respect-
ively. pH values were calculated from the concentration [Hϩ]
and mean activity coefficient fHCl of hydrochloric acid accord-
ing to eqn. (3). fHCl was calculated from literature data.4–6
pH = Ϫlog([Hϩ] fHCl/)
(3)
DO3 may be protonated both at the amino and at the azo
group, and the equilibrium spectra are well described by the
two dissociation constants given in eqns. (2) and (3), with
pKDO3H,1 = 2.42 0.03 and pKDO3H,2 = Ϫ0.53 0.05.
Fig. 2 εexp vs. pH for solutions of Diam at different wavelengths,
T = 25 ЊC: (᭹) λ = 393 nm; (᭺) λ = 460 nm; (ϩ) λ = 490 nm. The curves
are calculated with the dissociation constants given in the text. Insert:
spectra of 1 Diam, 2 DiamHϩ, 3 DiamH22ϩ and 4 DiamH3
.
3ϩ
[DO3][Hϩ]
[DO3Hϩ]
(4)
the concentration of cucurbituril was large compared to that of
the guest molecule or vice versa. In all experiments an exponen-
tially decaying curve was observed, i.e. the time dependence
of the absorbance is described by eqn. (1), where A0 and Ae are
KDO3H,1
=
[DO3Hϩ][Hϩ] fHCl
(5)
KDO3H,2
=
2ϩ
[DO3H2
]
Ϫt
(1)
A = (A0 Ϫ Ae)exp ͩ ͪϩ Ae
τ
The first dissociation constant was determined at a relatively
low ionic strength (pH < 1), where activity coefficients depend
predominantly on the charge of the ions, and thus they cancel
in eqn. (4). The second dissociation constant had to be deter-
mined at high ionic strength, where activity coefficients are
difficult to determine or to estimate. Therefore KDO3H,2 as
described by eqn. (5) (i.e. assuming that activity coefficients
the absorbances immediately after mixing the solutions and
after the reaction, when equilibrium is reached, respectively.
(A0 Ϫ Ae) and τ are referred to as relaxation amplitude and
relaxation time, respectively. pH values were measured with an
accuracy of 0.02 units.
for DO3Hϩ and DO3H2 cancel) is a conditional and not a
2ϩ
thermodynamic constant. This conditional constant is used for
determining the protonation of DO3, since it describes well the
pH-dependence of the absorption at high proton concentra-
tion, as can be seen in Fig. 1. The dissociation constants of
DO3 were determined at different temperatures. It should be
emphasised that for all three differently protonated species the
absorption coefficients do not depend on temperature. The
results (equilibrium constants, reaction enthalpies, reaction
entropies and absorption coefficients at λ = 526 nm) are sum-
marised in Table 1.
Analogously the spectra for Diam have been evaluated. Diam
may be protonated at one or both amino groups and at the
azo group. Thus three protonation steps have to be taken into
account. The absorbance is described well by the constants
defined in eqns. (6)–(8), with pKDiamH,1 = 3.54 0.02, pKDiamH,2
Results
Protonation equilibria
The host–guest complexes were studied at different proton
concentrations and therefore the protonation equilibria of
the guests have to be known. For the guests 4-amino-4Ј-
nitroazobenzene 2 (common name: Disperse Orange 3, and
therefore abbreviated as DO3) and 4,4Ј-diaminoazobenzene 3
(abbreviated as Diam) the visible spectra were measured at
varying proton concentrations. For selected wavelengths the
results are shown in Figs. 1 and 2.
Because of the low solubility of unprotonated DO3
(1.8 × 10Ϫ6 ) the measurements were performed at different
concentrations and different optical pathlengths (1–5 cm).  is
used as an abbreviation for mol dmϪ3. Correspondingly, in
530
J. Chem. Soc., Perkin Trans. 2, 1998

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[Diam][Hϩ]
[DiamHϩ]
(6)
(7)
(8)
KDiamH,1
=
2
[DiamHϩ][Hϩ] f1
[DiamH22ϩ] f2
KDiamH,2
=
[DiamH22ϩ][Hϩ] fHCl
KDiamH,3
=
3ϩ
[DiamH3
]
= 2.11 0.02 and pKDiamH,3 = Ϫ0.5 0.1; the agreement may
be seen in Fig. 2.
Again activity coefficients cancel in the determination of
KDiamH,1. KDiamH,2 was determined at low ionic strength, where
fi (i = charge of ion) can be calculated from eqn. (7) from the
ionic strength I.6
Fig. 3 Titration of solutions of DO3 with Cuc at T = 25 ЊC and
λ = 526 nm: (᭺) HCl0 = 0.125; (᭹) HCl0 = 2.0 and (ϩ) HCl0 = 5.0 .
The curves are calculated with the absorption coefficients and dissoci-
ation constants given in Table 2. Insert: spectrum of the complex at
HCl0 = 0.125 .
–
√I
Ϫlog( fi) = 0.509 zi2
ͩ
Ϫ 0.3I
ͪ
(9)
–
1 ϩ √I
KDiam,3 was determined at high ionic strength, and again
ϩ 2
εDO3KDO3,1
K
DO3,2 ϩ εDO3H
K
DO3,2[Hϩ] ϩ ε
[H ] fHCl
ϩ
2ϩ
DO3H2
it is a conditional constant due to neglecting the activity co-
εguest
=
2ϩ
efficients for DiamH2 and DiamH33ϩ. For λ = 481 nm the
KDO3,1
K
DO3,2 ϩ KDO3,2 [Hϩ] ϩ [Hϩ]2 fHCl
following values were determined: εDiam = 7800 200,
(15)
ϩ
2ϩ
3ϩ
εDiamH = 4100 200, εDiamH2 = 12 300 200 and εDiamH3
=
37 200 200 Ϫ1 cmϪ1. For 4-methylbenzylamine 4 (abbrevi-
ated as Met) the dissociation constant has been determined
previously to be pKMet,1 = 9.62.7
coefficients obtained as in the previous paragraph for DO3,
DO3Hϩ and DO3H22ϩ. The consistency of the evaluation is
proved by the good agreement of the values in Table 2. The
insert in Fig. 3 shows the spectrum of the complex, which may
be compared with the spectra of the differently protonated dye
shown in Fig. 1.
Analogously solutions of Diam were titrated with Cuc; see
Fig. 4. The binding was studied at both absorption maxima of
the complex, λ = 481 and 497 nm, see insert of Fig. 4. From the
titration curve it is evident that Cuc binds much more strongly
to Diam than to DO3. For λ = 481 nm the results are summar-
ised in Table 2. Again the absorption coefficient of εguest can be
calculated from the dissociation constants of Diam and the
absorption coefficients of the differently protonated species,
and comparison with fitted absorption coefficients shows good
agreement; see Table 2.
Stability of the host–guest complexes
For the determination of the stability of the host–guest com-
plexes solutions of the dyes were titrated with solutions of
cucurbituril at different concentrations of hydrochloric acid.
For constant concentration of hydrochloric acid the titration
curves agree with the simple reaction in eqn. (10). That means
kfQ
Guest ϩ Host
Complex
(10)
Q
kb
eqns. (11)–(14) describe well the absorption values at constant
wavelength.
Finally, the complexation equilibrium of Met with Cuc was
determined in aqueous 1  HCl. This amine absorbs only in the
UV region, where the absorption of Cuc also has to be taken
into account, with εhost = 280 cmϪ1 Ϫ1 at λ = 218 nm. The spec-
tra and titration curve are shown in Fig. 5 and the pQ-values
were evaluated at three wavelengths: λ = 216, 218 and 220 nm;
at all wavelengths the evaluation yields pQ = 5.0 0.1, for
T = 25 ЊC.
[guest] ϩ [complex] = D0
[host] ϩ [complex] = Cuc0
(11)
(12)
[guest][host]
Q =
(13)
(14)
[complex]
A
d
= εguest[guest] ϩ εcomplex[complex] ϩ εhost[host]
Kinetics
Assuming that the reaction proceeds according to the simple
scheme in eqn. (10), the relaxation time should be given by
eqn. (16), where the rate constants are related to Q according to
D0 and Cuc0 are the total concentrations of dye and cucurbi-
turil, respectively, d is the optical path length and the values of
Q, εguest and εcomplex were obtained by the fitting procedure. εhost
was measured separately. For DO3 and Diam the measure-
ments were performed in the visible range, where cucurbituril
does not absorb. Q (= quotient) is not a thermodynamic con-
stant, since it depends on proton concentration, and further-
more activity coefficients are not taken into account. For three
different proton concentration results are shown in Fig. 3. Due
to the dependence of the solubility of DO3 on the proton con-
centration the measurements were performed at different con-
centrations. Therefore εexp, as defined in eqn. (2), is plotted in
Fig. 3. The absorption was evaluated at λ = 526 nm, where the
complex absorbs most strongly. The results are summarised in
Table 2. For [Hϩ] р 0.1 the minor component is quantitatively
bound in the complex (i.e. either [guest] or [host] equals zero);
thus for Q only a lower limit can be obtained. The values of
εguest may also be calculated from eqn. (15) from the absorption
Q
1/τ = kfQ ([host] ϩ [guest]) ϩ kb
(16)
eqn. (17). The values of Q (see Table 2) indicate that for Diam
kbQ = kfQQ
(17)
and Met the contribution of kbQ to the reaction rate is negligible
in the concentration range of this investigation. The values of kfQ
were obtained by plotting the kinetic measurements according
to eqn. (18), and kbQ was calculated from kfQ and Q.
s
logͩ ͪ= log(kfQ/sϪ1 Ϫ1) ϩ log({[host] ϩ [guest]})
(18)
τ
J. Chem. Soc., Perkin Trans. 2, 1998
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Table 2 Results obtained for Q, εguest, εcomplex, kfQ and kbQ by fitting eqns. (14) and (17) to the values of optical absorption and to relaxation times.
The results refer to T = 25 ЊC if not indicated otherwise. The values in parentheses are calculated from eqn. (15) for εguest, eqn. (27) for pQ, eqn. (28)
Q
for kfQ and eqn. (17) for kb
Guest
DO3
DO3
DO3
DO3
DO3
DO3
DO3
DO3
DO3a
DO3b
DO3c
HCl/
0.050
0.100
0.125
0.250
0.50
εguest/Ϫ1 cmϪ1
εcomplex/Ϫ1 cmϪ1
55 600 500
55 600 500
55 500 500
55 300 500
54 600 500
53 800 500
52 900 500
49 550 500
53 800 500
53 800 500
53 800 500
pQ
log(kfQ/sϪ1 Ϫ1
)
log(kbQ/sϪ1
)
13 500 500
(13 800)
13 800 500
(14 400)
14 700 500
(14 650)
15 350 500
(15 400)
16 750 500
(16 700)
19 550 500
(19 100)
22 900 500
(23 800)
35 900 500
(34 800)
18 900 500
(18 500)
18 700 500
(18 150)
18 300 500
(17 900)
12 800 500
13 500 500
16 800 500
>6.9
(6.89)
>6.6
(6.60)
6.53 0.02
(6.51)
6.19 0.02
(6.20)
5.88 0.02
(5.88)
5.46 0.02
(5.54)
4.05 0.05
(4.09)
3.80 0.05
(3.80)
3.72 0.05
(3.71)
3.42 0.05
(3.40)
3.03 0.05
(3.08)
2.63 0.05
(2.73)
—
(< Ϫ2.9)
—
(< Ϫ2.8)
—
(Ϫ2.8)
—
(Ϫ2.8)
—
(Ϫ2.9)
Ϫ2.8 0.1
(Ϫ2.8)
Ϫ2.8 0.1
(Ϫ2.8)
1.00
2.00
4.80 0.02
2.00 0.05
5.0
3.25 0.02
5.17 0.02
5.00 0.02
4.87 0.02
—
—
1.00
2.89 0.05
3.00 0.05
3.10 0.05
Ϫ2.3 0.1
(Ϫ2.3)
Ϫ2.0 0.1
(Ϫ2.0)
Ϫ1.8 0.1
(Ϫ1.8)
—
1.00
1.00
Diam
Diam
Diam
0.100
0.200
1.00
58 000 500
58 300 500
58 900 500
>7.7
7.2 0.1
6.6 0.1
—
—
—
—
2.17 0.05
(Ϫ4.4)
—
Met
1.00
8 025 50
4 200 100
5.0 0.1
3.16 0.05
(Ϫ1.8)
a 35 ЊC. b 40 ЊC. c 45 ЊC.
Fig. 5 Titration of solutions of Met with Cuc at T = 25 ЊC, λ = 218 nm
and (᭹) HCl0 = 1.0 . The curves are calculated with the absorption
coefficients and dissociation constants given in Table 2. Insert: spectra
of solutions of 1  HCl containing 1 Met0 = 1.25 × 10Ϫ4, 2 Cuc0 =
1.25 × 10Ϫ4 and 3 Met0 = 1.25 × 10Ϫ4 and Cuc = 1.25 × 10Ϫ4 .
Fig. 4 Titration of solutions of Diam with Cuc at T = 25 ЊC, λ = 481
nm and (᭹) HCl0 = 1.0 . The curves are calculated with the absorption
coefficients and dissociation constants given in Table 2. Insert: spec-
trum of the complex at HCl0 = 0.2 .
Q
For DO3 in 1 and 2  HCl both values kfQ and kb may be
equilibria of DO3 are determined by the dissociation constants
in eqns. (4) and (5). (iii) The amino group of DO3 remains
protonated when forming a complex with Cuc due to the
favourable electrostatic interaction between the cationic group
and the carbonyl groups of Cuc. Moreover the azo group may
also be protonated. Thus the complex may be of the stoichi-
ometry CucDO3Hϩ or CucDO3H22ϩ. (iv) The solubility of Cuc
increases with proton concentration indicating that Cuc is pro-
tonated in solution, i.e. it is present as CucHϩ or CucH22ϩ. Thus
the overall reaction should follow the system of reactions in
eqns. (19)–(22).
obtained by fitting the relaxation times to eqn. (16), and Table 2
shows thegood agreement betweenkbQ and Q kfQ. For those solu-
tions the measurements are shown in Fig. 6.
Discussion
Table 2 shows that for DO3 the reaction quotient Q and the rate
constant kfQ depend strongly on the hydrogen ion concentration,
and these dependencies will be used to develop a mechanism for
the reaction of cucurbituril with substituted amines. The strong
dependence of εguest on [Hϩ] has already been discussed in the
previous section. εcomplex depends weakly on [Hϩ] only for con-
centrations larger than 0.5 .
The evaluation of the experiments is based on the following
considerations. (i) At constant proton concentration the meas-
urements agree with the simple mechanism in eqn. (10) indicat-
ing that Cuc and DO3 form a 1:1 complex. (ii) The protonation
KDO3H,1
KDO3H,2
2ϩ
DO3 ϩ 2Hϩ
DO3Hϩ ϩ Hϩ
DO3H2
(19)
(20)
(21)
KCucH,2
2ϩ
CucHϩ ϩ Hϩ
CucH2
KCucDO3,K
DO3 ϩ CucHϩ
CucDO3Hϩ
532
J. Chem. Soc., Perkin Trans. 2, 1998

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Fig. 6 Log(s/τ) vs. log({[host]e ϩ [guest]e}/) in 1  HCl for (᭺) DO3;
(᭞) Diam; (᭹) Met and in 2  HCl for (᭡) DO3. The curves are
calculated with rate constants given in Table 2. T = 25 ЊC if not indi-
cated otherwise.
Fig. 8 Degree of association vs. total concentration of Cuc for differ-
ent ligands at D0 = 10Ϫ5  and T = 25 ЊC
Q = KCucDO3,Kα
(27)
(28)
kf
kfQ
=
α
The fitting of eqns. (27) and (28) to the experimental data yields
pK = 8.05 0.05 and log(kf /sϪ1 Ϫ1) = 5.25 0.05. The con-
stants describe well the experiments up to 1  HCl as can be
seen in Fig. 7. From the temperature dependence of Q, kfQ,
KDO3H,1 and KDO3H,2 the following parameters were determined:
activation energies Ea,f = 18 2 kJ molϪ1 and Ea,b = 92 4 kJ
molϪ1, reaction enthalpy ∆fH0 = 79 4 kJ molϪ1 and reaction
entropy ∆fS0 = 112 10 J molϪ1 KϪ1.
For proton concentrations higher than 1  Fig. 7 shows
strong deviations of the calculated curves from the experi-
mental values of both absorbance and relaxation time. The
deviations seem to be too large to be attributed to a faulty
calculation of activity corrections, and therefore the deviations
may be caused either by neglecting species CucH22ϩ in eqn. (20)
Fig. 7 Double logarithmic plots of Q (scale on the left) and kfQ (scale
on the right) vs. pH. The solid curves are calculated according to eqns.
(27) and (28); the dashed lines are calculated with consideration of the
2ϩ
diprotonated CucH2
.
2ϩ
KcucDO3H,2
or by neglecting of species CucDO3H2 in eqn. (22). At high
2ϩ
CucDO3Hϩ ϩ Hϩ
CucDO3H2
(22)
proton concentration the deviations are due to a weaker com-
plex formation than expected from eqns. (19) and (21), whereas
the presence of CucDO3H22ϩ should lead to an increase in com-
plex formation at high proton concentration. The independence
of kbQ on pH indicates also that the product CucDO3Hϩ is not
further protonated, i.e. the concentration of CucDO3H22ϩ is neg-
ligible. Thus CucH22ϩ is included in the reaction scheme assum-
ing that (i) the equilibrium is determined by the stability con-
stant given in eqn. (29), where activity coefficients are included
analogously to eqn. (5) and (ii) the protonation rate of CucHϩ
is fast compared to the complex formation. Introducing species
The rate determining step of the overall reaction is given by
eqn. (21); the other reaction steps proceed by protonation with
diffusion controlled speed. The numerical evaluation of the
experimental data show that for proton concentrations smaller
than1thespeciesCucH22ϩ andCucDO3H22ϩ donotcontribute
to absorption and relaxation time [i.e. reactions (20) and (22) do
not need to be taken into account]. In this range the equilibrium
is determined by the dissociation constant in eqn. (23), and the
2ϩ
[DO3][CucHϩ]
[CucDO3Hϩ]
CucH2 with KCucH,2 = Ϫ0.25 0.08 [see eqn. (29)] into the
(23)
KCucDO3,K
=
[CucHϩ][Hϩ] fHCl
(29)
KCucH,2
=
rate law is given by eqn. (24). In eqns. (23) and (24) it is assumed
2ϩ
[CucH2
]
d[CucDO3Hϩ]
= kf[DO3][CucHϩ] Ϫ kb[CucDO3Hϩ]
(24)
dt
evaluation of absorbance and relaxation time leads to excellent
agreement between calculated curve and experimental values
both for Q and 1/τ, see Fig. 7. (Details of the evaluation are
available on request from the authors.)
that the activity coefficients of the monovalent ions CucHϩ and
CucDO3Hϩ and of the activated complex cancel.
In summary, for the reaction of Cuc with DO3 the mechan-
ism is given by eqns. (19)–(21). All constants involved are given
in Table 1.
Finally it should be discussed whether the guests studied can
be used as indicators. For that purpose the degree of associ-
ation is plotted versus the quotient of total concentration of
Cuc divided by D0 for the different ligands in Fig. 8.
In 0.1  HCl Cuc reacts nearly quantitatively with Diam as
long as [Cuc]0 < 0.95[Diam]0. (At higher proton concentrations
1
kf
(25)
(26)
=
(α[DO3] ϩ [CucHϩ]) ϩ kb
τ
α
[Hϩ]
[Hϩ]2fHCl
with α = 1 ϩ
ϩ
KDO3H,1 KDO3H,1KDO3H,2
Q and kfQ are related to equilibrium and rate constants by eqns.
(26) and (27)
J. Chem. Soc., Perkin Trans. 2, 1998
533

View Article Online
KCucDO3,K
the stability of the complex is reduced.) Thus the total concen-
tration of Cuc in aqueous solution may be determined by add-
ing HCl to obtain [Hϩ] = 0.1  and titrating the solution with
Diam. This method works for [Cuc]0 < [Diam]0, where the latter
value is restricted to [Diam]0 = 3 × 10Ϫ5 . Thus the solution
has to be diluted for higher concentrations of Cuc. For the
determination of the total concentration of Cuc the conditions
required above can always be established, and therefore the
reaction of Diam with Cuc has not been investigated at other
proton concentrations.
In Fig. 8 the curve for DO3 shows a degree of association
slightly higher than 0.5 for total concentration of approxi-
mately 10Ϫ5  both for Cuc and DO3. This means that DO3 is
an optimal indicator for the concentration of free cucurbituril
in this range, i.e. DO3 can act as an indicator for the study of
the binding of non-absorbing ligands to Cuc. For those studies
the concentrations of the reacting species cannot be changed,
and correspondingly the reaction of Cuc with DO3 has been
studied in detail over broad ranges of concentrations, pH and
temperature.
CucHϩ ϩ DO3 ϩ 2Hϩ
CucDO3Hϩ ϩ 2Hϩ
↑
KDO3H,1
↓
CucHϩ DO3Hϩ Hϩ
(30)
↑
KDO3H,2
↓
CucHϩ DO3H2
2ϩ
The constants involved are summarised in Table 1. In 2  and
5  HCl the presence of CuCH2 has to be taken into account.
For Diam the reaction with Cuc has been studied only in
0.1–1  HCl, where a very strong binding is observed. There-
fore Diam is a sequestering agent for Cuc, i.e. it is an indicator
for the total concentration of Cuc in 0.1  HCl. The absorption
coefficients at λ = 418 nm are εguest = 12 800 500 and εcomplex
= 58 000 500 Ϫ1 cmϪ1. The results of the measurements at
equilibrium are confirmed by the kinetic studies.
References
Fig. 8 also shows that Met binds only weakly to Cuc, i.e.
Met is not a suitable indicator (furthermore, it does not
absorb light in the visible range). The aptitude of Diam and
DO3 as indicators for total and actual concentrations is
studied in further investigations measuring pH dependence
of the solubility of Cuc and the binding of metal ions to Cuc,
respectively.
1 L. Mock, ‘Cucurbituril’, Top. Curr. Chem., Springer-Verlag, Berlin,
Heidelberg, 1995, vol. 175.
2 R. Hoffmann, W. Knoche, C. Fenn and H.-J. Buschmann, J. Chem.
Soc., Faraday Trans., 1994, 90, 1507.
3 P. Cintas, J. Incl. Phen. Mol. Recog. Chem., 1994, 17, 205.
4 CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton,
59th edn., 1978–79.
5 A. Robinson and R. H. Stokes, Electrolyte Solutions, Butterworth,
London, 2nd edn., 1970.
6 W. Davies, Ion Association, Butterworth, London, 1962.
7 W. Bunting and S. Dimitrios, J. Am. Chem. Soc., 1990, 112, 779.
Conclusions
In aqueous solutions of 0.05–1  HCl DO3 may be used as
indicator for the concentration of free Cuc in this range. The
reaction of Cuc with DO3 is well described by the following
mechanism in eqn. (30).
Paper 7/08015H
Received 6th November 1997
Accepted 14th November 1997
534
J. Chem. Soc., Perkin Trans. 2, 1998