Dynamics for the assembly of pyrene-γ-cyclodextrin host-guest complexes

Article abstract of DOI:10.1021/jp035544c

Pyrene and γ-cyclodextrin (γ-CD) form complexes with 1:1, 1:2, and 2:2 (pyrene/CD) stoichiometries. The complexation dynamics was studied using stopped flow. The dynamics for the higher-order complexes (1:2 and 2:2) occurs in the millisecond time domain, which contrasts with the much faster dynamics for the 1:1 complex. When pyrene is mixed with γ-CD, a transient enhancement of the concentration for the 2:2 complex was observed between 0.2 and 1 s, which at longer times leads to the formation of the 1:2 complex. This enhancement of the nonthermodynamic product is an example of the kinetic formation of a host-guest complex, and these types of processes may be explored to build self-assemblies under kinetic control.

Full text of DOI:10.1021/jp035544c

11652
J. Phys. Chem. B 2003, 107, 11652-11659
Dynamics for the Assembly of Pyrene-γ-Cyclodextrin Host-Guest Complexes
Andria S. M. Dyck, Ursula Kisiel, and Cornelia Bohne*
Department of Chemistry, UniVersity of Victoria, P.O. Box 3065, Victoria, B.C., Canada V8W 3V6
ReceiVed: June 2, 2003; In Final Form: August 5, 2003
Pyrene and γ-cyclodextrin (γ-CD) form complexes with 1:1, 1:2, and 2:2 (pyrene/CD) stoichiometries. The
complexation dynamics was studied using stopped flow. The dynamics for the higher-order complexes (1:2
and 2:2) occurs in the millisecond time domain, which contrasts with the much faster dynamics for the 1:1
complex. When pyrene is mixed with γ-CD, a transient enhancement of the concentration for the 2:2 complex
was observed between 0.2 and 1 s, which at longer times leads to the formation of the 1:2 complex. This
enhancement of the nonthermodynamic product is an example of the kinetic formation of a host-guest complex,
and these types of processes may be explored to build self-assemblies under kinetic control.
Introduction
Experimental Section
Materials and Sample Preparation. Pyrene (Polysciences
Inc. or Aldrich, 99%) was recrystalized once from 95% ethanol.
Its purity was checked by measuring the fluorescence decay in
water, where a monoexponential decay was observed for pure
samples. γ-CD (lots E 8056 and F 8025-12) was a generous
gift from Cerestar and was used without further purification.
Sodium iodide (BDH or Aldrich, g99%), tetrabutylammonium
iodide (Sigma-Aldrich), methanol (ACP, spectrograde), aceto-
nitrile (CALEDON, HPLC grade, g99.8%), sodium hydroxide
(ACP, g97%), and D2O (CDN Isotopes) were used as received.
Deionized water (SYBRON Barnstead system) was used for
all solutions.
Aqueous pyrene solutions (0.25-1 µM) were prepared by
injecting small amounts of a pyrene methanolic solution (1.5-
3.5 mM) into water and stirring the solution overnight. Two
different methods were employed to prepare the pyrene-γ-CD
solutions: (i) the pyrene methanol solution was injected directly
into an aqueous solution in which the desired amount of γ-CD
had been dissolved, or (ii) the appropriate amount of γ-CD was
dissolved in the aqueous pyrene stock solution. The samples
were stirred for at least 12 h. All measurements were performed
in aerated solutions. The second method was employed for the
preparation of the samples in D2O.
Supramolecular chemistry is an expanding field where many
different structural motifs have been explored.1-3 The principal
objective of supramolecular chemistry is to perform new
functions such as catalysis or transport that are not available
for the individual components of these structures. In contrast
to molecular chemistry, supramolecular architectures are always
reversible systems. This dynamic nature is frequently essential
for supramolecular function to be expressed. Dynamic processes
are also essential in self-assembly where frequent reversible
error-correction processes are required on the path to the final
self-assembly.4-6
The field of supramolecular chemistry has been driven by
the synthesis of elaborate and sophisticated structures. The
structures of supramolecular systems are routinely established
by NMR or X-ray crystallography, and the thermodynamics is
frequently reported. Kinetic measurements have been less
prevalent, in part, because many of the processes involved occur
on fast time scales (nano- to microseconds) and require fast
kinetic techniques.7 Kinetic information is unavailable from
thermodynamic measurements. For this reason, to exploit the
potential of supramolecular systems fully it is necessary to
characterize the structural, thermodynamic, and dynamic proper-
ties of each system.
Instrumentation. UV-vis absorption spectra were measured
with a Varian Cary 5 spectrophotometer at room temperature.
A PTI QM2 fluorimeter was employed for steady-state fluo-
rescence measurements (20.0 ( 0.2 °C). The excitation and
emission slits were set such that the bandpass for each was 3
nm. The solutions were excited at 331 nm, and the emission
was collected between 345 and 550 nm. Excitation spectra were
collected by monitoring the emission at 383 or 473 nm for the
monomer and excimer fluorescence, respectively. All pyrene
spectra were corrected by subtracting the collected spectra
containing all components except pyrene. Time-resolved fluo-
rescence decays were measured with a PTI LS-1 time-correlated
single-photon counter at 20.0 ( 0.1 °C. Samples were excited
at 331 nm, and the decays were deconvoluted from the
instrument response function.8,9
Self-assemblies are supramolecular architectures where struc-
tures with well-defined stoichiometries are formed spontane-
ously.1,2,5 Most self-assemblies are formed under thermodynamic
control. The type of structure and topology obtained for each
self-assembly can be controlled by changing the concentration
ratio of molecular building blocks. A larger number of structures
would become available if one could form assemblies under
kinetic control.
In this work, we describe the dynamics for the formation of
the complexes between pyrene and γ-cyclodextrin (γ-CD),
where one of the complexes is enhanced under kinetic control.
This work exemplifies with a very simple host-guest complex
the dynamic processes that will be required to explore the kinetic
control of self-assemblies.
Stopped-flow experiments were performed with a Bio-
Sequential DX-17MV spectrofluorimeter from Applied Photo-
physics. Data acquisition and analysis were done using the
* Corresponding author. E-mail: bohne@uvic.ca. http://www.foto.
chem.uvic.ca/. Phone: 250-721-7151. Fax: 250-721-7147.
10.1021/jp035544c CCC: $25.00 © 2003 American Chemical Society
Published on Web 09/30/2003

Pyrene-γ-Cyclodextrin Host-Guest Complexes
J. Phys. Chem. B, Vol. 107, No. 42, 2003 11653
SX.18 software from Applied Photophysics. Solutions were
mixed in a 1:1 ratio (10-mL syringes), and all measurements
were performed at 20.0 ( 0.8 °C. Solutions were kept for 10
min in the thermostated housing to ensure that the temperature
was equilibrated. The samples were excited with a 150 W Xe-
arc lamp at 331 nm. The entrance and exit slits were set to a
bandpass between 2.3 and 4.7 nm for the excitation monochro-
mator. Fluorescence was detected at 90° to the excitation beam.
The collected spectral region was selected using a cutoff filter
at 455 nm (GG 455) for the pyrene excimer emission and an
interference filter at 404 nm (fwhm of 38 nm, Melles Griot, lot
13637 (ANDV7248)) for the monomer emission. The PMT
voltage was set for each experiment by optimizing the emission
for the solution with the most intense fluorescence. An offset
(3-4 V) was used to bring the initial intensity to zero and to
maximize the dynamic range for the intensity changes (0.1-
1.5 V). The stopped-flow traces contained 1000 points and up
to 10 runs were averaged. The changes in the fluorescence
intensities (I) were analyzed (SX.18 MV software) for the sum
of exponentials (eq 1), where ai, ki, and b correspond to the
amplitude change, the relaxation rate constant, and the intensity
endpoint, respectively.
Figure 1. Corrected fluorescence spectra (λex ) 331 nm) for pyrene
(0.5 µM) in (a) water and in the presence of (b) 5 mM and (c) 20 mM
γ-CD. The inset shows the dependence of the intensity ratio for the
excimer (473 nm) and monomer (383 nm) (E/M) emissions for 0.5
µM (O) and 0.25 µM (b) pyrene on the γ-CD concentration. The error
bars correspond to the average deviation of two trials. Error bars smaller
than the symbols are not shown.
γ-CD but decreased when the CD concentration was raised
above 5 mM (inset of Figure 1). This result is consistent with
the formation of a CD complex containing monomeric pyrene
at high γ-CD concentrations, which corresponds to the formation
of the 1:2 complex. The assignment of the excimer emission to
the 2:2 complex is supported by a lack of growth for the excimer
emission with time, a shift in the excitation spectrum when
compared to that for the monomer emission, and a lower
quenching efficiency of the excimer emission by iodide in the
presence of γ-CD when compared to the efficiency in homo-
geneous solution.8 The involvement of two CD molecules in
the complex was confirmed by the disappearance of the excimer
emission when the pH was raised above the pKa of γ-CD (pKa
) 12.08).23
In water, the pyrene monomer emission had a high I/III
emission-intensity ratio (1.64 ( 0.02) (Figure 1). With increas-
ing γ-CD concentrations, the monomer emission intensities as
well as the I/III ratios changed. At each CD concentration, the
pyrene monomer spectrum corresponds to the sum of the
emission for each pyrene monomer species (i.e., free in water
and bound as 1:1 or 1:2 CD complexes), taking into account
their relative concentrations. At intermediate γ-CD concentra-
tions (5 mM, Figure 1), the monomer intensity was lowest and
a moderate decrease was observed for the I/III ratio (1.29 (
0.05), whereas at high CD concentrations (20 mM, Figure 1)
the monomer emission was raised and the I/III ratio decreased
significantly (0.71 ( 0.01). The latter value is close to the ratio
observed for pyrene emission in nonpolar solvents such as
cyclohexane (0.58-0.60).19,20 Steady-state and time-resolved
quenching experiments with iodide were performed in the
presence of 2 and 10 mM γ-CD.8 Iodide resides primarily in
the aqueous phase. A decrease in the monomer quenching
efficiency signifies the protection of the pyrene inside the CD
complex. Different singlet excited-state lifetimes were observed
for pyrene in water and when complexed in the 1:1 and 1:2
(pyrene/CD) complexes. A decrease by a factor of 5 was
observed for the quenching efficiency of the pyrene in the 1:1
complex, whereas the decrease was much larger for the 2:2
complex. The quenching results indicated that in the presence
of 2 mM γ-CD most of the complexed monomeric pyrene was
in the form of a 1:1 complex, whereas at high CD concentrations
the 1:2 complex was present in a significant amount.
i
I ) ( a e(-k t)) + b
(1)
i
∑
i
1
Results and Discussion
Thermodynamics of Complexation. The complexation of
pyrene to â-CD and γ-CD has been extensively studied.10,11 In
the case of â-CD, complexes with 1:1 and 1:2 (pyrene/CD)
stoichiometries are formed.12-15 Conflicting reports exist as to
the stoichiometry and equilibrium constants for the complexes
between pyrene and γ-CD.16-18 A knowledge of the concentra-
tion of the different pyrene-γ-CD species is essential to the
interpretation of the kinetic experiments. We studied the
thermodynamics of complexation using steady-state and time-
resolved fluorescence experiments combined with quenching
studies. Our results are consistent with the stoichiometries (eqs
2-4) and equilibrium constants reported by Hamai.18 Because
our experiments basically confirm the results of a previous
report, we presents details of the thermodynamic characterization
in the Supporting Information, and only a brief description
relevant to the kinetic studies is provided below.
K11
Py + CD y z PyCD
(2)
(3)
K12
PyCD + CD y z PyCD2
K22
PyCD + PyCD y z Py2CD2
(4)
The pyrene monomer emission shows vibronic structure, and
the ratio for the I (371 nm) to III (383 nm) bands is sensitive
to the solvent polarity. This property has been extensively used
to characterize the environment of pyrene when included in
microheterogeneous systems.19-22 In addition, singlet excited
pyrene in the presence of ground-state pyrene forms an excimer,
which shows a broad emission that is red-shifted from the
monomer emission.
In the presence of γ-CD, the monomer and the excimer
emissions of pyrene were observed (Figure 1). The excimer
emission was assigned to the emission of the pyrene dimer in
the 2:2 (pyrene/CD) complex. The ratio for the excimer emission
intensity to the monomer intensity increased in the presence of
Determination of the Equilibrium Constants for the
Pyrene-γ-CD Complexes. The excimer emission intensity is
proportional to the concentration of the 2:2 complex and the

11654 J. Phys. Chem. B, Vol. 107, No. 42, 2003
Dyck et al.
Figure 3. Dependence of the calculated concentrations of pyrene
species ([pyrene]total ) 0.25 µM) on the concentration of free γ-CD.
Figure 2. Numerical fit (s) to the change in excimer intensity with
the γ-CD concentration, fitted simultaneously for the total concentra-
tions of pyrene of 0.5 µM (b) and 0.25 µM (4) (K11 ) 280 M-1, K12
) 100 M-1, and K22 ) 1.3 × 106 M-1).
excitation spectrum for the excimer emission was broader than
for the monomer emission. Excitation at 331 nm led to the
excitation of the pyrene as a monomer and the pyrene dimer in
the 2:2 complex, whereas for an excitation wavelength of 350
nm only the dimer in the 2:2 complex was excited. The molar
absorptivity coefficients and fluorescence quantum yields for
pyrene in water and in each CD complex are different. The
samples were continuously irradiated during the stopped-flow
experiment, and changes in the fluorescence intensity with time
were measured. These fluorescence intensity changes were
related to changes in the concentrations of free and CD-bound
pyrene. This relationship is valid if one assumes that the molar
absorptivity coefficients and fluorescence quantum yields for
each pyrene-γ-CD species do not change with time. This
assumption predicts that normalized kinetic traces for each
mixing experiment should be the same when measured for
different excitation wavelengths and when recording the mono-
mer or excimer emissions (taking into account the inverse sign).
The different molar absorptivity coefficients and fluorescence
quantum yields have an effect on the amplitude of the signal,
but do not have an effect on the recovered rate constants.
Several relaxation processes were observed over different time
scales. The shortest relaxation process was complete within 200
ms (Figure 4). Three different mixing scenarios were employed,
where solutions were mixed in a 1:1 ratio. (i) A decrease in the
excimer emission was observed when the contents of one syringe
containing a solution with both pyrene and γ-CD was mixed
with the contents of a second syringe containing water (Figure
4A). In this case, the concentrations of pyrene and CD were
halved within the dead time of the stopped flow, and the
relaxation kinetics corresponds to a net decrease in 2:2
concentrations at the lower γ-CD concentrations. The effect is
more pronounced for the lower γ-CD concentrations where the
dependence of the 2:2 concentration on the CD concentration
is more pronounced. (ii) An increase in the excimer emission
intensity was observed when a solution containing pyrene was
emission quantum yield for the excimer. The variation in the
excimer intensity with the γ-CD concentration was determined
for pyrene concentrations of 0.5 and 0.25 µM (Figure 2). The
intensities at both pyrene concentrations were simultaneously
fitted numerically using the fitting routine in Scientist (Micro-
math v.2.02) (Figure 2). The expressions for the equilibrium
constants, defined by eqs 2-4, and the mass balance equations
for pyrene and cyclodextrins were used for the numerical
fitting.24 When all equilibrium constants (K11, K12, and K22) were
left as floating parameters, the recovered values had large
statistical errors. For this reason, several fits were performed
by fixing the parameter K11. Acceptable fits based on statistical
parameters, such as the squared correlation coefficient and the
coefficient of determination, were obtained for K11 values
between 240 and 320 M-1. In addition, for K11 values outside
this range systematic deviations from the experimental data
points were observed. The K12 and K22 values recovered for
the K11 range stated above were respectively 114 to 87 M-1
and 1.3 × 106 to 1.4 × 106 M-1. Although the range recovered
for the K22 values was narrow, the errors associated with this
parameter for each individual fit were much larger. The
equilibrium-constant values used for the calculation of the
concentration of the pyrene-γ-CD species present in the
dynamics studies were 280 ( 40 M-1 for K11, 100 ( 14 M-1
for K12, and (1.3 ( 0.5) × 106 M-1 for K22. These values are
similar to those reported previously by Hamai (K11 ) 300 M-1
K12 ) 170 M-1, K22 ) 1.3 × 106 M-1).18
,
The concentration of free pyrene decreased continuously as
the γ-CD concentration increased, whereas the concentrations
of the 1:1 and 2:2 complexes were at a maximum at intermediate
γ-CD concentrations (Figure 3). The concentration for the 1:2
complex was smaller than that of the 1:1 at low γ-CD
concentrations, but the 1:2 complex dominated at high host
concentrations (>10 mM).
Complexation Dynamics. The dynamics of pyrene com-
plexation to γ-CD was studied using the stopped-flow technique,
where two solutions were rapidly mixed (e1.5 ms) and the
relaxation processes toward an equilibrium were followed over
time. Changes in the excimer or monomer emission intensities
were measured. The changes in the excimer and monomer
intensities are coupled for the equilibria shown in eqs 2-4 (i.e.,
when the monomer intensity increases, one expects the excimer
intensity to decrease and vice versa). Changes in the concentra-
tion of the 2:2 complex were measured by monitoring the
excimer emission intensity above 455 nm, and the monomer
emission intensities were measured at 404 nm. From steady-
state fluorescence experiments,8 it was determined that the
mixed with a second solution containing γ-CD ([γ-CD]final e
5 mM, Figure 4B). For this mixing scenario, there were no CD
complexes formed before the solutions were mixed. The
amplitude of the relaxation process increased as the concentra-
tion of γ-CD was increased. (iii) An increase in the 2:2
concentration was observed when a solution containing pyrene
and γ-CD at a concentration greater than 2 mM was mixed with
a solution containing pyrene at the same concentration as in
the first syringe (Figure 4C). In this case, the pyrene concentra-
tion was kept constant, and the γ-CD concentration was halved
during the mixing. The increase in the excimer emission
intensity is related to the fact that once the solutions are mixed
the initial 2:2 concentration is half of that in the syringe (arrow

Pyrene-γ-Cyclodextrin Host-Guest Complexes
J. Phys. Chem. B, Vol. 107, No. 42, 2003 11655
Figure 5. Dependence of the observed rate constant for the change in
the excimer emission intensity on the final concentration of the 1:1
pyrene-γ-CD complex. The open symbols correspond to the mixing
of a solution containing pyrene ([pyrene]final: O, 0.25 µM; 0, 0.5 µM)
with a solution containing γ-CD. The closed circles correspond to the
mixing of water with a solution containing pyrene ([pyrene]final ) 0.25
µM) and γ-CD. The concentrations for the 1:1 complex were calculated
using K11 ) 280 M-1, K12 ) 100 M-1, and K22 ) 1.3 × 106 M-1
.
2:2 complex was then formed from the association of two 1:1
complexes (eq 5). After mixing, the kinetics proceeded im-
mediately to a decay of the monomer emission. This result
showed that the formation of the 1:1 complex occurred within
the mixing time of the stopped flow (<1.5 ms). This was
expected on the basis of the fact that the complexation dynamics
of other 1:1 CD complexes with guest molecules the size of
the CD cavity occurs in the microsecond time domain.25-34
22
k+
PyCD + PyCD y z Py2CD2
(5)
22
k-
For all mixing scenarios described, the kinetics followed a
monoexponential function. The formation of the 2:2 complex
is related to the association (k+22) and dissociation (k-22) rate
constants (eq 5), and the change in the 2:2 concentration is given
by eq 6:35,36
Figure 4. Changes in the excimer emission intensities measured in
the stopped-flow experiment for different mixing scenarios in a 1:1
ratio. (A) Mixing of a solution containing pyrene ([pyrene]final ) 0.25
µM) and γ-CD ([γ-CD]final: (a) 0.5 mM, (b) 1 mM, (c) 2.5 mM) in
one syringe with water in the second syringe. (B) Mixing of a solution
containing pyrene ([pyene]final ) 0.25 µM) with a solution containing
γ-CD ([γ-CD]final: (a) 0.5 mM, (b) 1 mM, (c) 2.5 mM, (d) 5 mM). (C)
Mixing of a solution containing pyrene ([pyrene]final ) 0.25 µM) and
γ-CD ([γ-CD]final: (a) 0.5 mM, (b) 1 mM, (c) 2.5 mM, (d) 5 mM)
with a solution containing only pyrene ([pyrene]final ) 0.25 µM). The
inset shows the variation of the 2:2 concentration during the stopped-
flow experiment. The arrow to point a corresponds to the instantaneous
decrease in the concentration of the 2:2 complex by half when a solution
containing pyrene and γ-CD was mixed with a solution containing only
pyrene. The arrow from a to b corresponds to the re-equilibration
process measured in the stopped-flow experiment.
d[2:2]
dt
-
) (4k+22 [1:1]final + k-22)[2:2] + 2k+22[2:2]2 (6)
The second term in eq 6 can be neglected when the
perturbation of the system is small35 (i.e., the change in the
concentration of the 2:2 complex is small when compared to
the total 1:1 concentration). In this case, the kinetics follows a
monoexponential function, and the observed relaxation rate
constant is given by
22
kobs ) 4k+22[1:1]final + k-
(7)
The concentration of the 1:1 complex for each pyrene and
γ-CD concentration was calculated using the equilibrium
constants determined from the fluorescence experiments. At each
final concentration of the 1:1 complex, similar kobs values were
obtained, regardless of the mixing scenario employed. This result
shows that the assumption made for the derivation of eq 7 (i.e.,
that the perturbation of the system was small) held even for the
scenario where no CD complex was present prior to mixing. A
linear relationship was observed for the dependence of kobs on
the final 1:1 concentration (Figure 5). The recovered values for
leading to “a” in the inset of Figure 4C). The system then
proceeds toward equilibrium (arrow leading to “b” in the inset
of Figure 4C), and the excimer intensity increases. The same
trends in the kinetics and observed rate constants were observed
when the samples were excited at 331 or 350 nm. The changes
in the monomer emission intensities were always in the opposite
direction from the change in intensity observed for the excimer
emission, but the recovered rate constants were the same. This
result is consistent with the coupling of the processes leading
to changes in the concentrations of free pyrene, 1:1 and 1:2
with changes in the 2:2 concentrations.
k+ and k- (eq 7) were respectively (6.3 ( 1.3) × 107 M-1
s-1 and 73 ( 5 s-1. The ratio of these two rate constants
corresponds to the equilibrium constants for the 2:2 complex
(K22 ) k+22/k-22). The value recovered from the kinetic studies
((0.9 ( 0.2) × 106 M-1) is in agreement, within experimental
22
22
No CD complexes were initially present for the mixing of
two solutions separately containing pyrene and γ-CD. For this
reason, the first complex that formed was the 1:1 complex. The

11656 J. Phys. Chem. B, Vol. 107, No. 42, 2003
Dyck et al.
Figure 7. Changes in the excimer (a, b) and monomer (c) emission
intensities measured in the stopped-flow experiment for the excitation
of pyrene at 331 nm (a, c) or 350 nm (b) when a solution containing
pyrene ([pyrene]final ) 0.25 µM) was mixed with a solution containing
γ-CD ([γ-CD]final ) 10 mM). The kinetic traces for the excimer
emission were normalized at the maximum observed before 1 s.
Figure 6. Changes in the excimer emission intensities measured in
the stopped-flow experiment when a solution containing pyrene
([pyrene]final ) 0.25 µM) was mixed in a 1:1 ratio with a solution
containing γ-CD ([γ-CD]final: (a) 5 mM, (b) 10 mM, (c) 15 mM, (d)
20 mM).
SCHEME 1
error, with the value determined from the thermodynamic
measurements ((1.3 ( 0.5) × 106 M-1). This agreement shows
that the monitored relaxation process indeed corresponds to the
formation of the 2:2 complex from the association of two 1:1
complexes.
The relaxation kinetics was also measured in D2O for a
mixing scenario where pyrene and γ-CD were contained in
separate syringes. The observed rate constants for the complex-
ation dynamics of the 2:2 complex were smaller in D2O than
in water. For example, the kobs values for final concentrations
of pyrene and γ-CD of 0.25 µM and 10 mM were 117 ( 5 s-1
in water compared to 70 ( 4 s-1 for the reaction in D2O. This
result suggests that the formation or cleavage of hydrogen bonds
is involved in the complexation dynamics of the 2:2 complex.
However, a quantitative evaluation was not possible because
the thermodynamics of the pyrene complexation to γ-CD in
D2O would have to be known in order to calculate the final
concentrations for the 1:1 complex.
For final γ-CD concentrations below 5 mM, the only observed
relaxation process was the formation of the 2:2 complex. The
monomer and excimer emission intensities were constant over
periods of time longer than 200 ms. However, at higher γ-CD
concentrations, a second relaxation process was observed that
corresponded to a decrease in the excimer emission after the
initial growth (Figure 6). This decrease was complete within
500 ms to 1 s. When the monomer emission was monitored, an
increase in the emission intensity was observed for the second
relaxation process, showing that the kinetics of the pyrene
monomers and excimer were coupled. The amplitude for the
second relaxation process increased as the γ-CD concentration
was raised. The rate constant for this process was obtained by
fitting the kinetic trace collected over 500 ms to the sum of
two exponentials and the kinetic traces measured for 2 or 5 s to
the sum of three exponentials. The observed rate constant for
the second process did not change significantly within the
experimental error (4.5 ( 1.5 s-1) for different final γ-CD
concentrations (7.5-20 mM) or different final pyrene concen-
trations (0.13-0.5 µM). When the experiments were performed
in D2O, no changes could be detected, within experimental error,
for the observed rate constants. Finally, when the excimer
emission intensity was normalized to its maximum within the
first 100 ms, the amplitude for the second relaxation process
was the same when the samples were excited at 331 or 350
nm. This control experiment is important because there was
always a small contribution of monomer emission in the excimer
detection region for samples excited at 331 nm.37 The fact that
the normalized amplitudes are the same for the different
excitation wavelengths showed that only changes in the 2:2
concentration were monitored.
A third relaxation phase was observed after the decay of the
excimer emission within 1 s. The kinetics for the excimer
emission were very dependent on the excitation wavelengths
(Figure 7). No changes were observed for excitation at 350 nm,
but substantial changes were seen when pyrene was excited at
331 nm. In addition, the changes in the excimer and monomer
emission intensities were not coupled. These effects were more
prominent at intermediate γ-CD concentrations ([γ-CD]final
)
7.5-10 mM) but were also present at higher CD concentrations.
The rate constant for the third relaxation process could be
reliably measured only for reasonably large amplitudes. No
discernible trends were observed with the CD or pyrene
concentrations. The average value for kobs was (0.4 ( 0.1) s-1
.
No deuterium isotope effect was detectable within the experi-
mental error.
Model for the Complexation Dynamics of Pyrene with
γ-CD. From the thermodynamic measurements, it was deter-
mined that three pyrene-γ-CD complexes are formed. The
possible reactions leading to these complexes are shown in
Scheme 1. Full equilibration requires a maximum of three
relaxation processes because one of the branches A, B, or C in
Scheme 1 is redundant. The species leading to monomer (free
pyrene, 1:1 and 1:2 complexes) and excimer (2:2 complex)
emission are coupled by the equilibria shown in Scheme 1.
Therefore, it is a necessary condition that the kinetics measured
for the monomer and excimer emission be coupled. Three

Pyrene-γ-Cyclodextrin Host-Guest Complexes
J. Phys. Chem. B, Vol. 107, No. 42, 2003 11657
different relaxation processes were observed for the kinetics of
pyrene complexation with γ-CD. The observed rate constants
for these three relaxation processes differ by at least 1 order of
magnitude, and as a first approximation, the kinetics for each
relaxation phase can be treated separately.
the 2:2 complex into two 1:1 complexes and the interaction of
a 1:1 complex with a free CD (branch B, Scheme 1). These
two pathways can in principle be distinguished because a
dependence on the γ-CD concentration was expected for the
observed rate constant in the case of the formation of the 1:2
complex through branch B, whereas for branch C the rate
constant is expected to vary with the pyrene concentration.
Unfortunately, the large errors associated with the rate constant
of the second relaxation process preclude this differentiation.
However, the upper limits for the association and dissociation
rate constants for each branch can be determined by assuming
that only one of the branches is responsible for the formation
of the 1:2 complex.
The observed relaxation rate constant for branch C in
Scheme 1 is related to the association (k+C) rate constant of
the 1:2 complex with pyrene free in solution, the dissociation
rate constants (k-C) for pyrene exiting the 2:2 complex, and
the final concentrations for free pyrene and the 1:2 complex
(eq 8).35,36
The formation of the 1:1 pyrene-γ-CD complex corresponds
to one of the three expected relaxation processes for the model
in Scheme 1. This relaxation process is fast and it is finished
within the mixing time of the stopped flow. Of the three
relaxation processed observed after mixing, the first two showed
coupled kinetics, whereas for the slowest one the kinetics for
the monomer and excimer emission were uncoupled. The
uncoupled kinetics suggests that this relaxation process is not
due to the formation of a complex with a stoichiometry different
from those shown in Scheme 1. A possible explanation for the
slow relaxation process is the slow internal rearrangement of
one of the complexes, which leads to a change in emission
quantum yields of pyrene without changing the concentration
of CD complexes. An example of such an rearrangement would
be the expulsion of water from the interior of the CD cavity
after the formation of the 1:2 complex, leading to an increase
in the pyrene monomer singlet excited-state lifetime. It will be
necessary to perform kinetic measurements at defined emission
wavelengths so that the species responsible for the change in
the emission intensities can be identified in order to explore
why these uncoupled relaxation processes occur. Unfortunately,
the capability for conducting such experiments is presently not
available. It is important to note that regardless of the origin of
the third relaxation process its lifetime was much longer than
for the first two processes, which occur within the first second
after mixing. For this reason, the kinetics for the first two
processes can be discussed within the framework of the model
presented in Scheme 1.
C
kobs ) k+C([1:2]final + [P]final) + k-
(8)
For the limited range of final pyrene concentrations employed,
the same value was observed for kobs within experimental error
(4.5 ( 1.5 s-1). For the calculations of k+C and k-C, the average
pyrene (0.25 µM) and CD concentrations (13 mM) were
employed. The concentrations of free pyrene and the 1:2
complex were calculated using the equilibrium constants
determined above, and these concentrations were respectively
0.025 and 0.116 µM. The equilibrium constant between the 1:2
and 2:2 complex (KC) can be expressed as a function of the
known equilibrium constants (KC ) (K22K11)/K12 ) (3.6 ( 1.6)
× 106 M-1). This equilibrium constant is equal to the ratio of
the association and dissociation rate constants (KC ) k+C/k-C).
The value for k-C (3 ( 2 s-1) was calculated from eq 8 for the
The formation of the 1:1 complex occurred within the time
resolution of the stopped-flow experiment, and for this reason
only estimates can be provided for the association and dissocia-
tion rate constants of this process (Scheme 1). The association
rate constants for guest molecules that are smaller than the
kobs value of 4.5 ( 1.5 s-1, and k+ (ca. 107) was determined
C
C
from the values of KC and k-
.
The second route for the formation of the 1:2 complex is
through branch B. The formation of the 2:2 complex is fast
and can be assumed to be in rapid equilibrium. The observed
rate constants for the process in branch B are given by eq 9
because the concentration of free CD is always present in large
excess over the concentration of the 1:1 complex:35,36
CD cavity are typically larger than 1 × 108 M-1 s-1 26-31,34
.
On the basis of the equilibrium constant for the 1:1 complex
(K11 ) k+11/k-11), the dissociation rate constant is estimated to
be larger than 3.6 × 105 s-1
.
At all γ-CD concentrations, an increase in the excimer
emission, and therefore in the 2:2 concentration, was observed
within the first 200 ms. This relaxation process was assigned
to the formation of the 2:2 complex from the association of
two 1:1 complexes. This assignment is consistent with the fact
that the value derived for K22 from the kinetic studies is the
same as the value measured from thermodynamic experiments.
At high γ-CD concentrations, a second relaxation process was
observed where the excimer emission decreased and the
monomer emission increased. At these CD concentrations,
fluorescence experiments indicated that the pyrene monomer
was mainly in a nonpolar environment. These results are
consistent with a decrease in the 2:2 concentration and a
concomitant increase in the 1:2 concentration. The formation
of the 2:2 complex is essentially finished within 200 ms, and
at high CD concentrations an accumulation of the 2:2 complex
is seen in excess of that observed for the thermodynamic
equilibrium because the formation of the 1:2 complex is slow.
The fast formation of the 2:2 complex is followed by the slower
re-equilibration, within 1 s, to the 1:2 complex. This re-
equilibration can occur either by the loss of pyrene from the
2:2 complex (branch C, Scheme 1) or by the dissociation of
12
kobs ) k+12[CD] + k-
(9)
The value for k-12 (2.0 ( 0.7 s-1) was calculated from eq 9
for a CD concentration of 13 mM and by substituting k+
12
)
12
12
K12 k- into the equation. The value for k+ was determined
12
to be 200 ( 80 M-1 s-1. It is worth noting that for these k+
and k-12 values, the kobs values calculated for γ-CD concentra-
tions of 7.5 and 20 mM were respectively 3.5 and 6 s-1. This
range is within the lower and upper limits of the value
determined for the relaxation rate constant (4.5 ( 1.5 s-1),
suggesting that the dependence of kobs on the CD concentration
would have been difficult to identify. As stated above, the values
12
12
for k+ and k- are upper limits because in the analysis that
was performed we assume that the formation of the 1:2 complex
occurs solely through branch B.
The dynamics for the pyrene-γ-CD complexes containing
two CD molecules is much slower than the dynamics for the
1:1 complex. The upper limit for the exit of pyrene from the
2:2 complex (k- < 3 s-1) is much lower than the exit from
C
the 1:1 complex (k- > 3.6 × 105 s-1). This result suggests
11
that pyrene enters the γ-CD cavity through the wider entrance

11658 J. Phys. Chem. B, Vol. 107, No. 42, 2003
Dyck et al.
containing the secondary hydroxyl groups. In the 2:2 complex,
the wider rims are facing each other and pyrene can exit only
through the narrower entrance, leading to a marked decrease of
the exit rate constant by at least 5 orders of magnitude. If the
γ-CD molecules were interacting either through the narrower
rims or through the interaction of one wide and one narrow
rim, then the exit of pyrene would be expected to happen with
the same rate constant as that estimated for the 1:1 complex.
The dissociation of a filled or empty CD from a complex
containing two γ-CD molecules is much slower than the
dissociation of guest molecules from 1:1 complexes. This result
suggests that in the dissociation processes for the complexes
with more than one CD the solvation of the CD is important
and slows down dissociation. The much slower dissociation for
the 1:2 complex compared to that for the 2:2 complex can be
explained by the higher energetic cost to solvate the empty CD
cavity compared to the cost to solvate the pyrene-γ-CD 1:1
complex. This explanation is correct only if the water content
in the 1:2 and 2:2 complexes inside the CD is smaller than for
the 1:1 complexes. On the basis of the I/III emission-intensity
ratio for monomeric pyrene, the polarity in the 1:2 complex is
indeed much lower than in the 1:1 complex.
Figure 8. Schematic representation of a self-assembly matrix, where
for each column the number of one component (squares) increases and
for each row the number of the second component (circles) increases.
The arrows show schematically two possible trajectories for the
formation of an n/n complex. The expanded view corresponds to the
part of the self-assembly matrix that describes the pyrene-γ-CD system.
There is a significant difference, by a factor of at least 3 ×
105, in the association rate constants of the 1:1 complex with
an empty CD or with another 1:1 complex. This large difference
is responsible for the observation of a transient excess of the
2:2 complex despite the large differential between the 1:1 (<0.1
µM) and the free γ-CD (>1 mM) concentrations. The associa-
tion rate constant of two 1:1 complexes is somewhat lower than
the diffusion-controlled limit for bimolecular reactions in water
(6.5 × 109 M-1 s-1).38 This rate constant is high considering
that the two CD molecules have to be aligned along an axis for
the complex to be formed. The only difference between the
reaction of a 1:1 complex with an empty CD and another 1:1
complex is that in the latter case the CD contains the guest.
The 1:1 complex will contain less water to be removed from
the interior of the cavity when compared to the empty CD. In
addition, in the 1:1 complex the rim of the CD will be more
rigid than in the empty CD, leading to a preorganization of the
CD to an optimal geometry for interaction with another 1:1
complex. Molecular mechanics calculations suggested that CDs
are flexible structures,39 and the inclusion of a guest will make
the rim of the CD rigid. This preorganization is akin to a
template effect,5,40 where the efficiency of the formation of a
supramolecular system, in this case, the dimerization of γ-CD,
is faster in the presence of a guest.
In a more general sense, this work has impact when
considering the kinetic control of structured assemblies. Kinetic
control of self-assemblies has not yet been achieved by rational
design. Self-assemblies are spontaneously formed by mixing
several building blocks.2,5,47 The stoichiometries of the various
architectures can be manipulated by changing the initial relative
concentrations of the building blocks because the final products
are thermodynamic. From an abstract point of view, all of the
possible structures for a self-assembly formed from two
components can be expressed as a 2D matrix (Figure 8), where
each column is related to an increased number of host molecules
(squares) and each row corresponds to an increase in the number
of guests (circles). After mixing the building blocks, we suggest
that each growing structure explores a trajectory on the matrix
until the thermodynamic product is formed. One of the condi-
tions for self-assembly to occur is that the system has to undergo
error corrections (i.e., trajectories not leading to the thermody-
namic product have to be reversible). The physical basis for
the formation of self-assemblies under thermodynamic control
has been explored to establish the necessary conditions for self-
assembly to occur.48-50 The formation of structured assemblies
under kinetic control has not been explored. The dynamics of
the pyrene-γ-CD system showed that the transient enhancement
of the kinetic (2:2 complex) product occurred on a time scale
(hundreds of milliseconds) that is amenable to performing
chemistry, as, for example, under continuous-flow conditions.
The ability to form structures under kinetic control would
provide access to a larger number of structures than available
when considering only thermodynamic products, and one could
conceivably work at mixtures of building blocks with very
different concentration ratios. To explore the formation of
structured assemblies under kinetic control, the dynamics of
systems that contain components on at least two rows of the
matrix (Figure 8) has to be investigated. This is the case for
the pyrene-γ-CD system we studied, where the 1:2 complex
is the thermodynamic product whereas the 2:2 complex is the
kinetic product. The next steps toward kinetic control of
structured assemblies is to establish the generality of the transient
enhancement of host-guest systems with different stoichiom-
etries, an understanding of how the competitive kinetic pathways
can be manipulated, and proof of the concept that chemistry on
a kinetically formed self-assembly is possible.
Consequences of the Slow Dynamics on the Function of
CD Systems and for Supramolecular Systems in General.
CDs are used as host systems to perform many different
functions. Two examples are the use of CDs to stabilize drugs
against their phototoxicity41-44 and the application of CDs to
achieve chiral separation in chromatography.45,46 For the drug-
stabilization function, it is important that the residence time of
the drug inside the CD be long enough to inhibit unwanted
interactions between the drug and biomolecules. The mixed
results in using CDs as photostabilization agents could be related
to a short residence time of the drug or reactive intermediates
inside the CD cavity. The photostabilizing effect of CDs as drug
carriers could be improved when using formulations that favor
the formation of higher-order CD complexes. The slower
dynamics of the complexes with two CDs when compared to
that of 1:1 complexes could also be employed to optimize
separation efficiencies when using CDs as separation agents in
chromatography.

Pyrene-γ-Cyclodextrin Host-Guest Complexes
J. Phys. Chem. B, Vol. 107, No. 42, 2003 11659
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Acknowledgment. C.B. thanks the Natural Sciences and
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for a PGSA scholarship, and U.K. thanks the NSERC for an
USRA award and the RISE program for a RISE award. We
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