LF Intermolecular Host-Guest Dynamics
J. Phys. Chem. B, Vol. 102, No. 27, 1998 5399
relaxation time corresponds to 350 ps. A double-exponential
fit is shown by the solid line. The best fit parameters for the
double-exponential form are 30% of a 26 ps component and
70% of 400 ps component. It is apparent from the plot that the
double-exponential decay law provides much better agreement
with the data. A comparison of the chi-square values for the
two fits shows that the chi-square for the double exponential is
5 times smaller than that for the single exponential. Figure 6B
shows the same data and fits as Figure 6A but the time axis is
logarithmic. This method of presenting the data makes the
deviations of the fitted curve from the measured data more
apparent. This difference in the quality of the fits and the large
time difference in the decay times found in the double-
exponential fit provide convincing evidence that the decay is
not a single exponential.
Figure 7. Computed geometry for the ADC:1 complex. The open
circles are hydrogen atoms, the shaded circles are carbon atoms, the
rectangular hatched circles are nitrogen atoms, and the diamond hatched
circles are oxygen atoms.
The similarity of the short time constant with that found for
the unbound ADC in DMSO motivated a detailed study of the
concentration dependence of the decay law. The anisotropy
decay was measured at four different concentration ratios (1:3,
1:9, 1:13, and 1:17). For the case where the concentration ratio
was 1:3, the anisotropy decay was fit by a double-exponential
decay law with 27 ps (28%) and 216 ps (72%). Using this
concentration ratio and the binding constants in Table 1, one
expects about 1% of the ADC to be unbound. At the higher
concentration ratios, the time constants were very similar to that
reported in Table 1 and the relative amounts of the short and
long time constants did not change over the range of concentra-
tion ratios. These data demonstrate that the signal’s charac-
teristics are not dependent on the concentration ratio of host to
guest, as long as the host is present in reasonable excess. Hence
the short time component of the anisotropy in Figure 6 reflects
dynamics involving the ADC bound to the host.
condition. It is clear that the long time constant measured has
a magnitude similar to that expected for a rigid body whose
size is similar to that of the entire complex.13 The complex
has a hydrodynamic boundary condition which is intermediate
between the slip and stick limits. It has been established that
as a rotating particle increases in size and roughness features
relative to the solvent the boundary condition progresses toward
the stick limit, even though it may be slip locally.13b In addition,
a body of data indicates that cations rotating in DMSO solvent
experience stronger frictional coupling than do anions.5,14 The
presence of local positive charges on the receptor would be
expected to increase its drag with the solvent and hence change
the effective hydrodynamic boundary condition. To conclude,
the value of the long time decay of the anisotropy is consistent
with that expected for the overall rotational relaxation of the
complex.
The assignment of the fast anisotropy decay to internal
motions of the chromophore in the complex is the most obvious
based on the knowledge concerning the binding and the known
mechanisms for the relaxation of the orientational anisotropy.
Nevertheless, other possible mechanisms for the anisotropy
decay were considered. Four possible sources for the fast
anisotropy, other than internal torsional relaxation, were con-
sidered.
It is well-known that electronic energy transfer between
chromophores can cause relaxation of the anisotropy.18 The
concentrations of the chromophore used here were ∼10-3 M,
which indicates that this mechanism should not be active for
the anthracene chromophore. Furthermore, the measurement
of the anisotropy decay at concentrations ranging from 10-3 to
10-4 M for the solute in free solution showed no influence of
concentration on the measured relaxation time.
A second mechanism for the decay of the anisotropy is by
fast population relaxation of the excited electronic state. The
fluorescence decay kinetics of the free chromophore and bound
in the complex reveal that the effect of the excited state lifetime
may be safely ignored. The excited state decay law of 1,3-
ADC does not change significantly from the free molecule to
that bound to the host molecules 1 and 2. The decays have a
mean fluorescence lifetime of 2.2-2.4 ns. In fact, the triplet
yield for the anthracene may be considerable and since the
OHPS method is probing ground state chromophores, the role
of population kinetics is even less significant.19 Another
possible origin for the fast anisotropy could arise from a rotation
of the transition dipole moment that is caused by a coupling
between electronic states of the anthracene. This mechanism
requires the presence of two low-lying electronic states, which
The anisotropy decay of ADC bound to host 2 was also
obtained with the host concentration present in large excess (1:
10) for both data sets. The anisotropy decay of the ADC when
it is bound in this host molecule is not exponential.
A
comparison of the fitting parameters to the anisotropy decays
of the two systems shows that the fast time component for ADC
in 2 is somewhat shorter than in 1, but that the long time
component is similar (see the data in Table 1). The short time
constant obtained for the complex with 2 is 14 ps with a standard
deviation of 4 ps, which is shorter than that found for the
complex with 1. The long time constant found for the
anisotropy is similar for the two complexes. This similarity is
consistent with the similarity in the overall size and shape
expected for these two systems. In addition, the slow time
constant is 10 times longer than that observed for the free ADC.
These results support the identification of the longer time decay
of anisotropy with the overall orientational relaxation of the
complex, and the faster time, partial loss of anisotropy with an
internal motion of the complex which occurs rapidly.
The assignment of the slow time constant to overall rotational
relaxation is supported by a quantitative analysis. As with the
rotational relaxation of the unbound chromophore molecules
(vide supra), it is possible to characterize the time scale for the
rotational relaxation of the complex by using the hydrodynamic
model. A geometry for the complex of ADC with 1 was
obtained by performing an ab initio calculation at the HF 3-21G
level. Figure 7 provides a three-dimensional rendering of the
complex. From this geometry one estimates the axial radii of
the complex to be 8.3:8.3:2.8 Å. The volume was estimated to
be 800 Å3 from van der Waals increments. Using these
geometric parameters, one computes a relaxation time of 590
ps for a stick boundary condition and 300 ps for a slip boundary