Angewandte
Chemie
rate (1/t) can be expressed as Equation (2), where E is the
not only favor the rotation of the rotator, but also weaken the
a
activation energy, w is a pre-exponential factor, and k is the
hydrogen-bonding interaction (F3···O1) between the rotator
and stator in 1, which, in turn, decreases the rotational
friction. Thus, the disorder of the fluorine atom in the rotator
increases with increasing temperature. The disappearance of
the fluorine atom from the F4 position in the rotator at lower
temperatures is unambiguously related to the formation
hydrogen bonds (F3···O1) between the rotator and stator in
1a, which prevents the fluorine atom at the F3 position from
becoming disordered or rotating. This deduction is consistent
with the occupancy of the fluorine atom at the F1 position,
which approaches that of the fluorine atom at the F2 position
at higher temperatures, and with the occupancy of the
fluorine atom at the F1 position, which diverges from that
of the fluorine atom at the F2 position at lower temperatures
(see section S2 in the Supporting Information).
0
B
1
4
ꢀ1
Boltzmann constant, an w value of 5.3 ꢁ 10 s , and an E of
0
a
ꢀ1
1
4.4 kcalmol were obtained from the plot of 1/Tpeak versus
ln(w) (Figure 2, inset).
Given the relationship between e’’ and T in Equation (1)
obtained under the assumption that all the rotators rotate at
the same frequency (i.e., that the thermodynamic rotation is
[
24]
a statistical result ), a distribution factor G(t) can be
introduced into Equation (1) to describe the distribution of
[19,25]
the rotational frequencies.
According to the time/temper-
ature superposition principle and Equation (2), the distribu-
tion factor G(t) can be transformed into a Gaussian-type
[
25–27]
energy function, G(E ).
Therefore, the simulated curves
a
for the test frequency can be plotted according to Equa-
tion (3)
To further confirm that the hydrogen-bonding interac-
tions between the rotator and stator are important in
enhancing the Ea in 1a, the molecular rotor 1b was
synthesized with the fluorine atom replaced by an amino
group. Single-crystal structural analysis revealed that 1b
Z
1
wtðTÞ
0
0
e ðTÞ ¼
GðtÞ
2dt
ð3Þ
2
0
1 þ w tðTÞ
ꢀ
1
using multiple energy barriers that range from 9.8 kcalmol
ꢀ
1
ꢀ1
[28]
to 18.8 kcalmol at 1.0 kcalmol intervals (Figure 2). As
indicated in Figure 2, the simulated curve for each test
frequency matches the experimental data.
ꢀ
crystallizes in space group P1. Although the space group of 1b
differs from that of 1a, the 1D chain in 1b can also be viewed
as the connection between adjacent APBP molecules through
the hydrogen bonding of two hydroxy groups (O-H···O =
2.801(4) ꢀ, H···O = 1.96 ꢀ, ]O-H···O = 168.28) from two
APBP molecules in a head-to-tail arrangement, similar to
that in 1a (Figure S2a). Moreover, the two compounds have
similar packing models (Figure S2). However, the hydrogen-
bonding interaction between the rotator (amino group) of one
APBP molecule and the stator (hydroxy group) of an adjacent
APBP molecule in 1b (O-H···N = 2.881(15) ꢀ, H···O =
2.13 ꢀ, ]O-H···O = 147.28; Figure 3) is significantly stronger
than that in 1a (Figure 3a). Therefore, we expected that the
ꢀ
1
The E value for 1a (14.4 kcalmol ) is significantly larger
than that for 1,4-bis[tri-(meta-methoxyphenyl)propynylben-
zene (11.7 kcalmol ) although the packing coefficient of
a (0.72) is smaller than that of 1,4-bis[tri-(meta-methoxy-
phenyl)propynylbenzene (0.73). Because a larger packing
coefficient often results in a larger E value for the rotation of
a molecular rotor, one can attribute the E in 1a, which is
larger than that in 1,4-bis[tri-(meta-methoxyphenyl)propy-
nylbenzene, to the hydrogen-bonding interaction between the
rotator (fluorine atom) and stator (hydroxy group) in 1a.
To determine how the hydrogen-bonding interactions
a
ꢀ1 [15]
1
[
29]
a
[
15]
a
between the rotator and stator enhance the E in 1a, the
a
crystal structures of a single 1a crystal were measured at
1
23(2), 213(2), 273(2), and 313(2) K (see section S2 in the
Supporting Information). These measurements indicate that
the occupancy of the fluorine atom at position F4 in 1a
decreases as temperature decreases. At and below 213 K, the
occupancy of the fluorine atom at position F4 becomes zero,
leaving three disordered F atoms (F1, F2, and F3) on the
phenyl ring. A further investigation of the crystal structures at
different temperatures revealed that the strength of the
hydrogen-bonding interaction (F3···O1) between the adja-
cent FPBP molecules in 1a increases with a decrease in
temperature (Table 1).
Figure 3. The hydrogen bonds between the hydroxy and amino groups.
The hydrogen atoms are omitted for clarity.
[
23]
Thus, the fluorine atom at the F4 position could be only
detected at higher temperatures because higher temperatures
E for the rotation of the rotator in 1b would be significantly
higher than that in 1a if the hydrogen-bonding interaction
a
between the rotator and stator are important in enhancing the
E value for the rotation of the rotor.
a
Table 1: Hydrogen-bonding interaction of F3···O1 in 1a at various
In fact, measurements of the e’’ values at various
frequencies and temperatures (Figure 4 and Figures S4 and
S5 in which the rapid increase in e’’ at temperatures above
370 K is due to an increase in the conductivity at high
temperatures) indicate that the maximum e’’ for 1b occurs at
a significantly higher temperature than that for 1a at the same
temperatures.
T [K]
F3···O1 [ꢀ]
F3···HO1 [ꢀ]
] F3···HꢀO1
1
2
2
3
23(2)
3.278(5)
3.303(8)
3.337(9)
3.333(9)
2.47
2.49
2.53
2.57
155.48
159.48
159.58
154.48
13(2)
73(2)
13(2)
4
test frequency. For example, at f = 10 Hz, the maximum e’’ for
Angew. Chem. Int. Ed. 2013, 52, 1 – 5
ꢀ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
3
These are not the final page numbers!
Zhang, Qian-Chong
