Throwing in a Monkey Wrench to Test and Determine Geared Motion in the Dynamics of a Crystalline One-Dimensional (1D) Columnar Rotor Array

Article abstract of DOI:10.1021/jacs.8b11385

Crystals of molecular rotor 1 with a central 1,4-phenylene rotator linked to two molecules of the steroid mestranol were prepared with 1%, 5%, 20%, and up to 40% of the analogous 2, which contains a larger 2,3-difluorophenylene rotator and effectively act

Full text of DOI:10.1021/jacs.8b11385

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Article
Throwing in a Monkey Wrench to Test and Determine Geared
Motion in the Dynamics of a Crystalline 1D-Columnar Rotor Array
Salvador Perez-Estrada, Braulio Rodríguez-Molina, Emily
F. Maverick, Saeed I. Khan, and Miguel A. Garcia-Garibay
J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 08 Jan 2019
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Throwing in a Monkey Wrench to Test and Determine GearedMotion
in the Dynamics of a Crystalline 1D-Columnar Rotor Array
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1
Salvador Pérez-Estrada, Braulio Rodriguez-Molina, Emily F. Maverick, Saeed I. Khan, Miguel A.
Garcia-Garibay *
1
1
Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United
2
States; Área Académica de Química, Centro de Investigaciones Químicas, Universidad Autónoma del Estado de Hidalgo,
Ciudad del Conocimiento, Hidalgo 42184, México; Instituto de Química, Universidad Nacional Autónoma de México, Cir-
3
cuito Exterior, Ciudad Universitaria, México, 04510, D.F., México
ABSTRACT:Crystals of molecular rotor 1with a central 1,4-phenylene rotator linked to two molecules of the steroid mestranol
were prepared with 1%, 5%, 20% and up to 40% of the analogous 2, which contains a larger 2,3-difluorophenylene rotator and ef-
fectively acts as a monkey wrench that affects the rotation of the host. The packing motifof the desired P3 crystal form consists of
2
1D columns of nested rotors arranged in helical arrays with the central aromatic rotators disordered over two sites related by 85º
2
rotation about their 1,4-axes. Rotational dynamics measured by quadrupolar echo H NMR line shape analysis were analyzed in
terms of a process model that involves degenerate180° jumps in the fast exchange regime combined witha highly correlated and
o
entropically demanding jump of 85 between the two dynamically disorderedsites. While theenthalpic and entropic barriersfor the
2
‡
-1
‡
-1
-1
1
80° jump estimated from H T measurements were H =2.7±0.1 kcal mol and S = -5.0±0.5 cal mol K , respectively,the
1
‡ -1 ‡
corresponding parameters forthe slower 85° jumps, determined by line shape analysis, wereH = 2.6 kcal mol and S = -23 cal
mol K . Increasing amounts of the larger molecular rotor 2in the solid solutionresults in significant dynamic perturbations as the
-
1
-1
guest, acting as a monkey wrench, reaches values of one outof everyfive molecular rotors in the chain.
INTRODUCTION
The last few years have witnessed an increased interest in the
1
field of amphidynamic crystals, and their applications for the
development of smart materials, crystalline molecular rotors,
2
,3,4
and molecular machines. In a previous communication we
reported the dynamics of molecular rotor 1 consisting of a 1,4-
phenylene rotator linked to two mestranol molecules that play
5
the role of the stator (Figure 1a, R=H). Molecular rotor 1can
be crystallized in the trigonal chiral space group P3 with
2
apacking structure that features a helical columnar array of
nested molecular rotors as shown in Figures 1b and 1c, which
respectivelyillustrate viewswith the 3-fold axis on the plane of
the paper, and down the direction of the channel. Rather than
having close face-to-face aromatic contacts, the phenylene
rotatorshave a center-to-center distance of ca. 4.9Å. This gene-
rates sufficient space for them to have some rotational free-
dom and adopt two equilibrium sites related by a rotational
5
displacement of 85°with45:55 occupancies (Figure 1d). One
of the most interesting features of the one dimension)al (1D
channel structure is the fact that the rotationalenergy potential
is not determined uniquely by steric and/or electronic interac-
tions from a relativelystatic structure,but rather by the variable
position of the neighboring rotators. This implies that rota-
tional motion in these crystalsrequires some degree of rotator-
rotator correlations. In fact, variable
Figure 1. (a) Line structure of mestranol molecular rotors with
phenylene1(R=H) and difluorophenylene2 (R=F) rotators.Side (b)
and top (c) views of the 1D columnar array of molecular rotors.(d)
Space-filling model ofphenylene rotators in the 1D chain illustrat-
ing the rotational disorder in the channel.
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temperature H NMR quadrupolar echo experiments with
titutional guest to crystals of 1. We reasoned that a 2,3-
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phenylene-d labeled samples revealed relatively narrow spec-
difluorophenylene rotator would result in a small perturbation
to the crystal lattice of 1 because the fluorine atom van der
Waals radius of 1.47 Å is close to that of the hydrogen atom of
4
tra (Figure 2).They could be simulated only with a somewhat
counterintuitive process involving two anisochronous, or ki-
netically distinguishable trajectories.
9
ca. 1.20 Å. Similarly, the C-F bond distance of ca. 1.34 Åis re
9
relatively close to the C-H bond length of ca. 1.09 Å. One
The observed spectrum is different from those of most crystal-
line phenylene rotators, which range between theones shown
in the top of Figure 2. The broad spectrum inFigure
should expect that a correlated rotational mechanism would be
subject to perturbations by the slightly larger guest, which can
10
be viewed as a monkey wrench. It may be expected that such
2
acorresponds to the Pake, or powder pattern, determined by
perturbation will beproportional to the number of rotors in-
volved in acooperative dynamic process. That is to say, if
there aren-rotors involved in a correlated process, the effect of
added2 would be significant when it approaches values of 1/n
(assuming a random distribution). An additional element of
interest in this study comes from the fact that the dipolar 2,3-
the full extent of the quadrupolar coupling interaction, and is
characteristic of samples where the phenylene groupsare either
static, orundergoing rotation in the slow exchange regime, i.e.,
0
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-1
krot ≤ 10 s (≤10 kHz). The spectrum in Figure 2bcorresponds
o
to samples where the phenylene rotator undergoes180 flips in
thefast exchange limit,which corresponds to rotational fre-
1
1
7
-1
6,7
difluorophenylene rotator ( ≈ 3 Debye) may provide us with
quencies thatare ca.≥10 s (≥10 MHz). By contrast, the am-
bient temperature spectrum recorded with samples of 1 can be
an alternative entry to materials with switchable macroscopic
1
2
o
polarization. Indeed, it can beshown that strongly interacting
dipole chains can spontaneously adopta ferroelectric aligne-
simulatedby a model that includes 180 rotations in the fast
exchange limit (k
≥ 10 MHz) combined with slower
fast
4
f
o
5
ment, whichin cases like thiswould be able toadopteither
directionalong the channel.
8
5 rotationsat a rate ofkslow≈ 1.5 MHz (Figures 2c and 2d). It
o
should be noted that this motion can take values of +85 or -
o
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5 depending on the direction of measurement, however, we
o
will simply refer to it as an 85 rotation. The trajectories sug-
gested by the spectral simulations are consistentwith therota-
tional C symmetry of the phenylene group, which accounts
2
o
o
for the 180 jumps, and the85 relation that exists between the
two disordered sites in crystal structure of 1 (Figures 1d and
3a). A schematic representation of the proposed anisochronous
trajectoriescan be visualized with the help of Figure 3, the
o
crystallographically distinct sites related by 85 (A and B) are
shown at the top (Figure 3a) and the relation that exists be-
tween the fast and slowmotion represented in Figure 3b. Con-
sidering the relativerotational frequencies, the ambient tem-
perature spectrumrequiresthe dynamic averaging of the qua-
o
drupolar coupling interaction caused by seven or more 180
rotationsfor every 85 jump between the A and B.
o
Figure 3. (a) Crystallographic sites A and B related by an angle of
8
5° and (b) the dynamicsof molecular rotor 1 described in terms
o
of fast 180 rotations that retain the identity of sites A and B,
combined with a much slower exchange between those two sites
(adapted from reference 3).
RESULTS AND DISCUSSION
Preparation and Characterization of Solid Solutions. Solid
solutions are single phase, crystalline materials that retain the
Figure 2. Representative quadrupolar echo spectra of thepheny-
13
crystal structure of the host with varying amounts of guest.
lene-d rotator in the (a) slow and (b) fast exchange regimes, and
4
Solid solutions where the guest occupies lattice positions in a
(
1
c) the experimental and (d) simulated spectra of molecular rotor
described in terms of fast 180 rotations and slow 85 jumps.
8,13b
random manner are known as substitutional solid solutions.
o
o
Solid solutions, or mixed crystals,have played an important
2
14
Further insightwas available from variable temperature
H
role in the development of solid state photochemistry, photo-
o
15
13,16
NMR measurements, which revealed that the 85 rotation oc-
physics and some areas of materials science. Kitaigorods-
ki suggested that substitutional solid solutions in molecular
crystals mayoccur between components that have a coefficient
curs with a relatively ―unfavorable‖activation entropy of -23
-1
-1
cal mol K , indicatingthatswitching between coordinates A
and B should be slow because the need for the correlated or-
concerted motion of several rotators.In this paper, searching
for further insight into the proposed anisochronous and corre-
8
of structural similarity that is greater than 85%. With a differ-
ence of only 2 small atoms in a relatively large structure, and
based on their molecular volumes, one can estimate a coeffi-
cient ofstructural similarity between 1 and 2 of ca. 98.6%,
which makes them excellent candidates.
lated model, we have explored the effects
a 2,3-
difluorophenylene rotator 2 (Figure 1a, R=F) added as a subs-
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To test that, samples of molecular rotors 1 and 2 and their
molecular rotor 2, the refinement was consistent with a fluo-
rine content of 0.4.While there is uncertainty related to the low
fluorine content and the quality of mixed crystal specimens,
the structure solution for the electron density of the fluorine
atoms at 100 K was localized in one of the four disordered
sites (Figure 5). Thisindicatesthat the four crystallographically
different positions are not isoenergetic.A simple computation-
al model was built with the X-ray coordinates of a central dif-
luorophenylene and two phenylene neighbors on each side but
with the full steroid structures included. This modelshowed
thatthe energetics of placing the fluorine atoms in sites 1-4
(Figure 5) have relative values of 0, 2.0, 2.8 and 3.8 kcal/mol.
These values are in good qualitative agreement with the X-ray
1
2
3
4
5
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phenylene deuterated isotopologues were obtained by Sonoga-
shira coupling of commercial mestranol with the correspond-
5
ing
1,4-dibromo-phenylene
and
2,3-difluoro-1,4-
trifluoromethansulfonylbenzene, respectively. We targeted
solid solutions in the columnar P3 lattice of molecular rotor1
2
with increasing amounts of 2, i.e.,1:2 = 99:1, 95:5, 80:20 and
6
0:40.Solid solutions 1(1-x)2x with x=0.01 and 0.05 were relia-
bly prepared by slow evaporation at room temperature from
:1 dichlomethane-acetonitrile solutions. In the case of x=0.2
and 0.4, solid solutions were also obtained by solvent (ace-
4
1
7
1
1
1
1
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2
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0
tone) assisted mechanochemical crystallization. We observed
thatthe slow evaporation method at ratios past 20% of molecu-
lar rotor 2resulted in phase segregation with concomitant crys-
2
structure and with H NMR results described below.
1
8
tallization ofthe alternative P2 2 2 polymorph. The formation
1
1 1
of theP3 phase could beconfirmed by powder X-ray diffrac-
2
tion (PXRD), infrared spectroscopy (IR) and
a)
b)
c)
Figure 5. View of the X-ray structure solution of the P3 mixed
2
single crystal 1(1-x)2x x=0.2at 100K illustrating the position of the
difluorophenylene rotator with respect to its two closest neigh-
bors. The figure suggests that the ortho-fluorine atoms, at equili-
brium, prefer one of the four possible sites (i.e., Site 1) at 100 K.
d)
5"
15"
25"
35"
45"
Comparing the unit cell parameters of 1(1-x)2x x=0.2 to those
2θ (°)
obtained from the pure molecular rotor 1 one can see that the
axes are slightly longer in the solid solution, resulting in a
larger unit cell volume (Table 1). We took advantage of single
crystalline specimens to document the macroscopic homo-
geneity of the solid solutions. We determined that different
crystals and different fragments of various single crystals have
the same composition, suggesting that the host composition
does not vary as the total concentration in solution changes
during crystallization, and that it does not accumulate in spe-
cific sectors of the crystal structure. With well characterized
samples in hand we proceeded to investigate the dynamics of
the host phenylene (Ph) and guest 2,3-difluorophenylene
Figure 4. Powder X-ray diffraction patterns of the P3 crystal
2
lattice of solid solutions 1(1-x)2x with a) x=0.01, b) x=0.05, c)
x=0.2 and d) pure molecular rotor 1.
differential scanning calorimetry (DSC). Diffraction patterns
of solid solutions 1(1-x)2xx=0.01, 0.05, 0.2 and 0.4 showed full
agreement with that of molecular rotor 1 in the P3 form (Fig-
2
ure 4 and Figure S19). Attenuated total reflectance Fourier
transform infrared spectroscopy (ATR-FTIR) can help distin-
guish between the P3 and P2 2 2 polymorphs which have
2
1 1 1
distinct fingerprint patterns, includinga characteristic OH
-
1
stretch band near 3530 cm for theP3 polymorph (Figures S7,
2
(
F2Ph) rotators in the solid solutions 1(1-x)2x.
Table 1. Unit cell parameters of the solid solution 1(1-x)2 ,
x
S8,and S9 SI section). As the DSC analysis of the solid solu-
tions 1(1-x)2x x=0.01, 0.05 and 0.2showed single endothermic
transitions (Figures S12-S18), the method was particularly
useful to identify mixtures of phases. DSC analyzes of pure 1
and 2 showed endothermic transitions between 250-255 °C
and 231-235 °C, respectively; whereas those of dilute solid
solutions 1(1-x)2x x=0.01, 0.05 are close to the pure 1 at 247-
x=0.2 and host crystal 1 in the P3
space group.
2
Crystal 1
Solid Solution
X-ray source
Wavelength (Å)
T (K)
Synchrotron
0.77490
100
Mo Kα
0.71073
100
2
54 °C and 246-254 °C, respectively. As expected, the solid
solution1(1-x)2x x=0.2 displayed an endothermic transition at a
lower temperatures of 231-239 °C. In the case of1(1-x)2x x=0.4
two close endothermic transition peaks were observed at 225
°C and 235 °C, suggesting that the sample crystallizes with
some degree of heterogeneity
a (Å)
b(Å)
14.7106(4)
14.7106(4)
14.6565(7)
2746.76(17)
14.758(4)
14.758(4)
14.683(4)
2769.7(12)
c (Å)
3
V (Å )
We were able to grow single crystals of the solid solution 1(1-
x)2x, x=0.2 and, as expected, the structure solution at 100 K
o
Activation Parameters for the 180 Rotation of Crystal
2
was obtained in the same space group as pure 1, P3 (Table 1
Host 1 by H NMR Spin-Lattice Relaxation. As previously
2
2
and Figure S20). Similarly, the phenylene rotator is disor-
dered over two positions with occupancies of 44:56 related by
an angle of 83.1°. As expected for the 20% mol content of the
noted, line shape analysis of quadrupolar echo H NMR spec-
tra required the 180° rotations in the P3
rotor 1 tooccur in the fast exchange regime (krot>10 s ) in the
form of molecular
2
7 -1
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temperature range between 155 K and 296 K. Knowing that-
Rotational Dynamics by Quadrupolar Echo H NMR Line
Shape Analysis of Solid Solutions. With dynamic informa-
tion for the pure crystals of 1 and the experimental tools nee-
dedto characterized the 180° and 85° rotational dynamics, we
moved on to characterize therotational motion of the host phe-
1
2
3
4
5
6
7
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9
1
1
1
1
1
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1
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2
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dynamic processes with rotational correlation times ( in Eq.
c
1) in this regime approach theLarmor frequency of common
magnetic nuclei(ω =2πν in Eq. 2), we decidedto take advan-
0
0
tage of variable temperature (VT) spin-lattice relaxation T1
measurements to determine the activation energy E and pre-
nylene and guest difluorophenylene in solid solutions 1(1-
a
-
1
19
2
exponential factor0 (Eq. 1). To accomplish that, one can-
x)
2
.Quadrupolar echo VT H NMR experiments were per-
x
1
9b
formed at 46 MHz (7.046 Tesla)with microcrystalline samples
using either of the two deuterated components,1-d4(1-x)2x or
substitute the in the Kubo-Tomita relaxation expression
c
(
Eq. 2) by Eq. 1.
1(1-x)
2-d2(x).
-
1
-1
c = o exp (-E /RT)
(Eq. 1)
(Eq. 2)
a
(a)
0
1
2
3
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9
0
1
2
3
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0
1
2
3
4
5
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9
0
1
-d4
-
1
2
2 -1
c
2
2 -1
c
T1 = C[ (1 +   ) + 4 (1 - 4  ) ]
c
o
c
o
1-d4(1-x)2x
To obtain information on the dynamicsof the phenylene rotator
2
2
werecorded H T experiments with a H Larmor frequency ν
1
0
kHz
=
ω /2π = 92 MHz at 14.092 Tesla onsamples of phenylene
0
(b)
rotator1-d . We collectedT data using a saturation recovery
4
1
pulse sequence in the temperature range of 160 K to 295 K.We
confirmed asingle exponential behaviorfor recovery kinetics at
1-d4(1-x)2x
1(1-x)
2-d2(x)
all temperatures measured and founda T minimum at 175 K.
1
As shown in Figure 6, the experimental T values as a function
1
of the temperature were fitted to the Kubo-Tomita equation
-
1
(Eq. 2), giving an activation energy of E =3.2±0.07kcal mol
kHz
a
-1
12 -1
and a pre-exponential factor τ =1±0.2x10 s .As expected,
o
2
Figure 7. H NMR spectra measured at 296 K of (a) 1-d (red
these values are greater than those previously determined by
4
2
dotted line) and1-d4(1-x)2xx=0.2 (black line), and (b) 1-d4(1-x)2
x
H NMR line shape analysisfor the 85° jump, which has as-
-
1
x=0.2 (blackline) and 1(1-x)2-d2(x) x=0.2 (red dottedline).
lightly smaller barrier ofE =2.6 kcal mol anda pre-exponential
factorτ =1.2x10 s , which is four orders of magnitude
smaller.
a
-
1
8
-1
0
Spectral changes as a function of increasing amounts of the
difluorophenylene rotor 2 resulted in some broadening that
depended on the amount of guest and the temperature of the
experiment. Effects on the rotational motion of the phenylene
host determined by measurements carried out with solid solu-
tions 1-d4(1-x)2x x=0.01, 0.05, 0.2 in the range of 145 K to 296
K were relatively small, as the spectra were very similar to
5
-1
2
The pre-exponential factor (τ ) arising from H T data for
0
1
o
the 180 rotations is consistent with an elementary process
determined by the frequency of the torsional mode that must
be thermally activated for the rotator to overcome the barrier,
-1
1,20
i.e., τ0 = torsion
.
This is in stark contrast with the pre-
-1 8 -1 o
exponential factor τ0 = 10 s for the 85 jumps, which re-
flects an entropically demanding process. It should be noted
that site exchange rates calculated from the activation parame-
ters for the 180 rotation, 4.9x10 s at 296 K and 3.9x10 s
at 155 K, are consistent with the fast exchange frequency
those reported for the host crystal 1-d
temperature spectra of the phenylene rotator in solid solutions
x=0.01 and 0.05 are identical to that of the pure
crystal host 1-d (not shown).However, an increase in the
amount of the difluorophenylene rotator to 20% in solid solu-
tion1-d4(1-x)2 x=0.2 resulted ina considerably broader spec-
x
4
. Particularly, the room
1-d4(1-x)2
x
o
9
-1
7
-1
4
7
-1
2
(>10 s ) required by the H NMR line shape simulations.
trum with a flatter top (Figure 7a,dotted), suggestingthat rota-
tional motion of the host rotators is affected when the guest
reaches values corresponding to one host for every four guests.
This initial resultindicated that perturbations at guest/hosts
loading levels of 1/100 and 5/100 are not significant to alter
the postulated correlated motions. However,perturbations at
loading levels of 1/5 are significant, indicatingthat correlated
motions involve a relatively small number of rotators in the
1D chain. Not surprisingly, when the rotational motion of the
6
5
4
3
2
1
fluorinated phenylene host2-d is analyzed at the same guest
2
loading of 20%(1(1-x)2-d2(x) x= 0.2), one can see significantly
more broadening(Figure 7b, red dottedline), which is an indi-
cation that the motion of the larger hostin the same channel
structureis more hindered.
2.5
3.5
4.5
5.5
6.5
7.5
1
000*T-1 (K-1)
2
Figure 6. H NMR Spin-lattice relaxation (T ) experiments with
1
Spectral changes as a function of decreasing temperature for
the solid solutions were similar to those previously observed
for crystals of host 1, with some broadening resultingfrom the
slowing rotations as the temperature changes from 296 K to
molecular rotor 1recorded at 92 MHz from 160-295 K. The solid
diamonds are the experimental data points and the red dotted line
is the Kubo-Tomita fit to the experimental data.
1
96 K. These results are illustrated in Figure 8with two sets of
spectra from measurements carried out with solid solutions
containing 20% of the difluorophenylene host (i.e., 1(1-x)2x
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x=0.2). The spectra shown in Figure 8a correspond to samples
Having established viable dynamic models for the motion of
the two components we collected data from the other solid
solutions. Variable temperature H NMR spectral data from
1
2
3
4
5
6
7
8
9
where the host phenylene rotator is deuterated (1-d4(1-x)2x
x=0.2), and those on the right (Figure 8b) to samples wherethe
NMR label is on the fluorinated guest(1(1-x)2-d2x x=0.2). One
can see that the spectra of the two solid solutions gradually
became broader at the lower temperatures as previously re-
ported for crystals of1-d4.
2
the phenylene rotator were obtained with samples 1-d4(1-x)2x
x=0.01, 0.05 and 0.2 and the Arrhenius and Eyring plots for
the dynamics of the slower 85° rotation gave results that are
5
similar to those observed in crystal host 1. The corresponding
Scheme 1
(a)
(b)
2
2
2
96 K
56 K
16 K
900 kHz
650 kHz
200 kHz
296 K
250 K
10 MHz
1.5 MHz
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
values, summarized in Table 2 in entries 3-5, showed a slight
increase in the activation enthalpies and activation entropies,
210 K
190 K
30 kHz
5 kHz
-
1
which take values that range from 1.6 to 2.4 kcal mol and -
-
1
-1
19.2 to -23 cal mol K , respectively. It is interesting to note
that the lowest concentrations of the difluorophenylene guest,
1
96 K
100 kHz
1
% and 5%, actually made the rotation of the host slightly
easier with slightly smaller activation enthalpies and activation
entropies that are slightly less negative, which also sup-
kHz
kHz
o
portsthesuggestionthat the 85 rotation occurs as a collective
2
event, rather than in an isolated manner.
Figure 8. H NMR spectra recorded at 46 MHz of solid solutions
a) 1-d4(1-x)2x x=0.2 and (b) 1(1-x)2-d2(x) x=0.2. The black solid
(
The spectra from solid solutions 1(1-x)2-d2(x) x=0.05, 0.2 did not
show significant changes between 296 K and 250 K, but broa-
dened significantly in going from 230 K to 190 K. We did not
lines correspond to the experimental spectra and the red dotted
lines to the simulation. The frequency shown in thesimulated
spectra corresponds to the 85° switch, as the 180° jumpsremain in
the fast exchange limit,above 10 MHz.
2
perform quadrupolar echo H NMR experiments with samples
of1(1-x)2-d2(x) x=0.01 because of the low concentration of deu-
terium in the sample. Interestingly, the Arrhenius plot for the
slow 85° difluorophenylene rotator jump in 1(1-x)2-d2(x) x=0.05
and 1(1-x)2-d2(x) x=0.2 revealed activation energies of
Line shape analysis of the spectra obtained from the phenylene
rotator in the solid solution1-d4(1-x)2x x=0.2 with the model
previously used for the host crystal gave good results with a
-
1
o
o
E =6.6±0.5 and8.4±0.5 kcal mol and pre-exponential fac-
fast 180 rotation and a slow 85 site exchange.The frequencies
of the latter varied from 100 kHz at 196 K to 900 kHz at 296
K, as indicated in Figure 8a. By contrast, spectral simulation
for the fluorophenylene rotator in samples of 1(1-x)2-d2(x) x=0.2
shown in Figure 8b turned out to be more complicated. Failed
attempts to reproduce the broader experimental spectra with
the same mechanism included trajectories where either or both
ofthe 180° and 85° jumps were considerably slower. After
that, we varied the magnitude of the short jump angle and ex-
plored distributions of frequencies that might arise from struc-
tural heterogeneities in the sample.Neither set of simulations
resulted in a spectrum that could match the experi-
ment.Eventually, recognizingthat the occupation of the fluo-
rine atoms in the crystal structure is notequally distributed
over all four previously degenerate sites, we found that a
three-site model involving180° rotation in the fast exchange
a
-
1
11
13
-1
tors of τ
and 7)which are considerably greater than those of the host
x=0.05 and 0.2. The corresponding
=7.5x10 ±3 and 2.3x10 ±3 s (Table 2, entries 6
0
phenylene in 1-d4(1-x)
2
x
enthalpies of activation for 1(1-x)2-d2(x) x=0.05 and 1(1-x)2-d2(x)
≠
-1
x=0.2are ΔH =6.0±0.5 and 8.0±0.5 kcal mol , and entropies
≠
of activation change to more positive values, ΔS =-6.0±2.1
-1
-1
and 1.0±2.2 cal mol K , suggesting that rotation of the dif-
luorophenylene group is more of an isolated event, unable to
participate in a correlated process that involves the collective
motion of several rotators. It is worth noting that the large pre-
exponentials for the 85° rotation in the case of 1(1-x)2-d2(x)
x=0.05 and 0.2 result in a relatively high ambient temperature
frequency despite its significantly higher energy barrier. How-
ever, with a high temperature coefficient, its rotational motion
decelerates rapidly as the temperature goes down.
o
regime, combined with slow 85° (or -95 )jumpsreproduced the
Rotational Dynamics of 2-d in Solid Solutions at Higher
2
experimental spectrawhen the slow process variedbetween 5
kHz and 10 MHz (Figure 8b). It appears that the broadening in
this case results from the sampling of orientations rather than
from slowing the dynamics of the original four sites. The pro-
posed difference between the trajectories responsible for the
spectra shown in Figure 8a and 8b is indicated in Scheme 1a
and 1b, respectively. The key distinction between the two
models is that the difluorophenylene rotator is unable to occu-
py one of the sites that is otherwise available to the phenylene
rotator.
Temperatures – TheLoss of Dynamic Order. When the
samples 1(1-x)2-d2(x) x=0.05 and 0.2 were heated in the range of
315 K to 395 K, we observed that the spectra gradually nar-
rowed, with a peak that emerges in the middle at ca. 375 K
(
Figure 9). We found that the model used to simulate the low-
er temperature spectra was no longer adequate. A solution
was found with a model that considers two different popula-
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Table 2. Activation parameters for the dynamics of the host phenylene and guest difluorophenylene rotators in the 1D col-
umn array of 1 and 1(1-x)2x x=0.01, 0.05, 0.2.
a
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
c
-1 -1
≠c
≠d
Sample
Jump
Angle
Ea
τ0 (s )
ΔH
ΔS
b
e
12 e
e
e
1
1
-d4
-d4
180
85
85
85
85
85
85
3.2 0.1
±
1±0.2x 10
2.7 0.1
±
-5.0 0.5
±
f
8 f
f
f
2.6
1.2x10
2.2
-23.0
8
1
-d4(1-x)2x
x=0.01
1-d4(1-x)2x
x=0.05
-d4(1-x)2x x=0.2
2.0 0.1
±
7.5x10 ±1
1.6±0.1
1.8±0.1
2.4±0.2
6.0±0.5
8.0±0.5
-19.0±0.5
-19.0±0.8
-23.0±0.9
-6.0±2.1
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
8
2.2±0.1
2.9±0.2
6.6±0.5
8.4±0.5
7.5x10 ±2
8
1
1.5x10 ±1
1
1
1(1-x)
x=0.05
1(1-x)
2-d2(x)
2-d2(x)
7.5x10 ±3
1
3
2.3x10 ±3
1.0±2.2
x=0.2
a
2
b
o
c
-1
d
-1
Unless indicated, data was determined by quadrupolar H NMR lineshape analysis. Units are degrees ( ) ; kcal mol ; cal mol K
-
1
e
2
f
;
Determined by H NMR spin-lattice relaxation; Reported in ref. 5.
tions with different dynamic characteristics and fractions that
vary systematicallyas a function of temperature. One popula-
tion is engaged in the original three site exchange model of
Scheme 1b, with fast 180° rotations and one site related by 85°
andjumps occurring at ca. 30 MHz (Figure 9). The second
population requires a trajectory that includes site exchange in
the low MHz regime between all four sites related by 85° (and
the guest:host ratio reaches the maximum value of 1:2 =
3:2,i.e., 1(1-x)2-d2(x) x=0.4. At 295K, the H NMR spectrumre-
2
corded at 92 MHz wasrelativelybroad with a feature that
projects from the center (Figure 10).The intensity of the cen-
tral feature decreased as the temperature was lowered to 253
K, and then to 233 K. While reasonable spectra were obtained
with simulations involving the three-site model, astatic com-
ponent with a increasing contribution was required as the tem-
perature was lowered.As shown in Figure 10,the dynamics of
the three site component were consistent with those observed
at lower (20%) loading, involving fast (≥10 MHz) 180° rota-
tions and slow 85° (30 KHz - 10 MHz) jumps (Figure 10).
This result suggest that jamming the channel does not have the
same effect as increasingtemperatures, supporting the sugges-
tion that correlated motion is an entropically determined
process and as such is primarily affected by increasing thermal
energies (TS).
-95°) jumps. The weight of the four-site population increases
with increasing temperature from 15% at 335K to 78% at 395
K. We find this result to be significant, as it implies that the
correlations responsible for the low temperature behavior be-
gin to disappear, which is reasonable for an entropically de-
manding process with S<0, as the -TS terms become in-
creasingly unfavorable. We propose the change in dynamics
from three sites to four sites indicates a transition from corre-
lated to independent rotations.
K = 4.0 MHz
K85= 1.5 MHz
K95= 1.5 MHz
8
5
K = 2.0 MHz
9
5
395 K
355 K
1
0 MHz
0%
500 kHz
40%
78%
20%
295 K
233 K
6
K = 2.0 MHz
K85= 1.0 MHz
K95= 1.0 MHz
8
5
K = 2.0 MHz
1.5 MHz
50%
30 kHz
35%
9
5
3
75 K
335 K
2
53 K
213 K
3
0%
15%
kHz
kHz
Figure 9. High temperature deuterium wideline spectra of the
solid solution 1(1-x)2-d2(x) x=0.2 recorded at 46 MHz that showthe
experimental spectra (black solid lines) and the simulated spectra
Figure 10. Experimental (black solid line) and simulated (red
dotted line) deuterium wideline spectra of solid solution 1(1-x)2-
d2(x) x=0.4 recorded at 92 MHz. The simulated spectra were pro-
duced considering two components of a three sites process, a stat-
ic at 10 kHz (not shown) and mobile component with fast 180°
jumps (≥100 MHz) and slow 85° jumps (30 KHz - 10 MHz). The
frequency displayed corresponds to the 85° jump and percentage
corresponds to the contribution of the mobile component.
(red dotted lines) obtained by considering a three sites process
with fast 180° and slow 85° jumps (not shown) and a four sites
process with consecutive 85° and 95° jumps. The percentage
shown corresponds to the contribution of the four sites process.
To further testthe emerging model, and to determine whether
the observed loss of order occurs primarily as a function of
temperature, or whether it can occur as a function of increas-
ing guest loading, we turned our attention to samples where
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amounts of the guest 2 as well as lowering the temperature
1
2
3
4
5
6
7
8
9
slows down the rotation of the host 1 and that the rotational
trajectory of the host phenylene rotators is not affected by the
guest 2,3-difluorophenylene rotators. Additionally, in solid
solutions
1(1-x)2-d2(x)
x=0.01 and 0.05 the 2,3-
difluorophenylene rotator appears to facilitate the 85° rotation
of the host phenylene rotator, as can be noted by smaller ener-
gy barriers than that of the pure molecular rotor 1. The host
phenylene rotators became slower at a ratio of 1:4 of molecu-
lar rotors 2 and 1. On the other hand, as a result of its slightly
larger size, the85° rotation of the 2,3-difluorophenylene rota-
tor is more encumbered and disengaged from the correlated
rotation of the host phenylene rotators.This is evident from
larger energy barriers and more positive entropies,
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
-
1
≠
E =6.6±0.5 to 8.6±0.5 kcal mol and ΔS =-6.0±2.1 to
a
-
1
-1
1.0±2.2 mol K .However it follows the same trajectory of
fast 180° and slower 85° rotation, without occupying one of
the four disordered positions.This work also suggests the value
of substitutional solid solutions as an additional strategy to
control the properties of amphidynamic crystals and crystal-
line molecular machines.
Figure 11. Mechanism for the rotation of the phenylene rotator in
the 1D column of molecular rotor 1.
ASSOCIATED CONTENT
A qualitative model that captures a plausible mechanism for
the correlated motion is shown in Figure 11 with three rotators
that have one phenylene edge labeled with a black dot. On the
top and bottom horizontal we represent a process where the
Supporting Information
Experimental procedures, spectral data, DSC and TGA analyses,
13
VT C CPMAS solid state NMR, and XRPD patterns (PDF). A
CIF file for single crystal X-tray analysis of solid solution solu-
tion 1(1-x)2x, x=0.2 is also included. This material is available free
o
reference rotator at the center of the triad undergoes 180 rota-
o
tion by a transition state (TS-180 ) that involves relatively
of charge via the Internet at http://pubs.acs.org.
small displacement of the two close neighbors. By adopting
orientations orthogonal to the chain direction while the central
ring rotates, they would disrupt the smaller number of neigh-
bors, making it a low entropy process. By contrast, to change
AUTHOR INFORMATION
Corresponding Author
* mgg@chem.ucla.edu
o
o
the tilt of the molecules by 45 (55 ) would require a transition
o
state (TS-45 ) where the two neighbors need to align along the
Funding Sources
This work was supported by National Science Foundation grants
DMR 1700471 and by the MRI program under grant 1532232.
direction of the channel, which is likely to disrupt more mole-
cules unless two or more are engaged in the process. The ef-
fect of these two processes on the next near neighbors is
represented in the center of the figure, suggesting why isolated
o
o
1
80 rotation would be faster than a collective motion of 45 .
ACKNOWLEDGMENT
CONCLUSIONS
In summary, we showed that in crystals of pure molecular
This work was supported by National Science Foundation grant
DMR 1700471.NMR work reported was carried out with an in-
strument purchased with funds from the MRI program under grant
1532232. Crystallographic data using synchrotron radiation were
collected through the SCrALS (Service Crystallography at Ad-
vanced Light Source) program at the Small-Crystal Crystallogra-
phy Beamline 11.3.1 at the Advanced Light Source (ALS), Law-
rence Berkeley National Laboratory. The ALS is supported by the
U.S. Department of Energy, Office of Energy Sciences Materials
Sciences Division, under contract DE-AC02-05CH11231. We
thank Dr. A. Carreras and Prof. P. Alemany from the Universitat
de Barcelona for many helpful discussions.
rotor 1 the barrier of the180° rotation is slightly greater,
-1
E =3.2±0.1 kcal mol , than that of the 85° rotation, E =2.6
a
a
-1
kcal mol , butits pre-exponential factor is four orders of mag-
nitude larger. The large and negative entropy of the 85° jump,
ΔS =-23 mol K is indicative of an entropically demanding
≠
-1
-1
process within the 1D column of phenylene rotators. By con-
≠
-1
-
trast, the entropy of the 180° jump,ΔS =-5.0±0.5 cal mol K
,
1
is considerably lessnegative. Mixed crystals of molecular
rotors 1 and 2, 1(1-x)2-d2(x) x=0.01, 0.05, 0.2 and 0.4, were reli-
ably prepared by slow solvent evaporation and solvent assisted
mechanochemical crystallization. Variable temperature qua-
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