Photoactivated directionally controlled transit of a non-symmetric molecular axle through a macrocycle

Article abstract of DOI:10.1002/anie.201200555

One-way path: A non-symmetric molecular axle threads a crown ether ring and is subsequently expelled along the same threading direction upon application of photochemical and chemical stimuli. The system relies on tailor-made control of the thermodynamic and kinetic properties of the system according to a flashing ratchet mechanism. Copyright

Full text of DOI:10.1002/anie.201200555

Angewandte
Chemie
DOI: 10.1002/anie.201200555
Molecular Devices
Photoactivated Directionally Controlled Transit of a Non-Symmetric
Molecular Axle Through a Macrocycle**
Massimo Baroncini, Serena Silvi, Margherita Venturi,* and Alberto Credi*
Dedicated to Professor Vincenzo Balzani on the occasion of his 75th birthday
The control of motion on the molecular scale is of funda-
mental importance for living organisms,[1] and one of the most
fascinating challenges in nanoscience.[2,3] Artificial molecular
machines have been realized on the laboratory scale,[4] and
utilization of such systems to construct responsive materials[5]
and surfaces,[6] control catalytic processes,[7] and develop test
structures for information storage devices[8] and drug deliv-
ery[9] has been investigated. Nevertheless, the construction of
synthetic nanoscale motors capable of showing directionally
controlled linear or rotary movements still poses a consider-
able challenge to chemists.[10] Moreover, the use of such
systems to perform the tasks that natural molecular motors
do,[11] namely active transport of substrates over long
distances or across membranes, remains a very difficult
endeavor that is further complicated by the fact that most
currently available synthetic molecular motors are based on
sophisticated chemical structures and/or operation proce-
dures.[4,10] In this context, the development of (supra)molec-
ular systems that exhibit directionally controlled relative
motions of their components based on a minimalist design
and activated by convenient inputs is of the highest impor-
tance.
Herein we describe the construction and operation of
a simple supramolecular assembly in which a molecular axle
Figure 1. a) Strategy for the photoinduced unidirectional transit of
passes unidirectionally through the cavity of a molecular ring
in response to photochemical and chemical stimulation. A
system of this kind constitutes a first step towards the
construction of an artificial molecular pump; it can also lead
to the realization of molecular linear motors based on
rotaxanes and rotary motors based on catenanes.[12]
a non-symmetric axle through a molecular ring. b) Simplified potential
energy curves (free energy versus ring–axle distance) for the states
shown in (a) describing the operation of the system in terms of
a flashing ratchet mechanism. Slower processes that do not take place
under our conditions are represented by shaded cartoons and dashed
lines.
The strategy that we have tackled is illustrated in Figure 1.
The system is composed of a molecular ring and a non-
symmetric molecular axle that comprises 1) a passive pseudo-
stopper (D) at one end; 2) a central recognition site (S) for
the ring; and 3) a bistable photoswitchable unit (P) at the
other end. Under the conditions employed, the axle pierces
the ring exclusively with the photoactive gate in its initial
form (a) for kinetic reasons,[13] affording a pseudorotaxane in
which the molecular ring encircles the recognition site S.
Subsequently, light irradiation converts the a-P end group
into the bulkier b form, a process which also causes
a destabilization of the supramolecular complex. Therefore,
a dethreading of the system is expected, which should occur
by extrusion of the D moiety of the axle. Reset is obtained by
photochemical or thermal conversion of the b-P gate back to
the a state, thereby regenerating the starting form of the axle.
Overall, the photoinduced directionally controlled transit of
the axle through the ring would be obtained according to
a flashing energy ratchet mechanism (Figure 1b).[4b,14]
[*] Dr. M. Baroncini, Dr. S. Silvi, Prof. M. Venturi, Prof. A. Credi
Dipartimento di Chimica “G. Ciamician”, Universitꢀ di Bologna
Via Selmi 2, 40126 Bologna (Italy)
E-mail: margherita.venturi@unibo.it
alberto.credi@unibo.it
Homepage: http://www.credi-group.it
Clearly, the success of such a strategy relies on two basic
requirements: 1) the kinetic barriers for the slippage of the
axle end groups through the ring[15] should follow the order:
E°a-P < E°D < E°b–P; and 2) the ring should form a more
[**] We thank the University of Bologna, MIUR (PRIN 2008), and
Fondazione CARISBO for financial support.
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.201200555.
Angew. Chem. Int. Ed. 2012, 51, 4223 –4226
ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
4223

.
Angewandte
Communications
stable pseudorotaxane with the axle bearing the a-P unit
compared to that bearing the b-P unit. From a practical
viewpoint, to enable a clean operation and characterization of
the system, it is important that the differences in the energy
barriers and stability constants are sufficiently large, and that
the photochemical interconversion of the P gate between
a and b forms is fast, efficient, and reversible.
It was shown earlier by Stoddart and co-workers[19] that in
chloroform/acetonitrile 3:1 the bis(cyclopentylmethyl)ammo-
nium ion 2H+ (Scheme 1) is complexed by R in a pseudo-
rotaxane fashion, with threading and dethreading rate-
constant values that fall in between those observed for EE-
1H+ and ZZ-1H+ with R.[16] Therefore, we envisaged that the
strategy shown in Figure 1 could be implemented with a non-
symmetric axle such as E-3H+ (Scheme 1).
In a previous investigation,[16] we studied the threaded
complex of axle EE-1H+, composed of a dialkylammonium
hydrogen-bonding site equipped with two azobenzene end
units, with the dibenzo[24]crown-8 ring R (Scheme 1).[17] We
The synthesis of E-3H+ was performed by reductive
amination of cyclopentanecarbaldehyde with (4-nitrophe-
nyl)methanamine, reduction of the nitro group to amine
through hydrogenation and subsequent Millꢀs coupling with
p-methylnitrosobenzene in acetic acid followed by anion
exchange with NH4PF6. The E-3H+·PF6 salt was fully charac-
1
terized by H and 13C NMR, DQF-COSY, ESI-MS, and UV/
Vis absorption spectroscopy.
1H NMR spectroscopic titration experiments in aceto-
nitrile show that E-3H+ and R self-assemble to yield a pseudo-
rotaxane (Supporting Information). The corresponding ther-
modynamic and kinetic data are reported in Table 1, together
with those for the threading–dethreading of the symmetric
axles EE-1H+, ZZ-1H+ and 2H+ with R. It can be noted that
the threading rate constant kin for E-3H+ is nearly half that for
EE-1H+, and two orders of magnitude larger than that for
2H+. This observation clearly indicates that on the observed
timescale, E-3H+ pierces the ring exclusively with its E-
azobenzene terminus. The decrease of the threading constant
by a factor of two compared with that for EE-1H+, which can
thread the ring with both its extremities, is fully consistent
with this picture.
Scheme 1. Structure formulas and cartoon representation of the exam-
ined axle and ring components.
Irradiation of E-3H+ at 365 nm affords Z-3H+ with
a quantum efficiency of 0.17 and a yield of over 95% at the
photostationary state. Also Z-3H+ forms a pseudorotaxane
with R, and it has a threading rate constant that is nearly half
that of 2H+ and almost 20 times larger than that of ZZ-1H+
(Table 1). These results show that Z-3H+ threads R from its
cyclopentyl terminus. It is noteworthy that the E!Z photo-
isomerization of the azobenzene end group of 3H+ also takes
place efficiently when this compound is surrounded by R.
Therefore, we can kinetically control the threading–dethread-
ing side of 3H+ by photoadjusting the steric hindrance of its
found that the threading–dethreading rate constants are
slowed down by at least four orders of magnitude when the
E-azobenzene end units are photoisomerized to the Z form,
practically transforming the complex into a rotaxane; more-
over, the stability constant drops by a factor of two
(Table 1).[18] The system exhibits excellent photoswitching
and reversibility, and it is easy to synthesize. Encouraged by
these results, we looked for a passive pseudo-stopper (D in
Figure 1) with steric hindrance for slippage through R that is
intermediate between that of the E- and Z-azobenzene end
units of 1H+.
Table 1: Kinetic and thermodynamic data for the self-assembly of the investigated complexes in CD3CN at 298 K.[a]
K[b]
[Lmolꢀ1
ꢀDG8[c]
kin
ꢀDG#
kout
[sꢀ1
ꢀDG#
t =
[d]
[e]
[d]
[e]
[f]
1
Complex
in
out
2
]
[kcalmolꢀ1
]
[Lmolꢀ1 sꢀ1
]
[kcalmolꢀ1
]
]
[kcalmolꢀ1
]
[EE-1HꢁR]PF6
[ZZ-1HꢁR]PF6
[2HꢁR]PF6
820
400
ca. 30
225
3.9
3.5
2
3.2
3.2
37[g]
15
4.5ꢁ10ꢀ2[h]
7.2ꢁ10ꢀ6
4.4ꢁ10ꢀ3
0.1[h]
19.3
24.5
20.7
18.8
22.3
15.4 s
27 h
2.6 min
6.3 s
2.9ꢁ10ꢀ3
1.3ꢁ10ꢀ1
22[g]
20.9
18.6
15.6
19.2
[E-3HꢁR]PF6
[Z-3HꢁR]PF6
230
5.1ꢁ10ꢀ2
2.6ꢁ10ꢀ4
46 min
[a] The reactions were followed with 1H NMR spectroscopy by monitoring the changes in the relative intensities of the signals associated with the
probe protons in the complexed and uncomplexed ammonium ions. [b] The K values were obtained from four single-point measurements of the
concentrations of the complexed and uncomplexed cations, in the relevant 1H NMR spectrum, by using the expression K=[complex]/[ring][axle].
[c] The free energies of association (DG8) were calculated from the K values by using the expression DG8=ꢀRTlnK. [d] The threading (kin) and
dethreading (kout) rate constants were calculated by fitting the concentrations of complexed and uncomplexed ammonium ions, extracted from
1H NMR kinetics experiments. [e] The free energies of activation for the threading (ꢀDG°in) and dethreading (ꢀDG°out) processes were calculated by
using the relationships ꢀDG°in =ꢀRTln(kinh/kT) and ꢀDG°out =ꢀRTln(kouth/kT), respectively, where R, h, and k correspond to the gas, Planck, and
1
Boltzmann constants, respectively. [f] The half-life of the complexes were calculated from kout values by using the expression t = =ln2/kout
.
2
[g] Determined by stopped flow UV/Vis absorption spectroscopy. [h] Calculated from the kin and K values by using the expression kout =kin/K.
4224 www.angewandte.org
ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2012, 51, 4223 –4226

Angewandte
Chemie
azobenzene end group below and above that of the photo-
inactive cyclopentyl pseudo-stopper located at the other end.
Unfortunately, in contrast with the results found for the
[EE-1HꢁR]+ and [ZZ-1HꢁR]+ pseudorotaxanes, the stabil-
ity constants of [E-3HꢁR]+ and [Z-3HꢁR]+ are identical
within errors (Table 1). Therefore, the dethreading of Z-3H+
from the ring cannot be caused by the same photochemical
stimulus that triggers the azobenzene E!Z isomerization. To
promote the disassembly of the complexes[20] we used K+ ions,
which act as competitive guests for R.[21,22] The addition of
three equivalents of KPF6 causes the complete dethreading of
both [E-3HꢁR]+ and [Z-3HꢁR]+; however, while the K+-
induced disassembly of the former complex is fast, the latter
exhibits a dethreading half-life of 51 min (Figure 2a). This
value is much shorter than the half-life of [ZZ-1HꢁR]+ in the
presence of K+ (ca. 25 h, Figure 2b)[16] and is in excellent
agreement with the half-life of Z-3H+ determined from the
self-assembly data (46 min, Table 1). These observations
indicate that the chemically induced disassembly of Z-3H+
and R takes place by extrusion of the cyclopentyl unit of the
former from the cavity of the latter.
Figure 3. Representation of the photochemically and chemically con-
trolled transit of 3H+ through R and relevant 1H NMR spectra
(400 MHz, CD3CN, 298 K). Conditions: i) 5.0 mm E-3H+ and 5.0 mm
R; ii) 365 nm, 15 min; iii) 10 mm KPF6; iv) 344 K, 2 h; v) 30 mm
[18]crown-6. Marked signals are due to the [KꢁR]+ complex.
threading event the system is “locked” by photoisomeriza-
tion, and the successive addition of potassium ions causes
dethreading in the same direction along which threading of E-
3H+ has initially occurred. The starting species E-3H+ can be
fully regenerated by thermal Z!E isomerization (half-life of
8 days at room temperature; see the Supporting Information).
Sequestration of K+ by an excess (3 equiv) of [18]crown-6
affords the re-assembly of [E-3HꢁR]+ and the full reset of the
system.
This molecular device, however, if it would be incorpo-
rated in a compartmentalized structure (for example, embed-
ded in the membrane of a vesicle), could not be used to pump
the molecular axle and generate a transmembrane chemical
potential[12] because the ring component has two identical
faces. However, we are ready to apply the strategy developed
in this work to supramolecular assemblies based on three-
dimensional non-symmetric macrocycles with lengths that can
approach the thickness of a bilayer membrane[23] and in which
face-selective threading can be realized.[24] Indeed, the
present system is characterized by a minimalist design,
facile synthesis, convenient switching, and reversibility: all
of these features can foster further research developments
and constitute essential requirements for future real-world
applications.
Figure 2. Concentration–time profiles, obtained from 1H NMR data in
CD3CN at 298 K, showing the K+-induced dethreading of a) [Z-3HꢁR]+
and b) [ZZ-1HꢁR]+. Conditions: a) 5.1 mm Z-3H+, 5.4 mm R (about
40% complexation of the axle molecules), 15.2 mm KPF6; b) 4.8 mm
ZZ-1H+, 7.6 mm R (about 65% complexation of the axle molecules),
16.7 mm KPF6.
The results of a summarizing experiment that illustrates
the directional transit of the axle through the ring are shown
in Figure 3. E-3H+ pierces R with its E-azobenzene side to
form the [E-3HꢁR]+ pseudorotaxane complex, which equi-
librates rapidly with its separated components. Irradiation in
the near UV converts quantitatively [E-3HꢁR]+ into
[Z-3HꢁR]+, which has much slower assembly–disassembly
kinetics. The successive addition of K+ ions promotes the
dethreading of Z-3H+ from R by the passage of the cyclo-
pentyl moiety through the cavity of the ring. It should be
noted that equilibration of the [Z-3HꢁR]+ complex with its
separated components, which would cause the loss of the
information on the threading direction of E-3H+, is much
slower than the time required for the activation of the
dethreading stimulus (addition of K+). Therefore, after the
Received: January 19, 2012
Published online: March 12, 2012
Angew. Chem. Int. Ed. 2012, 51, 4223 –4226
ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.angewandte.org
4225

.
Angewandte
Communications
Angew. Chem. 2005, 117, 5430 – 5433; Angew. Chem. Int. Ed.
2005, 44, 5296 – 5299; b) K. Hirose, Y. Shiba, K. Ishibashi, Y. Doi,
Y. Tobe, Chem. Eur. J. 2008, 14, 3427 – 3433; c) M. Hmadeh,
A. C. Fahrenbach, S. Basu, A. Trabolsi, D. Benꢃtez, H. Li, A. M.
Albrecht-Gary, M. Elhabiri, J. F. Stoddart, Chem. Eur. J. 2011,
17, 6076 – 6087; d) K.-D. Zhang, X. Zhao, G.-T. Wang, Y. Liu, Y.
Zhang, H.-J. Lu, X.-K. Jiang, Z.-T. Li, Angew. Chem. 2011, 123,
10040 – 10044; Angew. Chem. Int. Ed. 2011, 50, 9866 – 9870; e) T.
Avellini, H. Li, A. Coskun, G. Barin, A. Trabolsi, A. N. Basuray,
S. K. Dey, A. Credi, S. Silvi, J. F. Stoddart, M. Venturi, Angew.
Chem. 2012, 124, 1643 – 1647; Angew. Chem. Int. Ed. 2012, 51,
1611 – 1615.
Keywords: azobenzene · crown ethers · hydrogen bonds ·
molecular devices · supramolecular chemistry
.
[1] S. Mann, Angew. Chem. 2008, 120, 5386 – 5401; Angew. Chem.
Int. Ed. 2008, 47, 5306 – 5320.
[2] R. A. L. Jones, Soft Machines, Nanotechnology and Life, Oxford
University Press, New York, 2004.
[3] Recent outstanding examples: a) A. Ye, A. S. Kumar, S. Saha, T.
Takami, T. J. Huang, J. F. Stoddart, P. S. Weiss, ACS Nano 2010,
4, 3697 – 3701; b) P. Lussis, T. Svaldo-Lanero, A. Bertocco, C.-A.
Fustin, D. A. Leigh, A.-S. Duwez, Nat. Nanotechnol. 2011, 6,
553 – 557; c) T. Kudernac, N. Ruangsupapichat, M. Parschau, B.
Macia, N. Katsonis, S. R. Harutyunyan, K.-H. Ernst, B. L.
Feringa, Nature 2011, 479, 208 – 211.
[4] a) W. R. Browne, B. L. Feringa, Nat. Nanotechnol. 2006, 1, 25 –
35; b) E. R. Kay, D. A. Leigh, F. Zerbetto, Angew. Chem. 2007,
119, 72 – 196; Angew. Chem. Int. Ed. 2007, 46, 72 – 191; c) V.
Balzani, A. Credi, M. Venturi, Molecular Devices and
Machines—Concepts and Perspectives for the Nano World,
Wiley-VCH, Weinheim, 2008.
[5] a) R. A. van Delden, N. Koumura, N. Harada, B. L. Feringa,
Proc. Natl. Acad. Sci. USA 2002, 99, 4945 – 4949; b) D. L. Pijper,
B. L. Feringa, Angew. Chem. 2007, 119, 3767 – 3770; Angew.
Chem. Int. Ed. 2007, 46, 3693 – 3696; c) L. Fang, M. Hmadeh, J.
Wu, M. A. Olson, J. M. Spruell, A. Trabolsi, Y.-W. Yang, M.
Elhabiri, A. M. Albrecht-Gary, J. F. Stoddart, J. Am. Chem. Soc.
2009, 131, 7126 – 7134; d) H. Deng, M. A. Olson, J. F. Stoddart,
O. M. Yaghi, Nat. Chem. 2010, 2, 439 – 443; e) D. J. Mercer, V. N.
Vukotic, S. J. Loeb, Chem. Commun. 2011, 47, 896 – 898.
[6] a) J. Bernꢁ, D. A. Leigh, M. Lubomska, S. M. Mendoza, E. M.
Perez, P. Rudolf, G. Teobaldi, F. Zerbetto, Nat. Mater. 2005, 4,
704 – 710; b) Y. Liu, A. H. Flood, P. A. Bonvallett, S. A. Vignon,
B. H. Northrop, H.-R. Tseng, J. O. Jeppesen, T. J. Huang, B.
Brough, M. Baller, S. Magonov, S. D. Solares, W. A. Goddard,
C. M. Ho, J. F. Stoddart, J. Am. Chem. Soc. 2005, 127, 9745 –
9759; c) R. Eelkema, M. M. Pollard, J. Vicario, N. Katsonis, B. S.
Ramon, C. W. M. Bastiaansen, D. J. Broer, B. L. Feringa, Nature
2006, 440, 163; d) G. Pace, V. Ferri, C. Grave, M. Elbing, C.
von Hanisch, M. Zharnikov, M. Mayor, M. A. Rampi, P. Samorꢂ,
Proc. Natl. Acad. Sci. USA 2007, 104, 9937 – 9942; e) A. Harada,
R. Kobayashi, Y. Takashima, A. Hashidzume, H. Yamaguchi,
Nat. Chem. 2011, 3, 34 – 37.
[14] R. D. Astumian, Phys. Chem. Chem. Phys. 2007, 9, 5067 – 5083.
[15] M. Asakawa, P. R. Ashton, R. Ballardini, V. Balzani, M.
Belohradsky, M. T. Gandolfi, O. Kocian, L. Prodi, F. M.
Raymo, J. F. Stoddart, M. Venturi, J. Am. Chem. Soc. 1997,
119, 302 – 310.
[16] M. Baroncini, S. Silvi, M. Venturi, A. Credi, Chem. Eur. J. 2010,
16, 11580 – 11587.
[17] a) A. G. Kolchinski, D. H. Busch, N. W. Alcock, J. Chem. Soc.
Chem. Commun. 1995, 1289 – 1290; b) P. R. Ashton, P. J. Camp-
bell, E. J. T. Chrystal, P. T. Glink, S. Menzer, D. Philp, N.
Spencer, J. F. Stoddart, P. A. Tasker, D. J. Williams, Angew.
Chem. 1995, 107, 1997 – 2001; Angew. Chem. Int. Ed. Engl. 1995,
34, 1865 – 1869.
[18] For other pseudorotaxane-type systems in which threading–
dethreading processes can be photocontrolled, see: a) K. Hirose,
Y. Shiba, K. Ishibashi, Y. Doi, Y. Tobe, Chem. Eur. J. 2008, 14,
981 – 986; b) Y. Tokunaga, K. Akasaka, N. Hashimoto, S.
Yamanaka, K. Hisada, Y. Shimomura, S. Kakuchi, J. Org.
Chem. 2009, 74, 2374 – 2379; c) L. Zhu, D. Zhang, D. Qu, Q.
Wang, X. Ma, H. Tian, Chem. Commun. 2010, 46, 2587 – 2589;
d) T. Ogoshi, D. Yamafuji, T. Aoki, T. Yamagishi, J. Org. Chem.
2011, 76, 9497 – 9503.
[19] P. R. Ashton, I. Baxter, M. C. T. Fyfe, F. M. Raymo, N. Spencer,
J. F. Stoddart, A. J. P. White, D. J. Williams, J. Am. Chem. Soc.
1998, 120, 2297 – 2307.
[20] Deprotonation of the ammonium recognition site of [Z-3H]+
with a base causes the fast dethreading from R, thereby
neutralizing the stoppering ability of the Z-azobenzene unit. A
thorough discussion of this phenomenon, which was observed
also for [Z,Z-1H]+, can be found in Ref. [16].
[21] a) Y. Takeda, Bull. Chem. Soc. Jpn. 1983, 56, 3600 – 3604; b) Y.
Takeda, Y. Kudo, S. Fujiwara, Bull. Chem. Soc. Jpn. 1985, 58,
1315 – 1316.
[7] J. B. Wang, B. L. Feringa, Science 2011, 331, 1429 – 1432.
[8] J. E. Green, J. W. Choi, A. Boukai, Y. Bunimovich, E. Johnston-
Halperin, E. DeIonno, Y. Luo, B. A. Sheriff, K. Xu, Y. S. Shin,
H.-R. Tseng, J. F. Stoddart, J. R. Heath, Nature 2007, 445, 414 –
417.
[22] Although the use of competing potassium ions may be seen as
a disadvantage, it opens up the possibility to interpret the device
operation in terms of sequential logic. See, for example,
Ref. [13e] and: a) G. de Ruiter, E. Tartakovsky, N. Oded, M. E.
van der Boom, Angew. Chem. 2010, 122, 173 – 176; Angew.
Chem. Int. Ed. 2010, 49, 169 – 172; b) H. Tian, Angew. Chem.
2010, 122, 4818 – 4820; Angew. Chem. Int. Ed. 2010, 49, 4710 –
4712.
[23] A. Arduini, A. Credi, G. Faimani, C. Massera, A. Pochini, A.
Secchi, M. Semeraro, S. Silvi, F. Ugozzoli, Chem. Eur. J. 2008, 14,
98 – 106.
[24] A. Arduini, R. Bussolati, A. Credi, G. Faimani, S. Garaudee, A.
Pochini, A. Secchi, M. Semeraro, S. Silvi, M. Venturi, Chem. Eur.
J. 2009, 15, 3230 – 3242.
[9] M. W. Ambrogio, C. R. Thomas, Y.-L. Zhao, J. I. Zink, J. F.
Stoddart, Acc. Chem. Res. 2011, 44, 903 – 913.
[10] a) T. Fernꢁndes Landaluce, G. London, M. M. Pollard, P. Rudolf,
B. L. Feringa, J. Org. Chem. 2010, 75, 5323 – 5325; b) M.
von Delius, D. A. Leigh, Chem. Soc. Rev. 2011, 40, 3656 – 3676;
c) A. Coskun, M. Banaszak, R. D. Astumian, J. F. Stoddart,
Chem. Soc. Rev. 2012, 41, 19 – 30.
[11] Molecular Motors (Ed.: M. Schliwa), Wiley-VCH, Weinheim,
2002.
[12] R. D. Astumian, Annu. Rev. Biophys. 2011, 40, 289 – 313.
[13] For examples of kinetic control of molecular motions in
rotaxane-type systems, see: a) D.-H. Qu, Q.-C. Wang, H. Tian,
4226 www.angewandte.org
ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2012, 51, 4223 –4226