NMachines

Prepare as Communication or Concept(

Prepared as a Review article in Nature

Great expectations: Can artificial molecular machines deliver on their promise? Ali Coskun1, Michal Banaszak3, Raymond Dean Astumian4, J. Fraser Stoddart1*, and Bartosz A. Grzybowski1,2*1Department of Chemistry and 2Department of Chemical and Biological Engineering, Northwestern University, Evanston IL 60208

3 Faculty of Physics, Adam Mickiewicz University, Poznan, Poland

4Department of Physics, University of Maine, Orono ME 04469ABSTRACT: The development of mechanical devices powered by artificial molecular machines is one of the major goals of nano-science. Before the epiphany happens, however, we must learn how to both control the switching of individual molecules and also arrange them into organized, hierarchical assemblies from which significant packages of energy can be harnessed. While for individual molecular machines the effects of thermal noise are of paramount importance, the challenges inherent to machine ensembles lie in our ability to control their spatial ordering (e.g., into linear chains and then into muscle-like bundles) and mutual influence in terms of switching kinetics. In the latter context, situations where all modules switch synchronously appear desirable for maximizing mechanical power generated; when the units switch out of phase, the assemblies could develop intricate spatial or spatiotemporal patterns .Assembling and controlling synergistically artificial molecular machines housed in highly interactive architectural domains is a contemporary challenge for chemical synthesis and nanofabrication.

For over two decades now, the vision of switchable molecules acting as nanomachines of the future has inspired chemists ADDIN EN.CITE 1-4, physicists5,6, and nanoengineers ADDIN EN.CITE 7,8 alike. Despite tremendous progress in the synthesis of evermore complex molecular switches ADDIN EN.CITE 3,9, however, the aim of harnessing useful work/energy from these molecules has not yet been achieved. To be sure, there has been some ingenious examples of systems where molecules do act as primitive machines: bistable rotaxanes bending small cantilevers10, liquid crystals doped with molecular rotary motors spinning macroscopic objects11, liquid-crystal elastomers incorporating photochromic molecules driving macroscopic pulleys12, or molecular motors propelling nanoparticles in solution13. But these examples are few, and their performance characteristics (efficiency, power generated, etc.) are still far from those required of working machines. The question that naturally arises is whether future progress in the field will require only diligent optimization, or whether there are some fundamental roadblocks that need to be circumvented before synthetic molecular machines achieve their anticipated potential. An equally prominent and timely question is at what scales these machines should operate? As we see it, there are two parallel routes for further progress. The first is to develop molecular machines that would perform useful tasks at their own scales: transporting molecular or nanoscopic cargo, manipulating or fabricating other nanostructures. On the opposite end of the spectrum lie machines performing useful operations on scales much larger than molecular. In this regime, however, it is clear that individual molecules are not going to be able to move or manipulate loads orders of magnitude more massive than themselves. This, we argue, is going to be possible only if individual molecular machines are assembled into larger structures, within which they work in synchrony to perform macroscopic tasks or build macroscopic structures. The dichotomy between the micro- and macroscale uses of molecular machines is also reflected in the theory that needs to be developed with individual molecules, at the microscale, stochastic effects need to be considered; with machines assembled into larger structures, more deterministic models can become suitable. Overall, we suggest that the future of molecular machinery appears to be bright provided we can depart from the conventional thinking of these unique molecules as miniaturized machines and, instead, apply them in situations where their unique potential can be harnesses to the fullest possible extent.

The building blocks and the limitations of acting alone. Molecular switches come in a variety of forms and flavors (Table 1), and can be actuated chemically, electrochemically, or by light irradiation. The essence of switching is that an external stimulus causes a geometrical change depending on the specific system, switchable molecules can translate their internal parts from one station to another (as in bistable rotaxanes14), can shrink or expand (as in daisy-chains

15-19 ADDIN EN.CITE ), rotate (as in Feringas and Kelly`s molecular motor systems

11,13,20,21 ADDIN EN.CITE ), or pivot about an internal axis (as in Aida`s scissor-like molecules22). When these molecules are attached to external objects, their structural rearrangement can give rise to net translation, rotation, or both.

Let us consider a very simple switch

DEAN: I THINK WE NEED TO MENTION DAVID LEIGHS WORK HERE. MOST IMPORTANTLY, THE REST OF THIS PARAGRAPH, WHICH I COLOR YELLOW, PROBABLY HAS TO BE ENTIRELY REWRITTEN ALONG THE IDEAS YOU HAVE PRESENTED DURING YOUR VISIT. WE THINK THAT SOME EQUATIONS AND, SAY, ONE FIGURE WOULD ALSO BE VERY USEFUL. FRASER AND I LEAVE THIS PART ENTIRELY UP TO YOU. WE CONCENTRATE ON THE ASSEMBLY PART LATER IN THE TEXT Let us first consider (i) the typical forces the switches can generate, (ii) the typical actuation distances they can affect, and (iii) the amount of work they can generate. The forces have been measured directly in several model systems using atomic force microscopy (AFM). For example, Hugel et al.23 found that a polymer comprising ca. 50 azobenzene units can, upon light irradiation, generate a force of f ~200 pN, change the distance between its ends by ~0.22 nm, and perform useful mechanical work of 4.5(10-20 J or ~10-21J per one azobenzene unit. This result is certainly not a spectacular one, given that the characteristic thermal scale at room temperature is kT ( 4(10-21J it follows that an individual azobenzene molecule cannot even beat the thermal noise, which precludes its applicability as a sensus stricte machine. More promising are the switches based on the rotaxanes, where each rotaxane molecule can generate forces in tens of pN owing to large electrostatic effects and give rise to displacements of 1-2 nm

24,25 ADDIN EN.CITE . These parameters translate into characteristic work that a molecule can produce on the order of tens of kTs (e.g., 20 pN (2 nm ( 10kT at 293 K) which is, at least in principle, sufficient to overcome the effects of thermal noise and comparable to the typical work generated by biological motors such as dyneins26,27 (force ~ 6 pN, displacement per step ~8 nm, velocity ~5.3 ((m s(1, total travel distance up to 100 nm) or kinesins

28-31 ADDIN EN.CITE (force ~5-7 pN, step~8 nm, velocity ~ 570 nm s(1, total travel distance ~500 nm). Unfortunately, these promising estimates do not necessarily scale with the numbers of molecular machines present in the system. Since the forces add vectorially, random collections of individual, unconnected and/or uncorrelated machines give rise neither to net force nor to useful work. For practically relevant, macroscopic effects, molecular machines need to work in unison.Machine collections and the benefits of being ordered. Biological systems know these benefits well and virtually all collections of biological motors are spatially (and often temporally) synchronized dyneins and kinesins align along cytoskelatal fibers, rotary flagellar motors comprise a circular array of ion pumps and other proteins, while skeletal muscles can generate mechanical energy by the cooperative actions of myosins aligned parallel to one another within sarcomers building up myofibrils. The spatial arrangement is also crucial for the functioning of the few artificial systems in which molecules have been shown to move large loads. Although an individual azobenzene is not an efficient machine, a linear polymer of azobenzene unit can give rise to microscopic displacements (Fig. 1a); a monolayer of rotaxane molecules can bend a macroscopic cantilever (Fig. 1b); a liquid crystalline film doped with molecular motors11 can rotate objects 10,000 times more massive than the size of the individual motor molecule (Fig. 1c). These examples suggest that if arranged into large and ordered superstructures, molecular machines can, indeed, perform macroscopic tasks. An important theoretical observation here is that in such large collections, stochastic effects should be negligible as noise scales with inversely with the number N of individual molecules involved. REFERENCE TO LANDAU & LIFSHITZ, STATISTICSAL PHYSICS consequently, one can then describe such systems in terms of their bulk thermodynamics. Let us consider some possible arrangements.

Probably the most trivial ordered architecture is a monolayer comprising N switches assembled onto a solid surface. With modern surface chemistry, it is possible to graft or assemble up to ca. N = 1014 molecules per cm2 (as in SAMs on gold ADDIN EN.CITE 32,33). Assuming that the switches all stand up on the surface, and that upon stimulation each switch exerts 10 pN force (as in the case of rotaxanes24), one square centimeter of such a monolayer can push upwards an object weighting 100 kg! The problem is, of course, that for the typical switching distances, this heavy load is moved merely by |(L| ~ 1 nm (see above ADDIN EN.CITE 24,25) and the work performed is only 10-7J.

An improvement that naturally comes to mind, is an arrangement in which the switching units form linear chains attached to a supporting surface (n chains at grafting density, (). Approximating each switch as a cylinder of radius R and length L (upon stimulation, expandable or shrinkable byL) and assuming that each chain comprises N switching units (see Fig. 2a), the tools of polymer physics can be used to estimate the free energy, F, of the system, and the equilibrium height of the polymer brush, Heq. In the regime of sparse surface grafting, the chains are partly coiled (Fig. 2b), and the so-called Alexander model34 of polymer brushes can be applied to estimate equilibrium values and , where superscript i denotes the initial state, and w is the excluded volume (for derivation of this and other formulas, see Supporting Information, SI). When, upon stimulus, the switches expand (or contract) from L to L+L, then the polymer chain relaxes to a new equilibrium brush height, . Importantly, the work that can be retrieved in this process is . For typical dimensions of the switching unit (R, L, |(L| all on the order of 1 nm) and for sparse grafting densities of the brushes (dimensionless grafting density of, say, (w/L ~ 1/100), a chain of 50 switching units can extend/contract by |(H| ~ 3 nm and perform work (W ~10-3 kT (or 4(10-24 J). While the degree of extension/contraction is reasonably close to the experimental value recorded for azobenzene 50-mers, the predicted amount of work is four (!) orders of magnitude smaller than measured by Hugel et al.23.

The reason for the discrepancy is that in experiments, the azobenzene polymer was pre-stretched by the AFM probing tip in other words, it was substantially extended rather than coiled-up, and the individual displacements added up. This situation corresponds to the so-called strong-stretching regime of polymers35, where the work performed by the extending chains is well approximated by with and . For experimental parameters close to those of the azobenzene example (N = 50, NL = 90 nm, NL= -6 nm, Hi = 50 nm), the calculated work this expressions predicts is W ( 10 kT, close to the experimentally observed value.

The conclusion from these considerations is that in order to maximize the bang-for-the-buck, molecular machines should be lined-up along the direction of actuation as straight and stretched as possible. Experimentally, this objective can be achieved either by packing the chains densely on a surface (Fig. 2c) or by arranging them into muscle-like bundles (Fig. 2d). The close-packed surface grafts could perform substantial amounts of work for instance 1014 of 500-mer chains assembled onto 1 cm2 of area could perform work of W ( ~5x10-5 J, enough to actuate a small cantilever or a read/write head. Even higher values can be achieved with longer grafts (since W scales with N). On the other hand, miniaturization of such surface-based, planar systems could be problematic, since it would require either cutting the surface into smaller pieces or surface growth initiated from small islands from which the grafts could grow sideways rather than straight-up. In this respect, bundles of chains assembled in solution appear more promising, especially for applications such as molecular muscles actuating various nano- and micromachines. We note, however, that in such applications, the bundles should be relatively stiff, such that the underlying actions of the molecular switches/machines translate into productive displacement/work. Basic mechanical considerations tell us that the persistence length, ( i.e., the characteristic distance over which a tubular bundle does not wiggle (see Fig. 2d) scales as EI/kT 36 where E is the Youngs modulus and I is the moment of inertia proportional to the bundles cross-sectional area, A. This scaling of I with A implies that ( is proportional to the number, M, of individual chains forming a bundle. Since a typical polymer chain has a persistence length from about 1 nm (polystyrene) to about 50 nm (DNA), it then follows that, in order to make bundles stiff over micrometer distances, one should line up hundreds of individual chains of molecular machines. Developing self-assembly/synthetic methods that yield such structures without lateral entanglement of the individual chains should be a worthy challenge for supramolecular and mechanostereochemists.

Power generation and energy storage. Having outlined the possible strategies for making the operation of molecular machine assemblies efficient, let us now reflect on their capacity to generate power and to store energy. Relevant to our discussion is that irrespective of the exact molecular nature, molecular switches/machines can be characterized by a double-well free energy landscape whose minima corresponding to states before (Fig. 3a) and after (Fig. 3b) application of the stimulus and its removal (Fig. 3c). Typically, the difference between the free energies of these two forms, (F, is few kcal/mol (e.g., ~2 kcal/mol for bistable [2]rotaxanes and catenanes, and ~10 kcal/mol for azobenzenes), and the free energy barrier separating them, , is usually in the teens to few tens of kcal/mol (e.g., 23 kcal/mol for azobenzenes or 17 kcal/mol for rotaxanes37). The barrier height controls the rate of conversion, k, between the machines States and is important for its power output and also for potential energy storage characteristics.

For thermal relaxation, the rate of conversion from, say, State 2 to State 1 is given by the Eyring equation38, , which for the typical barrier heights and at room temperature is on the order of 0.1-1.0 s-1. This rate means that the characteristic relaxation times, (rlx = 1/k, are usually in seconds and the peak powers the machines can generate are on the order of P ( k(F ~ 1-10 kW/mol. For comparison, an insect weighting 4 g needs about 0.5 W to power its flight.

Some more practical observations regarding power generation are in order: Firstly, the effective heights of the barrier a separating machines energetic minima can be made relatively smaller by destabilizing one of these states this is a common strategy in donor-acceptor rotaxane-based systems38 where oxidation of one station increases the electrostatic potential energy and accelerates relaxation/switching toward the other station (Fig. 3b) to (rlx ~ ps for the bistable rotaxanes containing a redox-active tetrathiafulvalene station or (rlx ~ 3.7 s in surface-immobilized rotaxanes under electrical bias39. These rapid switching times correspond to powers well exceeding MW/mol! albeit delivered only during very short (rlx times, and thus of limited practical applicability. The second observation relates to systems in which switching is achieved either by chemical or by electrochemical means in such cases, it must be remembered that chemical switching involves diffusive transport, a phenomenon which limits the overall speed of the process. In our recent work40, we have shown that the switching in donor-acceptor pseudorotaxane-based aggregates is slowed down from milliseconds to minutes or even hours on account of diffusional limitations. While electrochemical control can be a viable alternative (e.g., with rotating-disk electrodes avoiding diffusion-related problems), the most rapid toggling of the machines could, in principle, be achieved using light stimuli, where delivery of the switching impulse is virtually instantaneous. Incidentally, it is the light switchable systems that also offer the highest measured efficiencies of over 40% (Table 1), a percentage which compares favorably with, for example, the 15% efficiency of car engines.

In some energy-related applications, however, high speed of switching is not always desirable. The case in point here is energy storage, where one would like to freeze the machines in the high energy state for a long time, and retrieve the energy only when needed and on demand. For this scenario to be realized, the rate of relaxation during the storage phase should be as small as possible this objective can be achieved by embedding the switches in a solid matrix (e.g., a polymer) or by dense packing (e.g., on a surface). For example, the relaxation times of azobenzenes co-polymerized with poly(dimethyl siloxanes) are tens of minutes. For donor-acceptor rotaxane-based systems, it has been shown38 that the values of (rlx increase by over three orders of magnitude from few seconds to ca. 1 h ( when these molecules are confined to a dense monolayer; in viscous polymer solutions, the values of (rlx are typically in tens of seconds. Another approach to increase (rlx is to incorporate into the machines switchable valve motifs. An illustrative example here is in some recently reported research41 where an azobenzene speed bump was introduced between the two stations in a donor-acceptor [2]rotaxane. In the more linear trans state of the azobenzene, the ring on the rotaxane system can shuttle between the two stations, but when the azobenzene valve is isomerized to the cis form, its steric bulk hinders the shuttling process and the rotaxanes states can be sustained in suspended animation for several hours at least.

Beyond mechanical function. In our discussion so far, we have tacitly assumed that when layered or bundled together, all the constituent molecules perform their switching functions synchronously and without mutual interference. While this mode of operation is ideal for performing mechanical work (everyone working together), interesting situations can arise if the molecules influence the switching kinetics of their neighbors. In the case of two-state switches, a switching of one molecule can either promote or hinder the switching of its neighbors. The first of these cases can be of interest in situations like chemical signaling, illustrated in Fig. 4a, where an impulse at one location of a monolayer of switches triggers a propagation of a switching front, much like in biological calcium waves and related phenomena S. Soh, M. Byrska, K. Kandere-Grzybowska & B.A. Grzybowski* Reaction-Diffusion Systems in Intracellular Molecular Transport and Control, Angew. Chem. Int. Ed. 49, 4170-4198 (2010). Since for some types of molecules we have been discussing, switching occurs on microsecond time-scales and the linear density of the switches within a densely-packed assembly is on the order of 107 molecules per 1 cm, one can approximate the speed of front propagation in mm/sec, which is comparable with the speeds achievable in the so-called active chemical media. By analogy to these media, one could also imagine that periodic forcing of the system would result in the development of spatiotemporal patterns. Such patterns could also form even without periodic forcing in situations when there is negative coupling between the switching units (i.e., one switch hapmers the switching of another). In this case, statistical-physical considerations suggest that if the system is spatially bound (e.g., a crystal in Fig. 4b), not all molecules can be in the same state but, instead, one should expect formation of finite size domains within the material. MICHAL, HERE WE NEED YOUR INPUT ON ANTIFFEROMAGNETS, FRUSTRATION EFFECTS ETC. ALSO, PLEASE SEE THE CAPTION TO FIG 4 These types of phenomena are largely unexplored but, we believe, the current solid-state synthetic methods are available to realize them. In particular, molecular organic frameworksALI, NEED ONE REF HERE, MOFs, appear to be very promising scaffolds whereby switchable molecules can be distributed on a regular grid and with distances (and, thus coupling constants!) adjusted precisely by the length of molecular struts.

In summary, we believe that the combination of structural and dynamic control offers some truly exciting challenges and, yes, opportunities! for molecular and macromolecular-level engineering, for self-assembly, and more generally, for chemistry and physics applied to molecules that can reside in and be toggled between non-equilibrium configurations. In the latter context, the field of non-equilibrium phenomena has been so far somewhat constrained by the scarcity of suitable molecules and experimental systems. Now, molecular machines and their assemblies can expand the available non-equilibrium toolbox well beyond the Belousov-Zhabotinski or Turing-type media.

Table 1. Popular switches categorized by the type of motion and mode of actuation. Energetic parameters are included when available. Symbols used: ( ; efficiency, (L; distance of actuation, (( ; angle of actuation, f (pN); force generated, W (kT); work performed.

TYPE OF

MOTIONTYPE OF ACTUATION

CHEMICALREDOXLIGHT

Rotaxanes; (i) (L = 1 nm, f = 200 pN42. (ii) (L = 1.3 nm, f = 145 pN24. Rotaxanes; (i) Metal-Templated43. (ii) H-Bonded44. (ii) Donor-Acceptor45. Rotaxanes: (i) ( = 0.4, W = 3.65 kT25 (ii) (L = 1.3 nm, ( = 0.1246. (iii) (L = 0.7 nm47.

NA Azobenzene48Azobenzene ADDIN EN.CITE 12,49-51: (i) ( = 0.152. (ii) (L = 0.7 nm, f ( 0.026 pN53. (iii) ( = 0.1, (L = 0.25 nm, W = 10.9 kT

23,54 ADDIN EN.CITE . Diaryethenes: ( ( 0.46, (( = 7o.55 Stilbene56.

Molecular Muscles: (i) (L = 1.8 nm

17,19 ADDIN EN.CITE . (ii) (L = 0.9 nm

15,16 ADDIN EN.CITE . Rotaxanes; (L = 1.4 nm, f ( 650 pN

10,57 ADDIN EN.CITE .

Molecular Muscles: (i) (L ( 0.7 nm18,58.

(c) Molecular Rotors: (i) ((= 120o21. (ii) ((= 360o20. (a) A [2]Rotaxane, ((= 180o59. (b) [2]Catenane; (i) ((= 180o60,61. (b) [3]Catenane, ((= 360o62. (c) Spiropyrans: ( = 0.1, ((= 180o63. Fulgides: ( = 0.12, (( ( 90o. Thioindigo: (( ( 180o64. Molecular Rotors: (i) ( = 0.07 0.5565, (ii) (( = 360o

11,13 ADDIN EN.CITE . Nanocars66.

NANAMolecular Scissors67. (i) (L = 0.7 nm, ( = 0.1, ((= 49o22,68.

References

1. Balzani, V., Credi, A., & Venturi, M., Molecular Devices and Machines, 2 ed. (Wiley, Weinheim, 2008).

2. Browne, W.R. & Feringa, B.L., Making molecular machines work. Nature Nanotech. 1, 25-35 (2006).

3. Kay, E.R., Leigh, D.A., & Zerbetto, F., Synthetic molecular motors and mechanical machines. Angew. Chem., Int. Ed. 46, 72-191 (2007).

4. Stoddart, J.F., The chemistry of the mechanical bond. Chem. Soc. Rev. 38, 1802-1820 (2009).

5. Duli, D. et al., One-way optoelectronic switching of photochromic molecules on gold. Phys. Rev. Lett. 91 (2003).

6. Astumian, R.D., Thermodynamics and kinetics of a Brownian motor. Science 276, 917-922 (1997).

7. Klajn, R. et al., Plastic and moldable metals by self-assembly of sticky nanoparticle aggregates. Science 316, 261-264 (2007).

8. Zheng, Y.B. et al., Active molecular plasmonics: Controlling plasmon resonances with molecular switches. Nano Lett. 9, 819-825 (2009).

9. Champin, B., Mobian, P., & Sauvage, J.P., Transition metal complexes as molecular machine prototypes. Chem. Soc. Rev. 36, 358-366 (2007).

10. Juluri, B.K. et al., A mechanical actuator driven electrochemically by artificial molecular muscles. Acs Nano 3, 291-300 (2009).

11. Eelkema, R. et al., Nanomotor rotates microscale objects. Nature 440, 163-163 (2006).

12. Yamada, M. et al., Photomobile polymer materials: Towards light-driven plastic motors. Angew. Chem., Int. Ed. 47, 4986-4988 (2008).

13. van Delden, R.A. et al., Unidirectional molecular motor on a gold surface. Nature 437, 1337-1340 (2005).

14. Stoddart, J.F. & Colquhoun, H.M., Big and little Meccano. Tetrahedron 64, 8231-8263 (2008).

15. Fang, L. et al., Acid-base actuation of [c2]daisy chains. J. Am. Chem. Soc. 131, 7126-7134 (2009).

16. Wu, J.S. et al., An acid-base-controllable [c2]daisy chain. Angew. Chem., Int. Ed. 47, 7470-7474 (2008).

17. Jimnez, M.C., Dietrich-Buchecker, C., & Sauvage, J.P., Towards synthetic molecular muscles: Contraction and stretching of a linear rotaxane dimer. Angew. Chem., Int. Ed. 39, 3284-3287 (2000).

18. Dawson, R.E., Lincoln, S.F., & Easton, C.J., The foundation of a light driven molecular muscle based on stilbene and alpha-cyclodextrin. Chem. Commun., 3980-3982 (2008).

19. Clark, P.G., Day, M.W., & Grubbs, R.H., Switching and extension of a [c2]daisy-chain dimer polymer. J. Am. Chem. Soc. 131, 13631-13633 (2009).

20. Fletcher, S.P., Dumur, F., Pollard, M.M., & Feringa, B.L., A reversible, unidirectional molecular rotary motor driven by chemical energy. Science 310, 80-82 (2005).

21. Kelly, T.R., De Silva, H., & Silva, R.A., Unidirectional rotary motion in a molecular system. Nature 401, 150-152 (1999).

22. Muraoka, T., Kinbara, K., & Aida, T., Mechanical twisting of a guest by a photoresponsive host. Nature 440, 512-515 (2006).

23. Hugel, T. et al., Single-molecule optomechanical cycle. Science 296, 1103-1106 (2002).

24. Brough, B. et al., Evaluation of synthetic linear motor-molecule actuation energetics. Proc. Natl. Acad. Sci. USA 103, 8583-8588 (2006).

25. Berna, J. et al., Macroscopic transport by synthetic molecular machines. Nat. Mater. 4, 704-710 (2005).

26. Vallee, R.B. & Hook, P., Molecular motors: A magnificent machine. Nature 421, 701-702 (2003).

27. Shingyoji, C., Higuchi, H., Yoshimura, M., Katayama, E., & Yanagida, T., Dynein arms are oscillating force generators. Nature 393, 711-714 (1998).

28. Svoboda, K., Schmidt, C.F., Schnapp, B.J., & Block, S.M., Direct observation of kinesin stepping by optical trapping interferometry. Nature 365, 721-727 (1993).

29. Higuchi, H., Muto, E., Inoue, Y., & Yanagida, T., Kinetics of force generation by single kinesin molecules activated by laser photolysis of caged ATP. Proc. Natl. Acad. Sci. USA 94, 4395-4400 (1997).

30. Meyhofer, E. & Howard, J., The force generated by a single kinesin molecule against an elastic load. Proc. Natl. Acad. Sci. USA 92, 574-578 (1995).

31. Vale, R.D. et al., Direct observation of single kinesin molecules moving along microtubules. Nature 380, 451-453 (1996).

32. Witt, D., Klajn, R., Barski, P., & Grzybowski, B.A., Applications properties and synthesis of omega-functionalized n-alkanethiols and disulfides - the building blocks of self-assembled monolayers. Curr. Org. Chem. 8, 1763-1797 (2004).

33. Campbell, C.J., Fialkowski, M., Bishop, K.J.M., & Grzybowski, B.A., Mechanism of reactive wetting and direct visual determination of the kinetics of self-assembled monolayer formation. Langmuir 25, 9-12 (2009).

34. Alexander, S., Adsorption of chain molecules with a polar head a scaling description. J. Phys. (France) 38, 983-987 (1977).

35. Kuznetsov, D.V. & Chen, Z.Y., Semiflexible polymer brushes: A scaling theory. J. Chem. Phys. 109, 7017-7027 (1998).

36. Grosberg, A.Y.K., A. R., Statistical Physics of Macromolecules. (AIP Press, Woodbury, 1994).

37. Flood, A.H. et al., The role of physical environment on molecular electromechanical switching. Chem. Eur. J. 10, 6558-6564 (2004).

38. Choi, J.W. et al., Ground-state equilibrium thermodynamics and switching kinetics of bistable [2]rotaxanes switched in solution, polymer gels, and molecular electronic devices. Chem. Eur. J. 12, 261-279 (2006).

39. Phoa, K., Neaton, J.B., & Subramanian, V., First-principles studies of the dynamics of [2]rotaxane molecular switches. Nano Lett. 9, 3225-3229 (2009).

40. Klajn, R. et al., Dynamic hook-and-eye nanoparticle sponges. Nature Chem. (in press) (2009).

41. Coskun, A. et al., A light-gated STOP-GO molecular shuttle. J. Am. Chem. Soc. 131, 2493-2495 (2009).

42. Badji, J.D., Balzani, V., Credi, A., Silvi, S., & Stoddart, J.F., A molecular elevator. Science 303, 1845-1849 (2004).

43. Durola, F. & Sauvage, J.P., Fast electrochemically induced translation of the ring in a copper-complexed [2]rotaxane: The biisoquinoline effect. Angew. Chem., Int. Ed. 46, 3537-3540 (2007).

44. Altieri, A. et al., Electrochemically switchable hydrogen-bonded molecular shuttles. J. Am. Chem. Soc. 125, 8644-8654 (2003).

45. Green, J.E. et al., A 160-kilobit molecular electronic memory patterned at 1011 bits per square centimetre. Nature 445, 414-417 (2007).

46. Balzani, V. et al., Autonomous artificial nanomotor powered by sunlight. Proc. Natl. Acad. Sci. USA 103, 1178-1183 (2006).

47. Qu, D.H., Wang, Q.C., & Tian, H., A half adder based on a photochemically driven [2]rotaxane. Angew. Chem., Int. Ed. 44, 5296-5299 (2005).

48. Liu, Z.F., Hashimoto, K., & Fujishima, A., Photoelectrochemical information-storage using an azobenzene derivative. Nature 347, 658-660 (1990).

49. Kausar, A., Nagano, H., Ogata, T., Nonaka, T., & Kurihara, S., Photocontrolled translational motion of a microscale solid object on azobenzene-doped liquid-crystalline films. Angew. Chem., Int. Ed. 48, 2144-2147 (2009).

50. Koshima, H., Ojima, N., & Uchimoto, H., Mechanical motion of azobenzene crystals upon photoirradiation. J. Am. Chem. Soc. 131, 6890-+ (2009).

51. Klajn, R., Bishop, K.J.M., & Grzybowski, B.A., Light-controlled self-assembly of reversible and irreversible nanoparticle suprastructures. Proc. Natl. Acad. Sci. USA 104, 10305-10309 (2007).

52. Ichimura, K., Oh, S.K., & Nakagawa, M., Light-driven motion of liquids on a photoresponsive surface. Science 288, 1624-1626 (2000).

53. Ferri, V. et al., Light-powered electrical switch based on cargo-lifting azobenzene monolayers. Angew. Chem., Int. Ed. 47, 3407-3409 (2008).

54. Holland, N.B. et al., Single molecule force spectroscopy of azobenzene polymers: Switching elasticity of single photochromic macromolecules. Macromolecules 36, 2015-2023 (2003).

55. Kobatake, S., Takami, S., Muto, H., Ishikawa, T., & Irie, M., Rapid and reversible shape changes of molecular crystals on photoirradiation. Nature 446, 778-781 (2007).

56. Waldeck, D.H., Photoisomerization dynamics of stilbenes. Chem. Rev. 91, 415-436 (1991).

57. Liu, Y. et al., Linear artificial molecular muscles. J. Am. Chem. Soc. 127, 9745-9759 (2005).

58. Tsuda, S., Aso, Y., & Kaneda, T., Linear oligomers composed of a photochromically contractible and extendable Janus [2] rotaxane. Chem. Commun., 3072-3074 (2006).

59. Letinois-Halbes, U., Hanss, D., Beierle, J.M., Collin, J.P., & Sauvage, J.P., A fast-moving [2]rotaxane whose stoppers are remote from the copper complex core. Org. Lett. 7, 5753-5756 (2005).

60. Cardenas, D.J., Livoreil, A., & Sauvage, J.P., Redox control of the ring-gliding motion in a Cu-complexed catenane: A process involving three distinct geometries. J. Am. Chem. Soc. 118, 11980-11981 (1996).

61. Asakawa, M. et al., A chemically and electrochemically switchable [2]catenane incorporating a tetrathiafulvalene unit. Angew. Chem., Int. Ed. 37, 333-337 (1998).

62. Leigh, D.A., Wong, J.K.Y., Dehez, F., & Zerbetto, F., Unidirectional rotation in a mechanically interlocked molecular rotor. Nature 424, 174-179 (2003).

63. Raymo, F.M. & Tomasulo, M., Fluorescence modulation with photochromic switches. J. Phys. Chem. A 109, 7343-7352 (2005).

64. Dinescu, L. & Lemieux, R.P., Photomodulation of the spontaneous polarization of a ferroelectric liquid crystal: Harnessing the transverse dipole modulation of a chiral thioindigo dopant. J. Am. Chem. Soc. 119, 8111-8112 (1997).

65. Feringa, B.L., The art of building small: From molecular switches to molecular motors. J. Org. Chem. 72, 6635-6652 (2007).

66. Morin, J.F., Shirai, Y., & Tour, J.M., En route to a motorized nanocar. Org. Lett. 8, 1713-1716 (2006).

67. Muraoka, T., Kinbara, K., & Aida, T., A self-locking molecule operative with a photoresponsive key. J. Am. Chem. Soc. 128, 11600-11605 (2006).

68. Muraoka, T., Kinbara, K., Kobayashi, Y., & Aida, T., Light-driven open-close motion of chiral molecular scissors. J. Am. Chem. Soc. 125, 5612-5613 (2003).

Supplementary Information accompanies the paper on www.nature.com/nature.Acknowledgements This work was supported by the Non-equilibrium Energy Research Center which is an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0000989.Author Contributions The ideas presented here were developed jointly by B.A.G and J.F.S.. B.A.G. , M.W. and R.D.A. developed the theoretical models for the manuscript. All authors participated actively in the writing of the manuscript.

Author Information Reprints and permissions information is available at www.nature.com/reprints. Correspondence should be addressed to B.A.G ([email protected]) and J.F.S. ([email protected]).

CAPTIONS TO THE FIGURES

Figure 1. Artificial molecular machines can perform mechanical work. (a) Schematic representation of the operation cycle for the polymer containing azobenzene units. Under light irradiation (h(), azobenzenes undergo trans(cis isomerization, resulting in force f and displacement (H of the attached object. (b) Electrochemically switchable palindromic bistable rotaxanes tethered onto the surface of a gold microcantilever control the cantilevers reversible bending (c) (i) Rotation of a glass rod on a liquid crystal layer doped with a motor molecule switchable by UV light. Frames are taken at 15 s intervals and show clockwise rotation of 0, 28, 141, and 226(, respectively. Scale bars: 50 (m.. (ii) Structural formula of the motor molecule. Principal axis indicates the clockwise rotation of the rotor part in a cycle of two photochemical steps (red arrows), causing the isomerization around the central double bond, and two thermal steps (blue arrows). The pictures in (C) are reprinted with permission from Ref 11.

Figure 2. Machine Assemblies Muscle-up. (a) An expandable muscle-like molecule (cf. Table 1) and its simplified representation as a cylinder of radius R and length L (upon stimulation, expandable by (L). The molecules form linear chains of N switching units. These polymers could be attached to a supporting surface as (b) sparsely, as partly coiled polymer brushes or (c) densely packed, as stretched chains. Another interesting arrangement is that of muscle-like bundles (d) comprising M chains, and with crossectional area A and persistence length (.

Figure 3. Qualitative free energy diagrams of a molecular switch (here, a bistable rotaxane) during actuation. (a) Ground-state co-conformation, in which the ring (blue) preferentially binds to the green station. (b) Oxidation of the green station (to yellow) causes the ring to shift over to the red station. (c) Upon reduction, the blue ring resides on the red station (metastable co-conformation) before relaxing back to the ground state. Figure 4. Possible collective phenomena in ensembles of coupled molecular machines. (a) When switching of one molecule causes the neighboring molecules to switch, it can create a domino-like affect propagating as a reaction-front. Here, this situation is illustrated for the case of a monolayer of two-state molecular machines. (b) When the switching of one unit hampers the switching of its neighbors, one can envision assemblies in which the states of nearby machines alternate, much like in a antiferromagnet. MICHAL, PLEASE DISCUSS THE RIGHTMOST PLOT THAT, IF THERE IS FRUSTRATION ON THE LATTICE, THE ORDERING CAN GIVE RIGHT TO LARGER-SIZE DOMAINS, YES? (c) ALI, PLS SEE BELOW FIG 4 EXPERIMETNAT 1010101010 CRYSTAL STRUCTURE, LIKE THE ONE DISCUSSED IN (b)

Figure 1

Figure 2

Figure 3

Figure 4.ALI: REMOVE A. RENUMBER B,C. AS NEW C, YOU MENTIONED YOU HAD SOME REAL CRYSTAL STRUCTURE ILLUSTRATING THE ALTERNATING ARRANGEMENT OF ON AND OFF ROTAXANES> COULD YOU INCLUDE THIS STRUCTURE AS C?

Supporting Information for Manuscript entitled On the energetics of molecular machines and of their assemblies by Ali Coskun, Michal Banaszak, J. Fraser Stoddart, and Bartosz A. GrzybowskiIn the following, we derive the equations describing free energy changes of grafted polymers of molecular switches.

(1) Sparse grafting. The first case we consider deals with the case of the sparsely-grafted polymer brushes and, in general terms, derives from the Alexanders coarse-grained model (33). The polymer brush is characterized by following parameters:

H brush height, polymer end-to-end distance

L length of single segment, assumed equal to the Kuhn length

N number of statistical segments (proportional to the degree of polymerization)

N L polymer contour length

n number of grafted chains

V total volume of the brush

S area of the surface from on which the brushes are grafted (note that V= S H) = N n /V (monomer concentration)

grafting density; n= Sw excluded volume parameter; w = (1-2) v, where v is of the order of the segments volume

Flory interaction parameter, a small number for a good solvent

This system can be described by the free energy, F, per chain in kT units, , where the elastic (entropic) contribution is and the interaction (enthalpic) contribution is . By minimizing F with respect to H we obtain the equilibrium brush height,

(S1)

and free energy

(S2)

where superscript denotes that this is the initial configuration. This free energy (S2) can be expanded around its equilibrium value to give the following quadratic approximation:

(S3)

Now, if L changes to L+L upon external stimulus, then free energy of the new, final state can be written using quadratic approximation as:

(S4)

where .Next, we calculate

(S5)

which is the expression used in the main text. Note that this expression is only an order-of-magnitude approximation, since the excluded volume parameter w is not known and is here assumed to be constant. Importantly, however, our estimates indicate only a small fraction of kT can be retrieved as useful energy from a single swichable polymer unit.

(2) Dense grafting. The model discussed in the previous section is applicable for extended but coiled polymer brushes of reduced grafting densities, w/L, considerably smaller than unity (sparse grafting). When polymer chains are very densely grafted, however, they should be almost fully extended (unless trapped kinetically by, for example, entanglements) with the brush height, H, close to the contour length, NL. The quadratic (in H) elastic term fails to describe properly the chains at strong extensions, and a different expression for entropic elasticity is used following Kuznetsov and Chen (34):

(S6)

This expression prevents the brush height, H, from exceeding the contour length, NL. Upon minimization of Fel with respect to H, the following results are obtained (up to multiplicative constants of the order of unity):

and

(S7)

Note that the free energy per segment is of the order of kT and so the corresponding free energy change upon stimulus can be a fraction of kT. Also, the formulas used in the main text can now be derived by assuming that the chain is extended as a result of a constant net force acting on it In this case, the force needed to keep the polymer at extension H is . Then, if L is changed upon stimulus from L to L+L, H has to change in linear proportion, , to maintain the constant force. Taking Hi=H, and Hf=H+H, we can calculate the work as

(S8)

with .

PAGE 20

_1315919774.unknown

_1316113715.unknown

_1318872721.unknown

_1318876781.unknown

_1318876782.unknown

_1318873087.unknown

_1318801356.unknown

_1316113670.unknown

_1315919790.unknown

_1315926512.unknown

_1314791024.unknown

_1315917599.unknown

_1315919755.unknown

_1314803469.unknown

_1313571640.unknown

_1313572752.unknown

_1313578258.unknown

_1313578846.unknown

_1313573985.unknown

_1313571776.unknown

_1313567846.unknown

_1313568465.unknown

_1313221314.unknown