Artificial Brownian Motors: Controlling Transport on the Nanoscale
Total Page：16
File Type：pdf, Size：1020Kb
Artificial Brownian motors: Controlling transport on the nanoscale Peter H¨anggi1, 2, ∗ and Fabio Marchesoni3, 4, y 1Institut f¨urPhysik, Universit¨atAugsburg, Universit¨atsstr.1, D-86135 Augsburg, Germany 2Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117542 3Dipartimento di Fisica, Universit`adi Camerino, I-62032 Camerino, Italy 4School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea (Dated: September 24, 2008) In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases, one speaks of \Brownian motors". In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cell molecular machinery: working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e. non-biological nanopores and optical traps, where single particle currents have been first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented hereby. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin or even heat and the assembly of chemical synthetic molecular motors. Our survey ends with a perspective for future roadways and potential new applications. PACS numbers: 05.60.-k, 47.61.-k, 81.07.-b, 85.25.-j, 85.35.-p, 87.16.-b 2. Vibrated ratchets 17 III. TRANSPORT IN NANOPORES 18 A. Ion pumps 18 Contents B. Artificial nanopores 19 C. Chain translocation 20 I. INTRODUCTION 2 D. Toward a next generation of mass rectifiers 21 1. Artificial nanodevices 3 1. Zeolites 21 2. Brownian motors 3 2. Nanotubes 22 II. SINGLE-PARTICLE TRANSPORT 5 IV. COLD ATOMS IN OPTICAL LATTICES 22 A. Symmetric substrates 5 A. Bi-harmonic driving 23 1. dc drive 5 B. Multi-frequency driving 23 2. ac drive 6 C. More cold atom devices 24 3. Diffusion peak 7 4. Single-file diffusion 7 V. COLLECTIVE TRANSPORT 25 B. Rectification of asymmetric processes 7 A. Asymmetric 1D geometries 25 C. Nonlinear mechanisms 8 1. Boundary effects 25 1. Harmonic mixing 8 2. Asymmetric patterns of symmetric traps 26 2. Gating 9 B. 2D lattices of asymmetric traps 26 3. Noise induced transport 10 C. Binary mixtures 28 D. Brownian motors 11 VI. MICROFLUIDICS 29 arXiv:0807.1283v2 [cond-mat.stat-mech] 24 Sep 2008 1. Rocked ratchets 11 2. Pulsated ratchets 13 A. Transporting colloids 29 3. Correlation ratchets 14 B. Transporting condensed phases 31 4. Further asymmetry effects 15 C. Granular flows 31 E. Efficiency and control issues 16 1. Optimization 16 VII. SUPERCONDUCTING DEVICES 33 A. Fluxon channels 34 B. Fluxon rectification in 2D arrays 36 C. Anisotropic fluxon rectifiers 38 ∗Electronic address: [email protected] VIII. QUANTUM DEVICES 39 yElectronic address: [email protected] A. Quantum dissipative Brownian transport 39 2 B. Josephson Brownian motors 40 pressure and temperature, a reasonable assumption when 1. Classical regime 40 dealing with the monster steam engines of the Victorian 2. Quantum regime 41 industry. A typical protein, however, is a few nanome- C. Quantum dot ratchets 42 ters in size and consists of just a few tens of thousands D. Coherent quantum ratchets 43 1. Quantum ratchets from molecular wires 44 of atoms. As a consequence the movements of a pro- 2. Hamiltonian quantum ratchet for cold atoms 44 tein engine are swamped by the fluctuations resulting from the Brownian motion of its surroundings, which IX. SUNDRY TOPICS 45 causes the energy of any its part to fluctuate continu- A. Pumping of charge, spin and heat 45 ally in units of kT , with k denoting the Boltzmann con- B. Synthetic molecular motors and machines 45 stant and T the temperature. The effects of such energy X. CONCLUDING REMARKS 46 fluctuations were brilliantly demonstrated by Yanagida's group (Nishiyama et al., 2002, 2001), who observed ki- Acknowledgments 47 nesin molecules climbing the cytoskeletal track in a jud- References 48 dering motion made up of random hesitations, jumps and even backward steps. Similar results have been reported for a host of protein engines. The key question in mod- I. INTRODUCTION ern thermodynamics is therefore how far energy fluctua- tions drive micro- and nano-engines beyond the limits of Over the past two decades advances in microscopy and macroscopic laws. microscale control have allowed scientists and engineers A revealing experiment was performed recently by Bus- to delve into the workings of the biological matter. One tamante et al. (2005), who first stretched a single RNA century after Kelvin's death, today's researchers aim to molecule, by optically tugging at a tiny plastic bead at- explain how the engines of life actually work by stretching tached to one end, and then released the bead to study thermodynamics beyond its 19th-century limits (Haw, the effect of random energy fluctuations on the molecule 2007). recovery process. By repeating many identical stretching Carnot realized that all engines transform energy from cycles, these authors found that the molecule \relaxation one form into another with a maximum possible efficiency path" was different every time. In fact, the bead was that does not depend on the technology developed or drawing useful energy from the thermal motion of the on the fuel utilized, but rather on fundamental quanti- suspension fluid and transforming it into motion. How- ties such as heat and temperature. Kelvin and Clau- ever, by averaging over increasingly longer bead trajecto- sius came up with two \rules of the engine", later known ries that is, approaching a macroscopic situation, Busta- as the first two laws of thermodynamics. The first law mante et al. (2005) were able to reconcile their findings states that energy cannot be destroyed or created but with the second law. These results lead to the conclu- only transformed; the second law sets fundamental lim- sion that the straightforward extension of the second law itations to what energy transformation can achieve in to microscopic systems was ungranted; individual small practical terms. Just as the first law was centered on the systems do evolve under inherently nonequilibrium con- notion of energy (from Greek for \work capability"), the ditions. second law revolved around the new concept of entropy (a However, a decade ago Jarzynski (1997) showed that term coined by Clausius also from Greek for \change ca- the demarcation line between equilibrium and non- pability"). 1 When expressed in such terms, the second equilibrium processes is not always as clear cut as we were law states that entropy cannot decrease during any spon- used to think. Imagining a microscopic single molecule taneous or natural process. Notably, within the whole, process, Jarzynski evaluated not the simple average of the virtual manufactory of all natural processes the first law change of the (random) work of the underlying perturbed takes on the role of an account clerk, keeping track of all nanosystem, as it was pulled away from equilibrium ac- energy changes, while the second law takes on the role of cording to an arbitrary protocol of forcing, but rather the director, determining the direction and action of all the average of the exponential of that tailored nonequi- processes. librium work. Remarkably, such a quantity turned out The fathers of thermodynamics developed their laws to be the same as for an adiabatically slow version of having in mind macroscopic systems that they could de- the same process, and most remarkably, equals the ex- scribe in terms of state (i.e., average) quantities such as ponential of the system's equilibrium free energy change. This result, also experimentally demonstrated by Busta- mante et al. (2005), came as much of a surprise because it meant that information about macroscopic equilibrium 1 Rudolf Julius Emanuel Clausius throughout his life allegedly pre- was somehow buried inside individual, randomly fluctu- ferred the German word \Verwandlungswert" rather than \en- ating microscopic systems far from equilibrium, see also tropy", although his colleagues suggested him to choose a name (Crooks, 1999; Gallavotti and Cohen, 1995; Jarzynski, for his new thermodynamic quantity \S" (his chosen symbol for labeling \entropy", possibly in honor of \S"adi Carnot) that 2007; Talkner et al., 2008, 2007). sounded as close as possible to the word \energy". There is an additional limitation of 19th-century ther- 3 modynamics that is potentially even more significant in be artificially manufactured by many orders of magni- the design