Periodic forcing of a Brownian particle

Faucheux, Luc P.; Stolovitzky, Gustavo; Libchaber, Albert

doi:10.1103/physreve.51.5239

Cited by 102 publications

(93 citation statements)

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“…Rather, this is an instance of a so-called drift ratchet [20]. Other pioneering implementations of classical force-free thermal ratchets also were based on asymmetric potentials, but did not exhibit flux reversal [21,22,23,24,25]. Figure 1 shows the principle upon which the three-state optical thermal ratchet operates.…”

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confidence: 99%

Observation of Flux Reversal in a Symmetric Optical Thermal Ratchet

et al. 2005

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We demonstrate that a cycle of three holographic optical trapping patterns can implement a thermal ratchet for diffusing colloidal spheres, and that the ratchet-driven transport displays flux reversal as a function of the cycle frequency and the inter-trap separation. Unlike previously described ratchet models, the approach we describe involves three equivalent states, each of which is locally and globally spatially symmetric, with spatiotemporal symmetry being broken by the sequence of states.Brownian motion cannot create a steady flux in a system at equilibrium. Nor can local asymmetries in a static potential energy landscape rectify Brownian motion to induce a drift. A landscape that varies in time, however, can eke a flux out of random fluctuations by breaking spatiotemporal symmetry [1,2,3,4]. Such flux-inducing time-dependent potentials are known as thermal ratchets [5,6], and their ability to bias diffusion by rectifying thermal fluctuations has been proposed as a possible mechanism for transport by molecular motors and is being actively exploited for macromolecular sorting [7].Most thermal ratchet models are based on spatially asymmetric potentials. Their time variation involves displacing or tilting them relative to the laboratory frame, modulating their amplitude, changing their periodicity, or some combination, usually in a two-state cycle. Chen demonstrated that a spatially symmetric potential still can induce drift, provided that it is applied in a threestate cycle, one of which allows for free diffusion [8]. This idea since has been refined [9] and generalized [10].The space-filling potential energy landscapes required for most such models pose technical challenges. Furthermore, their relationship to the operation of natural thermal ratchets has proved difficult to establish.This Letter describes the first experimental demonstration of a spatially symmetric thermal ratchet, which we have implemented with holographic optical traps [11,12,13]. The potential energy landscape in this system consists of a large number of discrete optical tweezers [14], each of which acts as a symmetric potential energy well for nanometer-to micrometer-scale objects such as colloidal spheres. We arrange these wells so that colloidal spheres can diffuse freely in the interstitial spaces but are localized rapidly once they encounter a trap. A threestate thermal ratchet then requires only displaced copies of a single two-dimensional trapping pattern. Despite its simplicity, this ratchet model displays flux reversal [5,15] in which the direction of motion is controlled by a balance between the rate at which particles diffuse across the landscape and the ratchet's cycling rate.Often predicted, and inferred from the behavior of some natural molecular motors and semiconductor devices [5], flux reversal has been directly observed in com- paratively few systems. Previous demonstrations have focused on ratcheting of magnetic flux quanta through type-II superconductors in both the quantum mechanical [16] and classical [17] regimes,...

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Observation of Flux Reversal in a Symmetric Optical Thermal Ratchet

et al. 2005

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“…This occupation number appears to be small enough for quantitative agreement with the singleparticle theory in Eqs. (11) through (15). Collisions arising in more highly occupied patterns could give rise to additional transport phenomena such as cooperative flux reversal of the type that is observed in ratchets for magnetic flux quanta [43,44] and bacterial swarms [45].…”

Section: Experimental Demonstrationmentioning

confidence: 99%

“…6(a) and (b) represent the numerical solutions of Eq. (12) and (15) for this set of conditions, again with no adjustable parameters. As in the deterministic limit, the optical Fibonacci spiral ratchet acts in quantitative agreement with theory when operated as a thermal ratchet.…”

Section: Experimental Demonstrationmentioning

confidence: 99%

“…Introduced with James Clerk Maxwell's thought experiments in the 1860's, thermal ratchets recently have enjoyed a resurgence of interest because of their relevance to biological molecular motors, and have been realized experimentally both for molecular [7,8], micrometer-scaled [9][10][11][12][13][14][15][16][17][18][19][20][21] and for quantum objects [22]. Virtually all of these studies, however, have focused on one-dimensional systems [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], or on systems that can be projected onto one dimension [7,21]. Comparatively little attention has been paid to thermal ratchets in two or higher dimensions.…”

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Two-dimensional optical thermal ratchets based on Fibonacci spirals

2011

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“…To date, LOTs have been used to construct thermal ratchets, 3 perform colloidal interaction measurements, [4][5][6][7][8] and produce passive "force clamps" ͑con-stant lateral force traps͒ for single molecule biophysics assays. 9 These traps were formed variously by scanning the laser using rotating mirrors, 3,10 galvanometer-driven mirrors, 2,5 or acousto-optical deflectors. 11 One-dimensional arrays of particles have also been trapped in the counterpropagating Gaussian beams of fiber optic traps.…”

Section: Introductionmentioning

confidence: 99%

Line optical tweezers instrument for measuring nanoscale interactions and kinetics

Biancaniello

Crocker

2006

Review of Scientific Instruments

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We describe an optical tweezers instrument for measuring short-ranged colloidal interactions, based on a combination of a continuous wave line optical tweezers, high speed video microscopy, and laser illumination. Our implementation can measure the separation of two nearly contacting microspheres to better than 4 nm at rates in excess of 10 kHz. A simple image analysis algorithm allows us to sensibly remove effects from diffraction blurring and microsphere image overlap for separations ranging from contact to at least 100 nm. The result is a versatile instrument for measuring steric, chemical and single-molecular interactions and dynamics, with a force resolution significantly better than achievable with current atomic force microscopy. We demonstrate the effectiveness of the instrument with measurements of the pair interactions and dynamics of microspheres in the presence of transient molecular bridges of DNA or surfactant micelles. We describe an optical tweezers instrument for measuring short-ranged colloidal interactions, based on a combination of a continuous wave line optical tweezers, high speed video microscopy, and laser illumination. Our implementation can measure the separation of two nearly contacting microspheres to better than 4 nm at rates in excess of 10 kHz. A simple image analysis algorithm allows us to sensibly remove effects from diffraction blurring and microsphere image overlap for separations ranging from contact to at least 100 nm. The result is a versatile instrument for measuring steric, chemical and single-molecular interactions and dynamics, with a force resolution significantly better than achievable with current atomic force microscopy. We demonstrate the effectiveness of the instrument with measurements of the pair interactions and dynamics of microspheres in the presence of transient molecular bridges of DNA or surfactant micelles.

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Periodic forcing of a Brownian particle

Cited by 102 publications

References 9 publications

Observation of Flux Reversal in a Symmetric Optical Thermal Ratchet

Observation of Flux Reversal in a Symmetric Optical Thermal Ratchet

Two-dimensional optical thermal ratchets based on Fibonacci spirals

Line optical tweezers instrument for measuring nanoscale interactions and kinetics

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