Dynamics, Rectification, and Fractionation for Colloids on Flashing Substrates A. Liba ´l, 1,2 C. Reichhardt, 1 B. Janko ´, 2 and C. J. Olson Reichhardt 1 1 Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 2 Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA (Received 11 August 2005; published 10 May 2006) We show that a rich variety of dynamic phases can be realized for mono- and bidisperse mixtures of interacting colloids under the influence of a symmetric flashing periodic substrate. With the addition of dc or ac drives, phase locking, jamming, and new types of ratchet effects occur. In some regimes we find that the addition of a nonratcheting species increases the velocity of the ratcheting particles. We show that these effects occur due to the collective interactions of the colloids. DOI: 10.1103/PhysRevLett.96.188301 PACS numbers: 82.70.Dd The motion and ordering of colloidal particles on two- dimensional (2D) periodic substrates has been attracting growing interest due to recent experimental breakthroughs that permit the creation of static 1D and 2D periodic substrate arrays using optical and holographic techniques [1– 8]. It is also possible to create dynamic periodic arrays, such as flashing or shifting traps [1,9–11]. Colloidal par- ticles interacting with periodic substrates are ideal model systems for studying general problems in condensed matter physics, such as the ordering and melting of commensurate and incommensurate elastic lattices on periodic surfaces. Problems of this type can arise in vortex crystal ordering in superconductors [12] or Bose-Einstein condensates (BECs) with periodic pinning sites [13] as well as mole- cules adsorbed on surfaces [14]. The dynamics of colloids moving over periodic substrates is also relevant to under- standing depinning phenomena [6,15] and phase locking [4]. In addition to the scientific interest in these systems, there are technical applications for colloids moving over periodic arrays, such as the fractionation or segregation of colloidal mixtures [4,5,7– 9]. For example, species fractio- nation can be achieved by flowing colloidal mixtures over an array at an angle such that the motion of one colloid species locks to a symmetry direction of the periodic array while the other species moves in the driving direction [4,7,8]. Other segregation phenomena occur when the substrate is dynamic, and rectification or ratchet devices can be constructed in which one species ratchets at a different velocity than the other [10]. New ratchet-based logic devices have also been realized [11] which may be useful for understanding similar solid state nanoscale de- vices [16]. Assemblies of interacting particles have been exten- sively studied for systems with random disorder and peri- odic substrates. Collectively interacting particles on a flashing substrate is a new class of problem that can be realized experimentally using dynamic substrates. For par- ticles interacting with optical traps, flashing can be achieved simply by modulating the laser power. It should be possible to create similar flashing potentials for vortices in BECs or ions interacting with optical arrays [13]. In this work we consider mono- and bidisperse assem- blies of charged colloids interacting with flashing 2D sym- metric periodic substrates. When a dc drive is applied to this system, phase locking in the velocity-force curves oc- curs. If an external ac drive is applied instead of a dc drive, we find that new types of ratchet effects can be realized. For bidisperse colloidal assemblies, the relative velocity between the two colloid species is affected by the density, number ratio, and charge disparity of the species. We find that collective effects play an important role in the ratchet- ing behavior. For a system containing a nonratcheting spe- cies A, the introduction of a second species B that does ratchet can induce ratcheting in species A due to the inter- actions between the colloid species. The effectiveness of the induced ratcheting goes through a peak as the fraction of ratcheting particles is changed at fixed colloid density. At high densities, the colloids reach a jammed state and both species ratchet at the same velocity. We also find a re- markable phenomenon for strongly interacting particles, where it is possible to increase the drift velocity of a rat- cheting species by adding nonratcheting colloids to the sys- tem. This effect occurs when the disorder introduced by the nonratcheting species breaks apart structures formed by the ratcheting species and allows the latter to couple more ef- fectively to the substrate. Our results can be tested experi- mentally for colloids interacting with flashing optical traps. We consider a 2D Brownian dynamics (BD) simulation of N interacting colloids with periodic boundary condi- tions in both the x and y directions. We neglect hydro- dynamic and excluded volume interactions, which are reasonable assumptions for strongly charge-stabilized par- ticles in the low volume fraction limit. The overdamped equation of motion [17] for colloid i is given by dR i dt F cc i F T i F s i F ext i ; (1) where the damping constant is set to unity. The colloid- colloid interaction force is F cc i q i P N i ij r i V r ij , where the colloid-colloid potential is a Yukawa or screened Coulomb interaction with the form Vr ij E 0 q j =jr i r j j expjr i r j j. Here, E 0 Z 2 =4 0 , where PRL 96, 188301 (2006) PHYSICAL REVIEW LETTERS week ending 12 MAY 2006 0031-9007= 06=96(18)=188301(4) 188301-1 2006 The American Physical Society