Kinetically Locked-In Colloidal Transport in an Array of Optical Tweezers

Korda, Pamela; Taylor, Michael B.; Grier, David G.

doi:10.1103/physrevlett.89.128301

Cited by 347 publications

(369 citation statements)

References 19 publications

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“…The deflection angle between the flux and the direction of F depends on the commensurability between the particle trajectories and the underlying periodic potential. This effect has been used for particle sorting [52][53][54]. Recent studies also showed that the multidimensional nonequilibrium steadystate distribution determines the ratio between the transport coefficients along different primitive crystal directions [55,56].…”

Section: Discussionmentioning

confidence: 99%

Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions

Lai

Ackerson

et al. 2015

Phys. Rev. E

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We report a systematic study of the effects of the external force F on the nonequilibrium steady-state (NESS) dynamics of the diffusing particles over a tilted periodic potential, in which detailed balance is broken due to the presence of a steady particle flux. A tilted two-layer colloidal system is constructed for this study. The periodic potential is provided by the bottom-layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top-layer diffusing particles. By tilting the sample at an angle θ with respect to the vertical (gravity) direction, a tangential component of the gravitational force F is applied to the diffusing particles. The measured NESS probability density function P ss (x,y) of the particles is found to deviate from the equilibrium distribution P (x,y) to a different extent, depending on the driving or distance from equilibrium. The experimental results are compared with the exact solution of the one-dimensional (1D) Smoluchowski equation and the numerical results of the 2D Smoluchowski equation. From the obtained exact solution of the 1D Smoluchowski equation, we develop an analytical method to accurately extract the 1D potential U 0 (x) from the measured P ss (x). This work demonstrates that the tilted periodic potential provides a useful platform for the study of forced barrier-crossing dynamics beyond the Arrhenius-Kramers equation.

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Section: Discussionmentioning

confidence: 99%

Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions

Lai

Ackerson

et al. 2015

Phys. Rev. E

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“…The direction of motion of the locked particles undergoes a series of steps as a func-tion of the effective angle of drive with respect to the substrate. The steps are centered at integer and rational ratios of the angle of drive and form a devil's staircase structure [46][47][48]50,51,53,54 . In the skyrmion system, we observe directional locking effects when the direction of external drive is fixed with respect to the substrate and the drive amplitude is varied.…”

Section: Introductionmentioning

confidence: 99%

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

2015

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We examine the dynamics of a skyrmion moving over a two-dimensional periodic substrate utilizing simulations of a particle-based skyrmion model. We specifically examine the role of the non-dissipative Magnus term on the driven motion and the resulting skyrmion velocity-force curves. In the overdamped limit, there is a depinning transition into a sliding state in which the skyrmion moves in the same direction as the external drive. When there is a finite Magnus component in the equation of motion, a skyrmion in the absence of a substrate moves at an angle with respect to the direction of the external driving force. When a periodic substrate is added, the direction of motion or Hall angle of the skyrmion is dependent on the amplitude of the external drive, only approaching the substrate-free limit for higher drives. Due to the underlying symmetry of the substrate the direction of skyrmion motion does not change continuously as a function of drive, but rather forms a series of discrete steps corresponding to integer or rational ratios of the velocity components perpendicular ( V ⊥ ) and parallel ( V || ) to the external drive direction: V ⊥ / V || = n/m, where n and m are integers. The skyrmion passes through a series of directional locking phases in which the motion is locked to certain symmetry directions of the substrate for fixed intervals of the drive amplitude. Within a given directionally locked phase, the Hall angle remains constant and the skyrmion moves in an orderly fashion through the sample. Signatures of the transitions into and out of these locked phases take the form of pronounced cusps in the skyrmion velocity versus force curves, as well as regions of negative differential mobility in which the net skyrmion velocity decreases with increasing external driving force. The number of steps in the transport curve increases when the relative strength of the Magnus term is increased. We also observe an overshoot phenomena in the directional locking, where the skyrmion motion can lock to a Hall angle greater than the clean limit value and then jump back to the lower value at higher drives. The skyrmion-substrate interactions can also produce a skyrmion acceleration effect in which, due to the non-dissipative dynamics, the skyrmion velocity exceeds the value expected to be produced by the external drive. We find that these effects are robust for different types of periodic substrates. Using a simple model for a skyrmion interacting with a single pinning site, we can capture the behavior of the change in the Hall angle with increasing external drive. When the skyrmion moves through the pinning site, its trajectory exhibits a side step phenomenon since the Magnus term induces a curvature in the skyrmion orbit. As the drive increases, this curvature is reduced and the side step effect is also reduced. Increasing the strength of the Magnus term reduces the range of impact parameters over which the skyrmion can be captured by a pinning site, which is one of the reasons that strong Magnus force effects reduce the...

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“…Experiments and computational studies have shown that in the absence of a drive, a variety of orderings can arise for colloidal particles interacting with one-dimensional (1D) periodic substrates [13,32,33], two-dimensional (2D) periodic substrates [15,20,21,[34][35][36][37][38], 2D quasiperiodic substrates [39][40][41][42][43], or 2D random substrates [44]. While these studies have provided a better understanding of several features of commensurateincommensurate behaviors, being able to dynamically control the particle ordering and dynamics could lead to a variety of applications, including self-assembled structures, particle separation, and photonic crystals.…”

Section: Introductionmentioning

confidence: 99%

“…Periodic pinning arrangements of this type have been experimentally realized in colloidal systems and studied in the range f = 4.0 to f = 5.5, with a triangular colloidal lattice observed at f = 4.0 when the pinning strength was such that each pinning site captures only one particle [48]. Such pinning arrays have also been used to study dynamical locking for colloidal particles driven over a substrate at different angles with respect to the substrate symmetry directions [34]. Experimental and numerical studies of vortex systems using similar 2D periodic pinning arrays also obtained a triangular vortex lattice at f = 4.0 and a square lattice at f = 5.0 [5,7] with domain wall and stripe states between these fillings [5].…”

Section: Introductionmentioning

confidence: 99%

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

2013

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We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.

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Kinetically Locked-In Colloidal Transport in an Array of Optical Tweezers

Cited by 347 publications

References 19 publications

Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions

Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

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