Depinning and Collective Dynamics of Magnetically Driven Colloidal Monolayers

Pietro Tierno

Phys. Rev. Lett. 109, 198304 – Published 9 November 2012

Abstract

We study the collective dynamics of interacting paramagnetic colloids transported via a magnetic ratchet effect above a modulated periodic potential. Upon increasing the modulation frequency, the particles undergo a series of dynamic transitions, from a continuous smectic flow to a disorder flow, and later enter into a two phase flow regime, ending in a complete pinned state. In the disordered phase, the system organizes into density waves due to traffic jams, as in granular systems, while the two phase flow regime shows strong similarities with plastic flow in vortex matter. Finally, it is shown that induced attractive interactions between the moving colloids lead to enhancement of the particle current due to formation of condensed chains traveling along the modulated landscape.

Received 20 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.198304

Authors & Affiliations

Pietro Tierno^*

Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain and Institut de Nanociència i Nanotecnologia IN2 UB, Universitat de Barcelona, 08028 Barcelona, Spain

^*ptierno@ub.edu

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Vol. 109, Iss. 19 — 9 November 2012

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Images

Figure 1
(a) Schematic showing the paramagnetic colloids above a FGF with spatial periodicity $λ = 2.6 μ m$ and subjected to an external magnetic field $H$ rotating in the ( $y$ , $z$ ) plane. (b) Microscope image showing a diluted sample of particles (areal density $ρ = 0.03 μ m^{- 2}$ ) and the magnetic pattern. Images (c)–(f) show experimental trajectories of the particles [one highlighted in gray (red), $ρ = 0.22 μ m^{- 2}$ ] in the various regimes of motion with $H_{0} = 900 A / m$ and $ω = 19 s^{- 1}$ (c), $251 s^{- 1}$ (d), $484 s^{- 1}$ (e), and $628 s^{- 1}$ (f). For clarity, the data show a small overview ( $44 \times 44 μ m^{2}$ ) of the whole observation area ( $140 \times 105 μ m^{2}$ ). Corresponding movies can be found in the Supplemental Material [13].Reuse & Permissions
Figure 2
(a) Average velocity $⟨ v_{y} ⟩$ in the driving direction ( $y$ ) versus $ω$ for a single particle (dashed line) and a collection of particles with density $ρ = 0.22 μ m^{- 2}$ (black squares). Gray (red) circles denote the location of the trajectories shown in Figs. 1c, 1d, 1e, 1f. Inset shows $⟨ v_{y} ⟩$ versus $ρ$ in the four regimes, with frequencies corresponding to Figs. 1c, 1d, 1e, 1f. (b) Average fraction of sixfold coordinated particles $⟨ P_{6} ⟩$ versus $ω$ . (c) Gray (green) empty squares denote the fraction of particles having the same velocity $ϕ_{s}$ , black points denote the fraction of particles having zero velocity $ϕ_{0}$ , both versus $ω$ . (d) Transversal diffusion coefficient $D_{x}$ versus frequency. Gray (blue) triangles indicate the values of $D_{x}$ for the mobile colloids in regime III.Reuse & Permissions
Figure 3
(a) Space-time diagram of the normalized density field $ρ (y, t) / ρ_{0}$ with $ρ_{0} = 0.15 μ m^{- 2}$ in regime II ( $ω = 251 s^{- 1}$ ). (b) $ρ (y, t) / ρ_{0}$ versus position $y$ at two different times. (c) Averaged velocity of the density waves $⟨ v_{w} ⟩$ normalized with respect to $⟨ v_{y} ⟩$ versus frequency in regime II. (d),(e) Normalized velocity distributions $P (v_{y})$ in the driving direction for regime II (d), and regime III (e). Inset shows the corresponding PDFs along the transversal direction.Reuse & Permissions
Figure 4
(a),(b) Microscope images of paramagnetic colloids subjected to an elliptic rotating magnetic field with frequency $ω = 314 s^{- 1}$ and ratio between components $H_{z} / H_{y} = 0.27$ (a) and $H_{z} / H_{y} = 3.6$ (b). (c) Average velocity $⟨ v_{y} ⟩$ versus $H_{z} / H_{y}$ for chains, inset shows $⟨ v_{y} ⟩$ for columns. (d) Average velocity of chains (empty squares and circles) and columns (filled triangles) $⟨ v_{y, N} ⟩$ composed of $N$ particles, versus $N$ . $⟨ v_{y, 1} ⟩$ denotes the average velocity of one particle under the same conditions.Reuse & Permissions

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