Reconfigurable microbots folded from simple colloidal chains

Abstract

To overcome the reversible nature of low-Reynolds-number flow, a variety of biomimetic microrobotic propulsion schemes and devices capable of rapid transport have been developed. However, these approaches have been typically optimized for a specific function or environment and do not have the flexibility that many real organisms exhibit to thrive in complex microenvironments. Here, inspired by adaptable microbes and using a combination of experiment and simulation, we demonstrate that one-dimensional colloidal chains can fold into geometrically complex morphologies, including helices, plectonemes, lassos, and coils, and translate via multiple mechanisms that can be varied with applied magnetic field. With chains of multiblock asymmetry, the propulsion mode can be switched from bulk to surface-enabled, mimicking the swimming of microorganisms such as flagella-rotating bacteria and tail-whipping sperm and the surface-enabled motion of arching and stretching inchworms and sidewinding snakes. We also demonstrate that reconfigurability enables navigation through three-dimensional and narrow channels simulating capillary blood vessels. Our results show that flexible microdevices based on simple chains can transform both shape and motility under varying magnetic fields, a capability we expect will be particularly beneficial in complex in vivo microenvironments.

Keywords: chain; colloids; directed assembly; magnetic field; microbot.

Fig. 1.

Folding of magnetic chains under precessing magnetic fields. (A) Snapshots showing the dynamics of chain folding in experiments (Left) and simulations (Right). (Scale bar, 10 µm.) (B) The phase diagram of chain morphologies with varying field strengths in B_yz and B_x. The regime highlighted in green corresponds to the helix morphology predicted by numerical simulation. The red dashed line corresponds to the magic cone angle β = 54.7°. (C) The helical geometry (p/πD) with magnetoelastic constant M_n. C, Inset shows all relevant geometric parameters. The snapshots show the helix geometry at corresponding points. (D) The propulsion efficiency (V/ωD) of the helix as a function of its geometry for several strengths of the magnetic field (Inset) keeping the ratio B_x/B_yz fixed. The solid line comes from Eq. 5 with measured helix parameters p and D.

Fig. 2.

Sequential folding and motion of a homogeneous chain under different magnetic-field conditions in experiments (upper or left half of images) and simulations (lower or right half of images). (A) Under a DC magnetic field, the chain can adopt line, U, and S shapes, depending on initial conditions. (B) By further applying an in-plane (x–y) undulatory magnetic field, they fold into oscillating arc, “U,” and “S” shapes, respectively. (C) The 3D precessing magnetic field makes the oscillating arc-, U-, and S-shaped chains fold into helical, plectoneme, and coiled structures. The arrows indicate the net propulsion direction. The scale bar (10 µm) applies to all images.

Fig. 3.

Multimodal motion of heterogeneous chains that mimic natural swimmers and propellers. Snapshots in equal time intervals of 0.44 s are shown top to bottom, with the red dashed line denoting a fixed reference position in the x direction. (A) Rotation of a single block chain (14-mer) with a malformed point defect (red arrow, between the fifth and sixth particles) under a 3D precessing field. (B) Helical motion of a diblock chain (54-mer tail with one 2.7-µm particle head) with a long and flexible tail under the same precessing field. Configs. 10 and 11 mimic rotating bacteria flagella. (C) In-plane undulatory motion of a diblock chain (13-mer tail with a 2 × 2.7-µm particle dimer head) under an x–y undulatory field, mimicking tail-whipping sperm. (D) Inchworm motion of a triblock chain (21-mer chain with a 2.7-µm particle head and a 2.7-µm particle tail) under an x–z undulatory field, mimicking arching and stretching inchworms. (E) Sidewinding of a diblock chain (29-mer tail with a 2 × 2.7-µm particle dimer head) under a 3D undulatory magnetic field, mimicking sidewinding snakes. The scale bar (10 µm) applies to all images.

Fig. 4.

Comparison of Configs. 4 to 14 with microswimmers in the literature. The radius axis of the polar plot is the length scale, angle axis the helical angle θ in Fig. 1 C, Inset. For 2D swimmers, θ = 90°. The propulsion efficiency V/ωD is marked with different color in the colormap. For helical swimmers, D is the helix diameter. For 2D swimmers, D is twice the actuation amplitude. Config. 15 is the result from Turner et al. (2000) (41), Config. 16 is from Gray and Hancock (1955) (37), Config. 17 is from Dreyfus et al. (2005) (6), Config. 18 is from Zhang et al. (2009) (8), Config. 19 is from Ghosh et al. (2009) (7), Config. 20 is from Tottori et al. (2012) (9), Config. 21 is from Jang et al. (2015) (12), and Config. 22 is from Yang et al. (2017) (34).

Fig. 5.

Navigation of microchains into complicated environments including narrow channels and 3D curved channels. (A) Typical dynamics of a defected linear chain (length ∼21 µm) passing through a narrow channel (width 9 µm) under an in-plane undulatory magnetic field $B_x\widehat{\mathit{x}}+B_y\sin \left({\omega }_{M}t\right)\widehat{\mathit{y}}$. The propulsion direction was controlled by the ratio of B_x and B_y. The red arrows indicate the point defect. (B) The dependence of chain-propulsion efficiency on the sperm number $S_p={\left(\frac{2\pi f_M{\zeta }_{\perp }{L}^4}{k_{bend}}\right)}^{\frac{1}{4}}$, in channels with different widths. The chain-beating amplitudes were measured in bulk. (C) Directed propulsion of a helical chain in bulk fluid by tuning the cone orientation α, including swimming against gravity (blue/green dots). We plot the 3D position of the center of mass of the chain as a function of time (indicated by the color scale). (D) Multimodal chain propulsion within a 3D curved channel (1.78 × 0.80 × 0.55 mm; 3D reconstruction from confocal microscopy images and labeled by green fluorescent dyes) under tilted precessing magnetic fields. The red dots indicate chain positions every 2 min. The segments connecting the red dots indicate sections of the trajectory where the chain is a helix (white) or a lasso (red), as controlled via the magnetic field.