Highly Efficient Freestyle Magnetic Nanoswimmer - Nano Letters (ACS

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Highly efficient freestyle magnetic nanoswimmer Tianlong Li, Jinxing Li, Konstantin Morozov, Zhiguang Wu, Tailin Xu, Isaac Rozen, Alexander M Leshansky, Longqiu Li, and Joseph Wang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02383 • Publication Date (Web): 05 Jul 2017 Downloaded from http://pubs.acs.org on July 5, 2017

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Highly efficient freestyle magnetic nanoswimmer Tianlong Li,1,2,† Jinxing Li,1,† Konstantin I. Morozov,3 Zhiguang Wu,1, 2 Tailin Xu,1 Isaac Rozen,1 Alexander M. Leshansky,3,* Longqiu Li,2,* and Joseph Wang,1,* 1 Department of Nanoengineering, University of California, San Diego, La Jolla, California 92093, USA. 2 State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China 3 Department of Chemical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel †

T. L .and J. L. contributed equally to this work.

*Correspondence to: [email protected], [email protected], [email protected].

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Abstract The unique swimming strategies of natural microorganisms have inspired recent development of magnetic micro/nanorobots powered by artificial helical or flexible flagella. However, as artificial nanoswimmers with unique geometries are being developed, it is critical to explore new potential modes for kinetic optimization. For example, the freestyle stroke is the most efficient of the competitive swimming strokes for humans. Here we report a new type of magnetic nanorobot, a symmetric multi-linked two-arm nanoswimmer, capable of efficient “freestyle” swimming at low Reynolds numbers. Excellent agreement between the experimental observations and theoretical predictions indicates that the powerful “freestyle” propulsion of the two-arm nanorobot is attributed to synchronized oscillatory deformations of the nanorobot under the combined action of magnetic field and viscous forces. It is demonstrated, for the first time, that the non-planar propulsion gait due to the cooperative “freestyle” stroke of the two magnetic arms can be powered by a plane oscillatory magnetic field. These two-arm nanorobots are capable of a powerful propulsion up to 12 body lengths per second, along with on-demand speed regulation and remote navigation. Furthermore, the non-planar propulsion gait powered by the consecutive swinging of the achiral magnetic arms is more efficient than that of common chiral nanohelical swimmers. This new swimming mechanism and its attractive performance opens new possibilities in designing remotely actuated nanorobots for biomedical operation at the nanoscale.

Keywords: Nanorobot, magnetic actuation, synchronized oscillation, non-planar propulsion, kinetic optimization

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Robotics deals with automated machines that can propel themselves and perform different tasks in various environments across different scales.1-11 Recent strides in micro- and nanofabrication technology have enabled researchers to design and develop highly capable micro- and nanoscale robotic systems for a growing number of medical applications.12, 13 These versatile robots, on the order of micrometers or lower, are highly promising for traversing biological tissue and are capable of localized diagnostics and treatment with remarkable specificity and efficacy.14-18 It is therefore of particular importance to develop micro- and nanoswimmers capable of rapidly propelling and accurately reaching the desired location. However, in these low Reynolds number environments, conventional propulsion strategies break down due to prominent viscous forces, which require new specialized swimming techniques. Unicellular living organisms have a particularly distinctive way to achieve efficient motion in such environments. Natural microorganisms generally utilize either a set of flexible flagella or rigid flagella to propagate planar or helical travelling waves, respectively. These natural swimming strategies have inspired the development of micro/nanorobots powered by artificial helical or flexible flagella.1, 19-23 Considerable attention has been directed towards engineering microswimmers that utilize these flagella hydrodynamics for their propulsion.14, 24-34

However, efficient propulsion gaits at the nanoscale are still quite limited. In his famous

article “Life at low Reynolds number”, E. M. Purcell outlined a new three-link swimmer, comprised of three slender rods connected with two joints, which is essentially a simple discrete flagellum.35 In recent studies, Nelson’s group and Wang’s group have demonstrated the undulatory locomotion of similarly-fashioned multilink magnetic nanoswimmers.36,37 The development of new efficient nanoswimmers requires critical evaluation of all potential modes of actuation38 For example, humans have fixed shapes but are capable of a wide range of swimming motions, such as freestyle, breaststroke, or butterfly. Of these forms, freestyle has been found to offer the fastest motion possible through kinematic optimization. Similar analysis directed towards micro- and nanoswimmers would allow researchers to focus their efforts on the most viable propulsion mechanisms. Here we introduce a novel propulsion strategy based on a powerful “freestyle” 3


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swimming motion in response to an oscillating magnetic field. The new multi-link two-arm artificial nanoswimmer consists of a central gold body segment and two nickel arm segments connected by flexible porous silver hinges. Remarkably, in response to a planar oscillating magnetic field, the two-arm nanorobot exhibits an efficient non-planar “freestyle” stroke, where the two arms swing cooperatively to push the middle link forward. The excellent agreement obtained between the experimental observations and the theoretical predictions confirms that this powerful “freestyle” gait is a result of the synchronized oscillatory deformation of the nanorobot under the combined action of magnetic field and viscous forces. Such “freestyle” swimming powered by an oscillating planar magnetic field is significantly more efficient than propulsion of existing helical (rigid or flexible) nanoswimmers driven by a rotating magnetic field. The powerful propulsion of the two-arm nanoswimmer demonstrates that kinematic optimization of nanoscale locomotion could be achieved by the new propulsion mode, while the propulsion driven by consecutive swinging of achiral bowed magnetic arms can be as efficient as chiral-driven propulsion in accordance with earlier theoretical predictions.39 This novel fuel-free “freestyle” nanoswimmer is thus expected to advance rapidly towards practical biomedical applications. Figure 1a illustrates the design of the two-arm nanoswimmer as well as the approach used for achieving freestyle strokes under an external oscillating magnetic field. The nanoswimmers consist of two magnetic metallic nanowire arms, and a gold metallic body, which are connected by flexible Ag hinges essential for generating periodic body deformations under an external oscillating magnetic field. As shown in the fabrication process of Figure 1b, the multilinked two-arm nanorobot are readily prepared with a template electrodeposition approach. The preparation involves sequential electrochemical deposition of the Ni, Ag, Au, Ag, and Ni segments into the 200-nm-diameter nanopores of a thin membrane of porous anodic alumina membrane. Dissolution of the alumina template releases the multi-segment nanowires, and the subsequent partial dissolution of the silver segment in hydrogen peroxide creates the porous Ag hinges. The resulting Ag hinges are essential for bending the nanoarms to generate non-reciprocal strokes. This fabrication strategy enables the construction of flexible structures with tailored length and desired components. The hinge 4


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length can be tuned to adjust the flexibility of the chain. The scanning electron microscopy (SEM) image of Figure 1c displays a two-arm nanoswimmer structure, consisting of two magnetic Ni arms with a length of ~1.3 µm, one ~1.3 µm long Au body, and two flexible Ag joints with a length of ~0.6 µm. The Ni, Au, and Ag compositions of the nanorobot are further confirmed by the corresponding energy-dispersive X-ray spectroscopy (EDX) mapping (Figure 1c).

Figure 1. Design and fabrication of two-arm magnetic nanoswimmers. (a) Schematic of two-arm nanoswimmers. Applying an oscillating the magnetic field on z direction leads to freestyle swimming of the nanorobot, with two nanoarms wobbling alternatively to generate actuation in the xy-plane. (b) Scheme showing the fabrication process of two-arm nanoswimmers: (I) electrochemical deposition of the Ni-Ag-Au-Ag-Ni segments in AAO membrane, (II) dissolution the membrane and release the of the nanorods, (III) etching the silver segment as deformable joints using hydrogen peroxide to obtain the two-arm nanoswimmer; (c) SEM image of a two-arm nanoswimmer and the corresponding energy-dispersive X-ray spectroscopy (EDX) mapping of elements Au, Ag, and Ni in the two-arm nanoswimmer. Scale bar, 500 nm.

The nanoswimmers are actuated through the application of an oscillating magnetic field (Figure 2a), which was generated using two sets of opposing electromagnetic coil pairs situated with a 180 deg phase shift. The dynamic body deformation of the nanorobot over 0.15 s is displayed in Figure 2b. Figure 2c shows the resulting continuous motion of a 5


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two-arm nanoswimmer via an external field with a frequency of 17 Hz over a 3 s period (taken from corresponding to SI Video 1). The speed of the nanorobot is 38.7 µm/s (~8 body length/s) at the frequency of 17Hz. Notably, the swimmer’s magnetic Ni arms continuously aligns with the orientation of the input field due to the exerted torque, while the whole swimmer body exhibits a forward motion. The oscillating magnetic field creates a wobbling of both magnetic arms. The nanoporous Ag’s elasticity allows the arm to flex during each stroke, thereby breaking the time-reversibility of the motion. To investigate the mechanism of freestyle nanoswimmer, we assume that the short flexible links made of porous silver can be modeled as elastic joints. The middle Au link of length l and the two Ni arms of length L are assumed to be rigid rods. Magnetization of the Ni arms is acquired in process of the nanoswimmer actuation in the external magnetic field H and their magnetic moments assumed to be equal to m1 and m2, respectively. The field oscillates along z-axis leading to oscillatory deformation of nanoswimmer in the xz-plane as shown in Figure 1a. Since the magnetic moments m1 and m2 of both arms tend to align with the magnetic field H parallel to z-axes, they oscillate in an anti-phase manner resulting in S-like shape of the nanoswimmer in the xz-plane owing to finite elasticity of the joints (Figure 2d).

Figure 2. Freestyle propulsion of two-arm nanoswimmer with an oscillating magnetic field. (a) Schematic showing the magnetic setup for propulsion along with the vibrating magnetic field. (b)Time lapse images (from SI Video 1) depicting the efficient propulsion of a freestyle nanoswimmer (magnetic frequency: 17 Hz). Scale bar, 2 µm. (c) Tracking lines (from video 1) 6


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illustrating the travel distances of the freestyle nanoswimmer over 1s, 2s and 3s. Scale bar, 2 µm. (d) Dynamics of two-arm nanoswimmer and its shapes in different planes.

Now we address the deformation in the xy-plane. As it can be seen in experiments, there is also a permanent bending of the nanoswimmer arms in the xy-plane perpendicular to the oscillating magnetic field in the direction opposite to the direction of propulsion. We choose y-axes as a direction of nanoswimmer propulsion and assume that both arms of the nanoswimmer are bent with the same (on average) angle with respect to the middle link as shown in Figure 2d. The original cause of this bending is probably the weak magnetic field gradient directed towards the center line of the electromagnetic coils. Such gradient results in the volumetric force = ∇ , where is the magnetic susceptibility,40 and the corresponding weak magnetic torques bending the arms towards the center line of the coils. This weak bending is further enhanced owing to viscous forces exerted on the arms once the nanoswimmer is set into motion in the y-direction. Thus, in the xy-plane the nanoswimmer adopts a Π-like shape (Figure 2d). It is important to notice that with each stroke of the magnetic arms with the external magnetic field, the middle link does not stay aligned with x-axis, but undergoes oscillations with respect to x-axis (SI Video 1). These oscillations might be attributed to alternating arm strokes in the vicinity of the surface. The estimated distance of the inactive nanowire from the bottom of the cell is = ⁄ ~ 200-300 nm

(sedimentation height); however, once the actuating field is turned on, the nanowire starts to hover above the surface at distance ~ 1.5-2 µm due to the stretch of the arm and the flexible link. With the field switching, each arm experiences slightly different viscous forces (arm swinging against the surface experiences higher viscous friction) and rotates with a somewhat different angular velocity. Propulsion in the vicinity of the surface breaks the symmetry of the nanoswimmer movement in the xy-plane, leading to the in-sync (with the field frequency) oscillations. As a result, the motion of each arm resembles in-sync wobbling driven by a rotating magnetic field. At low frequency of the actuating field they tumble in the plane of the field rotation in-sync with the field; at some actuation frequency ωt-w, the tumbling switches to in-sync wobbling, whereas the precession angle (i.e. the angle between the field rotation axis and the 7


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propeller’s easy-rotation axis) diminishes as driving frequency increases. At the so-called step-out frequency ωs-o the magnetic torque exerted on the propeller can no longer counter-balance the increased viscous torque and the synchronous regime switches to the asynchronous one. Typically, in-sync wobbling regime is accompanied by a considerable propulsive motion. Rotational dynamics of slender magnetic propellers steered by a rotating magnetic field is well understood:38 at low frequency of the actuating field they tumble in the plane of the field rotation in-sync with the field; at some actuation frequency ωt-w, the tumbling switches to in-sync wobbling, whereas the precession angle (i.e. the angle between the field rotation axis and the propeller’s easy-rotation axis) diminishes as driving frequency increases. At the so-called step-out frequency ωs-o the magnetic torque exerted on the propeller can no longer counter-balance the increased viscous torque and the synchronous regime switches to the asynchronous one. Typically, in-sync wobbling regime is accompanied by a considerable propulsive motion. The Ni-Ag-Au structure bends under the action of magnetic torque and viscous stresses and adopts the arc-like shape. Magnetized rigid arc-shaped objects have been recognized as rather efficient propellers, exhibiting propulsion speeds comparable to these of magnetic helix. The propulsion velocity of such arc-shaped object in the in-sync wobbling regime reads:39

=

&1 −

$ % $ !"#

$

$

) .

(1)

is the so-called pseudochirality Here l is the characteristic length of the filament, Ch

< 0.1). In the asynchronous regime beyond the step-out, > %1 , coefficient (typically Ch the average propulsion velocity in Eq.1 is reduced by a frequency-dependent multiplicative factor:38

2 = 31 − !1 −

$ "#

$

4.

(2)

Notice that a single Ni arm connected to the Au middle link via the flexible Ag filament closely resembles the arc shape, (Figure 2b). The major difference between the arc studied and the arc-shaped Ni–Ag–Au structure is the flexibility of the latter.39 It means that the 8


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, ωt-w and ωs-o, are not fixed, but depend on the actuating parameters of the problem, i.e., Ch frequency. For elongated body, the tumbling-to-wobbling transition takes place at small enough frequency ωt-w.41 At such frequencies the Ni-Ag-Au structure can be considered as a straight filament. The explicit relation for the tumbling-to-wobbling transition frequency reads

5%6 =

∥ 8 9:

(3)

where ∥ is the longitudinal magnetic moment of the body and ;< is the transverse viscous rotational friction coefficient. Our estimate of tumbling-to-wobbling transition frequency gives ωt-w = 87 s−1 or νt-w = ωt-w/(2π) ≈14 Hz (see SI for details). In the experiments propulsion in three different liquids have been examined – sea water, cell culture medium solution, and serum solution – with viscosities 0.9, 1.1 and 1.6 cP, respectively. For the tumbling-to-wobbling frequency of three samples we use the values 10, 8.2 and 5.5 Hz, correspondingly. The transition frequency of 10 Hz is the fitted, while the two other values are derived using the viscosity ratios. The explicit relation for the step-out frequency is given by:41

%1 =

: 8 9∥

(4)

where ;∥ is the viscous rotational resistance along the easy-axis of rotation and < is the transverse magnetic moment of the object. The step-out frequency ωs-o is the maximal frequency in the synchronous regime. For a flexible magnetic object its value cannot be estimate in simple manner as ωt-w since at elevated frequencies the filament deforms continuously so that < and ;∥ themselves are not fixed, but vary with actuation frequency. When matching the experimental results to the theory, we use the value of 25 Hz for νs-o = ωs-o/(2π) for all suspending media.

, can be determined unambiguously only for rigid The coefficient of pseudo-chirality, Ch

is due to the arc-like form of the filament. There are two main reasons objects. Generally, Ch for this form. First, the filament is slightly curved just after Ag dissolution (Figure 1c).

Second, it is deformed owing to interaction of magnetized arms with external magnetic field. For a flexible nanoswimmer one can argue, that the viscous stresses should diminish the 9


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, is filament deformations approaching a straight cylinder-like shape. We assume that Ch proportional to characteristic deformations. Since the later are determined by the balance of the elastic, magnetic and viscous stresses, one can expect that the deformations are inversely

∼ 1/@. Using Eqs. (3), (4) we find the following proportional to the viscous stresses, so Ch dependencies of the nanoswimmer velocity in synchronous and asynchronous regimes:

= A

B

$ %B $ !B"#

&1 −

2 = 31 − !1 −

$ B

)

(5)

$ B"#

4

(6)

B$

B$

Here C is the fitting constant independent on the liquid properties. Eqs. (5) and (6) describe the velocity of the Ni-Ag-Au structure towards the magnetic Ni-arm (see Figure 2d). The propulsion velocity of the nanoswimmer (in both the in-sync and a-sync regimes) composed of two conjugated Ni-Ag-Au structures follows from Eqs. (5) and (6) by multiplying by sine of the bending angle . Therefore, to find the velocity of the freestyle nanoswimmer one should determine the bending angle .

On the average the nanoswimmer propels in the xy-plane perpendicular to the oscillating magnetic field. Let C = 0, E, 0 be the net propulsion velocity. This motion results in drag

force exerted on each arm. According to the resistive force theory the normal component F
0 emerges. In sea water with η = 0.89 cP we estimate umin = 10


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10 µm s−1 (see SI for details). Similarly, for medium and serum we obtain umin = 8.2 and 5.5 µm s−1, respectively. Figure 3a, taken from SI Video 2, displays the moving trajectories of a freestyle nanoswimmer with magnetic field frequencies turning from 5 to 45 Hz, over a period of 1 s. The experimental speeds of the freestyle nanorobots in each experimental medium initially increase upon raising the input frequency of the oscillating magnetic field (Figure 3b). At the frequency of 5 Hz in water, the speed is 10.8 µm s−1, which is still significantly higher than Brownian diffusion. The freestyle nanorobot attains its fastest speed of 59.6 µm s−1 in water using a frequency of 25 Hz, with slower speeds observed at higher frequencies. At frequencies higher than the step-out frequency, the maximum available magnetic torque is insufficient to overcome the fluidic drag, leading to deceleration as the freestyle nanorobot moves out-of-sync with the applied magnetic field. The resulting system of Eqs. (7) and (5) is solved numerically with the indicated values of the parameters νt-w, νs-o and umin and the fitting constant C = 16.4 µm. The numerical speeds of the freestyle nanorobot under different magnetic field frequencies, shown also in Figure 3b, match well with the experimental results under the step-out frequency for each medium. Therefore, tuning the magnetic field enables rapid acceleration and deceleration of the freestyle nanoswimmer with precise speed control.

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Figure 3. Swimming performance of freestyle nanoswimmer under different magnetic frequencies. (a) Tracking lines (from SI video 2) illustrating the travel distances of freestyle nanoswimmer over a 1s period in the presence of an oscillating magnetic field with a frequency of 5 Hz(I), 15 Hz(II), 25 Hz(III), 35 Hz(IV) and 45 Hz(V). Scale bar, 5 µm. (b) Experimental and calculated freestyle nanoswimmer speeds upon varying the magnetic frequency from 5 to 45 Hz in sea water (blue), medium (red) and serum (pink) solutions.

Figure 4a, along with corresponding SI Video 3, displays the speed of a nanorobot in response to a square wave input over a 4 s period. At the frequency of 15 Hz, the nanoswimmer moves with a speed of 30.6 µm/s. An even more efficient propulsion, with a speed of ~60 µm/s, is observed at the frequency of 25 Hz. Figure 4b tracks the time-dependence of the nanorobot speed upon switching the frequency repeatedly between 15 and 25 Hz. This time-lapse image demonstrates that the freestyle nanoswimmer displays an instantaneous switching between different frequencies, with steady-state speeds reaching rapidly upon switching the frequency. The effect of driving signal of the oscillating magnetic 12


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field on the speed of freestyle nanoswimmer has also been investigated experimentally. As shown in Figure 4c, the different driving signals (square wave, triangle wave and sine wave) have minimal effect on the motion of freestyle nanoswimmer. To evaluate the critical role of the geometric parameters, such as arm length, on the propulsive efficiency, freestyle nanoswimmers with different arm lengths were fabricated and tested in different solutions. The speeds of freestyle nanoswimmers with longer (1.3 µm) arm are 34.8 µm/s, 19.8 µm/s and 12.6 µm/s in sea water, medium and serum solution, respectively. These speeds are larger than the speeds of freestyle nanoswimmers with shorter (0.8 µm) arm. These data indicate that freestyle nanoswimmers with longer arms are capable of more efficient propulsion at the low Reynolds number. The longer arms possess a higher magnetic moment while the longitudinal rotational resistance increases only marginally, so that the step-out frequency shifts towards higher frequency. Thus the propulsion velocity of the nanoswimmer with longer arms at the step-out is higher than that of the shorter-armed counterpart.

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Figure 4. On-demand speed modulation and control of the freestyle nanoswimmers: (a) Velocity modulation of the freestyle nanoswimmers in response to a 1 s 15 Hz-25 Hz-15 Hz-25 Hz step. (b) Time-lapse images (from SI video 3) showing the velocity modulation of the freestyle nanoswimmers. Scale bar 5 µm. (c) Quantitative velocity of the freestyle nanoswimmers at different frequencies using oscillating magnetic field generated by square wave, triangle wave and sine wave. (d) Quantitative velocity of the freestyle nanoswimmers with different length arms (long arms, Ni: 1.3 µm, short arms, Ni: 0.8 µm) in different media at the frequency of 15 Hz. (e) Scheme of the magnetic control of freestyle nanoswimmers. (f) Time-lapse images showing the magnetically guided propulsion of freestyle nanoswimmer in the frequency of 15 Hz over 20 s. Scale bar 5 µm.

Figure 4e-f presents the magnetic control of the directionality of the freestyle nanoswimmer. We observed that by changing the relative position between the electromagnet and the nanorobot in the xy-plane, the directionality of the nanoswimmer could be tuned. As indicated in Figure 4e, the nanorobot always tends to move away from the line of centers of the electromagnets in the x-y plane. This is due to weak gradient of the actuating field in the 14


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xy-plane resulting in arm bending towards the line of centers of the coils as explained above. Given that swinging of the bowed arms yields propulsion in the direction opposite to their bending, the nanoswimmer is always moving away from the line of center of the electromagnets. Thus, by relocating the electromagnets to change their center projection point in the xy-plane, the propulsion direction of the magnetic nanorobot could be altered. Figure 4f displays such real-time steering the freestyle nanorobot by relocating the electromagnets. Future efforts could lead to a more advanced control using multiple electromagnet pairs in the 3D space. Magnetic propulsion is highly promising for powering biomedical micro/nanorobots due to its noninvasive remote actuation and convenient navigation abilities. Recent advances in micro/nanofabrication has led to the successful engineering of bio-inspired helical propellers and flexible-body propellers which replicate bacterial hydrodynamics. Here, we have presented a two-arm nanorobot that achieves a high-speed “freestyle” swimming motion, a new microscale propulsion mode which has not been observed in nature. This nanoswimmer, composed of Ni nanorods linked by an Au nanowire body with flexible Ag joints, exhibits synchronized non-planar “freestyle” propulsion under a planar oscillating magnetic field. Our analytical modeling verifies that the observed propulsion is due to the synchronized oscillation of the nanorobot under the influence of the alternating magnetic field. In previous studies, the planar oscillating magnetic field could yield planar (wave-like) deformations of a flexible filament.34,35 In this work, for the first time, the oscillating magnetic field mimics the action of a rotating field, demonstrating that a planar oscillatory field is able to power non-planar propulsion stroke resembling freestyle swimming. The speed and the direction of the nanorobot can be remotely modulated by adjusting the magnetic field, with a maximum speed of 59.6 µm s−1, corresponding to a relative speed of ~12 body lengths/second. Such efficient swimming indicates that propulsion driven by the cooperative out-of-phase wobbling of the pseudo-chiral bowed arms can be more efficient than the rotation-driven propulsion of chiral nano-/microhelices. This efficient propulsion mechanism of the two-arm nanorobot holds considerable promise for a wide range of practical applications, from nanoscale manipulation and assembly to nanomedicine. We also envision that the presented innovative 15


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nanorobotic design, which has not been observed in natural microorganisms, would inspire even more powerful locomotion strategies at the nanoscale.

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Supporting Information Experimental methods, microscopy videos, the modeling about freestyle nanoswimmers. The Supporting Information is available free of charge on the ACS Publications website.

Corresponding Author *E-mail: [email protected], [email protected], [email protected].

Author Contributions J.L. and T.L. contributed equally.

Notes The authors declare no competing financial interest.

Acknowledgment: This project received support from the Defense Threat Reduction Agency-Joint Science and Technology Office for Chemical and Biological Defense (Grant no. HDTRA1-14-1-0064) National Natural Science Foundation of China (51521003 and 51175129), Key Laboratory of Micro-systems and Micro-structures Manufacturing of Ministry of Education (2016KM004). This work was supported in part by the Israel Ministry for Immigrant Absorption (K.I.M.).

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Highly Efficient Freestyle Magnetic Nanoswimmer - Nano Letters (ACS

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