Arti cial Flexible Sperm-like Nanorobot Based on Self-assembly and Its Magnetically Actuated Propulsion Property


 Sperm cells can move at a high speed in biofluids based on the flexible flagella, which inspire novel flagellar micro-/nanorobots to be designed. However, mass fabrication of vivid sperm-like nanorobots with flagellar flexibility is still challenging. In this work, a facile and efficient strategy is proposed to produce flexible sperm-like nanorobots with self-assembled head-to-tail structure. The nanorobots were composed of a superparamagnetic head and a flexible Au/PPy flagellum, which were covalently linked via biotin-streptavidin bonding. Under a precessing magnetic field, the head drove the flexible tail to rotate and generated undulatory bending waves propagating along the body. Bidirectional locomotion of the nanorobot was investigated, and moving velocity as well as direction varied with the actuating conditions (field strength, frequency, direction) and the nanorobot’s structure (tail length). Effective flagellar locomotion was observed near the substrate and high velocities were attained in both forward and backward directions. Typical modelling based on elastohydrodynamics and undulatory wave propagation were utilized for propulsion analysis. This research presents novel artificial flexible sperm-like nanorobots with delicate self-assembled head-to-tail structures and remarkable bidirectional locomotion performances, indicating significant potentials for nanorobotic design and future biomedical application.


Introduction
Micro-/nanorobots with excellent swimming capability in uids have become highly attractive due to their great potentials in biomedical applications [1][2][3][4][5] . These untethered robots can generate effective propulsion in uidic environment and access desired sites at small scale to achieve special tasks. To date, various types of micro-/nanorobots have been developed via taking biological inspiration from motile microorganisms 6-8 . For example, inspired by corkscrew propulsion of E. coli bacteria, several researches have presented helical micro-/nanorobots actuated by rotating magnetic elds [9][10][11][12][13] . In fact, undulating propulsion is an easy-to-think motion method which is commonly utilized in nature from shes to monotrichate eukaryotes [14][15][16][17] . In this case, sperm cell is typical with agellar self-propulsive capability, which can move forward in low Reynolds number bio uids through the agellum-generated transverse waves 18 , and also provides us with possibilities to realize effective agellar propulsion at micro-/nanoscale.
To date, many researches are focused on designing and fabricating sperm-based micro-/nanorobots. Among these researches, some are focused on direct utilization of living motile sperm's driving force, which can be integrated with magnetic guidance to form biohybrid microswimmers [19][20][21] . However, environmental sensitivity and inconsistent activity of the sperm cells greatly limit the practical applications. The other is to use the sperm's overall shape and morphology as biotemplates to synthesize microrobots with magnetized elastic agellar structures 22,23 , yet the fabrication is uncontrollable which hinders homogeneity in size as well as propulsion capability.
Enlightened by periodic undulations of the sperms, arti cial sperm-shaped micro-/nanorobots have also attracted much attention, aimed to achieve biomimetics in structure and function. Among these Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js researches, some are focused on integrated synthesis based on micro lithography or electrospinning technique, to construct a composite structure containing a magnetic head with a exible polymer tail [24][25][26][27] . However, the relatively large size and complex fabrication process greatly limit biomedical uses of such millimeter-sized microrobots. Thereon, sperm-shaped self-assembled nanorobots with modular designs stand out, which integrate a tiny head with a slender tail for agellar construction, and can be treated as an optimal way for essential imitation of the sperms. For example, a Fe 3 O 4 microsphere could be connected with rigid Ni nanorod for sperm-shaped con guration, yet the desired exibility was lacked; or be linked with repolymerized bacterial agellum to achieve agellar propulsion, yet great diversity existed compared with the sperm's shape 28-32 . Despite these tremendous efforts, to the best of our knowledge, no research has realized exible sperm-like nanorobots with assembled head-to-tail structures. Thus it is imperative to develop facile and reliable fabrication methods to construct arti cial sperm-like nanorobots, and study the corresponding agellar propulsion at low Reynolds numbers.
Here, we propose arti cial exible sperm-like nanorobot synthesized via a facile self-assembly strategy using Fe 3 O 4 nanobeads and exible polymer agella for the rst time, which can generate bidirectional agellar propulsion under precessing magnetic elds. Template-assisted electrochemical deposition was used to synthesize Au/PPy nanowires, and the streptavidin modi ed tails could be bonded with biotinylated magnetic nanobeads to form the sperm-like nanorobots. The self-assembled nanorobot was actuated in viscous glycerin and exhibited effective locomotion in forward or backward directions. A series of actuation experiments were conducted to characterize agellar propulsion of the nanorobots, and bidirectional locomotion velocity under precessing magnetic elds of diverse parameters (strength, frequency, precession angle and direction) were studied in detail. Under a magnetic eld of 70 Gs, 40 Hz and precession angle at 30°, the nanorobot could be actuated forward to reach a high velocity at 4.86 µm/s, and backward velocity at 3.17 µm/s could also be achieved when turning the precession axis around. Such vivid sperm-like nanorobot with exible propulsion performance under magnetic actuation provides possibilities for agellar nanorobot design and fabrication, and also indicates signi cant potentials for applications at low Reynolds numbers. placed in a self-made electrodeposition container, and Ag/AgCl reference electrode as well as Pt wire electrode was used for subsequent deposition. The Au-coated membrane was immersed in the prepared gold plating solution (containing 30 g/L H 3 BO 3 and 34 g/L HAuCl 4 ·4H 2 O), and the Au section was deposited at a DC voltage of -0.2 V. Next, deposition of PPy nanorods was conducted using prepared PPy plating solution (containing 19.25 g/L citric acid and 6.95 mL/L pyrrol) at + 0.8 V. PPy agella of various lengths could be synthesized via adjusting the deposition time. After that, mechanical polishing was conducted with 3-4 µm alumina powder to remove the sputtered sacri cial gold layer.

Methods
Modi cation process of the nanowires. Firstly, the Au ends of the nanowires (retained in the AAO templates) were exposed to a DMSO solution containing DTSP (4 mM), and immersed for 6 hours at 25°C to modify a self-assembled monolayer of DTSP on the end of gold segment. Then, streptavidin solution (0.5 mg/mL) was added to immerse the polished surface at room temperature for 6 hours, to covalently bond streptavidin to the DTSP modi ed Au ends. After streptavidin functionalization, template removing and nanowire releasing was achieved using NaOH (0.1 M) solution for 3 hours. Finally, the nanowires were washed with PBS solution (pH = 7.4) and centrifuged (10000 rpm, 5 min) for three times, and nally stored in PBS solution (4°C) for further uses.
Fabrication and characterization of the sperm-like nanorobots. The as-prepared Au/PPy nanowires and biotin modi ed Fe 3 O 4 nanoparticles were mixed in solution at a ratio of 1:1, and gently shaken at room temperature for 30 minutes. Due to the solid bonding between biotin and streptavidin, arti cial sperm-like nanorobots were formed via self-assembly and nanorobots with one single agellum could be mostly investigated in the experiments. The morphology and main elements of the as-prepared agella and nanorobots were characterized by a eld emission scanning electron microscope (SU-8010LA, Hitachi) equipped with an energy dispersive spectrometer.
Magnetic actuation experiments of the sperm-like nanorobots. A custom-made triaxial Helmholtz coil system was used to actuate the nanorobotic sperms, and the details were demonstrated in our previous published papers 10,35 . To actuate the sperm-like nanorobot and test its propulsion performance, a precessing magnetic eld was generated via the coils, in which the resultant eld vector at the head of the nanorobot was rotating in a cone-like path. The eld strength, frequency and spatial directions could be precisely tuned via a programmed current controller coupled with the coils. Locomotion of the nanorobots could be recorded in real time through a CMOS camera installed on the microscope. In our experiments, the as-prepared nanorobotic sperms were dispersed in 60% glycerin solution and transferred into a PDMS chamber at the coil center for magnetic actuation tests. In the viscous medium, the nanorobots could be considered as oating and adverse effect of the substrate surface was eliminated. For velocity measurement and locomotion direction tests, three times of experiments were conducted, and average velocity as well as standard deviations were calculated based on the experimental data.

Results And Discussion
Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js Preparation and characterization of the sperm-like nanorobot. The fabrication process of sperm-like nanorobots was brie y shown in Fig. 1a. Firstly, we prepared exible Au/PPy composite nanowires with the Au ends modi ed using streptavidin, which could act as arti cial agella of the nanorobots to generate undulatory wave propagation. Here, multi-step electrochemical deposition and monolayer modi cation were combined for fabrication. Au segments of 3 µm and PPy tails of given lengths were deposited in sequence. After mechanical polishing of the sacri cial gold layer, the Au tips of the nanowires were exposed and coated with monolayer of DTSP molecules, which could increase the contact area and improve the assembly e ciency for the following process. Then wet-etching of the Al 2 O 3 templates was conducted and the nanowires were released to be modi ed with streptavidin. After that, the nanowires were mixed with biotin-coated Fe 3 O 4 nanoparticles for bonding and formed the nal sperm-like nanorobots. In this case, the Fe 3 O 4 head endows the nanorobot with magnetic response and the exible agellum ensures undulatory propagation for effective propulsion.
Morphology and elemental analysis of the arti cial agella were conducted, and the SEM and EDS results were shown in Fig. 1b and 1c. Distinct two-stage structure can be observed on the nanowire, which corresponds to the Au tip and the PPy body, respectively. Flexibility of the arti cial agellum is presented with slightly bending in this view. Schematics of the self-assembled nanorobot's head-to-tail structure and the corresponding SEM image were shown in Fig. 1d and 1e, respectively. It can be observed that an intact self-assembled microstructure has been successfully achieved between the magnetic head and the exible agellum, to form the sperm-like nanorobot.
Theoretical analysis of the nanorobot's propulsion. The nanorobot in this study is fabricated via selfassembly using a superparamagnetic nanobead and an arti cial exible ultra-thin nanorod. Assuming the head has a magnetic moment M in the direction under the magnetic eld, the exible agellum has a body length L with a given elasticity modulus. For an arbitrary point P along the tail, we mark it with a generalized coordinate q respective to the head and describe its position at time t with vector p(q, t), which can also be transferred to the head's frame as where ϕ y (q,t) and ϕ z (q,t) represent the corresponding deformation along Y and Z axis, respectively.
Then the moving Frenet-Serret frame can be established on point P along local tangent, normal, and binormal directions: t = dp ( q , t ) / dq | | dp ( q , t ) / dq | | , n = dt / dq The head can orient itself to the time-varying magnetic eld due to the magnetic torque exerted on the dipole. Due to the head's rigid body rotation, bending waves are generated and can be propagating along Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js the exible agellum. According to the typical resistive force theory, the force and torque balance based on magnetic and uidic elds can be expressed as: Here, gravity is neglected, F m and T m are magnetic force and torque that can be expressed as: F d and T d are uidic drag force and torque, which can be decomposed into contributions of the head and the tail: where V and Ω are propulsion and rotation velocity matrices, D h and N h are resistance matrices for the head, and C represents the resistance coe cient matrix for the tail. Besides, R is the rotation matrix between the local Frenet-Serret coordinates and the nanorobot's frame, S h and S t are the corresponding position transformation matrices for the head and the tail.
The above equations describe the elastohydrodynamics of the sperm-shaped nanorobot swimming in viscous uids 27 . In the experiments, the nanorobot was actuated to swim in the horizontal plane (XY) and was investigated from the top view. Apart form the elastohydrodynamics, a simpli ed undulatory propagation modelling could also be used 33,34 . Swimming of the nanorobot in the X direction can be simpli ed into two orthogonal components in the XY and XZ planes. Motion of the nanorobot in each plane can be treated as a bending wave propagation across the two distal ends, and relative phase lag between the head and tail in two planes are noted as ϕ xy and ϕ xz . Here, agellar propulsion of the spermlike nanorobot along X direction can be ascribed to the overall oscillation along the body induced by two separate oscillations in both XY and XZ planes as: y(x, t) = a 1 sin(2πft) x L + a 2 sin(2πft + ϕ xy ) x L m (7) z(x, t) = a 3 sin(2πft) x L + a 4 sin(2πft + ϕ xz ) x L m (8) where a 1 and a 3 are amplitudes of magnetic oscillation that correspond to the head, a 2 and a 4 are amplitudes of uidic oscillation that correspond to the tail. Besides, f is the actuation frequency, and m is the curvature of bending deformation.
The propulsive forces in two planes can be expressed as where dl is an in nitesimal section along the body, C ∥ and C ⊥ are the drag coe cients in the tangential and normal directions. Besides, V x (xy) and V x (xz) are two contributions of the X-direction velocity resulted from oscillations in XY and XZ planes, respectively. When the nanorobot reaches a steady swimming state, the total force equals zero, and the velocity components can be calculated to be And the resultant velocity along X-direction can be expressed as Hence, we can deduce that a phase difference in oscillation is requisite to generate effective locomotion with a nonzero velocity. The oscillations in two perpendicular planes undergo different uidic drag conditions due to the substrate-induced asymmetry, and diverse amplitudes as well as phase lags are stimulated. The resultant motion of the nanorobot is determined by combination of the decomposed oscillations, which can result in a balance between propulsion and retarding in the form of forward or backward locomotion. In this case, dynamic magnetic eld with a precessing angle is essential for swimming direction reversal since spatial oscillations become accessible to lead to bidirectional resultant.
Propulsion performance of the sperm-like nanorobot. To actuate the sperm-like nanorobot and test its propulsion performance, a precessing magnetic eld or a so-called conical rotating magnetic eld was applied using a custom-made triaxial Helmholtz coil system. The externally actuated magnetic eld can be expressed as where The resultant eld vector at the head of the nanorobot was rotating in a cone-like path, and the angle between the eld vector and the cone axis was noted as the precessing angle (θ) of the actuation eld. For agellar propulsion of sperm-like nanorobots, undulatory motion theory has been developed as described above, which is focused on the bending wave propagating process along the body. Actuated by the magnetic torque exerted on the head, continuous rotation is triggered to drive the body to uctuate. The stimulated wave propagates along the agellum yet different oscillating amplitudes are generated from the head to the tail. Flexibility of the arti cial agellum contributes to effective undulatory propagation and a constant phase lag exists compared to the magnetic head. Here, time-dependent deformation of the exible agellum was measured over one whole period and morphing changing process of the body was also illustrated. The nanorobot was actuated to oscillate by a 2 Hz precessing eld (B = 100 Gs, θ = 30°) (Movie 1). The results indicate the whole propagating process of the generated wave during helical agellar propulsion, and a distinct oscillating angle can be observed from the superimposed image as shown in Fig. 2a. Such nanorobot could be actuated to precess synchronously with the low-frequency alternating magnetic eld. A planar coordinate system was de ned to facilitate position recording and calculation. In this view, the upward tail tip of the nanorobot corresponds to a positive value of oscillating angle yet the downward tail tip corresponds to a negative one. As shown in Fig. 2b, we measured the oscillating angle change of the nanorobot in a given time period, which exhibited a sinusoidal pattern with time and kept consistent with the precessing eld's oscillation. To investigate the relative position relations between the nanorobot's head and agellum, we further recorded the displacements of the head and the tail tip along the Y axis, with respect to the original position (Y = 0) at t = 0 s. As shown in Fig. 2c, the displacement waveforms near the distal end as well as the head were recorded. Both the head and the agellum undergo a sinusoidal waving locomotion in the direction perpendicular to the cone axis, and a xed phase diversity ) ] Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js exists between them. The head and the agellum exhibit diverse oscillation amplitudes during propulsion, in which the tail tip oscillates with a larger amplitude compared with the head. In this case, the nanosphere head dominates the magnetic response and acts as an oscillation source. It is actuated to precess around and drives the agellum to rotate in the same pattern with a phase lag under the sinusoidal alternating magnetic eld. It also proves that asymmetrical shape deformation occurs to cater the scallop theorem and achieve effective locomotion as a result. At the same time, a negative positional offset of the swimmer's body can be observed, which is related to the minor lateral drift during swimming.
Bidirectional locomotion property of the nanorobot. For magnetic actuation of the sperm-like nanorobot, four types of spatially oriented precessing magnetic elds were de ned according to the corresponding directions (Fig. 3a). When the eld vector exhibited an acute angle with the agellum-head direction, the eld was de ned as a "Head-pointing Field" (HF), and the rotating direction was further classi ed into counter-clockwise (CCW) or clockwise (CW) types on the basis of the right-hand rule. Schematics of the sperm-like nanorobot actuated by a HF type eld with a precessing angle θ was shown in Fig. 3b.
Similarly, when the eld vector was pointing in the head-agellum direction, it could be de ned as a "Flagellum-pointing Field" (FF) with a CCW or CW rotating directions. In our experiments, the nanorobotic sperms would not easily turn around for coincident magnetic alignment when the precessing axis of the high-frequency eld (f > 5 Hz) was abruptly turned in an opposite direction. This could be ascribed to the relatively low magnetic torque as well as the encountered uidic drag of the slender nanorobot near the substrate surface, which induced the insensitive magnetic response under high-frequency dynamic elds. This was also con rmed using magnetic nanowires actuated under 3 Hz and 5 Hz precessing elds for comparison (Movie 5 and 6). Both HF and FF type elds could be used to actuate the nanorobot and the exible agellum could be driven to oscillate around with the precessing magnetic head. Effective locomotion can be observed near the substrate due to periodic nonreciprocation that breaks the time symmetry, which is depended on integrated effects of elastic agellum, hydrodynamic resistance as well as uidic ows generated by the moving head. Due to continuous interactions with the viscous uids, helical agellar propulsion was generated for the nanorobot.
To study the motion directionality, diverse precessing angles and directions were adopted for experimental comparison (Movie 2). As shown in Fig. 3c, the eld strength and frequency were set to be constant at 100 Gs, 40 Hz, yet the spatial directions were different. In Fig. 3c-1, when a eld of HF-CCW at θ = 10° was applied, backward locomotion in the agellum-pointing direction could be observed, which corresponded to a negative velocity (V < 0). However, when the eld was set to be precessing in the CW direction, the nanorobot changed to swim forward on the contrary. In this case, the nanorobot was capable to move in an opposite direction without a U-turn trajectory, which was different from other onetail magnetic microswimmers. This property could be attributed to the chirality of the sperm-like nanorobot, which was a combined effect of the nonideal self-assembled structural con guration as well as the time-dependent undulatory dynamics. Thus magnetic elds of diverse precessing directions were capable to drive the nanorobot to rotate and achieve bidirectional locomotion. In Fig. 3c-2, the magnetic eld (θ = 10°) was tuned to be a FF type, the nanorobot kept the original pointing direction without turning around. As for magnetic eld transformation, a HF-CW type eld could be tuned to FF-CW type as just Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js turning the precessing axis 180°, yet the nanorobot could be driven to oscillate and move in an opposite direction as a result. Therefore, a FF-CW and FF-CCW type of precessing magnetic eld could actuate the nanorobot to move in the same direction with the results of HF-CCW and HF-CW cases, respectively.
In addition, the in uence of the actuation eld's precession angle was also investigated as shown in Fig. <link rid=" g3">3</link>c-3. Under a HF type eld at θ = 30°, the nanorobot could be effectively actuated forward in both CCW and CW directions, which was quite different with the results demonstrated in Fig. 3c-1. It could be explained that actuation eld of a large precessing angle induced relatively violent precession with higher oscillation frequency, and the chirality was no longer valid in this case. The results con rmed that exible switching between swimming forward and backward could be achieved via tuning the actuation eld parameters, including precessing direction and angle as well as eld frequency. In the future, such bidirectional propulsion property can be applied to control multiple sperm-like nanorobots with distinguished strategies and complete cooperative tasks.
Based on the preliminary actuation study above, actuation experiments under elds of various parameters were conducted, and locomotion directions as well as resultant velocities were systematically measured. As shown in Fig. 4a-1 to 3, the eld strength was set to be constant at 50 Gs, yet the precessing angles were 10°, 30°, 60°, respectively. Four types of elds (HF-CCW, HF-CW, FF-CCW, FF-CW) at a given frequency ranging from 5 Hz to 40 Hz were applied to actuate the nanorobot. The positive velocity corresponded to swimming forward yet the negative velocity represented backward propulsion. At a lower value of precession angle (θ = 10°), the nanorobot was actuated to swim backward over the frequency range regardless of spatial directions of the elds. However, the results at higher precession angles (θ = 30° and 60°) were completely different since both forward and backward locomotion could be observed. Speci cally, the nanorobot was actuated forward under HF-CW or FF-CCW elds, yet backward under HF-CCW or FF-CW elds. A highly effective forward velocity of 2.11 µm/s and backward velocity of 2.77 µm/s could be easily obtained at θ = 30° via tuning the precession directions of the eld, indicating distinct bidirectional propulsion property which was different from previously reported sperm-shaped microswimmers.
As shown in Fig. 4b-1 to 3, under precessing magnetic elds of 70 Gs, the propulsion results were similar with the cases in 50 Gs when other parameters kept the same. The nanorobots still kept swimming backward at θ = 10°, yet locomotion differentiation occurred when θ = 30° or 60°. However, when the eld strength was large enough (100 Gs), it turned to be much easier for the nanorobots to move forward. Speci cally, both HF-CW and FF-CCW elds could successfully drive the nanorobots forward at θ = 10°, despite backward locomotion was still destined under HF-CCW or FF-CW elds. A large forward velocity of 2.96 µm/s and backward velocity of 4.26 µm/s could both be achieved at 40 Hz using the opposite precessing directions (HF-CW and FF-CW elds, respectively). As increasing precessing angle of the 100 Gs elds (θ = 30°, 60°), robust forward propulsion turned to be dominated regardless of the spatial directions of the actuation elds. In this case, a signi cantly high forward velocity could be obtained over a wide frequency range.
Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js Thereon, we measured and summarized locomotion directions of the nanorobot actuated by precession magnetic elds of diverse parameters, and the results were listed in Table 1. From the observations in our experiments, it can be deduced that locomotion direction of the sperm-like nanorobot is determined by multiple actuation parameters including eld strength, frequency, precessing angle as well as direction. In the experiments, the sperm-like nanorobots generally tended to move forward under precessing magnetic elds of HF-CW or FF-CCW types. To propel the nanorobots forward, precessing magnetic elds of an intensi ed strength as well as a large precessing angle were desired for actuation, which was also consistent with the velocity measurement results in Fig. 4. Table 1 Locomotion directions of the sperm-like nanorobot actuated by a precessing magnetic eld of given parameters over a frequency range (5-40 Hz). Here, "+" represents forward locomotion yet "-" represents backward locomotion. Similarly, four directional types of elds and precessing angles of 10°, 30°, 60° were applied successively for agellar propulsion. Bidirectional locomotion could be distinctly observed under elds of any precession angles, which was quite different compared with the long-tailed nanorobots that tended to move forward under the same actuation condition. Under the 100 Gs magnetic eld of a moderate precessing angle (θ = 30°), typical bidirectional property could be observed and relatively high locomotion velocity exceeded 2 µm/s could be achieved both in forward and backward directions. The nanorobot could be actuated to move forward under precessing magnetic elds of HF-CW or FF-CCW types, and move backward under HF-CCW or FF-CW elds, which were still similar with the experimental results of Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js long-tailed ones actuated under 70 Gs elds. With diversity in body length, the sperm-like nanorobots exhibited different sensitivity to the dynamic elds yet the locomotion directions kept basicly consistent. It can also be predicted that short-tailed nanorobots tend to move forward under precessing elds of an enhanced intensity.

Conclusion
In summary, we presented novel exible sperm-like nanorobots based on a simple and facile preparation method. Based on tunable electrochemical deposition of exible agella and self-assembled bonding with magnetic nanobeads, the mass produced sperm-like nanorobots were endowed with exible head-to-       Locomotion velocity of the short-tailed nanorobot actuated under a 100 Gs precessing magnetic elds (HF-CCW, HF-CW, FF-CCW, FF-CW) over a frequency range (5-