Lightweight and drift-free magnetically actuated millirobots via asymmetric laser-induced graphene

Millirobots must have low cost, efficient locomotion, and the ability to track target trajectories precisely if they are to be widely deployed. With current materials and fabrication methods, achieving all of these features in one millirobot remains difficult. We develop a series of graphene-based helical millirobots by introducing asymmetric light pattern distortion to a laser-induced polymer-to-graphene conversion process; this distortion resulted in the spontaneous twisting and peeling off of graphene sheets from the polymer substrate. The lightweight nature of graphene in combine with the laser-induced porous microstructure provides a millirobot scaffold with a low density and high surface hydrophobicity. Magnetically driven nickel-coated graphene-based helical millirobots with rapid locomotion, excellent trajectory tracking, and precise drug delivery ability were fabricated from the scaffold. Importantly, such high-performance millirobots are fabricated at a speed of 77 scaffolds per second, demonstrating their potential in high-throughput and large-scale production. By using drug delivery for gastric cancer treatment as an example, we demonstrate the advantages of the graphene-based helical millirobots in terms of their long-distance locomotion and drug transport in a physiological environment. This study demonstrates the potential of the graphene-based helical millirobots to meet performance, versatility, scalability, and cost-effectiveness requirements simultaneously.

The motion of a magnetically actuated millirobot can be described using a speed vector  ⃗ ⃗ (  ,     ), where   is the rate of lateral drift due to near-wall effects and wall-induced friction,   is the rate of propulsion induced by the rotating magnetic field, and   is the rate of sinking, if gravity dominates over buoyancy.
For a C-Millirobot, as there is a certain distance between the millirobot and the bottom wall (h>>0) at the initial, the near-wall effect is avoided.Therefore, the motion of the millirobot can be categorized as motion far away from bottom wall which can be subdivided into the sinking movement (  ) due to the imbalance between gravity and buoyancy, and the propulsion (  ) induced by the magnetic torque resulted from the rotating magnetic field.While millirobots is near the bottom wall (h≈0), its motion is categorized as motion near the bottom wall which can be divided into two parts as well, including the lateral drift (  ) due to near-wall effects and friction between the millirobot and the bottom wall, and the propulsion (  ) driven by the magnetic driving torque of the rotating magnetic field.
Each motion of the C-Millirobot can be given as follows: where  1 and  1 are constants;  is the friction coefficient between the millirobot and the bottom wall; ℎ and  are the chiral coefficient and the "steerability" parameter, respectively, which are both related to the geometry of the millirobot;  is the viscosity coefficient related to the properties of the liquid and the geometry of the millirobot.
The aforementioned paradigm can be altered by reducing the density of the millirobot so that the buoyant force is greater than the gravitational force.In this case, the millirobot maintains floating and the wall effects are negligible, resulting in close-to-zero rates in both the x-and z-directions, i.e., the rate vector becomes (0,   , 0) and a straight trajectory can be obtained.Considering a liquid density of 0.998 g/cm 3 (assuming the liquid is deionised water), the density of the millirobot should ideally be below 1.000 g/cm 3 to reach the float state.On the other hand, to enable magnetic field control, a high enough loading of magnetic nanoparticles is required.Here, we use nickel nanoparticles, which have a bulk density of 8.902g/cm 3 , and take the volume fraction () of nanoparicles 58 as  = 0.06, the average density of the millirobot,   , can be calculated as   =   (1 − ) +   * .Accordingly, the density of the helical scaffold (  ) must have a density below 0.5 g/cm 3 to render the millirobot floating in the liquid.Such a low density can be obtained from highly porous structures composed of light elements.As such, porous graphene becomes our choice of material for creating the helical scaffold.
In this case, the millirobot maintains floating and the wall effects are negligible, resulting in close-tozero rates in both the x-and z-directions, i.e., the rate vector becomes (0,   , 0) and a straight trajectory can be obtained.
Thus for a GH millirobot, because of the balance between the gravity and the buoyancy, each axis of the GH millirobot is only affected by the magnetic driving torque and the torque induced by the viscous force.Thus, each motion of the GH millirobot can be given as: The GH millirobot steps out when the magnetic field's magnetic torque is not able to maintain a synchronous relationship between the magnetic moment and the applied rotating magnetic field.
Therefore, the geometry of the helix, the viscosity of the liquid, the magnetic materials characteristics and the strength of the magnetic field are the main factors that influence the step-out frequency, which can be formulated as 57 : where ∆ and  are effected by saturation magnetization and magnetic materials, respectively, and Φ is the angle between helical axis and axis of rotating magnetic field.The forward swimming velocity after step out can be predicted by the formula as 58 : The normalizing radiu  = 2, where r is the rediu of GH millirobot.The "steerability" parameter  used in prediction curve are 15.76, 11.10, 9.49, 8.26, 6.60.And the chirality coefficients ℎ used in prediction curve are 0.185, 0.169, 0.16, 0.153, 0.147 depending on the geometric parameters of GH millirobot, respectively.

Note S2. Drug release of GM-Millirobot
To verify whether the drug release of each GH millirobot was consistent among different batches, we randomly selected ten GH millirobots from Batch 1 and five GH millirobots from Batch 2, respectively, for comparison (Fig. 5d).Under the same NIR irradiation intensity, the ten GH millirobots from Batch 1 released 0.32 μg of drug in total and the five GH millirobots from batch 2 released 0.15 μg of drug in total, both to 2 mL of deionized water in 5 min, corresponding to an average release amount of 0.032 μg per GH millirobot for Batch 1 and 0.030 μg per GH millirobot for Batch 2. The results confirm that the drug release performance of the GH millirobots is consistent among different batches.
Besides, to characterize the fall-off of the loaded drugs, we monitored the drug concentration in the liquid environment where the DOX-HCl-loaded GH millirobots were suspended for 90 minutes.As shown by the green curve in Fig. 5d, only 0.188 μg DOX-HCl was dislodged from a total of ten GM-Millirobots after the 90-min movement.Note that the GH millirobots can move very fast with a maximum speed of 3.1 mm/s, thus they can reach the target position in a very short time (usually less than thirty seconds).Therefore, there will be extremely little drug dislodged during the delivery process.When the defocus distance increased from 3 mm to 9 mm, the sheet width increased from 86 ± 4 μm to the largest value of 117 ± 3 μm at 8 mm and then slightly decreased to 110 ± 6 μm, the helix diameter correspondingly increased from 167 ± 4 μm to 498 ± 10 μm.d, Effects of laser power and scanning speed on the helix diameter and e the corresponding optical microscope image.The laser power and scanning speed had minor effects on the helix diameter of the helical LIG sheets.The helix diameter was within the range of 300 ± 20 μm with a deviation of less than 6.7% under different laser powers.
The helix diameter varied no more than ± 10 μm with a deviation within a range of less than 3.4% under different scanning speeds.f, Effect of laser power and scanning speed on the helix pitch and g the corresponding optical microscope image.Laser power had little effect on the helix pitch: when the laser power was varied from its minimum to maximum values, the helix pitch varied no more than ± 20 μm (i.e. with less than 1.3% variation).When the scanning speed increased from 85 mm/s to 130 mm/s, the helix pitch increased from 986 ± 6 μm to 1792 ± 20 μm.h, Smallest millirobot processed at a defocus distance of 3 mm, a scanning speed of 85 mm/s, and a laser power of 2 W. Scale bars: 500 μm.Firstly, a planar LIG sheet was processed with a laser power density of 35 J/cm 2 ; subsequently, a pressure of 10 tons was applied to the planar LIG sheet for 10 min.Then the resulted high density planar LIG sheet was processed using the same laser parameters used in the processing the low-density one, resulting in a high density helical LIG sheet.
After that, it was coated with nickel resulting in a density of approximately 1.42 g/cm 3 .Note that we used a higher magnetic field strength as compared to some other works because of the low loading of the magnetic metal particles in the GH millirobots (i.e., the magnetic metal Ni layer taking only 6% volume fraction).The low loading ensures the full suspension mode of the of millirobots and thus enables fast movement and precise trajectory control; however, due to the reduced magnetic content, the magnetic field strength has to be increased.

Fig. S2 .
Fig. S2.Raman and wetting property characterizations of LIG sheet Fig. S3.Schematic diagram of a LIG sheet processed by the circular laser spot Fig. S4.Ablation shapes of defocused laser spots on PI film Fig. S5.Batch processing for the porous helical LIG sheets Fig. S6.Effects of laser processing parameters on the geometrial configurations of the helical LIG sheet Fig. S7.Porous helical LIG sheets with sputtered metal Ni Fig. S8.Elemental composition on the surface of GH millirobot Fig. S9.Magnetic driving system used in the experiment Fig. S10.Processing high-density GH millirobots Fig. S11.Rotation of GH millirobots with right-handed (blue) and left-handed (red) chirality under the same magnetic field Fig. S12.Time-lapse photographs of the motion of a DOX-HCl@GH millirobot, controlled by a rotating magnetic field of 12 mT, in an isolated porcine bladder Fig. S13.Safety verification of GH millirobot for living mice Fig. S14.Safety verification of GH millirobot for living mice: the routine hematological analysis and the biopsies H&E staining of organs Fig. S15.Safety verification of GH millirobot for living mice: biochemistry analysis Fig. S16.Mice tumor therapy Fig. S17.Routine hematological analysis of mice tumor therapy Table S1.Comparison of swimming speeds and lateral drift rates of millirobots of conventional materials

Fig. S1 .
Fig. S1.Principle of shaping the laser beam.a, In a conventional setting, the deflected laser beam is focused to a circular spot at the working plane, so the spot on the defocus plane Ⅰ is simply the magnification of that on the focus plane Ⅱ. b, By deliberately tilting one of the F-θ lenses, the laser beam is shifted away from the original focusing plane, and introducing asymmetric distortions which are magnificated by the defocuse distance to the laser spot on the working plane.

Fig. S2 .
Fig. S2.Raman and wetting property characterizations of LIG sheet.a, The Raman spectrum demonstrates that the characteristic peaks of LIG sheets include the D (~1350 cm -1 ), G (~1584 cm -1 ) and 2D (~2695 cm -1 ) peaks, which indicates that the sheets are indeed composed of graphene.b, Hydrophobicity test of LIG sheet.c, Effects of power density on the surface wettability.

Fig. S3 .
Fig. S3.Schematic diagram of a LIG sheet processed by a circular laser spot.a, When the laser spot is circular, the gas formation along the scanning line is uniform, therefore, only a bended LIG sheet is formed.b, Optical image of a LIG sheet processed by the circular laser spot.

Fig. S5 .
Fig. S5.Batch processing for the porous helical LIG sheets.a, The helical LIG sheets were highly reproducible and b had controllable lengths.

Fig. S6 .
Fig. S6.Effects of laser processing parameters on the geometrical configurations of the helical LIG millisheet.a, Geometric configuration definition of the helical LIG millisheet.b, Effects of defocus distance on the helix diameter and sheet width and c the corresponding optical microscope images.

Fig. S7 .
Fig. S7.Porous helical LIG sheets with sputtered metal Ni. a, The pristine porous helical LIG sheet induced from amber PI film and b its surface structure.c, After sputtering a metallic nickel layer on helical LIG sheets, their surface color converted to a silvery white with a metallic sheen and d SEM image shows dense nickel nanoparticles were loaded on the surface.

Fig. S8 .
Fig. S8.Elemental composition on the surface of GH millirobot.a, The SEM-EDS mappings of the GH-Miccrorobots cross-section shows carbon and nickel are the main elements distributed on the surface of the LIG sheet.Scale bar: 20 μm.b, The SEM-EDS mappings at a larger magnification shows the same distrbutions.Scale bar: 5 μm.

Fig. S9 .
Fig. S9.Magnetic driving system.Magnetic driving system used in the experiment, includes the signal generator, power amplifiers and Helmholtz coils.The combined effect of these components creates a uniformly strong rotating magnetic field within its working area.

Fig. S10 .
Fig. S10.Processing high-density GH millirobots.Firstly, a planar LIG sheet was processed with a

Fig. S11 .
Fig. S11.Rotation of GH millirobots with right-handed (blue) and left-handed (red) chirality under the same magnetic field.

Fig. S13 .
Fig. S13.Safety examination of GH millirobots on living mice.a, Body weight of mice during 7 consecutive days gavage of millirobots (control group, mice in other groups were in gavages of 1000, 2000 and 4000 GH millirobot, respectively) and follow-up 14 days monitoring, (n=4/group).b, Comparison of organ weights of mice at the end of the safety experiment, (n=4/group).Data are presented as the means ± s.e.m.

Fig. S14 .
Fig. S14.Safety examination of GH millirobots in living mice: routine hematological analysis and biopsies H&E staining of organs.a, Blood routine examination results of mice at 14th day.There were different numbers of pristine GH millirobots by gavage in mice and the safety test performed continuously for 7 days at a volume of 0.2 mL per mice in each day, and all the mice were continuously observed for 14 days, (n=4/group).Data are presented as the means ± s.e.m. b, Tissues' biopsies (including heart, liver, spleen, lung, kidney) for H&E staining, which were collected from group iv (4000 GH millirobots) in safety experiments.

Fig. S15 .
Fig. S15.Safety examination of GH millirobots in living mice: biochemistry analysis.The serum samples were collected for biochemistry analysis at 14th day, (n=4/group).Data are presented as the means ± s.e.m.

Fig. S16 .
Fig. S16.Mice Tumor Therapy.a, Gastric tumor weight of mice in different groups, (n=5/group).Data are presented as the means ± s.e.m. b, Body weight of mice during the tumor treatment, (n=5/group).

Fig. S17 .
Fig. S17.Routine hematological analysis of mice tumor therapy.Whole blood was collected for routine hematological analysis at 14th day which is the end of treatment, (n=5/group).Data are presented as the means ± s.e.m.

Table S1 .
Comparison of swimming speeds and lateral drift rates of millirobots of conventional materials