robotics.sciencemag.org/cgi/content/full/4/33/eaax7112/DC1

Supplementary Materials for

Soft phototactic swimmer based on self-sustained hydrogel oscillator

Yusen Zhao, Chen Xuan, Xiaoshi Qian, Yousif Alsaid, Mutian Hua, Lihua Jin, Ximin He*

*Corresponding author. Email: ximinhe@ucla.edu

Published 21 August 2019, Sci. Robot. 4, eaax7112 (2019)

DOI: 10.1126/scirobotics.aax7112

The PDF file includes:

Materials and Methods Section S1. General Section S2. Fabrication of materials Section S3. Characterization of materials Section S4. Characterization of oscillation Section S5. Theory and simulations Fig. S1. UV-visible absorption spectrum of AuNPs. Fig. S2. The schematic of the measurement of hydrogel deswelling/swelling ratio and rate. Fig. S3. Deswelling/swelling kinetics of oscillating hydrogel and tracking hydrogel. Fig. S4. Scanning electron microscope images of hydrogels. Fig. S5. The stress-strain curves of hydrogels with different cross-linking densities. Fig. S6. Photo-tracking versus photo-oscillation. Fig. S7. Comparisons of the bending and unbending kinetics of oscillating pillar and tracking pillar. Fig. S8. Switch from tracking to oscillation by tuning light power. Fig. S9. Fishhook-shaped oscillator and position independency. Fig. S10. Schematic of lower-biased (case I), upper-biased (case II), and symmetric flapping (case III). Fig. S11. Range of operation input correlated to the dimension and the photothermal properties. Fig. S12. Realization of oscillation under ambient white light. Fig. S13. The hydrogel oscillator floating on the surface of water in the container. Fig. S14. Maneuverability of the OsciBot. Table S1. Summary of effect of cross-linking density on materials properties and oscillation performance. Legends for movies S1 to S11 References (38–40)

Other Supplementary Material for this manuscript includes the following: (available at robotics.sciencemag.org/cgi/content/full/4/33/eaax7112/DC1)

Movie S1 (.mp4 format). Hydrogel-based light-driven oscillator. Movie S2 (.mp4 format). Comparison of light-induced tracking and oscillation. Movie S3 (.mp4 format). Fishhook-shaped hydrogel oscillator. Movie S4 (.mp4 format). Position independency. Movie S5 (.mp4 format). Realization of omnidirectional oscillation. Movie S6 (.mp4 format). Oscillation frequency as a function of geometry. Movie S7 (.mp4 format). Initialization: From tracking to oscillation. Movie S8 (.mp4 format). Long-term stability of the oscillation. Movie S9 (.mp4 format). OsciBot: Continuous swimming. Movie S10 (.mp4 format). OsciBot: Controllable motion. Movie S11 (.mp4 format). Oscillation under ambient white light.

Materials and Methods

1. General

PDMS prepolymer (Sylgard 184 Silicone Elastomer kits) was purchased from Ellsworth.

Chloroauric acid, sodium citrate dehydrate, N,N’-Methylenebis(acrylamide) (BIS), dimethyl

sulfoxide (DMSO), 3-(Trimethoxysilyl)propyl methacrylate (TMSPMA) and allyl disulfide were

purchased from Fisher. 2-Hydroxy-2-methylpropiophenone (Darocur 1173) was purchased from

TCI. N-isopropylacrylamide (NIPAAm) was purchased from Sigma Aldrich and recrystallized

using n-Hexane. Except for NIPAAm. All chemicals were used as received.

The templates for molding the hydrogel pillars were disposable hypodermic needles purchased

from Exel International. The masters of soft swimmer were prepared by 3D printing using

Stratasys 3D printer, Objet 24. The Green laser (532nm) was generated by Genesis MX532-1000

STM. The temperature measurement used the K-trype thermocouple coupled with the DC millivolt

amplifier and the oscilloscope (Wavesurfer 454, Lecroy). Videos were recorded using a digital

camera with a red color filter. The tip displacement and angle were measured by using tracking

software.

2. Fabrication of Materials

2.1 Fabrication of gold nanoparticles (AuNPs)

250 μL of chloroauric acid was added to 250 ml water to make a seed solution. The seed solution

was then heated to its boing point with a stirring speed of 400 rpm. 20 ml of 1 wt.% sodium citrate

dihydrate solution was then added into the seed solution followed by an immediate increase in the

stirring speed to 800 rpm. The solution was left to boil for another 6 minutes, after which the

hotplate was switched off. After cooling, the solution was centrifuged at 6000 rpm. Finally, the

AuNPs were collected and stored in the 4℃ fridge. The absorbance of AuNPs was measured by

using a UV-Vis-NIR spectrometer (Shimadzu uv-3101) and shown in Fig. S1.

Fig. S1. UV-visible absorption spectrum of AuNPs.

2.2 Fabrication of PDMS molds

The masters of pillar structure used hypodermic needles with different gauges. Consider the

swelling of the hydrogel after curing, needle gauges of 21-Gauge (0.81 mm), 22-Gauge (0.71 mm),

23-Gauge (0.64 mm), 25-Gauge (0.50 mm) and 30-Gauge(0.315 mm) were used to prepare pillars

with the diameter of 1.03mm, 0.91mm, 0.78mm, 0.56mm and 0.36mm. The masters of OsciBot

were prepared by 3D printing.

The PDMS molds were replicated from the masters. To fabricate the PDMS molds, the Sylgard

184 silicone prepolymer and curing agent were mixed with the weight ratio of 10:1 and cured at

45°C for four hours.

2.3 Preparation of TMSPMA treated cover glass

The cover glass was sonicated in acetone and ethanol for 15 mins, alternatively. Then the cover

glass was treated with oxygen plasma at 600 mTorr for 5 min, followed by immersion in a mixture

of 3 ml of TMSPMA, 9 ml of 10 vol.% acetic acid solution and 300 ml of ethanol overnight. After

treatment, the cover glass was rinsed in ethanol and dried subsequently.

2.4 Fabrication of the hydrogel pillars under green light

For oscillating pillar, the poly(N-isopropylacrylamide) (PNIPAAm) precursor solution was

synthesized by mixing 40 wt.% NIPAAm monomer, 1.5 wt.% BIS in DMSO. For tracking pillar,

the concentration of BIS was increased to 2.0 wt.% and 3.0 wt.%, leaving others unchanged. Then,

0.5 wt.% AuNPs, 0.07 vol.% Allyl disulfide and 0.5 vol.% photoinitiator Darocur 1173 were added

in PNIPAAm precursor solution, respectively. The prepolymer solution was injected into PDMS

mold and covered by TMSPMA-treated cover glass. The UV polymerization was undergone for

80 seconds. Then, the cured AuNP/PNIPAAm pillar gel was carefully squeezed and pulled out

from the mold and immersed in DI water to remove the DMSO residue.

2.5 Fabrication of the hydrogel pillars operated under white light

The PNIPAAm precursor solution was prepared by mixing 40 wt.% NIPAAm monomer, 1.5 wt.%

BIS in DMSO, followed by the addition of 0.5 vol.% photo-initiator Darocur 1173 prior to use.

The prepolymer solution was injected into PDMS mold and covered by TMSPMA-treated cover

glass. The UV polymerization was undergone for 40 seconds. Then, the cured PNIPAAm gel was

carefully pulled out from the mold and immersed in DI water to remove the DMSO solvent.

Subsequently, to incorporate polyaniline (PANi) into the as-prepared PNIPAm hydrogel, we used

the in-situ polymerization method. Typically, 182 μL (0.2 M) of aniline monomer were dissolved

in 5 mL of a 1M HCl aqueous solution to form Solution A. The PNIPAm hydrogel pillar was placed

into the solution A for 2 hours. After the two-hour soaking, 456 mg of ammonium persulfate (APS,

0.2 M) was dissolved in another 5 mL of 1M HCl aqueous solution, to form Solution B. Mix

solution B into Solution A under stirring at room temperature for 8 hours to in-situ grow

polyaniline in the PNIPAm gel. Then, the PANi-embedded PNIPAm gel was taken out of the

solution and rinsed with water to remove excess reactants. The dimension of the PANi-PNIPAm

pillar for testing was 29 mm in length and 0.48 mm in diameter.

2.6 Fabrication of the OsciBot

The OsciBot was made by injecting the prepolymer solution in the PDMS mold, covered with

cover glass without treatment. To polymerize the hydrogel homogeneously, the UV light was

irradiated from the top and bottom of the PDMS mold for 40 s each.

3. Characterizations of Materials and Oscillation

3.1 Characterization of hydrogel (de)swelling kinetics

Three different hydrogel pillars of different crosslinker concentrations (1.5 wt.%, 2.0 wt.%, and

3.0 wt.% BIS) were prepared in the PDMS mold, via the same procedure of preparing all hydrogel

pillars. Subsequently, a segment from each cured hydrogel pillar was cut into a rod with a diameter

of 0.53 mm and length of 0.90 mm. As shown in Fig. S2, The hydrogel rod was fully swollen in

its original state and placed in a pertri-dish. The kinetics of deswelling and swelling were

characterized by recording the volume changes of the hydrogel rod during temperature change

under an optical microscope (Leica DMI 6000B). 45℃ hot water was poured into the petri dish to

heat up the gel rod instantly. At 35 seconds, when the hydrogel swelling reached equilibrium, the

hot water was quickly removed and subsequently water at room temperature was instantly injected

into the Petri dish. The video recording was kept for 270 seconds, for the entire the deswelling and

swelling process.

As shown in Fig S3, the test of deswelling and swelling rates indicated that the 1.5-wt.% BIS

hydrogel shrunk to 33.7±1.7% of its original swollen-state volume when submerged in 45 ℃ water

bath for 30 seconds. By contrast, the 2.5- and 3.0-wt.% BIS hydrogels shrunk to 48.7±4.9% and

62.3%±2.1%.

Fig. S2. The schematic of the measurement of hydrogel deswelling/swelling ratio and rate.

The hydrogel rod was placed in an inner cylinder container which protected the rod from being

detached as the water was added and removed. The 45 ℃ hot water and 25 ℃ water was poured

to instantly heat and cool materials with a relatively constant temperature condition.

Fig. S3. Deswelling/swelling kinetics of oscillating hydrogel and tracking hydrogel. Volume

changes of reversibly actuating hydrogel disks below/ above the LCST (25 and 45℃) are shown

with 1.5% wt.% BIS (red square), 2.0 wt.% BIS (blue) and 3.0% wt.% BIS (black square). The

AuNP/PNIPAAm composite hydrogel with low crosslinking density possesses a faster deswelling

rate and ratio.

3.2 Characterization of hydrogel microscopic morphologies

The morphologies of the tracking and oscillating hydrogels were observed via Supra 40VP

scanning electron microscope. The SEM images used secondary electron mode, with the working

distance (WD) of 8.9 mm and Acceleration Voltage of 10.0 kV. As Fig. S4 shows, the average

pore sizes of hydrogels were 4.61 μm, 3.58 μm and 2.07 μm for 1.5, 2.0 and 3.0 wt.% BIS

hydrogels, respectively. Hydrogels with higher crosslinking density had smaller pores.

Fig. S4. Scanning electron microscope images of hydrogels with (A) 1.5 wt.% BIS, (B) 2.0

wt.% BIS, (C) 3.0 wt.% BIS.

3.3 Characterization of hydrogel mechanical properties

The stress-strain curve of AuNP/PNIPAAm hydrogel was measured using the dynamic mechanical

analyzer (DMA, TA Instruments, Q800). Hydrogel samples were cured together with the treated

glass slides which acted as the holders at two ends of hydrogel. As Fig. S5 shows, the hydrogel

with lower crosslinking density (1.5 wt.% BIS, the oscillating hydrogel) has a higher fracture strain

of 63% and Young’s modulus of 6.3 kPa.

Fig. S5. The stress-strain curves of hydrogels with different cross-linking densities: 1.5, 2.0,

and 3.0 wt.% BIS, respectively.

4. Characterization of oscillation

4.1 Time-resolved temperature/ tip displacement of the hydrogel pillar

The temperature was measured by thermocouple connected to an oscilloscope (wavesurfer 454,

Lecroy). The tip of the thermocouple was placed on the hydrogel, as close to the illumination spot

as possible. The time dependent tip displacement and temperature were recorded simultaneously.

Pillar dimensions: L=17 mm, d=0.90 mm and input power = 500 mW.

4.2 Influence of deformation kinetics and geometry on photo-tracking vs. photo-oscillation

As Fig. S6 shows, with the negative feedback loop built in the dynamic light-material interactions,

the hydrogel pillar has been noticed capable of performing either photo-tracking (in-equilibrium

actuation, steadily pointing to the light source) or photo-oscillation (out-of-equilibrium actuation,

bouncing between two kinetically stable states around the light source), depending on the

(un)bending kinetics of hydrogel and the power of light source. To understand how of these two

key factors determine the pillar to perform photo-tracking or photo-oscillation, we systematically

investigate the conditions required for realizing the two behaviors.

Fig. S6. Photo-tracking versus photo-oscillation. Hydrogel pillars can realize either photo-

tracking (in-equilibrium actuation, A) or photo-oscillation (out-of-equilibrium actuation, B)

depending on the actuation kinetics and the input energy.

4.2.1 Influence of (un)bending kinetics

To understand the bending and unbending kinetics of oscillating pillar and tracking pillar,

hydrogels with different responsive volume-change rates were prepared by tuning their cross-

linking densities (i.e., different water diffusivities and moduli) and tested on their photo-actuation

behaviors. Three pillars with respectively 1.5, 2.0, and 3.0 wt.% BIS cross-linker concentrations

were actuated by a 300-mW light which was turned on at the 5th second and turned off in 60

seconds. Pillars experienced bending, tracking/oscillation and recovery. The pillar (L = 17 mm, d

= 0.9 mm) was placed vertically at the bottom of a water bath.

As Fig. S7 shows, the 1.5 wt.%-BIS hydrogel pillar could bend towards the 90o incident light

within 8.7±1.3 s and then started oscillating. By contrast, the 2.0 wt.%- and 3.0 wt.%-BIS pillars

bent to 90° more slowly, within 15.7±1.3 s and 56.7±2.9 s respectively and both remained static,

aiming at the light in its incident direction. As the light was turned off (t = 60 s), the oscillating

pillar abruptly recovered towards the original upright position within the first few seconds, since

the initial velocity of the upstroke (unbending) motion promoted the water diffusion into the

hydrogel and tip promptly bounced up due to the inertia. The light-tracking pillars, however,

swelled progressively back to the vertical state.

Fig. S7. Comparisons of the bending and unbending kinetics of oscillating pillar and tracking

pillar. The hydrogel pillar with 1.5 wt.%-, 2.0 wt.%- and 3.0 wt.%- BIS could bend towards the

90° incident light within 8.7±1.3 s, 15.7±1.3 s and 56.7±2.9 s, respectively. Only the 1.5 wt.%-BIS

sample could oscillate, and 2.0 wt.%-BIS, 3.0 wt.%-BIS samples tracked to the light.

Based on the experimental results above, we have summarized the effect of crosslinking density

on materials properties and the boundaries of oscillation and tracking. We found that with a lower

crosslinker density, the pore sizes from SEM images were increased, indicating a macroporous

structure to enhance the diffusion. Due to the larger pores with lower crosslinker density, we

observed that the hydrogels became softer from 27.3 kPa of Young’s modulus for 3.0 wt.% BIS to

6.3 kPa for 1.5 wt.% BIS. In the meantime, the elasticity of hydrogels is also enhanced from 12%

to 63%. We thereafter found that the volume changes of 1.5 wt.% BIS was 1.84 times greater in

comparison to the 3.0 wt.% BIS. The volume shrinkage time scale of 1.5 wt.% BIS was 2.69 times

faster than that of 3.0 wt.% BIS. Under the fixed laser intensity, only the 1.5 wt.% BIS hydrogel

was capable to oscillate, whereas the other two stayed as tracking. It is worth pointing out that

even though the hydrogels with crosslinking density smaller than 1.5 wt.% is expected to have

faster response kinetics and magnitude. However, it is experimentally difficult for hydrogels with

such small crosslinking density to be cured and come off from the mold. The materials would also

be too soft to be able to realize robotic functions or other practical applications. Based on the

materials characterization and oscillation examination, we conclude that the hydrogels with such

large pore sizes (>4.5 um), large volume shrinkage magnitude (<33.7% in 30 seconds), fast

response kinetics (t<7s) can produce the oscillatory motion.

Table. S1. Summary of effect of cross-linking density on materials properties and oscillation

performance.

crosslinking density 1.5% 2% 3%

Pore sizes (um) 4.61 3.58 2.07

Young's modulus (kPa) 6.3 16.3 27.3

Elongation at break 63% 37% 12%

Deswelled volume/original volume 33.70% 48.70% 62.30%

Volume shrinkage time scale (s) 7.14 9.22 19.2

Tracking time (s) 8.7 15.7 56.7

Oscillation vs. Tracking Oscillation Tracking Tracking

4.2.2 Influence of light power

To understand the stimulus conditions required for the initialization of oscillation with a certain

hydrogel (i.e., with fixed volume-change ratio and rate), we tuned the input power of the light and

observed the switching from photo-tracking to photo-oscillation. As Fig. S8 shows, originally the

pillar was tracking the light source with an input power of 150 mW. At the 2nd second, the input

power was instantly increased from 150 mW to 300 mW. As a result, the pillar started to oscillate

with the amplification increasing for about five cycles and eventually reaching steady oscillation,

presenting the initiation process of oscillation.

Fig. S8. Switch from tracking to oscillation by tuning light power. The pillar tracked the light

source with the input power of 150 mW. When the input power was instantly increased to 300 mW,

the pillar started oscillating with the amplification for about five cycles and eventually reaching

the steady oscillation.

4.3 Independency of pillar geometry and orientation for oscillation generation

To demonstrate that oscillation can be generated and maintained independent of pillar geometry,

a hydrogel pillar of irregular shape, such as with a fishhook-shaped tip, was prepared and tested.

Oscillation was successfully realized. As Fig. S9A shows, only the hinge and tip were alternatively

exposed to the light, whereas the front and back sidewalls of its arm (or cantilever) were not

exposed to light. This proves that the hinge participates into the deformation and the tip facilitates

the self-shadowing, rather than the pillar arm.

To demonstrate that oscillation can be generated and maintained independent of pillar orientation

(horizontal or vertical, upward or downward), the pillar was originally placed horizontally (Fig.

S9B) and upside down (Fig. S9C), respectively, with a 90° illumination angle for both. Oscillation

occurred for both pillars, independent of the original pillar orientation at any arbitrary deflection

angle, for example 90° in this demonstration.

Fig. S9. Fishhook-shaped oscillator and position independency. (A) Realization of the

oscillation with fishhook tip, proving that only the hinge participated into the deformation, rather

than the pillar arm (sidewalls of pillar). Dimensions: L=17 mm, d=0.9 mm. Input power = 500

mW. (B, C) The oscillation can be realized independent of the original pillar orientation, either

horizontal (B) or downward (C) at any arbitrary deflection angle, for example 90° in this

demonstration. All images are superimposed photos of pillars of different configurations at

different time points during oscillation to show the relative positions.

4.4 Realization of omnidirectional oscillation

4.4.1 Oscillation at different zenith angles

A pillar of 0.9 mm diameter was originally placed upright with the light from different zenith

angles, thus different deflection angles. The deflection angle was gradually changed from 90° to

59° but the light always shined on the same spot. Each measurement started from a fully unbent

state. Lower amplitude was observed at small deflection angle, because as the input power of the

beam was fixed, smaller angle gave a larger exposed area on the pillar, diluting the intensity of the

light in the unit surface area. A deflection angle smaller than 59° resulted in tracking instead of

oscillation.

Since the smaller diameter pillar required a smaller volumetric deformation to achieve a given

bending angle, the diffusion time scale tdiff = t2/D was relatively smaller. When the diameter of the

hydrogel pillar was reduced to 0.36 mm, the oscillation could be maintained from a deflection

angle of 90° to nearly 0° under the same input power.

To realize oscillation with 0° deflection angle, the pillar was placed horizontally with the light

shining on its tip. We speculate that the achievement of the 0° oscillation is attributed to more

participation of gravity on the cantilever to contribute to the driving force for bending. The regular,

upper-biased, and lower-biased oscillations were achieved by fine-tuned the relative height of light

source with respect to the root (central axis) of the pillar. For the light beam positioned slightly

higher than the horizontal pillar (Fig. S10, Case I), the pillar could receive more light exposure

when above the horizontal position of pillar) than the light-exposure time period when the pillar

was lower than the equilibrium horizontal level. Then, the pillar will receive more energy for it to

bend down during the downstroke and be inhibited from going upward too far during the upstroke.

Therefore, the pillar would more significantly bend down and the oscillation was referred as lower-

biased. In contrast, the oscillation would be upper-biased when the light beam was positioned

relatively lower than the pillar (Fig. S10, Case II). The symmetric oscillation was observed when

light precisely shined on the root (central axis) of the pillar (Fig. S10, Case III).

Fig. S10. Schematic of lower-biased (case I), upper-biased (case II), and symmetric flapping

(case III).

4.4.2 Oscillation at different azimuthal angles

The 0.9 mm diameter pillar was originally placed upright and the 500 mW light came from four

different azimuthal angles, covering the whole horizontal plane of the pillar. The pillar bent down

to the corresponding direction of light and started oscillating. The camera was placed on the plane

of a 360° continuous rotation stage together with the water bath for testing. Therefore, the camera

and the sample were always in the same reference frame.

4.5 Oscillation frequency as the function of diameter and arm length

The oscillation frequency was measured for different pillar geometries. In the Movie S6, pillars

with L=13, 17, and 22 mm, d=0.56 mm were utilized to explore the arm-length frequency

dependence. Then, the pillars with d=0.56, 0.78, and 1.03 mm and L=17 mm were tested to explore

the frequency dependence on the diameter.

4.6 Optimal operation conditions of oscillation

The diameter, arm length, and the photo-absorption are the key parameters that affect the range of

operation input power. We have conducted experiment using a series of light intensities on

hydrogel pillars of different arm lengths, diameters and photo-absorber concentrations. Below we

summarized their effects and identified the optimal operation conditions of oscillation.

Before the analysis, we define the range of operational input power for clarification. For photo-

induced oscillation, there exists a threshold intensity beyond which the self-sustained oscillation

occurs. The threshold intensity determines the lower limit of the operation window of oscillation.

Below the threshold intensity of oscillation, there is a range of intensity that the pillar can steadily

track to the laser direction, as shown in the yellow regime in Fig. S11. When the laser intensity is

overly low, the energy is not sufficient to induce tracking or oscillation, shown in the grey regime

in Fig. S11. By contrast, if the light intensity is overly high, we observed unstable oscillation with

chaotic behavior, as shown in the red regime in Fig. S11. This implies the deviation of oscillation

from steady position is amplified and the pillar tip may not perfectly shadow the hinge if any lateral

fluctuation happens. Here, the unstable intensity determines the upper limit of the operation

window. Thus, we determine the range of operation input power between the threshold intensity

of oscillation and unstable intensity, as shown in the blue regime in Fig. S11.

To investigate the effects of the key parameters on the operation input condition, we first fixed the

diameter of the pillar as 0.9 mm and changed the arm length from 17.7 mm to 10.6 mm, equivalent

to the aspect ratio changing from 20 to 11.8. With a higher aspect ratio, the threshold intensity was

gradually reduced, especially to be 122 mW for the aspect ratio of 20. In the meantime, the unstable

intensity was also reduced. It is noteworthy that when the aspect ratio was decreased to 10.6, no

oscillation was observed even if the highest laser intensity was applied. This may be because the

oscillation can be generated only if the pillar has a sufficiently high aspect ratio to provide inertia.

Second, we carefully examined the correlation between the operation condition and arm diameter

(pillar thickness). As expected, with a smaller diameter of pillar, a lower threshold intensity was

needed to realize oscillation, due to the lower tdiff. Also, for the thin pillar, the unstable intensity

was also lower. Beyond the unstable intensity, we observed that the pillar started to oscillate

irregularly, with more random and chaotic motion. This implies that when the diameter is smaller,

the water damping part (eq. 2) becomes more significant. And such thin pillar could induce larger

actuation magnitude (Fig. 4A), indicating larger amplitude. As both the driving force and

resistance increase, the deviation of oscillation from steady position is amplified, resulting in more

unstable oscillation.

Third, we investigated the correlation between operation condition and photo-absorber (AuNPs)

concentration. As expected, higher concentration of AuNP had lower threshold intensity, due to

the stronger photothermal effect. On one hand, it is interesting to point out that the absorber

concentration (0.5 mg/mL) with 10 times diluter than current recipe (5 mg/mL) could still provide

sufficient photothermal efficiency to initiate the oscillation, indicating the robustness of our

oscillation system. On the other hand, an absorber concentration higher than 5 mg/mL would cause

increased aggregation and undesirable segregation of AuNP during the centrifuge and hydrogel

photo-curing process. Without such a technical limit in the fabrication process or with photo-

absorbers of higher photothermal efficiency, a higher light absorption effect together with lower

threshold intensity to start oscillation could be expected.

Fig. S11. Range of operation input correlated to the dimension and the photothermal

properties. (A) Arm length, (B) diameter and (C) AuNP photo-absorber concentration. The grey,

yellow, blue and red regimes stand for non-tracking, tracking but oscillation, oscillation and

unstable oscillation, respectively.

4.7 Realization of oscillation under ambient, white light

To realize operation using ambient environment light source for more practical applications, we

systematically optimized the design of materials and geometry. Since the ambient environment

usually has lower light intensity and diffusive direction, achieving oscillation under such condition

requires lowering the threshold intensity of oscillation. Here, we have successfully demonstrated

a hydrogel pillar oscillating under diffusive (non-parallel) and broadband white light, which has

the spectrum close to sunlight and the intensity of 2.5 suns (Fig. S12 and Movie 11). To respond

to this white light, we utilized PANi as absorbers for its high photo-absorption efficiency over

broad wavelength. We also made the pillar slightly thinner and longer in arm length (see SI 2.5 for

dimension and fabrication) to further lower the threshold intensity. Thus, the oscillation of

hydrogel pillar was achieved. In the demonstration, the hydrogel pillar was taped on a PDMS

substrate to fix the position without movement laterally. The pillar was originally upright and

incident light came from a deflection angle of 70°. (The reason for not using horizontal 90° light

is because the areal light would cause the pillar to completely bend down and attach to the ground.)

Although the light did not shine vertical to the pillar, the pillar could still successfully oscillate.

The superimposed picture in fig S12A indicates the upper and lower position of pillar during one

cycle. Interestingly, the tip displacement was not as regular as under laser. Instead, the amplitude

oscillation was relatively small and slightly chaotic. The small amplitude arose from the relatively

lower intensity of the white light used, compared to the laser operation. The amplitude fluctuation

might be due to the diffusive light direction that made the shadowing less regular and the actuation

less defined. However, the oscillation frequency maintained at ~0.085 Hz and did not vary much,

indicating that the oscillation frequency still obeyed the quasi-harmonic model.

Fig. S12. Realization of oscillation under ambient white light. (A) The superimposed snapshots

of the setup consisting of the oscillating pillar and the white LED. The pillar was taped on a PDMS

substrate at the side. Under the area light of an optical beam size larger than the pillar dimension,

the entire pillar (without a sharp bend as seen under a small-area spot light from laser) actuated

towards the light and oscillated around the incident direction. (B) Time-dependent tip displacement

of oscillation in vertical direction.

4.8 Characterization of the OsciBot

The OsciBot was placed in a thin long container (Fig. S13). The hydrophobic glass sidewalls lead

to a concave water surface due to the water tension present on the interface of water, air and the

glass wall. The OsciBot was able to float on the surface along the central axis of the consistently.

The light was applied along the central axis of the container, enabling the OsciBot to move always

aligning the direction of the light.

For the characterization of the swimming speed of the OsciBot, 450 mW of green light was applied

and the swimming motion was recorded from the side. For the characterization of the controllable

swimming motion via intermittent illumination, the light was switched on at 20, 230, 450 seconds

and turned off at 200 and, 415 seconds. The OsciBot could constantly swim with the light on and

gradually stopped once the light was turned off.

Fig. S13. The hydrogel oscillator floating on the surface of water in the container. The

OsciBot was able to float on the surface always along the central axis of the container due to the

meniscus of the water surface. The light was shone on the hydrogel sheet along the central axis of

the container, enabling the OsciBot to move always following the direction of the light.

4.9 Effects of oscillation parameters on swimming performance of the Oscibot

In order to obtain a general principle of swimming performance, the experiment we have

conducted here is to use the same Oscibot and change the amplitude. We fixed the thickness and

aspect ratio of the beam to be the same. Then, we observed that with a larger amplitude (bending

angle), the swimming velocity of Oscibot could increase linearly (Fig. 6A). It is because the beam

propelled more water backwards during one cycles. Whereas, a larger amplitude indicates longer

distance for the beam tip to travel, leading to a slight frequency drop, consistent with our

experimental observation in Fig. 4B. Therefore, the swimming velocity inversely correlates with

the oscillation frequency in this particular case (Fig. 6B), mainly due to that the amplitude and

frequency are bound variables, hard to be increased at the same time. Overall, the Oscibot swims

faster with higher amplitude, while the frequency unavoidably decreases slightly.

We further investigated the dependence of average velocity of beam tip in the vertical direction to

the velocity of the Oscibot in the horizontal direction (swimming direction). Here we simplify the

average velocity of beam tip (vbeamtip) as 2 times of amplitude (A) divided by the time period

(Tb=1/f). We find that although the larger amplitude (A) situation has low frequency (f) and longer

time period (Tb), the average velocity of beam tip (vbeamtip=2A/Tb=2Af) at vertical direction is still

higher. It’s because the frequency drop and time period increase are negligible in comparison to

the increase of amplitude. When plotting the velocity of the Oscibot and the velocity of beam tip,

we found that the velocity of the Oscibot increases as the velocity of beam tip.

4.10 Maneuverability of the Oscibot

From the preliminary test, we have realized the directional control of the swimming robot guided

by light. Particularly, we designed the container into a V-shape with an angle. The entire Oscibot

was made of the same hydrogel including the strip and substrate. The substrate floated on the water

due to surface tension. Guided by light, the Oscibot swam along the long axis of container as

shown in Fig. S14 1-4. As the Oscibot swam to the corner, the light direction changed to allow the

Oscibot to steer its body and turn left (Fig. S14 5-8), to continue swimming to another end of

container. Notably, current design of flipper part of OsciBot is rectangular shape in cross-section

to enlarge the propulsion force at the same frequency condition. Therefore, rotation step requires

to be finely tuned. Instead, if a cylindrical pillar is designed as the flipper of the swimmer, merely

changing in the direction of incident light can allow for the change of the swimming direction.

Fig. S14. Maneuverability of the OsciBot. As the OsciBot swims to the corner of a V-shape

container, the light direction is changed to allow the OsciBot to steer its body to swim to another

end of container, demonstrating the direction controllability of the phototactic locomotion.

5. Theory and simulations

5.1 Theory and simulation of the oscillation frequency

Classical vibration theory suggests that the frequency of a damped single degree of freedom system

(with damping ratio , undamped natural frequency ) is 21d . Since our hydrogel

cantilevers are submerged in water, their motion is damped by water. The above relationship

between the undamped and damped frequencies for single degree of freedom systems holds true

for cantilevers, with infinite degrees of freedom as well, since frequencies of linear systems do not

interfere with one another. With the current material and geometric parameters, we hypothesize

that the total resistance force from water to the cantilever roughly falls into the Stokes flow limit

so that the force is proportional to the velocity and length of the cantilever (34). Therefore, the

frequency of a damped cantilever with damping coefficient per unit cantilever length c is

2 4

1 14

d

c L

AEI

(SI.1)

where 4

1 3.5 /EI AL is the angular frequency of the 1st bending mode of a cantilever beam.

If the cantilever has a circular cross-section of diameter d, by using 4 / 64I dp and

2 / 4A d, we obtain the angular frequency and frequency of the vibration

2 4

2 2 6

3.5 641

4d

d E c L

L E d

, (SI.2)

2 4

2 2 6

3.5 641

8d

d E c Lf

L E d . (SI.3)

Next we fit the frequency-diameter and frequency-arm length curves with Eq. (SI.3), by

introducing an artificial prefactor A

2 4

2 2 6

3.5 641

8d

d E c Lf A

L E d . (SI.4)

As a result, the best fitting to the frequency-arm length curve gives rise to c=1.272×10-4, A=0.9421,

R2=0.99894, given the material and geometric parameters E=6.3 kPa, ρ=103 kg/m3, d=0.6 mm

(Fig. 3A). The best fitting to the frequency-diameter curve gives rise to c=3.265×10-4, A=0.89692,

Coefficient of determination R2=0.99917, given the material and geometric parameters E=6.3 kPa,

ρ=103 kg/m3, L= 17mm (Fig. 3C). Both fitting gives the damping coefficient c on the same order

of magnitude, and A close to unity, which verifies our model.

5.2 Modeling of the oscillator

Here we model the photo-responsive cantilever vibration in water triggered by constant light

illumination. The vibration is governed by

2

2

1/ ph

tt t xxxx

RAw cw EIw EI

x

, (SI.5)

where x is the axial direction of the cantilever, the density, A cross section area, E Young’s

modulus, and I area moment of inertia. The boundary conditions are one end clamped and the

other end free

(0, ) (0, ) 0, ( , ) ( , ) 0x xx xxxw t w t w L t w L t . (SI.6)

The eigen-radius of bending curvature ph1/ ( )R t arises from spontaneous deformation

inhomogeneous through the thickness direction z,

/2

ph ph/2

1/ ( ) ( , ) /h

hR t z t zdz I

. (SI.7)

Light causes the hydrogel to deswell, a spontaneous isotropic volumetric deformation as can be

quantified by an eigen-photo-strain ph 0( , ) [ ( , ) / 1] / 3z t C z t C , where 0C is the pre-

illumination solvent concentration. The concentration C is governed by a one-dimensional

diffusion relation in the thickness z direction,

B

C DC

t k T z z

, (SI.8)

with the boundary conditions ph 0 on the illuminated surface and 0 on the non-

illuminated surface. Light raises the surface temperature, reducing the chemical potential from 0

to ph , equivalent to reducing the swelling ratio of the illuminated surface (with width

phd ) on

the hydrogel, making the hydrogel shrink in volume on the illuminated surface and bend towards

the incoming light direction. The cantilever turns out to vibrate up and down periodically due to

inertia and illumination collectively.

Both equations (SI.5) and (SI.8) are solved by the forward-time central-space finite difference

method. The solution of Eq. (SI.8) will enable one to calculate Eq. (SI.7) as an input to the right

hand side of Eq. (SI.5) at every time step. The parameters we use in the simulation are: laser

diameter ph / 20d L , crosslink number per monomer volume

310N , polymer-solvent

interaction constant 0.3 , photo chemical potential 4

ph B/ 5 10k T , diffusivity D=10-7 m2/s,

density 103 kg/m3, Young’s modulus E=6.3 kPa, unless otherwise stated. The simulation

results suggest that the cantilever roughly vibrates periodically within the 1st vibration mode, with

frequency shown in Eq. (SI.2) (Fig. 3B, D).

5.3 Scaling analysis of vibration frequency (eq.1)

From Eq. (SI.5), it is a standard practice in mechanics of vibration textbooks to derive the 1st,

2nd, 3rd, … natural frequencies of such a vibration system, 1

dw,

2

dw,

3

dw and so on, where the

subscript ‘d’ stands for damping and 1 2 3

d d dw w w. The

1

dw is just the ‘ dw

’ in Eq. 1 and (SI.1),

omitting the superscript ‘1’ as no other higher modes are discussed in this work.

The vibration is driven by 2 factors: the inertia of the beam itself and the forcing term on the right-

hand side (RHS) of Eq. (SI.5). The RHS of Eq. (SI.5) is caused by solvent transport/diffusion.

When the RHS forcing is of moderate (like in this work) or low frequency, the beam vibrates under

the 1st vibration mode with the lowest possible intrinsic natural frequency 1

dw (‘ dw

’ in Eq. 1).

When the solvent transport/diffusion is much faster than it is now, the system is likely to vibrate

under the 2nd vibration mode with frequency 2 1

d dw w or even higher. That is because under faster

solvent transport, the solvent migrates into/out of the illuminated spot of gel more frequently, then

the RHS of Eq. (SI.5), the forcing term will have a higher forcing frequency, perturbing the

bending shape of the 1st vibration mode into the 2nd mode or higher.

There is a simple scaling analysis to tell when the system should adopt the 1st vibration mode in

Eq. 1 or other higher order modes, by comparing the inertia time scale 4

i /t AL EI and the

diffusion time scale 2

diff /t d D (defined at the start of P.6 in manuscript). When i difft t=

,

namely diffusion is very slow, the beam adopts the 1st vibration mode with frequency 1

dw (‘ dw

’ in

Eq. 1); When i difft t?, namely diffusion is very fast, the beam adopts the 2nd vibration mode with

the frequency 2 1

d dw w or 3rd vibration mode with the frequency

3 2

d dw w , etc. Hence, from the

experimental data provided at the end of P.5 and start of P.6 in the manuscript, though the solvent

transport in this work is already quite fast for typical hydrogels, it is still slow enough to keep the

beam vibrating in the 1st mode.

In summary, Eq. 1 which is generally valid for slow or moderate speed solvent transport, is enough

to describe the phenomenon in this work where the solvent transport is quite fast but not fast

enough to trigger higher order frequencies.

5.4 Explanation of effect of inertia and diffusion on oscillation

During the oscillation, the diffusivity and speed of bending determines whether there is oscillation

or tracking while the inertia determines the frequency of the oscillation. The physical picture is

that the oscillator is operated in damping condition and there is large friction. This indicates that

the oscillation will stop without fueling it with energy input. To realize the perpetual oscillation,

energy input is needed to compensate the resistance. In this case, the energy input is provided by

light. Then, in the photo-thermal-mechanical energy conversion, the diffusion of water will affect

the kinetics of thermal-mechanical actuation and help compensate the energy loss from the system

(i.e., friction). A larger diffusivity can better compensate the resistance and help maintain the

oscillation. By contrast, a lower diffusivity would result in tracking. However, it turns out that the

actuation by diffusion is only sufficient to compensate the resistance, with little impact on boosting

the frequency, i.e., further forcing the oscillation to be faster. Therefore, parameters like fast

volume change or large diffusivity can help overcome the damping and maintain the oscillation,

but the overall frequency of oscillation is still quasi-harmonic (Eq. 1), which is mainly governed

by inertia.

Besides hydrogels, interestingly this scenario was also found in the oscillatory liquid crystal

elastomer films (18, 19, 20). With the input energy, the film was able to oscillate following the

harmonic oscillation frequency, which was consistent with ours. Although their actuation

mechanism is not driven by diffusion, we believe the physical picture of using the input energy to

compensate the resistance is highly close to our model.

5.5 Estimation of the correlation of the thrust and the velocity of the Oscibot

To analyze how the thrust (the force generated by a stroke) affects the speed of the Oscibot, we

first estimate the mean thrust T produced by the oscillator as (39, 40)

2 2

21 ( , ) ( , )m -

2v

x L

x t x tT U

t x

(SI.9)

, where U is the swimming speed of the Oscibot and approximates to a negligible number (U →

0) for analyzing the thrust, w(x,t) is the tip displacement in vertical direction. Overbar denotes the

mean values for the time derivative and spatial derivative of tip displacement, mv is virtual mass

of the oscillator and can be estimated as

2

4v m

bm c

(SI.10)

, where ρw is the density of water, b is the width of the oscillator, cm is the virtual mass coefficient.

From the equation of thrust of oscillator (Eq. (SI.9)), a higher beam tip velocity can provide larger

thrust with a quadratic law. From the experiment (Fig. 14C), we observed that with a higher beam

tip velocity, the overall Oscibot velocity was increased in a linear fashion. Therefore, a larger thrust

results in higher overall velocity of the Oscibot.

Movie Description

Movie S1. Hydrogel-based light-driven oscillator. Light-driven self-sustained oscillation of a

gel-made pillar with the dimensions 14 mm (L)×0.9 mm (d) and the scale bar is 10 mm (also see

Fig. 1B). The light source is a green laser (532nm) with the diameter of 1 mm and the input power

of 500 mW.

Movie S2. Comparison of light-induced tracking and oscillation. Three pillars (L = 17 mm, d

= 0.9 mm) of different cross-linking densities (with 1.5, 2.0, and 3.0 wt.% BIS respectively) were

placed at the bottom of a water bath. Pillars were actuated by a 300 mW light which was switched

on at the 5th second and off at 60th second. Pillars were bent towards the light, started tracking or

oscillation and recovered once the light was switched off. The tip displacement analysis is shown

in Fig. S7.

Movie S3. Fishhook-shaped hydrogel oscillator. Self-shadowing is hypothesized to be the

governing mechanism for oscillation, since the hydrogel cantilever recovers when the hinge is

blocked by the tip (Fig. S9A). Here we simplify the model to a two-irradiation-spots case, where

the light only shine on the tip and hinge, yet the pillar still exhibits oscillation. This demonstrates

it is the shrinkage and relaxation of the hinge that enables the oscillation.

Movie S4. Position independency. The pillar was placed horizontally and upside down, while the

light was approaching from the top and right, respectively, ensuring that the deflection angle is 90°

(Fig. S9B, S9C). This demonstrates that the oscillation can be maintained only if the deflection

angle is fixed, and that oscillation is independent of initial pillar orientation.

Movie S5. Realization of omnidirectional oscillation. The video showcases two demos of

oscillation at different zenith angles and different azimuthal angles, aiming to reflect the

omnidirectional response of the pillar to the stimuli from the entire 3D space.

• Demo 1, The pillar with 0.9 mm in diameter was originally placed upright. As the 500 mW light

came from different zenith angles and shined on the same spot of the pillar, the pillar oscillated at

different deflection angles following these incident directions. Each measurement started from

fully unbent vertical state and oscillation was initiated after achieving the light tracking (Fig. 2C,

2D, 2E).

• Demo 2, The pillar with 0.9 mm in diameter was originally placed upright and the 500 mW of

light came from four different azimuthal angles, covering the whole horizontal plane of the pillar.

The pillar bent down to the corresponding direction of light and started oscillation (Fig. 2F).

Movie S6. Oscillation frequency as a function of geometry. The video exhibited the oscillation

of pillars with L =13, 17, and 22 mm, d=0.56 mm to explore the arm length frequency dependence.

Then, the pillars with d=0.56, 0.78, and 1.03 mm, L=17 mm were used to explore the diameter

frequency dependence (Fig. 3A, 3C).

Movie S7. Initialization: From tracking to oscillation. Originally, 150 mW of light shined on a

pillar and the pillar tracked the light source. Then, the input power was instantly increased from

150 mW to 300 mW. As a result, the pillar started oscillating with the amplification increasing for

about five cycles and eventually reaching a steady oscillation state (Fig. S8).

Movie S8. Long-term stability of the oscillation. With a diameter of 0.56 mm and a length of 22

mm, the hydrogel oscillation can be maintained for more than 3600 seconds at 200 mW (Fig. 4D).

The amplitude of oscillation was around 0.5 mm. We observe a slight amplitude increase together

with frequency drop at the first 10 minutes of the oscillation, after which the frequency curve was

flattened (Fig. 4E). This is because it takes some time for the oscillator to reach dynamic

equilibrium. When water-induced kinetic energy dissipation is relatively small, the oscillation

amplitude grows as vibration goes on, until the amplitude reaches a certain stable value, when the

dynamic equilibrium is reached. The growth of amplitude naturally causes a longer traveling

distance of water damping, enlarging the time period of each cycle, and lowering the frequency.

The specific analysis of amplitude variation over time will be discussed in our correlated paper.

Movie S9. OsciBot: Continuous swimming. The OsciBot floated on water surface in a

rectangular water container (Fig. S13). Once light (input power = 450 mW) was shone on the

paddle part of the OsciBot continuously, the OsciBot gradually swam away from the light (Fig.

5C). The typical swimming behavior was recorded with the side.

Movie S10. OsciBot: Controllable motion. The OsciBot was originally placed on the water

surface and the paddle part was exposed to the 450 mW light. The light was switched on at the

different time points of 20, 230, and 450 seconds, and the OsciBot started oscillating and constantly

swimming away from the light source. By turning the light off at the 200 and 415 seconds, the

OsciBot gradually reduced its speed and eventually stopped (Fig. 5F).

Movie S11. Oscillation under ambient white light. The self-sustained oscillation of a PANi-

PNIPAm pillar with the dimensions 29 mm (L)×0.48 mm (d). The light source is a white LED and

the input power is about 2.5 suns. The pillar was originally upright and incident light came from a

deflection angle of 70°. The amplitude of oscillation was relatively small and slightly chaotic,

respectively due to the lower light intensity in comparison to the laser operation and the diffusive

light direction that made the actuation less regular.