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: [email protected]
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.
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