Self-oscillating Gel Accelerated while Sensing the Shape of an

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Self-oscillating Gel Accelerated while Sensing the Shape of an Aqueous Surface Miyu Yoshii, Hiroya Yamamoto, Yutaka Sumino, and Satoshi Nakata Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b00337 • Publication Date (Web): 31 Mar 2016 Downloaded from http://pubs.acs.org on April 1, 2016

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Self-oscillating Gel Accelerated while Sensing the Shape of an Aqueous Surface

Miyu Yoshii1, Hiroya Yamamoto1, Yutaka Sumino2, and Satoshi Nakata1,3,*

1. Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan

2. Department of Applied Physics, Faculty of Science, Tokyo University of Science, 6-3-1 Niijuku, Katsushika, Tokyo 125-8585, Japan 3. Research Center for the Mathematics of Chromatin Live Dynamics, Japan

*To whom correspondence should be addressed.

Tel. & fax: +81-824-24-7409

E-mail: [email protected]

1

ACS Paragon Plus Environment

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ABSTRACT: The

reciprocating

motion

of

a

self-oscillating

square

gel

Belousov-Zhabotinsky (BZ) reaction was investigated on an aqueous surface.

induced

by

the

The chemical wave

propagated from the side at which the oxidation of the Ru-catalyst in the gel started.

As the

chemical wave propagated, the gel moved in either the opposite (Mode I) or the same (Mode II) direction as the chemical wave propagation.

The gel then went back as the Ru-catalyst in the gel

was slowly reduced. We examined the relationship between the modes of motion (Mode I or II) and the shape of the aqueous BZ solution surface.

The mode selection was discussed in relation to

the contact angle around the gel which was changed by the BZ reaction; i.e., the lateral imbalance of surface tension and the capillary interaction.

KEYWORDS.

oscillation, polymer gel, Belousov-Zhabotinsky reaction, self-propelled system

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1. INTRODUCTION Autonomous actuators or self-propelled motors that can move themselves or transport objects to a target location in a narrow space have attracted interest in medicine and engineering.1-4 The movement of these actuators or motors is externally controlled, so precise design and manufacture are needed for complex functions, such as taxis in living organisms that exhibit characteristic responses to the physicochemical environment.

This is a major challenge in creating

complex machinery in nonliving systems. Nonlinear chemical reaction can produce self-organization such as spatio-temporal patterns.5-9

These nonlinear effects can allow actuators or motors to respond to their

environment.10, 11

In this way, complex functions in living organisms are mimically reproduced by

using self-organization even without precise design nor manufacture. self-oscillating

polymer

gel

composed

of

N-isopropylacrylamide

For this purpose, a (NIPAAm)

and

[Ru(bpy)2(4-vinyl-4’-methylbpy)]2+ (Ru(bpy)2(vmbpy)) catalyst has been investigated as an autonomous actuator.12-18

The Ru-catalyst periodically alternates between oxidation (Ru3+: green)

and reduced (Ru2+: orange) states in the Belousov-Zhabotinsky (BZ) reaction inside of an appropriate solution (BZ solution).

The gel containing the Ru-catalyst swells or shrinks depending

on whether the Ru-catalyst is in the Ru3+ or Ru2+ state. self-oscillation in BZ solution.19-21

Hence, the gel shows periodic

Several applications of such self-oscillating gels as chemical

robots have been developed including using a the self-oscillating gel on a solid ratchet,13 and the peristaltic motion of the self-oscillating gel in BZ solution.14 In this study, we examined the motion of the gel floating on an aqueous BZ solution. gel showed reciprocating motion synchronized with the BZ reaction. modes of motion during the chemical wave propagation.

The

In addition, there were two

These modes were characterized by the

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directions of the chemical wave propagation and the gel motion. surfaces were changed to clarify the selection of modes.

The shapes of the aqueous

We discuss the mechanism of the mode

selection based on the lateral imbalance of surface tension and the capillary interaction.22-24

2. EXPERIMENTAL SECTION A NIPAAm gel sheet was prepared based on a previous procedure.13,

24, 25

We used

NIPAAm (Wako Pure Chemical Industries, Ltd., Osaka, Japan), Ru(bpy)2(vmbpy) (Fuji Molecular Planning Co., Ltd., Yokohama, Japan),

2-acrylamido-2-methylpropanesulfonic acid (AMPS)

(Tokyo Chemical Industry Co., Ltd., Japan), N,N’-methylenebisacrylamide (MBAAm) (Kanto Chemical Co., Inc., Tokyo, Japan) as a cross-linker, and 2,2’-azobis (isobutyronitrile) (AIBN) (Wako Pure Chemical Industries, Ltd.) as an initiator.

The Ru-catalyst was chemically

immobilized in the gel; i.e., there was no catalyst in the aqueous phase. chemical wave propagated only inside of the gel. pure water.

For this reason, the

The gel sheet was stored at room temperature in

The stored sheet was used for experiments within several months after it was prepared.

The gel sheet was cut into pieces with a razor (blade thickness: 0.1 mm, Feather Safety Razor Co., Ltd., Osaka, Japan).

A square of the gel sheet (3 × 3 × 1 mm) as a self-oscillating object was

floated on the aqueous BZ solution. acid, and 0.894 M nitric acid.13-18

BZ solution consisted of 0.084 M NaBrO3, 0.0625 M malonic The experiments were performed in a thermostat water bath at

291 ± 1 K (TGB045AE, Advantec, Tokyo, Japan).13-17 The motion of the gel was monitored with a digital video camera (HDR-CX590, SONY; minimum time-resolution, 1/30 s), and the images were analyzed with an image processing system (ImageJ, National Institute of Health, Bethesda, MD, USA). state.

The color of the gel changed from orange to green as it changed from reduced to oxidation Therefore, we measured the ratio of the green area, φg.

As the chemical wave propagated,

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φg increased 0 to 100%. To obtain a desired local shape of the aqueous surface, we prepared three different geometries, i.e., concave, horizontal, and convex (see Figure 1).

Figure 1 shows the measurements of

the water level, ∆h, with a laser confocal displacement meter. We set the height of the edge of the Petri dish as ∆h = 0. We measured three geometries of (a) concave for a glass Petri dish (ID = 16 mm), (b) horizontal for a Petri dish (ID = 34 mm) of which inside was placed in a silicon seat (thickness: 1 mm), and (c) convex for the glass Petri dish (ID = 34 mm, volume: 12.7 mL) when a larger amount of the BZ solution (volume: 13 mL) was poured. The sloped regions of concave and convex geometries were 3.0 < r < 8.0 mm and 10.0 < r < 17.0 mm, respectively, and the flat region of horizontal geometry was 0 < r < 14 mm, where r is the radial distance from the center of the Petri dish in the shaded regions in Fig. 1. The geometry of the surface was prepared by

changing the wall of the container or the amount of solution.

For the concave geometry, BZ

solution (1 mL) was poured into a glass Petri dish (inner diameter (ID) = 16 mm) (Fig. 1a).

For

the horizontal geometry, a silicon seat (thickness: 1 mm) was placed in the Petri dish (ID = 34 mm), and BZ solution (5 mL) was poured into it (Fig. 1b).

For the convex geometry, BZ solution (13

mL) was poured into a glass Petri dish (ID = 34 mm) (Fig. 1c). shapes of the surfaces as sloped and flat.

and |

Next, we classified the local

Sloped and flat surfaces have gradients of |

dz | ≥ 0.03 dx

dz | < 0.03, respectively, where x and z are the horizontal and vertical positions of the surface, dx

respectively.

Concave and convex geometries were used for the sloped surface, whereas horizontal

geometry was used for the flat surface.

The sloped regions of concave and convex geometries had

3.0 < r < 8.0 mm and 10.0 < r < 17.0 mm, respectively, and the flat region of horizontal geometry was 0 < r < 14.0 mm, where r is the radial distance from the center of the Petri dish (shaded regions in Fig. 1).

The size of the sloped surfaces in a container corresponds to that of meniscus which is 5


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scaled by the capillary length (about 2 mm).26

Figure 1. Experimental results on the water level, ∆h, which was classified as three geometries of (a) concave (ID = 16 mm), (b) horizontal (ID = 34 mm), and (c) convex (ID = 34 mm). We defined the height of the edge of the Petri dish as ∆h = 0. The shaded regions indicate the sloped and flat surfaces. The used aqueous surfaces in (a), (b), and (c) correspond to those in Figs. 3, 4, and 5, respectively. r is the radial distance from the center of the Petri dish.

3. RESULTS Reciprocating motion of a gel synchronized with the BZ reaction When a gel was placed on the aqueous BZ solution, oxidation started from one side of the gel.

The green area, which corresponded to the oxidation region (chemical wave), propagated on

the gel.

The whole of the gel was oxidized as the chemical wave swept across the gel.

the gel slowly returned to the reduced state with orange color. and periodically.27

Finally,

This process occurred repeatedly

The direction of motion was maintained as the chemical wave propagated

(forward motion), and the direction was reversed when the gel returned to the reduced state (reverse motion).

The forward motion and the chemical wave can be in the opposite direction (Mode I: 100

≤ |θd| ≤ 180°) or the same direction (Mode II: 0 ≤ |θd| ≤ 80°) (Figure 2).

Here, θd is the angle

between the directions of the forward motion and the chemical wave propagation. We defined the 6


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marginal case (80 ≤ |θd| ≤ 100°) as Mode III.

If the direction of the motion is determined by

chance, the ratio of θd for Mode I is calculated as ((180° − 100°)/180°) × 100 = 44.4%, and as 44.4 and 11.2% for Modes II and III, respectively.

Figure 2. Schematic of (a) the forward motion of the gel on an aqueous surface coupled with the BZ reaction (slanted view) and (b) definition of the three modes of motion (Modes I, II, and III) of the gel (top view) by the angle between the directions of the forward motion and chemical wave propagation (θd).

Reciprocating motion of a gel on a sloped surface Figure 3 shows the typical reciprocating motion of a self-oscillating gel on a sloped surface in the concave geometry (Movie S1 in SI).

Here, D is the distance between the center of the Petri

dish and the center of the gel from the top view, and v (= dD/dt) is the velocity of the gel. Synchronization between the reciprocating motion and the BZ oscillatory reaction was observed. Periodic oscillation of the ratio of the green area in the gel, φg, reflects the chemical wave propagation. When φg increased to about 15%, the forward motion started.

In Fig. 3, the forward

motion was in the opposite direction to that of the chemical wave propagation (|θd| = 162°, Mode I). The gel then slowly went back to the center of the Petri dish (reverse motion), whereas φg started to decrease from 100%.

We confirmed that the gel did not collide with the wall of the Petri dish 7


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when v was zero (D was at its maximum) (Fig. 3b-3).

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The forward motion resumed from the

reverse motion before the gel reached the center of the Petri dish.

Although the forward motion

lasted for a shorter time, it was faster than reverse motion.

The amplitude and baseline of D were

almost maintained for the individual reciprocating motion.

The number of oscillation was at least

8-10 times for 1 hour observation in the individual experiments. for 1 hour, but after that, decreased with time.

Period of oscillation maintained

Therefore, we selected 3-4 oscillations as the

stationary experimental results.

Figure 3. (a) Snapshots of the reciprocating motion of a gel on a sloped surface (top view), (b) time-course of (b-1) the ratio of green area, φg, (b-2) the velocity of the gel on the BZ solution, v, and (b-3) the distance between the center of the Petri dish (×) and that of the gel, D (Mode I). ID = 16 mm (Fig. 1a). The horizontal bar in (b-1) corresponds to the timespan shown as the snapshots in (a). The dotted line in (a) was drawn from the center to a wall of the Petri dish via the center of 8


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the gel at t = 17 min. v is positive when the gel moves from the center to the wall of the Petri dish. The red dotted lines denote the time at v = 0.

On the sloped surface in the concave geometry, Mode I was mainly observed, although Mode II was also observed sometimes (Fig. S1).

The forward motion of the gel was in the same

direction as the chemical wave propagation in Mode II.

The gel began moving forward when φg

reached around 5%, whereas corresponding φg was around 15% for Mode I. frequently observed (probability: 56%) on the sloped surface.

Notably, Mode I was

The gel moved forward toward the

higher water level even for Mode II.

Reciprocating motion of a gel on a flat surface Figure 4 shows the reciprocating motion of a self-oscillating gel on a flat surface in the horizontal geometry (Movie S2 in SI).

In this case, the forward motion of the gel was in the same

direction as the chemical wave propagation (|θd| = 18°, Mode II). mainly observed (probability: 77%).

On the flat surface, Mode II was

This result is consistent with our previous report,24 which

was mainly conducted on a flat surface.

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Figure 4. (a) Snapshots of a gel on a flat surface (top view), (b) time-course of (b-1) φg, (b-2) v, and (b-3) D (Mode II). ID = 34 mm (Fig. 1b). The horizontal bar in (b-1) corresponds to the timespan shown as the snapshots in (a). The dotted line in (a) was drawn from the center to a wall of the Petri dish via the center location of the gel at t = 39 min. The definition of v and the meaning of the red dotted line are the same as those in Fig. 3.

Probabilities of Mode I and II on a sloped and a flat surface Table 1 shows the probabilities of finding each motion, for a sloped and a flat surface. The probability of Mode I was higher than that of Mode II for the sloped surface, whereas Mode II was dominant for the flat surface.

Table 1. Probabilities of selection for Modes I, II, and III when the gel showed its reciprocating motion on sloped and flat surfaces. The probabilities were obtained from 46 experiments (113 oscillations) for the sloped surface and 7 experiments (30 oscillations) for the flat surface. The data for “sloped” and “flat” surfaces were used at ID = 16 mm and 34 mm, respectively.

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Forward motion of a gel toward a higher water level To confirm the mechanism of the forward motion of a gel toward a higher water level, we performed the experiment with a convex geometry.

Figure 5 shows the reciprocating motion of the

gel on a sloped surface in the convex geometry (Movie S3 in SI).

The slope existed as in the

concave geometry, although the water level at the center of the Petri dish was higher than that around the wall for the convex condition (see Fig. 1c).

When the chemical wave was generated

from the side of the gel, the direction of the forward motion was up the slope; that is, toward the center of the Petri dish.

This motion was classified as Mode I (|θd| = 139°).

Interestingly, the

maximum speed of the forward motion was lower than that of the reverse motion.

The

probabilities of observing Modes I and II were 91% and 9%, respectively, i.e., Mode I was preferred on the sloped surface.

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Figure 5. (a) Snapshots of a gel on a sloped surface (top view), (b) time-course of (b-1) φg, (b-2) v, and (b-3) D (Mode I). ID = 34 mm (Fig. 1c). The horizontal bar in (b-1) corresponds to the timespan shown as the snapshots in (a). The dotted line in (a) was drawn from the center to a wall of the Petri dish via the center of the gel at t = 48 min. The definition of v and the meaning of the red dotted line are the same as in Fig. 3.

4. DISCUSSION We discuss the mechanism of the forward motion of a gel (Mode I and II) synchronized with the oxidation of the gel based on our experimental results and related studies.22-24, 27-30

Figure 6

shows a schematic of two kinds of the lateral force around the gel, namely the lateral imbalance of surface tension (Fs)24 and the capillary interaction (Fc).28 positive and left in Fig. 6.

The direction of the forward motion is

Contact angle θ is defined as γaw cosθ = γag − γwg, where γaw, γag, and γwg

denote the interfacial tensions of the air-water, air-gel, and water-gel interfaces. the position on the contact line as well as time.

θ is a function of

The driving force of the gel (F) is expressed as the 12


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sum of Fs and Fc, F = Fs + Fc,

(1)

where Fs is the difference between the lateral forces on the left (FL) and right (FR) sides of the gel (Fig. 6a), and is given by Fs = FL − FR = lw γaw (sinθL − sinθR),

(2)

where lw is the width of the contact line of the gel, and θL and θR are the contact angles at the left and right sides, respectively. When the whole gel is in the reduced state, the lateral force is balanced, Fs = FL − FR = lw γaw (sinθred − sinθred) = 0, where θred is the contact angle in the reduced state.

When

the chemical wave was generated on the right side of the gel, i.e., the right side of the gel is oxidized, the left side remains reduced.

In this situation, the contact angles for the two sides are different.

As we reported in our recent paper,24 the contact angle of the gel in the oxidation state (θox) is smaller than that in the reduced state (θred).23 Therefore, the lateral imbalance of surface tension (Fs) appears; the lateral force of the oxidation side, FR (= lw γaw sinθox), is lower than that of the reduced side, FL, (= lw γaw sinθred). lw γaw (sinθred − sinθox) > 0.

The driving force of the difference in the contact angle is Fs =

Thus, the gel moves in the same direction as the chemical wave

propagation. The capillary interaction, Fc, can be estimated by taking a far field approximation of the meniscus shape.28

In this approximation, Fc is determined by the contact angle around the gel, and

the hypothetical slope of the air-water interface, in the absence of the floating gel.

dz , which corresponds to the shape of the interface dx

Here, we take x and z as the horizontal and vertical position of

the interface, respectively, as in Fig. 6b, and gravity acts in the z direction.

The total gravitational

force, including buoyancy, acting on the gel should be balanced by the vertical surface force acting on the contact line.

Thus, we have, 13


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~ g = −γ m aw ∫ cos θ (l ) dl ,

(3)

~ is the effective mass considering buoyancy, and g is the gravitational acceleration. where m integral is taken over the contact line around the gel. float on the aqueous surface.

The

If this balance is disrupted, the gel cannot

Thus, the effective potential, U(z(x)), of the floating gel is expressed

as28 ~ gz ( x ) = −γ z ( x ) cos θ (l ) dl . U ( z ( x )) = m aw ∫

(4)

By taking the derivative of U with respect to x, we obtain the capillary interaction as

Fc = −

d dz U ( z( x)) = γ aw ∫ cosθ (l )dl . dx dx

For example, Fc, red = γ aw

(5)

dz dz cosθ red L when the gel is fully reduced, and Fc, ox = γ aw cosθ ox L dx dx

when the gel is fully oxidized, where L = 4l w = ∫ dl is the peripheral length of the square gel. Therefore, we have Fc, red < Fc, ox, from cosθred < cosθox.

Thus, the attractive force in the uphill

direction increases as the contact line of the gel changes from the reduced to the oxidation state, irrespective of the initiated position of the wave (Fig. 6b).

The attractive force reaches the

maximum when the gel is fully oxidized. When the gel is on a flat surface, dz/dx = 0, Fc = 0 from eq 5, so from eq 1, the driving force F = Fs.

Owing to this lateral imbalance of surface tension, the gel is propelled in the same direction

as the chemical wave propagation (Mode II).

Because the shape of the gel is not perfectly smooth

and symmetric, the probability of Mode II on the flat surface is not 100%; nonetheless, Mode II was dominant. In contrast to the flat surface, the gel always climbed the sloped surface (Figs. 3 and 5) when the gel became the oxidation state. Both the lateral imbalance of surface tension, Fs, and the capillary interaction, Fc, occur on the sloped surface.

The time profile of velocity, v, was different

14


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for Modes I (Fig. 3) and II (Fig. S1).

In Mode I, the gel descended the hill from φg ~ 0% to 15%,

even after the chemical wave was generated.

This can be explained by Fs, which pushes the gel in

the opposite direction to the wave generation point, initially overwhelmed Fc. gel went upward, and Fc became larger than Fs.

After φg ~15%, the

However, the gel immediately accelerated uphill

after the chemical wave was generated (φg ~ 5%) in Mode II (Fig. S1). forces, Fs and Fc, act cooperatively to propel the gel uphill.

In this situation, the two

Using the typical value, we obtain Fs =

6 µN, and Fc, red = 32 µN, Fc, ox = 35 µN, based on eqs 2 and 5.

To obtain these values, we used

dz/dx = 0.149 at D = 2.3 mm (x = 4.3), and lw = 2 mm for the experimental data of Fig. 3, and the value γaw = 40 mN m-1, θred = 48 rad, θred = 42 rad.24

The orders of Fc are similar to that of Fs.

However, we should further consider the resistive force around the gel on eqs 2 and 5 since the actual driving force (~ nN), which is obtained based on the experimental results on Fig. 3, is significantly smaller than that for Fc as the future work.

Figure 5 suggests that the gel moves in the direction of

the higher water level, and the gel is not pulled toward the glass wall by the electrostatic force because of the increase in valence of the Ru-catalyst in the gel.

The low speed of the forward

motion in Fig. 5 can be explained by the dependence of Fc on the local slope of the aqueous surface. The size of the slope was smaller at the center of the Petri dish, so Fc and v for the forward motion decreased. Therefore, Mode II should be observed frequently on the flat surface, whereas the probability of observing Mode I increased on the sloped surface. observed on the sloped surface.

Modes I and II were both

Our consideration of the mechanism based on the combination of

the lateral imbalance of surface tension and the capillary interaction should lead to the conclusion that the probability of Mode I should be equal to that of Mode II even on the sloped surface.

Thus,

the slight preference for Mode I on the sloped surface cannot be explained by our simplified 15


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mechanism.

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In future work, we may need to consider the near field effect in the capillary

interaction30 to explain the preference for Mode I.

Figure 6. Schematic of forces of (a) the lateral imbalance of surface tension, Fs, and (b) the capillary interaction, Fc. When the gel is oxidized (green), the contact angle changes from θred to θox. In (a), Fs propels the gel by Mode II motion on an arbitrary surface. The change in the contact angles also induces the capillary interaction that makes the oxidized gel climb the slope.

5. CONCLUSIONS Our main finding is that there are two types of reciprocating motion for a gel synchronized with the BZ oscillatory reaction.

The modes of the gel motion are characterized by the directions

of the forward motion and the chemical wave propagation. I and the same in Mode II motion. for Mode II on a flat surface.

These directions are opposite in Mode

We observed a preference for Mode I on a sloped surface and

The selection of two reciprocating motions depending on the shape

of the aqueous surface was discussed based on the change in the contact angle around the gel. Only the lateral imbalance of surface tension was significant on a flat surface, whereas both the lateral imbalance of surface tension and the capillary interaction acted cooperatively on a sloped surface. This study suggests that two different forces originating from the change in surface tension 16


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can act on the floating gel accompanied by oscillatory swelling.

This complex behavior was

achieved by introducing the nonlinear reaction, i.e., the BZ oscillatory reaction.

We expect that

accumulation of the many gels on the same aqueous surface will produce to self-organized collective motion.

ACKNOWLEDGMENTS We thank Dr. R. Yoshida (The University of Tokyo, Japan), Dr. Y. Hara (AIST, Japan) for providing important suggestions about the synthesis and properties of polymer gels, Prof. H. Kitahata for his technical assistance with the measurement of water levels, and Prof. K. Ito for his technical assistance with the motion analysis.

This study was supported in part by a Grant-in-Aid

for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 25410094) to SN, a Grant-in-Aid for Young Scientists B (No. 24740287), the Cooperative Research Program of "Network Joint Research Center for Materials and Devices" to SN, YS and MY, Platform for Dynamic Approaches to Living System from the Ministry of Education, Culture, Sports, Science and Technology, Japan, the Sasakawa Scientific Research Grant from The Japan Science Society to MY, and JSPS Bilateral Joint Research Project between Japan and the Polish Academy of Sciences.

ASSOCIATED CONTENT Supporting Information.

Movies S1, S2, and S3 of reciprocating motion, which correspond to Figs.

3, 4, and 5, are shown.

This information is available free of charge via the Internet at 17


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http://pubs.acs.org.

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Mode selection of the forward motion of the self-oscillating gel on an aqueous surface coupled with the BZ reaction. 467x217mm (300 x 300 DPI)


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Self-oscillating Gel Accelerated while Sensing the Shape of an

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