Direct Observation of Periodic Swelling and Collapse of Polymer

Article pubs.acs.org/JPCB

Direct Observation of Periodic Swelling and Collapse of Polymer Chain Induced by the Belousov−Zhabotinsky Reaction Yusuke Hara,*,† Hiroyuki Mayama,‡ Yoshinori Yamaguchi,§ Yoshiko Takenaka,† and Ryushi Fukuda⊥ †

Nanosystem Research Institute (NRI), National Institute of Advanced Industrial Science and Technology (AIST), Central 5-2, 1-1-1 Higashi, Tsukuba 305-8565, Japan ‡ Department of Chemistry, Asahikawa Medical University, 2-1-1-1, Midorigaoka-Higashi, Asahikawa 078-8510, Japan § Photonics advanced research center (PARC), Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita-city, Osaka 565-0871, Japan ⊥ MEIWAFOSIS CO., LTD, 1-14-2 Shinju-ku, Tokyo 160-0022, Japan S Supporting Information *

ABSTRACT: By utilizing a quartz crystal microbalance with dissipation (QCM-D), we directly observed the self-oscillating behavior of a polymer chain induced by the Belousov− Zhabotinsky (BZ) reaction. We succeeded in measuring selfoscillations of the resonance frequency (Δf) and dissipation (ΔD), which originate in the self-oscillating behavior of the polymer chain on a gold surface induced by the BZ reaction. We synthesized a self-oscillating polymer chain with Ru as the catalyst of the BZ reaction and a chemical adsorption site, so as to directly observe its periodic swelling and collapse on the gold surface. Distinct self-oscillation of ΔD synchronized with the selfoscillation Δf was observed. The period of the Δf self-oscillation was about 400 s, and the induction time was about 6.5 h. In QCM-D measurements, we found that the peaks of Δf and ΔD oscillations did not coincide in time because the state of the Gaussian chain did not coincide with the maximum value of Δf. Moreover, examination of the relationship between Δf and ΔD revealed that their oscillatory waveforms were identical in frequency but differed in phase and amplitude.

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INTRODUCTION Many types of nanosized molecular machines have been developed by utilizing intelligent materials such as stimulusresponsive polymer systems.1−8 The conformations of these polymer systems vary with changes in external conditions such as solvent composition, ionic strength, electric field, temperature, and pH. Therefore, stimulus-responsive molecular machines show promise for application to soft actuators, micropumps, microvalves, soft robots, and other medical related devices by leveraging their lightweight, flexibility, and low noise.9 To drive these molecular machines, external devices to control the external stimuli are indispensable. In contrast, living bodies possess intrinsic mechanisms that generate autonomous activities. Moreover, living organisms have an isothermal conversion system to convert chemical energy into mechanical work, which underlies their motility. The efficiency of this process, in which a chemical reaction is directly converted into mechanical energy, is significantly higher than that of a conventional stimulus-responsive material, because the process in a living organism does not have intermediate steps. If autonomous nanosized molecular machines with high efficiency could be realized by tailor-made molecular designs, unprecedented nanodevices that do not require external control devices © 2013 American Chemical Society

could be created. To construct an autonomous molecular machine with high energy efficiency, we selected the Belousov− Zhabotinsky (BZ) reaction as an energy source. In this reaction, temporal and spatial oscillating phenomena such as spirals or target patterns can be observed in an unstirred solution.10−16 In addition, many researchers have regarded the BZ reaction as analogous to the TCA cycle (Krebs cycle). In previous studies, the BZ reaction, which can be considered a simple model for analyzing how spatiotemporal structures are formed, has been extensively investigated by experimental and theoretical approaches. In this reaction, organic matter is oxidized by an oxidizing agent in the presence of a metal catalyst and strong acid, and the oxidation number of ruthenium tris(2,2′bipyridine), which is the metal catalyst of the reaction, exhibits oscillations. As the redox number of the Ru catalyst changes autonomously, a concomitant change occurs in the solubility of the Ru catalyst. To convert the autonomous solubility change in the Ru catalyst in polymer chain self-oscillations, a polymer chain that consists of poly-(N-isopropylacrylamide) (PNIReceived: June 17, 2013 Revised: October 18, 2013 Published: October 22, 2013 14351

dx.doi.org/10.1021/jp408417h | J. Phys. Chem. B 2013, 117, 14351−14357

The Journal of Physical Chemistry B

Article

gold surface sensor was installed in the QCM-D with one side exposed to the solution. The QCM-D can measure the change in adsorbed mass with ng/cm2 sensitivity by determining the frequency shift to within ±1 Hz in aqueous solution. In the QCM-D measurement, the resonant frequency (Δf) decreased as a substance was absorbed onto the sensor gold surface. Δf has been found to vary in proportion to the change of mass (Δm). The Sauerbrey equation is shown to be satisfied when the added mass is distributed on the gold surface and much smaller than that of the quartz crystal.28

PAAm) covalently bonded to ruthenium tris(2,2′-bipyridine) (Ru(bpy)3) was synthesized. Soluble−insoluble self-oscillation of the polymer chain occurred because of the autonomous change in the solubility of Ru(bpy)3 induced by the BZ reaction under constant temperature.17,18 Previously, there have been many reports on various functions of the self-oscillating polymer chain.19−24 Hara et al. demonstrated on−off switching of the self-oscillating behavior of the polymer chain25 and a selfoscillation of viscosity at a high concentration of the polymer solution.26 To control the behavior of the autonomous molecular machine precisely, a detailed analysis of the selfoscillating behavior of the polymer chain is important. However, few studies have directly observed the periodic swelling and collapse of a polymer chain induced by the BZ reaction.27 In this study, we directly observed self-oscillation of water adsorption−desorption on the polymer chain by utilizing a quartz crystal microbalance with dissipation (QCM-D). QCMD measurements can detect changes in the mass and structure of a polymer chain on a gold surface. We synthesized a selfoscillating polymer chain composed of PNIPAAm, a thermoresponsive molecule, covalently bonded to the Ru catalyst in the BZ reaction and an N-succinimidyl group as the gold-surface adsorption site to observe the periodic swelling and collapse of the polymer chain. By utilizing the QCM-D, we succeeded in observing self-oscillations that involved the periodic swelling and collapse of the polymer chain induced by the BZ reaction on a gold surface.

Δm = C

Δf n

(1)

Here, C, n, and Δf are the constant of the quartz crystal, the overtone number (n = 1, 3, 5, 7, ...), and the frequency shift in the measurement. In this study, C was set to 17.8 ng/(cm2 Hz). The QCM-D also measures ΔD of the quartz crystal by periodically switching the voltage on and off. ΔD is defined as: ΔD = −

Edissipated 2πEstored

(2)

where Edissipated is the energy lost during one oscillation cycle and Estored is the energy stored in the oscillator.29,30 As the driving voltage of the piezoelectric oscillator is turned off, the driving voltage over the quartz crystal is attenuated exponentially as a damped sinusoidal function.30,31 ΔD is considered an indicator of viscoelasticity of the substance absorbed on the gold surface. ΔD is not connected to any quantitative theory. In previous investigations, a dense and compact polymer was shown to have a smaller D value than an extended and flexible polymer.29,30,32,33 This is due to the friction between the polymer and the solvent molecules. Therefore, the change in ΔD was assumed to be caused by the conformational change in the polymer chain adsorbed on the gold surface. QCM-D Measurements. The gold-coated resonator was cleaned by using an ultrasonic bath sonicator for 3 h, rinsed with ethanol, and blown dry. The gold surface was modified by using 8-amino-1-octanethiol hydrochloride (−SH chemical agent). The −SH chemical agent was dissolved in 100 mM ethanol/water (50/50) solution. The gold surface, which was protected on one side, was immersed in the thiol solution at 20 °C. The QCM-D can maintain the temperature of the solution to within ±0.02 °C. The gold surface was then washed with ethanol. The mass of the −SH chemical agent chemically bonded to the gold surface was 11.2 ng/cm2. The gold surface with the −NH2 surface was again immersed in a 5 wt % poly(NIPAAm-co-Ru(bpy)3-co-NAS) solution, after which it was washed with the ethanol solution. The polymer solution was prepared by dissolving the polymer in the ethanol/water (50/50) solution. The mass of the self-oscillating polymer chain chemically bonded to the gold surface was 48.9 ng/cm2. The polymer chains were chemically bonded to the gold surface with a loop-train-tail structure because the NAS adsorption site is randomly incorporated into the polymer chain. Figure 2 shows the procedure to prepare the gold surface with the selfoscillating polymer chain for QCM-D measurements. In present investigation, the masses of the −SH chemical agent and self-oscillating polymer chain were acquired from the third overtone (n = 3). QCM-D measurements of the self-oscillating behavior were conducted in an aqueous solution that included three BZ substrates (nitric acid ([HNO3] = 0.3 M), sodium

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EXPERIMENTAL SECTION Polymerizations. The self-oscillating polymer chain (see Figure 1) was prepared as follows. 4-Vinyl-4′-methyl-2,2′-

Figure 1. Chemical structure of the self-oscillating polymer chain.

bipyridinebis(2,2′-bipyridine)bis(hexafluorophosphate) (Ru(bpy)3; 1.6 g), N-isopropylacrylamide (NIPAAm; 12.6 g), Nsuccinimidyl acrylic acid (NAS; 0.8 g), and 2,2′-azobisisobutyronitrile (0.2 g) were dissolved in ethanol (59.8 g) under a total monomer concentration of 20 wt %. Poly(NIPAAm-coRu(bpy)3-co-NAS) was synthesized by free-radical polymerization at 60 °C for 8 h under N2 bubbling. The resulting reaction mixture was dialyzed against ethanol for 30 days by repeatedly exchanging the ethanol. QCM-D Technique. QCM-D systems (Q-Sense, Sweden) enable time-resolved measurements of the changes in both resonance frequency (Δf) and energy dissipation (ΔD), where Δf relates to added mass (including coupled water) and ΔD relates to frictional (viscous) losses in the added layer on the gold surface of the sensor. In this study, QCM-D measurements were performed at 20 °C in a liquid environment. In the QCMD system used here, an AT-cut quartz crystal with a fundamental frequency ( f 0) of 5 MHz was adopted. The 14352



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Figure 2. Schematic illustration of the procedure for polymer layer on a gold surface. Figure 3. (A) Self-oscillation at the resonance frequency (Δf) for fixed initial concentrations of the BZ substrates ([MA] = 0.1 M, [HNO3] = 0.3 M, and [NaBrO3] = 0.5 M) at 20 °C. (B) Period of self-oscillation of the resonance frequency (Δf).

bromate ([NaBrO3] = 0.5 M) and malonic acid ([MA] = 0.1 M)) under constant temperature (20 °C).

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RESULTS AND DISCUSSION We measured time-dependent changes in the resonance frequency (Δf) of the self-oscillating polymer chain under constant temperature (20 °C) by using a QCM-D. Figure 3A shows the self-oscillation of Δf, which originates from the selfoscillation of water adsorption−desorption on the polymer chain induced by the BZ reaction. As the self-oscillation of the polymer chain occurs induced by the BZ reaction, the density of the polymer layer periodically changes to a small extent because the density of the polymer is close to that of water. As a simple approximation, the change in frequency can be used to obtain the change in mass of the polymer layer, which includes the self-oscillating polymer chain and the hydrated water molecules.30,32,33 Since the self-oscillating polymer chains are chemically bonded to the gold surface, the mass of polymer hardly changes. Therefore, we consider the dominant factor affecting the Δf self-oscillation to be water adsorption− desorption on the polymer chain. During the BZ reaction on the gold surface, the Ru catalyst moiety in the polymer chain caused periodic changes in solubility because its solubility differs in the reduced and oxidized states; that is, the periodic change in the solubility of the Ru catalyst moiety causes corresponding changes in the solubility of the polymer chain.18−21 In the oxidized state, the solubility of the polymer chain is higher than in the reduced state; hence, Δf decreased because the number of water molecules coupled with the polymer chain increased owing to the hydrophilic property of the Ru(bpy)3 moiety. In the reduced state, Δf increased owing to the dehydration of the water molecules on the polymer chain. In addition, the waveform of the Δf self-oscillation was

asymmetrical. In the BZ reaction, the rates of reduction and oxidation of the Ru(bpy)3 moiety in the polymer chain differ,18−21 and the oxidation rate is significantly higher than the reduction rate. Therefore, the rate at which Δf decreases is greater than the rate at which it increases (Figure 3A). The period of Δf was stable at about 400 s (Figure 3B). This stability strongly suggests that the periodic change in Δf is synchronized with the cyclic change in solubility of the polymer chain induced by the BZ reaction. In this experiment, the Δf self-oscillation was obtained from only the fundamental tone; it was not detected in the case of higher overtones (third, fifth, and seventh). As shown in Figure 4A, the induction time of the Δf self-oscillation was about 6.5 h. Subsequently, the Δf selfoscillation with a stable period began. During the induction time, there was no Δf self-oscillation. This result indicates that the Δf self-oscillation obtained from the fundamental tone was not noise but self-oscillating behavior of the polymer chain due to the water adsorption−desorption induced by the BZ reaction.34 In general, the fundamental tone senses the two liquid layers. The higher overtones (third, fifth, and seventh) are more sensitive to the surface region. Therefore, the selfoscillation of water adsorption−desorption on the polymer chain occurred mainly at a position elevated from the gold surface. In Figures 4 and 5, we plot time-dependent changes in the Δf and dissipation (ΔD) to understand the relationship between the self-oscillation of water adsorption−desorption and the polymer structure. ΔD reflects the conformation of the polymer chains on the gold surface. Figures 4 and 5 show the distinct 14353



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Figure 6. (A) Temporal changes in Δf and ΔD obtained from Figure S3. (B) Magnification of the peaks of ΔD. Spikes are observed at the front edge of the peaks.

Figure 4. Time dependence of the (A) resonance frequency (Δf) and (B) energy dissipation (ΔD). The initial concentrations of the BZ substrates were fixed to [MA] = 0.1 M, [HNO3] = 0.3 M, and [NaBrO3] = 0.5 M at 20 °C.

Figure 7. Plots of ΔD against Δf for the self-oscillating polymer chain on the gold surface in the BZ reaction. The notations 1, 2, and 3 coincide with those in Figure 5

Conversely, as Δf increased owing to the detachment of water molecules from the polymer chain, ΔD decreased because the rigidity of the polymer chains increased. These phenomena are observed in the thermoresponsive poly(N-isopropylacrylamide) (PNIPAAm) chain at a lower critical solution temperature (LCST) around 32 °C.30 The solubility of PNIPAAm is changed by the solution temperature because the PNIPAAm chain is in the coiled state below 32 °C and in the globular state above 32 °C. In QCM-D measurements of PNIPAAm, at temperatures below 32 °C, Δf decreases because of water molecules adsorbed on the polymer chain and ΔD increases owing to the increase in flexibility of the polymer chain.

Figure 5. Time dependence of the resonance frequency (Δf) and energy dissipation (ΔD).

self-oscillation of ΔD. As shown in Figure 4, after the induction time, the ΔD self-oscillation occurred in synchrony with the Δf self-oscillation. As Δf decreased owing to the adsorption of water molecules on the polymer chain, ΔD increased because the flexibility of the polymer chain increased (Figure 5). 14354



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freely move. In other words, α is the normalized polymer size. RG is related to the polymer length and number of the sticks as follows:35 R G ∼ lKN1/2

(4)

where lK is the Kuhn length and N is the number of Kuhn segments in the chain. As stated above, Δf and ΔD are directly correlated with changes in the mass and energy dissipation, respectively, where the mass and energy dissipation are proportional to the volume and conformational entropy, respectively, of the polymer chain. In our experiments, the self-oscillating polymer chain was chemically bound to the gold surface, and the Ru(bpy)3 moiety in the polymer chain reacted with the other three substrates of the BZ reaction (NaBrO3, malonic acid (MA), and HNO3). As the polymer chain undergoes periodic conformational changes, α and the volume of the polymer chain also change, where the volume is proportional to α3. Therefore, Δf is roughly related to α as follows: Δf ∼ −α 3

(5)

Δf becomes maximal when α becomes maximal (α > 1). On the other hand, ΔD is related to flexibility of a polymer chain, where the degree of flexibility is defined as Sconf, i.e., the conformational entropy of the polymer chain.35 Sconf ∼

(6)

Here, Sconf is maximal in the Gaussian state (α = 1). Since energy is wasted by the flexibility (the number of conformations) in the Gaussian state maximal, ΔD becomes maximal in the Gaussian state. Therefore, the maximum condition of ΔD is different from that of Δf. The time lag between the peaks of Δf and ΔD, as observed in Figure 5, can be thus understood. In the Supporting Information, we describe how α can be connected to the BZ reaction.36 The temporal changes of Δf and ΔD with a discrete change in α are shown in Figure 6A, whereas Figure 6B shows the peaks of ΔD at a higher magnification. In the transition between the coiled and globular states under suitable conditions, the polymer chain conformation passes through the Gaussian one in the pathways from the coiled to globular state and vice versa. The sharp and dull spikes that appear in Figure 6B reflect these changes. In particular, sharp spikes appear at the front edge of the peaks when the polymer chain is in the Gaussian state. As the hydrophilicity of the polymer chain increases in the oxidized state, α increases. Sconf is maximal in the Gaussian chain state (RG); hence, RG did not coincide with the maximum value of α. Therefore, the peaks of Δf and ΔD waveforms did not coincide in time. As shown in Figure 5, the lag between the peaks is 21 s in the first wave, 27 s in the second wave, and 17s in the third wave. The shape of a theoretical ΔD peak is rectangular unlike the obtained ΔD, presumably because we assume a homogeneous change in the polymer conformation in the calculation. The behavior of the polymer chain in the BZ reaction (in Figure 5) is thus explained. Figure 7 shows the relationship between Δf and ΔD. The elliptical shape of the graph indicates that the oscillatory waveforms of Δf and ΔD are identical in frequency but differ in phase and amplitude. To verify the frequencies of the Δf and ΔD self-oscillations, the values of Δf and ΔD were subjected to

Figure 8. Fourier transform of the (A) resonance frequency (Δf) and (B) energy dissipation (ΔD).

Conversely, at temperatures above 32 °C, Δf increases owing to the detachment of water molecules and ΔD decreases because of the increase in rigidity of the polymer chain. In the case of PNIPAAm, the solubility of the polymer chain is determined by the temperature. In this QCM-D measurement under a fixed temperature, the solubility of the polymer chain depends on the Ru(bpy)3 moiety. This is because a change in the solubility of the Ru(bpy)3 moiety in the polymer chain is induced by the BZ reaction. Therefore, the oscillatory changes in Δf and ΔD due to the periodic change in the solubility of the Ru(bpy)3 moiety originate from the same cause as the change in PNIPAAm. Figure 5 shows a time lag between the peaks of Δf and ΔD. To understand the behavior of polymer chains under the BZ reaction, this phenomenon needs to be explained. Here, we present a simple scenario based on polymer physics. To state a previous conclusion, Δf and ΔD are directly correlated with the volume and conformational entropy of a polymer chain, respectively, where the hydrodynamic volume and conformational entropy can be explained by α, the ratio of the size of the polymer chain to the size of the Gaussian chain. Because α oscillates under the BZ reaction, the key is how it relates to the size of the polymer chain. α is defined as follows:35

α = R /R G

3 2 (α + α − 2 ) 2

(3)

Here, R and RG are the sizes of the polymer chain and Gaussian chain, respectively, where the Gaussian chain is an ideal polymer chain in which sticks (Kuhn segments) linearly joined 14355



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(7) Kwon, G. H.; Park, J. Y.; Kim, J. Y.; Frisk, M. L.; Beebe, D. J.; Lee, S. H. Biomimetic Soft Multifunctional Miniature Aquabots. Small 2008, 4, 2148−2153. (8) Sidorenko, A.; Krupenkin, T.; Taylor, A.; Fratzl, P.; Aizenberg, J. Reversible Switching of Hydrogel-actuated Nanostructures into Complex Micropatterns. Science 2007, 315, 487−490. (9) Nakamaru, S.; Maeda, S.; Hara, Y.; Hashimoto, S. Control of Autonomous Swelling-deswelling Behavior for a Polymer Gel. J. Phys. Chem. B 2009, 113, 4609−4613. (10) Zaikin, A. N.; Zhabotinsky, A. M. Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System. Nature 1970, 225, 535−537. (11) Reusser, E. J.; Field, R. J. The Transition from Phase Waves to Trigger Waves in a Model of the Zhabotinskii Reaction. J. Am. Chem. Soc. 1979, 101, 1063−1094. (12) Gyorgyi, L.; Turanyi, T.; Field, R J. Mechanistic Details of the Oscillatory Belousov−Zhabotinskii Reaction. J. Phys. Chem. 1990, 94, 7162−7170. (13) Scott, S. K. Chemical Chaos, 1st ed.; Oxford University Press: Oxford, U.K., 1991. (14) Field, R. J.; Burger, M. Oscillations and Traveling Waves in Chemical Systems; John Wiley & Sons: New York, 1985. (15) Nicolis, G.; Prigogine, I. Self-Organization in Nonequilibrium Systems; John Wiley & Sons: New York, 1977. (16) Murray, J. D. Mathematical Biology; Springer-Verlag:: Berlin, 1990. (17) Ishiwatari, T.; Kawaguchi, M.; Mitsuishi, M. Oscillatory Reactions in Polymer Systems. J. Polym. Sci., Part A: Polym. Chem. 1984, 22, 2699−2704. (18) Yoshida, R.; Sakai, T.; Ito, S.; Yamaguchi, T. Self-oscillation of Polymer Chains with Rhythmical Soluble-insoluble Changes. J. Am. Chem. Soc. 2002, 124, 8095−8098. (19) Hara, Y.; Yoshida, R. Self-oscillating Polymer Fueled by Organic Acid. J. Phys. Chem. B 2008, 112, 8427−8429. (20) Hara, Y.; Yoshida, R. Self-oscillation of Polymer Chains Induced by the Belousov-Zhabotinsky Reaction under Acid-free Conditions. J. Phys. Chem. B 2005, 109, 9451−9454. (21) Hara, Y.; Yoshida, R. Damping Behavior of Aggregation− disaggregation Self-oscillation for a Polymer Chain. Macromol. Rapid Commun. 2009, 30, 1656−1662. (22) Hara, Y.; Yoshida, R. Influence of a Positively Charged Moiety on Aggregation−disaggregation Self-oscillation Induced by the BZ Reaction. Macromol. Chem. Phys. 2009, 210, 2160−2166. (23) Ito, Y.; Nogawa, N.; Yoshida, R. Temperature Control of the Belousov−Zhabotinsky Reaction Using a Thermo-responsive Polymer. Langmuir 2003, 19, 9577−9579. (24) Hara, Y.; Jahan, R. A. Activation Energy of Aggregationdisaggregation Self-oscillation of Polymer Chain. Int. J. Mol. Sci. 2012, 13, 16281−16290. (25) Hara, Y.; Yoshida, R. Control of Oscillating Behavior for the Self-oscillating Polymer with pH-control Site. Langmuir 2005, 21, 9773−9776. (26) Hara, Y.; Yoshida, R. A Viscosity Self-oscillation of Polymer Solution Induced by the BZ Reaction under Acid-free Condition. J. Chem. Phys. 2008, 128, 224904. (27) Ito, Y.; Hara, T.; Uetsuka, H.; Hasuda, H.; Onishi, H.; Arakawa, H.; Ikai, A.; Yoshida, R. AFM Observation of Immobilized Selfoscillating Polymer. J. Phys. Chem. B 2006, 110, 5170−5173. (28) Sauerbrey, G. Z. The Use of Quartz Oscillators for Weighing Thin Layers and for Microweighing. Phys. 1959, 155, 206−222. (29) Rodahl, M.; Hook, F.; Krozer, A.; Kasemo, G.; Breszinsky, P. A. Quartz Crystal Microbalance Setup for Frequency and Q-factor Measurements in Gaseous and Liquid Environments. Rev. Sci. Instrum. 1995, 66, 3924−3930. (30) Zhang, G. Sensitive Linear Grafted Poly(N-isopropylacrylamide) Chains by Quartz Crystal Microbalance. Macromolecules 2004, 37, 6553−6557. (31) Hook, F.; Voros, J.; Rodahl, M.; Kurrat, R.; Boni, P.; Ramsden, J. J.; Textor, M.; Spencer, N. D.; Tengvall, P.; Gold, J.; Kasemo, B. A

Fourier transformation. As shown in Figure 8, the frequencies of the Δf and ΔD self-oscillations were in good agreement. Furthermore, the size of the ellipse differed. This result demonstrates that the rates of oxidation and reduction of the Ru(bpy)3 moiety per cycle in the BZ reaction were different.

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CONCLUSIONS By utilizing QCM-D measurements, we succeeded in directly observing the self-oscillation of swelling and collapse for the polymer chain induced by the BZ reaction. Self-oscillation of Δf occurred after a long induction time (about 6.5 h). The period of the self-oscillation was stable at about 400 s. ΔD exhibited a distinct self-oscillation that was synchronized with Δf. We found that the peaks of the Δf and ΔD oscillations did not coincide in time. This is because the Gaussian chain state does not coincide with the maximum value of Δf. Moreover, we demonstrated a relationship between Δf and ΔD. This relationship indicates that the oscillatory waveforms of Δf and ΔD are identical in frequency but differ in phase and amplitude.

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ASSOCIATED CONTENT

S Supporting Information *

Theoretical part for the BZ reaction and conformation of a polymer chain. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-29-861-9318. Fax: +8129-861-6236. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out under the auspices of the New Energy and Industrial Technology Development Organization (NEDO) of Japan under the Industrial Technology Research Grant Program in 2011. The study was also supported by Grants-in-Aid (KAKENHI) for Challenging Exploratory Research (24656178) and Scientific Research on Innovative Area (25104501) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan (MEXT).

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Direct Observation of Periodic Swelling and Collapse of Polymer

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