Article pubs.acs.org/JPCB
Generative Force of Self-Oscillating Gel Yusuke Hara,*,† Hiroyuki Mayama,‡ and Keisuke Morishima§ †
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 § Department of Mechanical Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita 565-0871, Japan
ABSTRACT: We succeeded in measuring the generative force of a self-oscillating polymer gel in an aqueous solution comprising the three substrates of the Belousov−Zhabotinsky (BZ) reaction (malonic acid, sodium bromate, and nitric acid) under constant temperature. In this study, we developed an apparatus with a microforce sensor for measuring the generative force of small-sized gels (1 mm3). The self-oscillating polymer gel directly converts the chemical energy of the BZ reaction into mechanical work. It was determined that the generative force of the self-oscillating gel was 972 Pa, and the period of selfoscillation was 480 s at 18 °C. We demonstrated that the generative force of the gel was about a hundredth the generative force of a muscle in the body. We analyzed the time dependence of the color change in the self-oscillating polymer gel. The color of the gel changed periodically owing to the cyclic change in the redox state of the Ru moiety, induced by the BZ reaction. The peaks of the waveforms of the generative force and color change were almost identical. This result showed that the generative force was synchronized with the periodical change in the oxidation number of the Ru catalytic moiety in the gel. To understand a theoretical basis for the generative force of a self-oscillating gel, we considered a general theory that is based on the volume phase transition of gel and the two-parameter Oregonator model of the BZ reaction.
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INTRODUCTION A gel consists of a cross-linked network of polymer chains filled with solvent molecules in its interstitial space. Since the volume phase transition (discontinuous change in volume with an infinitesimal change in the external environment) of gels was discovered, polymer gels have been used as drug delivery systems, actuators, soft robots, matter transporting devices, etc.1−12 The phase transition of polymer gels can be induced by hydrogen bonds, Coulombic, hydrophobic, or van der Waals interactions. Muscles in the body, one of nature’s greatest inventions, are a type of gel. They are hierarchical molecular assemblies of motor proteins and actin filaments. The muscle involves an isothermal transducer that converts chemical energy into mechanical work, and generates motion without an external control apparatus.13−15 This transducing mechanism has high energy efficiency because the chemical energy is converted directly into mechanical energy without intermediate steps. The development of an autonomous polymer gel that does not need an external control device and battery is important in order to decrease its weight and improve its © 2014 American Chemical Society
energy efficiency. A self-oscillating polymer gel that converts the chemical energy of the Belousov−Zhabotinsky (BZ) reaction into mechanical volume change was developed.16−18 The BZ reaction is a well-known nonlinear reaction that accompanies the spontaneous redox oscillations of a metal catalyst.19−25 The overall process of the BZ reaction is the oxidation of an organic substrate by an oxidizing agent in the presence of a metal catalyst under strongly acidic conditions. In the BZ reaction, as the redox number of ruthenium tris(2,2′bipyridine), the BZ catalyst, changes cyclically, the solvation state of the Ru catalyst changes concurrently. Since the Ru catalytic moiety is covalently bonded to the polymer main chain in the gel, the gel undergoes a swelling−deswelling selfoscillation, which is synchronized with the cyclic change in the solvation state of the Ru catalyst, induced by the BZ reaction under constant temperature. Previous investigations have Received: December 31, 2013 Revised: February 12, 2014 Published: February 13, 2014 2576
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EXPERIMENTAL SECTION Polymerizations. Synthesis of Self-Oscillating Polymer Gel (Poly(NIPAAm-co-Ru(bpy)3-co-AMPS) Gel). In order to synthesize the self-oscillating polymer gel (poly(NIPAAm-coRu(bpy)3-co-AMPS) gel (see Figure 1)), the monomers,
applied the periodic change in the volume of the gel to soft actuators.26,27 The self-oscillating gel actuators require a strong acid (HNO3 or H2SO4) because strongly acidic conditions are indispensable to cause the BZ reaction. However, the presence of a strong acid in the operating environment of a selfoscillating gel can be risky. Hara et al. developed a selfoscillating polymer system that operates under more moderate pH values in an attempt to improve the operating environment of a self-oscillating polymer system.28−32 The strong-acid-free polymer chain was composed of 4-vinyl-4′-methyl-2,2′bipyridinebis(2,2′-bipyridine)bis(hexafluorophosphate)Ru (Ru(bpy)3), N-isopropylacrylamide (NIPAAm), and a large amount of 2-acrylamido-2-methylpropane sulfonic acid (AMPS) (more than 30 mol %) to control the pH value. It was clarified that the strong-acid-free self-oscillating polymer chain undergoes the on−off switching of the self-oscillation and the viscosity self-oscillation under strong-acid-free conditions.31,32 Recently, we succeeded in synthesizing a strongacid-free gel with a semi-interpenetrating network structure.33 The novel gel that undergoes the self-oscillation under the strong-acid-free conditions has the first network with 100 mol % AMPS moiety. However, the displacement observed for the novel gel was quite small to be applicable to soft actuators and robots. In addition, the displacement of conventional selfoscillating gels (poly(NIPAAm-co-Ru(bpy)3) gel) is too small (about 10 μm at 1 mm3 gel). In the previous study, we attempted to modify the displacement of the self-oscillating polymer gel.34−37 When a small amount of AMPS (about 2 mol %) was incorporated in the self-oscillating gel, the displacement of the gel was dramatically improved (about 200 μm at 1 mm3 gel) under the strong-acid conditions. A self-walking gel robot34 and matter transport system35 were created using the large displacement of the AMPS-containing self-oscillating gel (poly(NIPAAm-co-Ru(bpy)3-co-AMPS) gel). In order to expand the utility of self-oscillating gels, it is important to accurately measure the generative force because the design of soft robots requires an exact value of the generative force in the gel. Unfortunately, however, the generative force of the AMPScontaining gel actuator was not determined because the apparatus for measuring the generative force of the small gel actuator in water was not commercially available. It is important to measure the generative force of the gel in water, as the gel can undergo swelling and collapse only in water. In this study, we succeeded in the in-water measurement of the generative force of the AMPS-containing self-oscillating polymer gel (1 mm3) under constant temperature by using an in-house designed apparatus with a microforce sensor. Furthermore, in order to theoretically understand the generative force of the self-oscillating gel, we considered a general theory that is based on the volume phase transition of gel and the two-parameter Oregonator model of the BZ reaction. The volume phase transition in gels can be discussed in terms of a first-order phase transition using the Ginzburg− Landau way. In contrast, the change in the valency of the metal catalyst in the BZ reaction, which corresponds to a change in solvent quality, has been discussed by the two-parameter Oregonator model, one of the mathematical models of the BZ reaction. On the basis of free-energy arguments and the model, we could explain the experimental results and the force generation of the self-oscillating BZ gel.
Figure 1. Chemical structure of the self-oscillating polymer gel.
NIPAAm (0.78 g), Ru(bpy)3 (81.3 mg), N,N′-methylenebisacrylamide (MBAAm) (14.0 mg) as a cross-linker, and azobisisobutyronitrile (AIBN) (33.2 mg) as the initiator were dissolved in ethanol (2.4 g). AMPS (27.6 mg) was dissolved in water (2.4 g). The two solutions were then mixed together, and nitrogen was bubbled through the solution. The solution was injected between two glass plates separated by a silicone spacer (thickness: 0.5 mm), and then, radical polymerization was allowed to proceed for 20 h at 60 °C. The resulting gel membrane was soaked in pure ethanol for a week to remove unreacted monomer, and then gradually hydrated by sequential immersion in decreasing concentrations of ethanol in H2O (75, 50, 25, and 0%) for 1 day each. Measurements of the Generative Force. Figure 2 shows a schematic illustration of the apparatus for the (in-water) measurement of the generative force of the self-oscillating gel (1 mm3) under constant temperature. As shown in Figure 2, the apparatus consisted of a jig, water bath controlled by a Peltier, temperature indicator, microforce sensor, an XYZ-axis controller to adjust the jig positions when setting the gel, and a jig position controller to adjust the jig positions when immersing the gel in the water tank. The gel actuator was sandwiched between the jigs and immersed in the water bath filled with an aqueous solution comprising malonic acid (MA) (0.05 M), sodium bromate (0.1 M), and nitric acid (0.9 M). The temperature of the aqueous solution comprising the three BZ substrates was controlled at 18 °C by the Peltier control system. To sandwich the gel between the jigs, the X and Y positions of the jig on the right were adjusted by the Y- and Zaxis controllers, respectively (see Figure 2B). The X position of the jig on the left was adjusted by the X-axis controller. For immersing the gel into the water tank, the two jigs were moved into the water tank simultaneously by the jig position controllers (see Figure 2B). The generative force of the selfoscillating gel was detected by the microforce sensor. The microforce sensor consists of a distortion-generating element and an electrostatic capacitance displacement meter. Cyclic changes in gel color were observed using a microscope (WAT250D, Fortissimo Corp, Japan). We conducted an RGB analysis of the cyclic color change in the gel.
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RESULTS AND DISCUSSION The self-oscillating polymer gel (poly(NIPAAm-co-Ru(bpy)3co-AMPS) gel) (Figure 1) has a different equilibrium swelling 2577
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Figure 2. Schematic illustration of the apparatus used for measuring the generative force of the gel in water at a constant temperature: overall view (A) and close-up view (B).
ratio in the reduced and oxidized states.34−37 The oscillation of the self-oscillating gels in the reduced and oxidized states was adjusted by the Ce(III) and Ce(IV) solutions under strong acidic conditions. The gel had an orangish tinge in the Ce(III) solution, indicating that the copolymerized Ru(bpy)3 moiety in the gel was in the reduced state. The gel quickly turned from orange to green in the Ce(IV) solution, showing that the Ru(bpy)3 moiety in the gel was now in the oxidized state. The lower critical solution temperatures (LCSTs) of the selfoscillating polymer gel in the reduced and oxidized states were different because the Ru(bpy)32+ and Ru(bpy)33+ moieties in the gel have different solvation states. The solvation state of the Ru(bpy)3 moiety in the reduced state is lower than that in the oxidized state.28−32 At temperatures below the LCST, the equilibrium volume of the gel in the oxidized state is larger than that in the reduced state owing to the difference in the solvation states of the reduced and oxidized Ru(bpy)3 moiety. This difference in the solvation state of the Ru(bpy)3 moiety is the origin of the driving force for the periodic volume change in the
self-oscillating gel induced by the BZ reaction under constant temperature. Figure 3 shows the time dependence of the generative force of the self-oscillating polymer gel and the green value originating from the periodical color change of the Ru(bpy)3 moiety. From Figure 3, it can be seen that the generative force of the poly(NIPAAm-co-Ru(bpy)3-co-AMPS) gel is 972 Pa, while the period of oscillation is 480 s at 18 °C. The generative force of the gel was about a hundredth that of a muscle. In previous studies, Sasaki et al. determined the generative force of a conventional self-oscillating polymer gel (poly(NIPAAm-coRu(bpy)3) gel) to be 20 Pa.38 Therefore, this study demonstrated that the generative force of the AMPS-containing gel was about 50 times as large as that of the poly(NIPAAm-coRu(bpy)3) gel. Furthermore, the peaks of the waveform of the color change in the gel were almost coincident with those of the generative force. This result demonstrated that the force of the gel was generated synchronously with the periodical change in the oxidation number of the Ru(bpy)3 moiety in the gel. 2578
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Fforce = −
Ntot (α − α −3) + λNtotNsub−1/2α −4 Nsub
+ 2NtotNsub−1C*α −7 + 3λ 2NtotNsub−1/2α −10 λNtot + 1/2 4 Nsub α − λα
By defining the number of subchains nsub = Ntot/Nsub, Fforce is described as Fforce = −nsub(α − α −3) + λnsubNsub1/2α −4 + 2nsubC*α −7 + 3λ 2nsubNsub−1/2α −10 +
Figure 3. Time dependences of the generative force and the green value for the poly(NIPAAm-co-Ru(bpy)3-co-AMPS) gel.
⎡ 3 Fgel[α] ≈ Ntot⎢ (α 2 + α −2) + λNsub−1/2α −3 ⎢⎣ 2Nsub
dz =x−z dt
(5)
(7)
where x and z are the normalized concentrations of bromous acid HBrO2 and Ce4+, respectively; ζ is the stoichiometric factor between bromomalonic acid BrCH(COOH)2 (BrMA) and Ce4+, and ε is the tuning parameter. Here, z corresponds to the normalized concentration of Ru3+. That of Ru2+ can be obtained from ([Ru2+] + [Ru3+])/[Ru2+(t = 0)] = constant. The Ru3+ form of the Ru catalyst acts as a good solvent for the BZ gel. The black curve in Figure 4 shows the numerical results of the temporal change in Ru3+ concentration, where ε = 0.01, q =
(1)
where α is defined as follows.40,41
α = R /R G
Nsub1/2α 4 − λα
The two-parameter Oregonator model can be used to explain the periodical volume change induced by the BZ reaction. Temporal changes in the concentration of the chemical species in the BZ reaction can be described as follows. x−q dx ε = x(1 − x) − ζz dt x+q (6)
Next, we try to explain the experimental results by a simple model. In a previous study,39,40 we obtained the free energy of gel Fgel[α] as
+ Nsub−1C*α −6 + λ 2Nsub−1/2α −9 ⎡ ⎤⎤ λ ⎥⎥ − ln⎢1 − ⎢⎣ Nsub1/2α 3 ⎥⎦⎥⎦
λnsubNsub−1
(2)
Here, RG is the size of the Gaussian chain that is an ideal polymer chain and R is the size of the polymer chain. In the Gaussian chain, the sticks (Kuhn segments) linearly join and freely move. That is, α indicates the normalized polymer size. In addition, C* is a parameter that affects solvent quality. In this case, it corresponds to the change in the valency of the metal catalyst in the BZ reaction. Stable states of the subchain with a change in C* can be determined from ∂Fsingle[α]/∂α = 0. ⎡ ⎤ λ ⎥α 3 2C* = α8 − α 4 − Nsub1/2⎢λ + − − 1/2 3 ⎢⎣ 1 − λNsub α ⎥⎦ − 3λ 2Nsub1/2α −10
(3)
Figure 4. Temporal changes in solvent quality (black solid curve) and the gel size ratio (red solid curve). The inset shows the relationship between the solvent quality and the gel size ratio.
Thus, the conformational change of a subchain between the elongated and collapse states is equal to the volume phase transition of the gel. Next, we discuss the force generated from a discrete change in the volume of a gel. Force, Fforce, is simply described from Fgel as Fforce = −
1 ∂Fgel[α] 3 ∂α
0.0008, x(t = 0) = 0.1, ζ = 1, z(t = 0) = 0.01, [Ru2+(t)]/[Ru2+(t = 0)] + z = 0.28, and −2C* = 2[Ru2+(t)]/[Ru2+(t = 0)]. On the basis of this and eq 3, the change in the size ratio α is given by the red curve in Figure 4, and the relationship between solvent quality and α is illustrated in the inset, where λ = 0.04, Nsub = 10, and nsub = 109. It can be clearly seen that the BZ gel shows a rhythmic change between the coil and globule states in a discrete manner with change in the Ru3+ concentration. Figure 5 shows the numerical results of the force Fforce generated by the self-oscillating gel, where we assumed, for simplicity, that a global oscillation occurs in the self-oscillating
(4)
where the factor of 1/3 arises from the principle of equipartition. Therefore, Fforce is 2579
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Figure 5. Temporal change in the force generated by the swelling of the BZ gel.
gel. It can be seen that the waveform of the force generated is rectangular. Compared to Figure 4, it can be seen that the selfoscillating gel is generating the force in the swollen state. This qualitatively explains the experimental results of force generation in Figure 3.
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CONCLUSIONS In this study, we determined that the generative force of a selfoscillating poly(NIPAAm-co-Ru(bpy)3-co-AMPS) gel was 972 Pa, which is about 50 times as large as that of a conventional self-oscillating polymer gel (poly(NIPAAm-co-Ru(bpy)3) gel). The peaks of the waveform of the color change in the gel were almost coincident with those of the generative force. This result demonstrated that the generative force of the gel was synchronized with the periodical color change in the gel. Moreover, in this study, we also explained the generative force of the self-oscillating gel theoretically.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. 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. We were supported also by Grants-inAid (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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