J. Phys. Chem. B 2008, 112, 1777-1782
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Direction Control of Chemical Wave Propagation in Self-Oscillating Gel Array Shinji Tateyama, Yasushi Shibuta, and Ryo Yoshida* Department of Materials Engineering, Graduate School of Engineering, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ReceiVed: October 10, 2007; In Final Form: NoVember 16, 2007
A chemomechanical actuator utilizing a reaction-diffusion wave across gap junction was constructed toward a novel mircoconveyer by micropatterned self-oscillating gel array. Unidirectional propagation of the chemical wave of the Belousov-Zhabotinsky (BZ) reaction was induced on gel arrays. In the case of using a triangleshaped gel as an element of the array, the chemical wave propagated from the corner side of the triangle gel to the plane side of the other gel (C-to-P) across the gap junction, whereas it propagated from the plane side to the corner side (P-to-C) in the case of the pentagonal gel array. Numerical analysis based on the KeenerTyson model was done for understanding the mechanism of unidirectional propagation in triangle and pentagonal gel arrays. The swelling and deswelling changes of the gels followed the unidirectional propagation of the chemical wave.
Introduction Communication via diffusion of a chemical messenger is a fundamental process in living organisms. In the nervous system, neurotransmitter diffuses across the synapse between adjacent neurons and transmits signals. Recently, such reaction-diffusion systems free from complex wiring have attracted attention for the realization of new computing structures such as diodes or logic gates.1-3 For example, a chemical diode1 was constructed by utilizing the Belousov-Zhabotinsky (BZ) reaction.4 Unidirectional propagation of the chemical wave was demonstrated by arranging the two square BZ mediums asymmetrically with a small gap junction: one medium was oriented to the contact area by the plane side, and the other was oriented by the corner side. The limit size of the gap for propagation of the chemical wave from the plane side to the corner side (P-to-C) was wider than that for propagation from the corner side to the plane side (C-to-P). Hence, unidirectional P-to-C propagation of the chemical wave was observed under an appropriate gap size. By utilizing the unidirectional propagation of chemical wave, applications to computing systems5 are attempted. On the other hand, we are attempting to construct an actuating system using self-oscillating gel6,7 as a novel microconveyer to transport substances with the propagation of chemical wave. So far, we have developed a novel polymer gel that changes its volume periodically under constant conditions (called a self-oscillating gel) by constructing a built-in system of energy conversion from chemical oscillation of the BZ reaction to mechanical oscillation of polymer chains. The catalyst of the BZ reaction, ruthenium(II) tris(2,2′-bipyridine) (Ru(bpy)32+), was covalently bonded to the polymer chain of N-isopropylacrylamide (NIPAAm) in the gel. The gel has a volume phase transition temperature because of the thermosensitive NIPAAm constituent. The phase transition temperature in the oxidized Ru(III) state becomes higher than that in the reduced Ru(II) state due to the charge increase of the catalyst. As a result, under constant temperature, swelling-deswelling changes of the gel occur with redox * To whom correspondence should be addressed. Phone and Fax: +81-3-5841-7112. E-mail:
[email protected].
changes of the Ru(bpy)3 site. In the solution containing the BZ substrates, therefore, the gel autonomously repeats swelling and deswelling with redox changes of Ru(bpy)3 sites induced by the BZ reaction inside the gel. By arraying the self-oscillating gel as an element with a gap junction, unidirectional propagation of swelling could be achieved with chemical wave, and it may bring forth an autonomous microconveyer actuating by oneself. In this study, such a novel chemomechanical actuator was constructed by a micropatterned self-oscillating gel array. The chemical wave was induced on the gel array, and the direction of propagation was controlled by changing the geometry of the gels. In addition to experimental approaches, unidirectional propagation processes were analyzed by numerical simulation. The BZ reaction can be explained by the FKN mechanism8 and the Oregonater model9 including three variables. The simulation was done by using the two-variable version of the Oregonater model (KeenerTyson’s model10). Experimental Section Fabrication of a Self-Oscillating Gel Array. NIPAAm (2.5 M), Ru(bpy)3 monomer (9 wt %), N,N′-methylenbis(acrylamide) (MBAAm) (5 mol %) as a cross-linker, and 2,2dimethoxy-2-phenylacetophenone (5 mol %) as a photoinitiater were dissolved in a mixture of ethanol (540 µL) and dimethylsulfoxide (DMSO) (60 µL). The pregel solution was injected between two glass plates (the surface of the lower glass plate was treated with a silane coupling agent) separated by a spacer with 300 µm thickness. Figure 1 shows the fabrication process of the gel array. The plate was set up on a motor-driven x-y sample stage equipped with a fluorescence microscope (DIAPHOT, Nikon). A photomask with triangle or pentagonal shape was inserted in front of the N-D filter. The UV light from an Hg lamp (100 W, 300 cd, peak wavelength 365 nm) was condensed by a 10× objective lens (Plan 10, Nikon) to focus on the stage, and the spotlight was irradiated to the plate for 90 s. By irradiating UV light right through the photomask, a triangle- or pentagonal-shaped gel with a size of millimeter order
10.1021/jp709882h CCC: $40.75 © 2008 American Chemical Society Published on Web 01/19/2008
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Figure 1. Schematic image of the experimental apparatus for fabricating microgels by irradiating a UV spotlight locally to the pregel solution through a photomask.
Figure 3. Propagating behavior of the chemical wave on the (a) triangle gel array and (b) pentagonal gel array.
Figure 2. (a) Gray scale image of a triangle gel array with a gap of 177 µm. (b) A spatiotemporal pattern constructed by lining up oneline (dotted line in part a) images across the triangle gel array for 180 min. The lateral dotted line represents a gradient of white and black stripes in the image. (c) Time change of gray scale intensity at a centroid of the triangle gel represented by the vertical dotted line in part b.
was obtained. Gel arrays were prepared by repeated on-off switching of UV irradiation and moving the sample stage. Observation of Chemical Wave Propagation. The gel array on the glass plate was immersed into the BZ substrate solution containing malonic acid (MA) (62.5 mM), sodium bromate (NaBrO3) (84 mM), and nitric acid (HNO3) (0.6-1.4 M) in the microchamber maintained at 20 °C. The chemical wave propagation on the gel array was observed under a microscope equipped with a black-white CCD camera and a video recorder. For the observation, monochromatic light (390 nm) passed through a blue filter was used. Results and Discussion Unidirectional Propagation of a Chemical Wave on a Triangle and Pentagonal Gel Array. At first, a triangle gel array was fabricated and immersed in the solution containing the BZ substrates. Figure 2a shows the gray scale image of the gel array with a gap of 177 µm in the substrate solution ([HNO3] ) 0.9 M). Figure 2b shows a spatiotemporal pattern constructed
by sequentially lining up one-line image across the triangle gel array (dotted line in Figure 2a) for 180 min. White and black stripes indicate oxidation and reduction states, respectively. Chemical waves propagated from the left to right direction, which was recognized by right-downing stripes. The wave velocity was estimated to be 16.5 µm/s from the gradient of the stripes. The period of the reaction was estimated to be 31.2 min from the change of intensity of gray scale at a centroid of the triangle gel (Figure 2c). Figure 3a shows the behavior of a chemical wave unidirectionally propagating across the gap between triangle gels. At the gap, the chemical excitation jumps from the corner side of the left gel to the plane side of the right gel (C-to-P), which settled the propagation to the left-to-right direction. The C-to-P propagation of chemical excitation observed here was the opposite direction (P-to-C) supposed by the previous report of chemical diode1 despite having the same P-C gap structure. The unidirectional propagation was not observed in the case of a wider gap of 220 µm with the same HNO3 concentration, and the BZ reaction occurred at each gel independently. As a result of investigating various combinations of gap spacings and HNO3 concentrations, the maximum gap for unidirectional propagation was 80, 177, and 215 µm when the HNO3 concentration was 0.6, 0.9, and 1.4 M, respectively. The gap limit for unidirectional propagation increases with the concentration of HNO3, whereas the direction of propagation (C-to-P) was not changed in any case of concentration. Next, a pentagonal gel array with a C-P junction was fabricated in order to investigate the effect of gel shape on propagation direction. Figure 3b shows the chemical wave propagation on the pentagonal gel array immersed in the BZ substrate solution. The chemical wave propagated from the right to left, and the chemical excitation jumped from the plane side of the right gel to the corner side of the left gel (P-to-C) at the gap. It is opposite the case of the triangle gel array and the same as the previously reported chemical diode.1 Pentagonal gel has two parallel sides and two orthogonal corners. The
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chemical diode1 made from two square gels also has such parallel sides and orthogonal corners. In general, substrate penetrates easier from the corner side than from the plane side. Also, it is known that products like bromomalonic acid (BrMA) or bromide ion inhibit the BZ reaction. The concentration of these product components outside of the gel is negligible, but it can reach much higher levels inside the gel where they are produced. Obviously the steady-state concentration of these inhibitory products should be lower in the corners. Hence, the chemical wave tends to arise at the corner side compared with the plane side in both triangle and pentagonal gels. In the case of an isolated triangle gel, the probability as a start point of the chemical wave is equivalent among three corners. However, when triangle gels are aligned as in Figure 3a, the probability for the two left corners is higher than that for the right corner, since some of the substrate near the right corner penetrates the plane side of the right-hand neighbor. Hence, the chemical wave arises from the left and propagates to the right in each triangle gel. The directional waves in each gel are amplified due to the sequence of the gel array with small gaps. Finally, unidirectional propagation of a chemical wave across gaps was observed: the direction was from the corner side of the left gel to the plane side of the right gel (C-to-P). On the other hand, the pentagonal gel has three different angles in five corners. The substrate penetrates easier to the corner with a sharp angle than to that with an obtuse angle, since the corner with a sharp angle contacts with much substrate area. Hence, the chemical wave tends to arise at the right corner and propagate to the left side in each pentagonal gel. As in the case of the triangle gel mentioned above, the directional waves in each gel were amplified and unidirectional propagation across gaps was observed. The propagation direction was from the plane side to the corner side (P-to-C), which was opposite the propagation in the triangle gel array. These interesting results indicate the propagation direction of a chemical wave depends not only on the combination of shapes in a gap junction but also on the gel shape itself, since the starting point of a chemical wave depends on the gel shape. In order to confirm the above discussion based on the experimental results, the propagation process of a chemical wave on triangle and pentagonal gel arrays was analyzed by numerical simulation in the following section. Numerical Analysis by Keener-Tyson’s Model. The unidirectional propagation of a chemical wave was analyzed by numerical simulation using the Keener-Tyson model,10 which is the two-variable version of the Oregonater model.9 The Oregonater model is a variables-reduced model from the FKN mechanism,8 which captures the essential features of chemical waves in the BZ reaction with three variables. The Keener-Tyson model is described as following two reactiondiffusion equations:
(
)
fV(u - q) 1 ∂u ) Du∇2u + u(1 - u) ∂t u+q
(1)
∂V ) DV∇2V + (u - V) ∂t
(2)
where u and V represent the concentrations of the activator, HBrO2, and the oxidization catalyst Ru(bpy)33+ as an inhibitor. Du and DV represent the diffusion coefficient of the activator and inhibitor. The parameters , q, and f are for the excitability, the nondimensional reaction rate, and the threshold of the excitability. The physical aspect of these parameters was defined in the original paper.10 The parameters used in the
TABLE 1: Parameters Employed in the Numerical Calculation diffusion coefficient of activator diffusion coefficient of inhibitor excitability non-dimensional reaction rate threshold of the excitability
Du DV q f
1.0 0.0 0.01 0.0008 1.0
simulation are listed in Table 1. DV is set to be zero because the polymer chain of NIPAAm fixes the oxidization catalyst in the gel media. f is set to reproduce oscillatory reaction because the self-oscillating gel actuates under oscillatory conditions. A finite-difference scheme is employed for the solution of the differential equations with a time step of 1.0 × 10-3 s. Seven triangle and pentagonal gels are arrayed in the two-dimensional system of 4 cm × 1 cm, expressed by 400 × 100 mesh points. The area of the gel media was recognized by way of neglecting the reactive term in eqs 1 and 2 outside of the gel media; that is, standard diffusion equations are employed outside of the gel media. A Neumann boundary condition is used for conservation of the concentrations as a closed system. First, the propagation process of a chemical wave on a triangle gel array was examined. As an initial condition, the concentrations u and V were set to be zero at all of the simulation areas. As a starting point of the chemical wave, perturbation of concentrations (u ) 0.5 and V ) 0.15) was added at corners facing a gap in triangle gels, as shown in Figure 4a. Figure 4b shows the snapshots of the propagation process of the chemical waves on the triangle gel by showing the contour of the concentration u. At first, the chemical wave propagated on each gel independently. Then, two chemical waves from the plane side on the far left gel and from the corner side on the far right gel were observed around 100 s: the far left and far right gels became the controllers of the chemical wave as starting points. Finally, the wave arising from the far left gel overcame the wave arising from the far right gel by annihilation of the chemical wave and the direction of wave propagation became stable going from left to right around 300 s. The chemical wave propagated across gaps from the corner side of the left gel to the plane side of the right gel. It is in good accordance with the experimental result; unidirectional propagation of the chemical wave on a triangle gel array from the corner side of the lefthand gel to the plane side of the right-hand gel (C-to-P) was observed. Next, the propagation process of a chemical wave on a pentagonal gel array was examined. The calculation condition was the same as the above calculation for the triangle gel array expect for gel shape. Figure 4c shows the snapshots of the propagation process of the chemical waves on the pentagonal gel array by showing the contour of the concentration u. As in the case of the triangle gel array, two chemical waves from the far left and far right gels were observed. Finally, the direction of the chemical wave became stable going from right to left, which is opposite the direction on the triangle gel array. It is also in good accordance with the experimental result; unidirectional propagation of the chemical wave on a pentagonal gel array from the plane side of the right gel to the corner side of the left gel (P-to-C) was observed. The time for settling to the unidirectional chemical wave on the pentagonal gel array was about one-third the time in the case of the triangle gel array. It was confirmed by numerical simulation that the propagation direction depends on the shape of the gels. The reason will be discussed by detailed analysis of the starting point of the chemical wave in the following section.
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Figure 4. Numerical analysis of unidirectional propagation of the chemical wave using Keener-Tyson’s model. Propagation of the chemical wave was shown by the contour of the concentration u. (a) Initial condition for the numerical simulation. Snapshots of the propagation process on (b) the triangle gel array for 300 s and (c) the pentagonal gel array for 100 s. Red and green color represents high and low concentration, respectively.
Figure 5. (a) The time series of the concentration of the activator u at the three different points (the midpoint of the left side, the corner not facing the gap, and the corner facing the gap) on the far left gel in the triangle array during the first two cycles. Magnified views at starting up of the chemical wave were added for clarity.
According to the former simulation, the pacemaker of the BZ reaction in the triangle array was the far left gel in the triangle gel array and the far right gel in the pentagonal gel array. Figure 5 shows the time series of the concentration of the activator u at the three different points on the far left gel in the triangle array during first two cycles. Though the chemical wave was artificially perturbed at the corner facing the gap (point 3) as an initial condition, the second wave started from the corner not facing the gap (point 2) and it lasted to the end,
as shown in magnified views. The amplitude of the midpoint of the left side (point 1) was smallest, and that of point 3 was largest. Figure 6a shows the snapshots of a contour plot of the concentration V during a half-cycle on the far left, center, and far right gel in the triangle gel array around 100 s. In this stage, two chemical waves of different directions were observed in Figure 4b. On the far left gel, the chemical wave arose at the two corners not facing the gap and propagated to the corner facing the gap and it arose at the right corner not facing the gap and propagated to another side facing the gap on the far right triangle gel. On the other hand, the chemical wave increased from the midpoint of the left side on the center. Figure 6b shows the snapshots of a contour plot of the concentration V during a half-cycle on the far right gel in the triangle (300 s) and pentagonal (100 s) gel array after unidirectional direction was observed. The propagation direction on the far right triangle gel followed that on the center gel during unidirectional propagation. It shows the far left gel on the triangle gel array becomes a pacemaker of the chemical wave. On the other hand, the chemical wave arose at the right sharp corner during all process in the case of the pentagonal gel array. Hence, the far right gel on the pentagonal gel becomes a pacemaker of unidirectional propagation of chemical wave from right to left. Volume Changes of a Self-Oscillation Gel during the Wave Propagation Process. In addition to the direction of chemical wave propagation, volume changes of the gel array during the wave propagation process were investigated. Vertical displacement of the pentagonal gel array was observed from the crosssectional images (upper view in Figure 7a). The lower views
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Figure 6. Snapshots of the contour plot of the concentration of the inhibitor V during a half-cycle (a) on the far left, center, and far right gel in the triangle gel array when two chemical waves of different directions were observed in Figure 4b and (b) on the far right gel in the triangle and pentagonal gel array after unidirectional propagation. Red and green color represents high and low concentration, respectively.
Figure 7. (a) Cross-sectional image of the pentagonal gel (upper view) and a sequence of the observation views during the wave propagation process (lower views). (b) Spatiotemporal pattern constructed by a sequential one-line gray scale image of a cross section on the pentagonal gel. (c) Schematic image of controlling physical waves derived by self-oscillation gels as a microconveyer by controlling the direction of chemical waves.
in Figure 7a shows a sequence of the observation view of the pentagonal gel array during the wave propagation process. Unidirectional propagation of the swelling region from right to left was observed, which is the same as the propagation of a chemical wave. Hence, it was found that volume change of the gels followed the unidirectional propagation of a chemical wave. Figure 7b shows the spatiotemporal pattern constructed by sequential gray scale images of the pentagonal gel. Periodical height change between 55.7 and 73.3 µm was observed, whereas volume change to the horizontal direction did not occur, since the gel was bonded chemically to the silanized glass plate. The proportion of the volume change was estimated to be 31.6% from the change of the vertical direction, which is larger than that of the isotropic volume change in the self-oscillatig gel,11
since the volume change concentrated on the vertical direction because of obligation to the horizontal direction. These results mean controlling the direction of the propagation of the chemical wave makes it possible to control the physical wave derived by self-oscillating gels, as shown in the schematic image in Figure 7c. Conversion of unidirectional chemical wave to unidirectional physical wave may be applied to a new intelligent microconveyor. Conclusion Unidirectional propagation of the chemical wave by the Belousov-Zhabotinsky (BZ) reaction was induced in the gel array. In the case of using triangle gels, the chemical wave
1782 J. Phys. Chem. B, Vol. 112, No. 6, 2008 propagated from the corner side to the plane side (C-to-P), whereas it propagated from the plane side to the corner side (P-to-C) on the pentagonal gel array. From numerical simulation, it was found that the gel at the end of array becomes a pacemaker of the chemical wave. The direction of propagation on the gel array was determined by the event probability of the trigger of chemical wave. The probability depends on the gel shape itself rather than the gap structure. Hence, by fabricating different shapes of gel arrays, control of the direction is possible. The volume change of the self-oscillating gels followed the unidirectional propagation of the chemical wave. Application to novel microconveyers is expected. Acknowledgment. Authors thank Prof. Toshio Suzuki (The University of Tokyo) for useful discussion in numerical simulation.
Tateyama et al. References and Notes (1) Agladze, K.; Aliev, R. R.; Yoshikawa, K.; Yamaguchi, T. J. Phys. Chem. 1996, 100, 13895. (2) Toth, A.; Showalter, K. J. Chem. Phys. 1996, 103, 2058. (3) Dupont, C.; Agladze, K.; Krinsky, V. Physica A 1998, 249, 47. (4) Zaikin, A. N.; Zhabotinsky, A. M. Nature 1970, 255, 535. (5) Aoki, T.; Hiratsuka, M.; Higuchi, T. IEE Proc.-Curcuits DeVices Syst. 1998, 145-4, 264. (6) Yoshida, R.; Takei, K.; Yamaguchi, T. Macromolecules 2003, 36, 1759. (7) Sakai, T.; Yoshida, R. Langmuir 2004, 20, 1036. (8) Field, R. J.; Ko¨ro¨s, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94, 8649. (9) Field, R. J.; Noyes, R. M. J. Chem. Phys. 1975, 60, 1877. (10) Keener, J. P.; Tyson, J. J. Physica D 1986, 21, 307. (11) Yoshida, R.; Tanaka, M.; Onodera, S.; Yamaguchi, T.; Kokufuda, E. J. Phys. Chem. A 2000, 104, 7549.
