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Articles Controlled Motion of Solvent-Driven Gel Motor and Its Application as a Generator Tetsu Mitsumata, Kazuo Ikeda, Jian Ping Gong, and Yoshihito Osada* Division of Biological Sciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan Received April 22, 1999. In Final Form: July 29, 1999 Attempts have been made to control the spontaneous random motion of a tetrahydrofuran-swollen amphiphilic polymer gel on a water surface. By allowing the ejection of tetrahydrofuran through spouting holes, the gel showed an improved translational motion with a velocity of 77 mm/s or rotation with a rotation rate of 394 rpm. The controlled rotation showed an energy efficiency of 4.5 × 10-3%, which was 10 times of that of random motion. On the basis of the improved rotational motion of the gel, a generator consisting of a gel rotor equipped with a pair of permanent magnets and a solenoid coil has been constructed. The generator rotor which was 40 mm long, 6 mm wide, and 2 mm thick, produced an alternative electric power with an instantaneous electromotive force as high as 15mV for a period of over 30 min. Such behaviors as the controlled motion, the spreading rate of tetrahydrofuran on the water surface, the crystallization and texture of gel surfaces, and the power generated have been described.
1. Introduction When a drop of a liquid with a lower surface tension is placed on a plane surface of a liquid with a higher surface tension, a rapid spreading of the former liquid on the latter liquid surface is observed.1-5 The phenomenon is wellknown as the Marangoni effect6 and originated from the difference in the surface tension between two liquids. The spreading rate depends mainly on the Harkins spreading coefficient,1 and the motion of the free surface is mainly associated with the variation of surface tension along this free surface. If there exist any materials that are able to float on the supporting liquid surface and release continuously another liquid capable of spreading along the surface, the material should spontaneously move as a result of the reaction of the surface spreading. We have reported previously that the cross-linked amphiphilic polymer gels prepared by copolymerizing acrylic acid (AA) with stearyl acrylate (SA) [poly(AA-coSA)], acryloyl hexadecanoic acid (AHA) [poly(AA-co-AHA)], or 12-acryloyl dodecanoic acid (ADA) [poly(AA-co-ADA)] swollen in water miscible organic solvent undergo prolonged translational and rotational motions if they are placed on supporting water.7,8 The prolonged motion of the gel on the water surface is chemically driven and it is different from the motion observed in an oil/water system where repetitive changes * Corresponding author. E-mail:
[email protected]. (1) Harkins, W. D.; Feldman, A. J. Am. Chem. Soc. 1922, 44, 2665. (2) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; John Wiley & Sons: New York, 1990; Chapter 4, p 116. (3) O’Brien, R. N.; Feher, A. I.; Leja, J. J. Colloid Interface Sci. 1976, 56, 474. (4) Saylor, J. E.; Barnes, G. T. J. Colloid Interface Sci. 1971, 35, 143. (5) Troian, S. M.; Wu, X. L.; Safran, S. A. Phys. Rev. Lett. 1989, 62, 1496. (6) Marangoni, C. M. Ann. Phys. Chem. 1871, 143, 337. (7) Osada, Y.; Gong, J. P.; Uchida, M.; Isogai, N. Jpn. J. Appl. Phys. 1995, 34, L511. (8) Gong, J. P.; Matsumoto, S.; Uchida, M.; Isogai, N.; Osada, Y. J. Phys. Chem. 1996, 100, 11092.
in the interfacial tension at oil-water interface causes a self-movement of the oil drop.9,10 The driving force of the present case is the surface spreading of the organic solvent released from the gel. The process of the gel motion on the water surface was related to two steps.8 The first step is the release of organic solvent from the gel by osmotic pressure and hydrostatic pressure. When an amorphous gel which has been highly swollen in organic solvent is placed on water, it quickly forms a crystalline skin layer and an osmotic pressure is produced between the inside and outside of the gel. As reported earlier,11-13 long alkyl side groups in the gels can form a tail-to-tail structure aligned perpendicular to the main chain in water.14 The diffraction peaks of the wet poly(AA-co-SA) gels (the molar fraction of the hydrophobic monomer ) 0.5), for example, corresponded to a spacing of 0.41 nm and were characteristic of hexagonal packing of long alkyl side groups. The lamellar distance of the swollen gels was found to be almost 0.8 nm larger than in their dry state. Since the formation of the crystalline surface skin layer additionally produces a large hydrostatic pressure difference, the organic solvent was ejected for a prolonged period of time from the gel. The organized layer behaves as a perm selective membrane, which allows the organic solvent to diffuse out but does not allow the water to come in. The formation of an organized structure of the gel starts from the outer surface of the gel and develops into its inner part. By virtue of this, the skin layer keeps “pumping out” the organic solvent for a prolonged period of time. (9) Yoshikawa, K.; Magome, N. Bull. Chem. Soc. Jpn. 1993, 66, 3352. (10) Yoshikawa, K.; Magome, N. J. Phys. Chem. 1996, 100, 19102. (11) Matsuda, A.; Sato, J.; Yasunaga, H.; Osada, Y. Macromolecules 1994, 27, 7695. (12) Tanaka, Y.; Kagami, Y.; Matsuda, A.; Osada, Y. Macromolecules 1994, 28, 2574. (13) Osada, Y.; Matsuda, A. Nature 1995, 376, 6537. (14) Uchida, M.; Kurosawa, M.; Osada, Y. Macromolecules 1995, 28, 4583.
10.1021/la990483o CCC: $19.00 © 2000 American Chemical Society Published on Web 11/16/1999
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Here, an important fact is that the crystalline skin layer formed at the gel-water interface can act as a “molecular orifice” through which the organic solvent in the gel flows out. The second step is the spreading of the organic solvent on the surface of the water by the Marangoni effect, which imparts motion to the gel. Once the organic solvent is ejected out of the gel, it rises up onto the water surface because of its lower density and rapidly spreads on water because of the large difference in their surface tensions. The surface spreading of the organic solvent imparts a reaction force to the gel and makes the gel perform motion. The mode of motion depends on the shape of the gel: a disk-shaped gel exhibits translational motion while a triangular or a cubic gel shows rotation with an occasional change in direction. Thus, the motion was random and irregular, both in time and in space, owing to the cancellation of momentum by random spouting. Accordingly, the energy efficiency was very low. If the spouting direction can be controlled, not only the controlled motion of gels but also an enhanced energy efficiency will be realized. We have briefly reported that the motion of gels can be controlled by permitting the organic solvent to eject through a spouting hole.15 This investigation clarified that we can obtain a stable electric power only by diluting the organic solvent, such as an alcohol or tetrahydrofuran (THF), with water. In this paper, we have made detailed investigations of the controlled motion of amphiphilic polymer gels. The effect of size rotor, the time dependencies of crystallization and surface morphology of gel, and the effect of surface tension or contamination of water have been described. On the basis of these investigations, a generator has been constructed and the energy efficiency has been discussed.
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Figure 1. Time dependence of the velocity of translational motion. Inset: Schematic illustration of the model showing translational motion (type 1).
2. Experimental Procedure Poly(n-stearyl acrylate) gel (PSA) was prepared by radical polymerization in ethanol in the presence of N,N′-methylenebisacrylamide (MBAA) (1 mol %) as a cross-linking agent. The monomer concentration was 3 mol/L, and polymerization was carried out at 58 °C for 20 h to give the chemically cross-linked polymer gel. After polymerization, the gel was immersed in a large amount of THF for 3 days to remove unreacted chemical residuals and then was immersed in fresh THF for a week until it reached equilibrium. The motion of a gel was recorded by a digital video camera. The translational velocity was calculated from the drift distance per second. The rotation rate was calculated from the average values of three rounds. The surface morphology of the gel was observed by using a Hitachi S-2250N scanning electron microscope. Gels were quenched at the temperature of liquid nitrogen after being immersed in water for a certain time, dried in a vacuum at room temperature, and provided for microscope observation after coating with gold. Optical observations of the PSA crystalline were made with an Olympus BH-2 polarizing microscope through crossed polarizers. The electromotive force was measured by using a digital voltage meter. The electromotive force data were recorded automatically by a personal computer. The load of the circuit used in this experiment was 30 Ω.
3. Results and Discussion 3.1. Controlling the Motion of Gels. Two types of model, showing a translational motion (type 1) and a rotational one (type 2), have been prepared and schemati(15) Mitsumata, T.; Ikeda, K.; Gong, J. P.; Osada, Y. Appl. Phys. Lett. 1998, 73, 2366.
Figure 2. Time profiles of rotation rate as a function of rotor weight. (]): large rotor, (0): medium rotor, (O): small rotor. Inset: Schematic illustration of the model showing rotational motion (type 2).
cally illustrated in the insets of Figures 1 and 2, respectively. In the type 1 model, the polymer gel is wrapped in aluminum foil, and a spouting hole is opened at the rear of the model. The flux of THF solvent can only spread out via this spouting hole. The type 1 model, which resembles a water beetle, has a pair of rudders that enable the gel to undergo a translational motion, and it behaves like the tail of a kite. The width, length, and weight of the model are 7 mm, 30 mm, and 129 mg, respectively. It is noted that the role of the aluminum foil is not only to float the gel on the water surface but also to control the flow of the solvent that the polymer gel releases. The motion could be observed as long as the gel floated on the supporting water surface. Once the gel totally sinks into the water, it stops moving. The type 2 model shows rotational motion around a center pivot that serves as a stator. Two polymer gels are wrapped together by aluminum foil, with the two spouting holes settled at opposite sides of the rotor to generate the torque. The width and length are 3 mm and 9 mm, respectively, and the weight is 25 mg. The rotational motion is caused by the coupling of forces that are generated by spreading the organic solvent from the two spouting holes on the rotor. The type 1 model moves forward in a straight with spreading ripples on the water surface, and reaches a
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Figure 4. Relationship between the volume fraction of THF and the degree of swelling of the gel. Figure 3. Time profiles of the amount of THF released from the gel as a function of rotor weight. Inset shows the releasing rate of THF normalized by gel weight. (]): large rotor, (0): medium rotor, (O): small rotor. Table 1. Size and Weight of Rotors rotor size
length (mm)
width (mm)
weight (mg)
large medium small
78 39 9
7 6 3
238 115 25
maximum velocity of 77 mm/s. The kinetic energy of the translational motion was estimated under the assumption of constant velocity. The kinetic energy is given by the following formula.
1 Ek ) Mv2 2
(1)
Here, M is the mass of the type 1 model and v is the mean velocity of the translational motion. We get Ek as 3.8 × 10-7 J by substituting M ) 129 mg and v ) 7.7 × 10-2 m/s into the equation. The time profile of the translational velocity is shown in Figure 1. The type 1 model starts to move as soon as it is put on the water. The velocity increases until 60 s and then decreases with the elapse of time. It keeps on moving smoothly for over 30 min. 3.2. Effect of the Size of the Rotor. The effect of the size of the rotor on the rotation rates has been investigated. Three kinds of rotors, which are listed in Table 1, were used in this experiment. The time profiles of the rotation rates are shown in Figure 2. Like the translational motion, the rotation rate increases until 60 s and then decreases gradually with time. In the case of the small rotor, the rotation rates strongly depend on time with a maximum rotation rate of 400 rpm at 60 s. Figure 3 shows the time changes of the amount of THF, ∆n, released from the gel. ∆n was evaluated by measuring the rotor weight using an electronic balance from time to time. The inset of the figure shows a normalized amount of THF released at every 30 s. It is seen that the gel ejects THF extensively during the first 3 min with a maximum between 30 and 60 s. This indicates that a considerable amount of the organic solvent is released particularly in this interval. This coincides well with the time change of the rotation rates, which shows a maximum at around 60 s. There is no large difference in the THF releasing rate, ∆n/∆t, among three kinds of rotors, indicating that the largest rotation rate of the smallest rotor is attributed to the highest acceleration by the large ∆n/∆t value.
The time change of the rotation rates appearing around 60 s might be associated with the change in hydrostatic pressure caused by the extensive shrinkage of the gel. As mentioned in the Introduction section, a PSA gel undergoes an amorphous-crystalline transition depending on the volume fraction of THF, and shows an abrupt change in the degree of swelling. The relationship between the volume fraction of THF and the degree of swelling, q, is shown in Figure 4. q was calculated using the relationship q ) (swollen sample weight)/(dry sample weight). As shown in this figure, an abrupt shrinkage of the gel occurs if a small amount of water is introduced, which in turn produces a large hydrostatic pressure and enables THF to be ejected most efficiently. Since the collapse of the gel could be related to the orderdisorder transition by the presence of water, the time dependence of the crystallization of the gel was studied using a polarizing microscope. Figure 5a-e shows micrographs of the gel immersed in water for various times. The micrographs were obtained by using a polarizing microscope under crossed nicols. No clear image of the gel is observed at 0 s in Figure 5a, indicating that the gel is entirely amorphous at the beginning. The gel image becomes clear at 30 s, from the outer to inner part of the gel, indicating that the crystallization progresses from the outer surface toward the inner part of the gel. Figure 5 shows that extensive crystallization occurs between 30 and 60 s, which coincides with the maximum rotation rate and the maximum value of ∆n/∆t observed in Figures 2 and 3, respectively. However, no anisotropy in the crystalline orientation was observed in the direction from outer to inner gel. Since the rate of THF spreading depends on the surface morphology of the gel, the surface texture of the gel have been studied using scanning electron microscopy (SEM) and the results are shown in Figure 5f-j. One can observe that the surface is plain without any particular texture at 0 and 30 s, while it shows fibril textures after 60 s. This fibril-like structure becomes denser and more fine with the elapse of time. We have attempted to characterize the morphological texture of the surface in terms of the fractal dimension. According to the fractal theory,16 the relation between the scale of each segment r and the number of fittings N(r) is expressed by the following equation
N(r) ) r-DH
(2)
(16) Mandelbrot, M. M. The Fractal Geometry of Nature; Freeman: San Francisco, 1982.
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Figure 6. Time profile of the fractal dimension DH of the gel. Inset: Relationship between the number of segments and the scale.
Figure 5. Polarizing microscope micrographs of PSA gel after being immersed in water for (a) 0, (b) 30, (c) 60, (d) 75, and (e) 600 s (×4). SEM micrographs of the gel surface after being immersed in water for (f) 0, (g) 30, (h) 60, (i) 75, and (j) 600 s (×2000).
where DH represents the fractal dimension (Hausdorff dimension). The obtained patterns satisfys the above relation as shown in the inset of Figure 6. The fractal dimension DH was estimated by calculating the slope using the least-squares method. The time profile of the fractal dimension is shown in Figure 6. DH shows a sudden increase at around 45 s and saturates afterward. This means that the gel has a smooth surface structure (DH ≈ 1.0) in the swollen state and becomes complicated around 45 s, which almost coincides with the time when an extensive crystallization occurs. Figure 7 shows the dependence of the maximum rotation rate, ωmax, on the rotor weight. The rotation rate increases rapidly with the decrease in rotor weight. A large rotor rotates slowly with a long duration, while the small one rotates rapidly for a restricted time. The solid line in the figure represents the result of power fitting [ωmax ) 4889/ (rotor weight)0.85 ]. This fact suggests that by decreasing the rotor weight, a chemically driven micromotor with high rotation rate might be realized.
Figure 7. Rotor weight dependence of the maximum rotation rates. Inset: Relationship between the rotor weight and the energy efficiency.
The torque, τ, for the rotation was estimated from the relationship between ω and t by using the following formula:
τ)I
dω dt
(3)
where I is the momentum of inertia of the rodlike rotor. We can express I for rectangular shape approximately as follows assuming that the rotor is a fine uniform rigid body for simplicity:
I)
1 Ml2 12
(4)
where M is the rotor mass and l is the longitudinal length of the rotor. The momentum of inertia I was estimated as 1.7 × 10-10 kg m2 for the small rotor. The torque was calculated, at a minimum, to be in the range of 10-9-10-7 N‚m. The actual torque must be larger than this value if we take into account of the drag force of water.
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Langmuir, Vol. 16, No. 2, 2000 311 Table 2.
not controlled controlled
∆n (×10-5 mol/s)a
∆Es (×10-2 J)b
ωmax (rpm)c
Ek (×10-7 J)d
ηeff (×10-3%)e
0.95 1.68 0.78 0.13
2.32 4.08 1.91 0.32
180 34.9 75.0 394
0.92 8.47 4.50 1.45
0.4 2.1 2.4 4.5
large medium small
a ∆n is the maximum THF releasing rate. b ∆E is the energy of THF spreading. c ω s max is the maximum rotation rate. energy of the rotor at ωmax. e ηeff is the energy efficiency.
d
Ek is the kinetic
Figure 9. Effect on the rotation rates by placing the rotor in fresh water. Figure 8. Rotor weight dependency of kinetic energy Ek and the energy of THF spreading Es.
An attempt to determine the efficiency of the process of converting chemical energy into mechanical energy has been made. The energy efficiency largely depends on how to define the energy, Es, consumed by the gel. If we suppose that the spreading of the organic solvent is an ideal 2-D isothermal expansion, we have the following relation:8
Es ) nRT
(5)
Here, n is the molar number of the organic solvent doing the 2-D spreading, and R and T are the gas constant andthe absolute temperature, respectively. The kinetic energy of rotation, Ek, can be expressed as
1 Ek ) Iω2 2
(6)
Figure 10. Time profiles of the rotation rate in salt solution. (O): 5 mol/L NaCl; (b): water.
The dependence of the kinetic energy and spreading energy on rotor weight is shown in Figure 8. Both the kinetic and the spreading energies decrease with the decrease in rotor weight with different slopes, suggesting that the energy efficiency is dependent on the rotor weight. The energy efficiency, ηeff, can be written by the ratio of the kinetic energy to the spreading energy of the organic solvent, which are defined by eq 5 and 6
to a gel without controlling. We have also compared the ηeff values between controlled and uncontrolled gels, and the calculated results are listed in Table 2. One can see that the energy efficiency increases up to 10 times by controlling the motion. As shown in Figures 1 and 2, the translational velocity and rotation rate decrease extensively with time. We assume that the decrease in the rate is associated with the decrease in the surface tension due to water contamination by THF with time. Therefore, we placed the gel in fresh water and observed the change in the rotation rate (Figure 9). As shown in the figure, the rotation rate increases considerably after being placed in fresh water. This result suggests that the rotor would move quickly for a much longer period of time if the surface is kept fresh during the course of the experiment. Figure 10 shows time profiles of the rotation rate when the gel was placed on saline instead of pure water. The closed circle represents the motion in pure water, and the open circles indicate the motion in 5 mol/L NaCl solution.
ηeff )
Eκ × 100% Es
(7)
The relationship between the rotor weight and the energy efficiency is shown in the inset of Figure 7. The energy efficiency increases with the decrease in rotor weight. The energy efficiency of the smallest rotor is larger than that of the largest rotor by 2 times. The energy efficiency of the rotor with a weight of 100 µg has been estimated in a similar manner as used in Figure 7 and was calculated as 0.5%, which exceeded more than 100 times compared
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Figure 11. Electromotive force generated by the gel generator.
It is obvious that the rotor on the salt solution rotates almost two times quicker than in pure water for a longer duration, presumably due to increased surface tension of the salt solution. The surface tension of saline is 83 dyn/ cm and that of water is 73 dyn/cm at 25 °C. 3.3. Application as a Generator. We have constructed a generator using a rotor, a pair of permanent magnets, a solenoid coil, a stator, and a schale filled with pure water. The rotor is made from two pieces of polymer gels, a pair of permanent magnets with a flux density of 2300 Oe (Hitachi Metals, Ltd.), and a piece of aluminum foil. The size and the weight of the magnet are 4 × 4 × 1 mm3 and 175 mg, respectively; the total weight of the rotor is 434 mg; and the longitudinal and transverse length of the rotor are 40 and 6 mm, respectively, with a thickness of 2 mm. The stator is made of copper wire. The solenoid coil is made from a copper lead of 8.3 × 103 turns/m, and the two ends of the coil are connected to an amplifier. When the rotor was placed on water, it rotated on the surface of water by spreading organic solvents, and the change of magnetic flux in the solenoid coil generated an electromotive force, which is shown in Figure 11. The instantaneous electromotive force reaches a maximum of about 15 mV using four pieces of solenoid coil without load. The electromotive force attenuates with time, and the amplitude falls off to a few millivolts after 20 min, while the rotor maintains rotational motion over 30 min. We have calculated the energy efficiency of the conversion of the chemical energy to the kinetic and the electric energies. The electric power Ee is expressed by the following formula:
Ee ) i0ν0
(8)
Here, i0 and v0 are the instantaneous induced current and electromotive force, respectively. i0 ) 8.3 × 10-5 A and v0 ) 2.5 × 10-3 V at the maximum rotation rate. Accordingly, the maximum electric power during 1 s was calculated as 2.1 × 10-7 J. The kinetic energy of rotation was 3.2 × 10-7 J, and the energy of spreading was calculated as 2.1 × 10-2 J, which was obtained from the result of Figure 8. The effect of the magnet on the surface tension of the water is negligible. Therefore, the energy efficiency was calculated as 2.5 × 10-3%. We should emphasize here that the energy source of this generator was simply obtained from the free energy change of solvent dilution. It has similarities to biological motors, which also work through the dissipation of chemical energy. Such chemomechanical transduction produces no noise, no air pollution, and no unnecessary exhaust products such as combustion or other chemical reactions do. Acknowledgment. This research is supported by a Grant-in-Aid for the Special Promoted Research Project “Construction of Biomimetic Moving Systems Using Polymer Gels” from the Ministry of Education, Science, Sports, and Culture, Japan. This research is also financially supported by a Grant-in-Aid for the Novel HighFunctional Materials from NEDO (New Energy and Industrial Technology Development Organization). We are grateful to Professor M. Ido and Professor M. Oda of the Department of Physics of Hokkaido University for their kind and useful discussions. We are also grateful to Mr. M. Nishi (Hitachi Metals, Ltd.) for his kind offer of magnets. LA990483O
