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Fabrication and actuation of ionic polymer metal composites patterned by combining electroplating with electroless plating
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Composites: Part A 39 (2008) 588–596 www.elsevier.com/locate/compositesa
Fabrication and actuation of ionic polymer metal composites patterned by combining electroplating with electroless plating Jin-Han Jeon, Sung-Won Yeom, Il-Kwon Oh
*
School of Mechanical Systems Engineering, Chonnam National University, 300 Yongbong-dong, Buk-gu, Gwang-Ju 500-757, Republic of Korea Received 14 March 2007; received in revised form 21 June 2007; accepted 27 July 2007
Abstract The novel fabrication technique that patterns the multiple electrodes of the ionic polymer metal composite actuators was developed to mimic the swimming and flapping locomotion of a living thing. The developed method is to combine electroplating with the electroless chemical reduction using the patterned mask. The advantages of this fabrication method are that the initial compositing between the polymer and platinum particles can be assured by the chemical reduction method, and the thickness of each electrode can be controlled easily and rapidly by electroplating. By using the fabricated actuator with a multiple degree of freedom, the oscillatory and undulatory waves of the flexible membrane actuator was generated and a twisting motion was also realized to verify the possibility of mimicking the fish-like locomotion. Present results show that this novel method combining electroplating with electroless plating can be a promising technique to easily pattern multiple electrodes and to implement the biomimetic motion of the polymer actuators with good mechanical bending performance. 2007 Elsevier Ltd. All rights reserved. Keywords: A. Smart materials; B. Electrical properties; IPMC; E. Surface treatment
1. Introduction The ionic polymer metal composites (IPMCs) that can be applied to smart structures, bio-medical devices and biomimetic robots have been extensively investigated [1–4]. Those electroactive polymers with high reliability and flexibility can be used as novel sensors and actuators, which are on much demand in several industrial fields. Fig. 1 shows a schematic illustration of the bending principle of the IPMC actuators under the electric fields. As shown in Fig. 2a, there are mobile cations, water molecules and sulfonate side-chains in the ionic polymer membrane. As the electrical current is applied to the electrode surfaces, the metallic cations and water molecules move to the anode. Therefore, one side will swell and the other side will shrink, resulting in the mechanical bending of the cantilevered actuators as shown in Fig. 1. Fig. 2b shows the layer-up *
Corresponding author. Tel.: +82 62 530 1685; fax: +82 62 530 1689. E-mail address: [email protected] (I.-K. Oh).
1359-835X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2007.07.013
structure that is composed of the surface electrodes, the polymer-metal composite layer and the ionic polymer membrane. Actually, the polymer-metal composite layers, which are built up in the primary process of the electroless chemical reduction, play an important role in interfacial bonding, electrical conductivity and mechanical bending performance of the IPMC actuator. So, the electroless chemical reduction method has several advantages in comparison with other deposition techniques such as evaporating and sputtering. Biomimetic engineering, which is biologically inspired by the natural selection mechanism, has become a new and challenging research topic. The fish-like biomimetic locomotion can be artificially mimicked by using flexible polymer actuators. Especially the propulsive and maneuvering abilities are very important and prerequisite to toy robots, bio-medical devices and micro-manipulators. Most fish generate thrust by bending their bodies into a backward-moving propulsive wave that extends to its caudal fin; this type of swimming is called a body and caudal fin
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IPMC actuators, in-phase and out-of-phase activation and a twisting motion were generated. 2. Patterning of multiple electrodes of IPMC 2.1. Existing fabrication techniques
Fig. 1. A schematic illustration of actuation principle.
locomotion (BCF) [5]. Fish can also swim by using their median and pectoral fins, thus called a median and paired fin locomotion (MPF). BCF and MPF propulsions are the combination of two motions; undulatory motion involves the passage of a wave along the propulsive structure, while oscillatory motion involves the swivel of the propulsive structure on its base without formation of waves. In the undulatory BCF mode, the propulsive wave traverses the fish’s body in a direction opposite to the overall movement and at a speed greater than the overall swimming speed. In order to smoothly mimic the biological locomotion of crawling and flying insects, swimming fish and walking animals, the patterning technique of multiple electrodes in the electroactive polymers should be developed to control the shape of the actuator surface. In this study, the novel method combining electroplating technique with the electroless chemical reduction was newly developed to pattern the IPMC actuators with a multiple degree of freedom. This method can assure the strong interfacial bonding between the ionic polymer membrane and the electrodes and can control the stiffness of the local area in the process of electroplating. To validate the actuation of the patterned
There are several methods for metal deposition on polymer membranes such as electroless chemical reduction, electroplating, physical deposition, electrochemical deposition and so on. The patterning method based on electroless chemical reduction is simply applied by using a masking technique, which uses a special mask tape, crepe paper [6], and jig. Guilly et al. [7] developed a masking technique using a hydrophobic silicon rubber. And Nakano et al. [8] proposed a similar masking technique, which uses an adhesive tape, 3M Polyethylene Film Tape 480. But, the tapes in all these masking techniques are frequently peeled off because the patterned polymer tapes can shrink and expand due to changes of environmental temperature under the fabrication process. Therefore, it is very difficult to precisely pattern the multiple electrodes by using the previous masking tapes. Jeong [9] fabricated a simple pattern shape of the IPMC actuator by a pressing process using a mechanical jig. But, this method also produced a wrinkling problem of the polymer membrane. Also, a laser cutting method can be used for the electrode patterning of the IPMC fabricated by electroless chemical reduction. In view of preventing damage of the ion exchanging membrane, laser cutting is not proper for patterning. Also, the laser beam has to be precisely controlled by trial and error. Sewa et al. [10] proposed excimer laser processing. And, Nakabo, et al. [11] achieved sufficient insulation at the minimum groove size of 50 lm in width and approximately 20 lm in depth by optimizing the conditions of the bursts of the laser beam. But, this method damaged the ionic polymer membrane and the laser beam cutting required a high fabrication cost. All methods addressed in this section are not adequate enough to pattern the ionic polymer metal
Fig. 2. Ion-exchangeable polymer membrane and layer-up of IPMC: (a) chemical structure of Nafion, and (b) cross-sectional view of IPMC ( , surface electrode; , polymer-metal composite; , membrane).
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bered from 1 to 6 as shown in Fig. 3. This multiple electrodes enable the IPMC actuator to naturally mimic the flexible motion of fish including oscillatory, undulatory and twisting waves. A picture of the expected undulatory wave is shown in Fig. 4. Our goal is to eventually create the motion with a multiple degree of freedom. Details of the fabrication procedures and experimental results are described in the following sections. 3. Fabrication methods of electrode patterning Fig. 3. An improved pattern design of multiple electrodes of IPMC actuator.
Fig. 4. An expected motion of IPMC actuator with multiple DOFs.
composite actuators. Therefore, a novel method to rapidly pattern the multiple electrodes and to minimize the damage of the ionic polymer membrane should be developed. 2.2. Design of multiple electrodes of IPMC In this section, an electrode pattern shape for implementation of a fish-like bio-mimetic motion is addressed. The overall pattern design of the membrane is shown in Fig. 3. All patches have a number from 1 to 6. In several previous fabrication results, some cracks were observed at the sharp corners of the original pattern as shown in Fig. 3. Therefore, the pattern shape was slightly modified with round corners as shown in Fig. 3. The corner of the masking tape was trimmed to 2 mm diameter. The pattern on the membrane consists of two parts; one is the electrical connecting part and the other is the flexible body of the IPMC actuator. The patterned shape for the top and bottom surfaces consists of six isolated electrode patches num-
3.1. Method 1: electroless chemical reduction with masking tapes The simplest patterning method is to stick masking film tapes on both sides of the Nafion film as shown in Fig. 5a and to apply the electroless chemical reduction. Three different tapes were compared and evaluated to find more reliable masking film in Table 1. Although the polyimide film tape 5413 has the best performance for high temperature and chemical resistance among the three tapes, it is too thin to adhere to the Nafion membrane. In many experiments, the tape 5413 was wrinkled and torn in the chemical reduction process. Also, the plastic film tape 472 begins to soften at 107 C and is too sensitive to the change of environmental temperature. However, the UHMW polyethylene tape, 3M 5423, kept proper adhesion between the Nafion membrane and the masking film in the chemical reactions. The patterned shapes by the chemical reduction with the 3M 5423 tape are shown in Fig. 5b. But, there are two problems; the platinum particles permeated into the micro chasm between the Nafion membrane and the masking tape because of long fabrication time, and the edge of the patterned shape was not sharp due to shrinkage and expansion of the tape in the chemical reduction processing. Rough edges with black color in Fig. 5c indicate the infiltration of the platinum. Therefore, the pattern shape of the masking tape was changed as explained in Section 2.2. The width of electrical insulation lines increased slightly and the rectangular edges were changed to round edges. Through trial and error, we got precise and clear
Fig. 5. Patterned IPMCs by electroless chemical reduction with masking tape: (a) bonded tapes to Nafion; (b) infiltration and rough edges; (c) patterning by previous masking tape and (d) patterning by improved masking tape.
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Table 1 Basic characteristics of masking film tapes Product
Thickness (mm)
Temperature range (C)
Adhesion (g/in)
Characteristics
Polyimide film tape 5413
0.07
73 to 260
566
Plastic film tape 472 UHMW polyethylene tape 3M 5423 [16]
0.26 0.28
107 34 to 107
652 737
Stable at high temperature Resistive to the chemical Sensitive to temperature Resistive to the chemical A little trace
Table 2 The process of electroless chemical reduction for platinum layers Formula of reaction
Process
Order
þ ½PtðNH3 Þ4 þ 2Cl þ NHþ 4 þ OH þ H ðinside NafionÞ 2þ ! ½PtðNH3 Þ4 ðinside NafionÞ þ NH4 Cl2 þ H2 O ðlÞ þ NaBH4 þ 8OH ! BO 2 þ Na þ 6H2 O þ 8e 2þ 0 ½PtðNH3 Þ4 þ 2e ! Pt þ 4NH3 NaBH4 þ 2H2 O ! NaBO2 þ 4H2 þ NaBH4 þ 4½PtðNH3 Þ4 2þ þ 8OH ! 4Pt0 ðsÞ þ 16NH3 ðgÞ þ BO 2 þ Na þ 6H2 O ðlÞ
Ion-exchange process and hydrolysis Oxidation response Reduction response Additional response Total response
(1)
patterned electrodes of the IPMC actuators as shown in Fig. 5d. The chemical reduction procedure is separated into two steps; one is the initial platinum compositing process (IPCP) and the other is the surface electroding process (SEP). IPCP reduces the platinum complex to deposit platinum nanoparticles into the ionic polymer whereas SEP grows the platinum on top of the initial platinum surface to reduce surface resistance. In this method, the IPMC was fabricated through 3 times IPCP and 2 times SEP. The electroless chemical reduction procedure is briefly introduced as follows: first, the surfaces of Nafion-117 film are roughened by sandblasting; then a platinum–ammine complex salt is adsorbed onto the membrane. The hydrophilic ion cluster (H+, Nafion) is exchanged for the platinum complex cations ((Pt(NH3)4)2+) using a platinum complex (Pt(NH3)4Cl2) and adding ammonia water as shown in Table 2(1). In the next step, the reduction of the platinum–ammine complex salt deposits metallic nuclei on the surfaces, and then this metal deposition forms thin electrode layers. A proper reducing agent like NaBH4 is used to metalize the polymeric materials by the molecular plating as shown in Table 2(2)– (4). Proper repetition of the absorption-primary plating process, so called IPCP, can make the polymer-platinum composite layer grow with reliable composition in the depth of the membrane. And then, an additional amount of platinum is plated on the deposited platinum layer by the secondary plating process. Then the surface resistance of surface electrodes can be reduced. The final step is to exchange H+ with other counter ions (Li+). The thickness of the platinum electrode layer, formed by the electroless chemical reduction was about 6 lm from SEM pictures. 3.2. Method 2: combining electroplating and electroless plating with masking tape Method 1 requires a long fabrication time of about seven days and has the infiltration problem previously
(2) (3) (4) (5)
described. In this study, a novel method to pattern the multiple electrodes is proposed by combining electroplating with the electroless plating technique. The main advantage of Method 2 is that we can control the thickness of the local electrodes of the patterned IPMC actuators by using electroplating. The electroless chemical reduction, which makes composite layers between the ionic polymer and metallic electrodes, can give better mechanical adhesion and bending performance than other methods like evaporation and sputtering. In Method 2, the electroplating technique follows the electroless chemical reduction via three times IPCP and one time SEP. Electrical currents for electroplating processing are listed in Table 3. The plating bath was prepared with 1 N hydrochloric acid, 2 mM lead (II) nitrate, 20 mM nitric acid and dissolved 5 g Hexachloroplatinate(IV) (H2PtCl6) [13]. The solution composition and operating conditions were carefully controlled to attain the maximum ductility in the deposited platinum electrode layer. First, the proper current density was found to form a consistent and reliable microstructure and to reduce the electrical resistance of the surface electrodes. The recommended electrical operation is that a constant 0.1 A current is applied for 30 min and are repeated seven times [12]. Present results show that current electroplating can save three days worth of time as compared the electroless chemical reduction. Also, the infiltraTable 3 Operating conditions of electroplating Electroplating operating conditions Plating bath Temperature, C Agitation General current density range Anode electrode Proper current density
2.5% Hexachloroplatinic acid plating solution [H2PtCl6, 20 g/L] 30 Mechanical stirring system 0.1–1 A/dm2 [17] Titanium expanded mesh plate coated by platinum Reference to Table 4
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Fig. 6. Patterned IPMC by combining electroplating and electroless plating with masking tapes: (a) specimen by Method 2; (b) SEM cross-section of IPMC sample by Method 2; (c) picture of uneven plating surface; (d) optical microscope picture of plating line disconnected and (e) the direction of electroplating.
Table 4 Current density conditions of electroplating Specimen
1
2
3
4
Unit
Current density Supplied current Operating time (1 time) Supplying quantity (1 time)
0.33 0.04 1382 456
0.58 0.07 786 456
0.83 0.1 549 456
1.08 0.13 422 456
A/dm2 A s C/dm2
Voltage(V) & Displacement (mm)
4 3 2 1 0 -1 -2
Input Voltage Specimen 1 Specimen 2 Specimen 3 Specimen 4
-3 -4 0
2
4
6
8
Time (s)
Fig. 8. Comparison of bending performance according to current density of electroplating; driving voltage: 1.5 * sin(2p * 0.2 * t). 120
100
Surface Resistance (Ohms/cm)
tion problem was solved as shown in Fig. 6a. In Fig. 6b, the thickness of the platinum electrode is about 20 lm. However, a few problems in electroplating were observed. The IPMC made by electroplating was slightly twisted due to residual stresses and showed a reduced bending performance. Above all, the narrow electric insulation line was frequently disconnected during electroplating as shown in Fig. 6c–e. Therefore, insulation lines were widened and the electric connection was separately applied according to patch size. Additionally, four IPMC specimens, which were fabricated by three times IPCP and one time SEP, were prepared to investigate the effect of current density on the bending performance. To find the optimal the current density, the pretest on the electroplating was performed with simple cantilevered beam specimens. The specimens have the same size of 4 mm · 70 mm as shown in Fig. 7. Fig. 7b–c shows the cross-sectional SEM micrographs of the IPMC actuators after the electroplating process according to different current densities listed in Table 4. The platinum layer through the electroless chemical reduction was deposited up to about 5 lm. And the electrode thickness of all specimens increased up to 6 lm through the electroplating process regardless of applied current densities. The thickness growth by electroplating was mainly affected by the supplying quantity rather than the current density. The harmonic excitation of these samples was applied with peak voltage of 1.5 V and exciting frequency of 0.2 Hz. The second specimen fabricated under
80
60
40
20
Fig. 7. IPMC samples used to find proper current density: (a) strips for observing the microstructure; (b) cross-sectional SEM of three times ICPC and one time SEP; (c) cross-sectional SEM after electroplating.
0 Specimen 1
Specimen 2
Specimen 3
Specimen 4
Fig. 9. Surface resistance of specimens according to current density.
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4.1. Experimental setup An integrated experimental setup was used to measure the transverse displacement and to capture the moving shape of the patterned IPMC actuators in aqueous condition. Therefore, in all experiments, the electrical connecting parts of the IPMC actuators are out of water for insulation. However, all IPMC actuators are immersed in water. The overall measurement system is shown in Fig. 10. Input signals were generated by a NI-PXI 6733 board, which was connected to the terminal BNC-2210 output channel and its electric current was amplified by UPM 1503. The NIPXI acquisition board 4472 and a laser displacement sensor, LK 301, were used to measure the tip displacement of the actuators. And the NI-PXI 1409 image acquisition board and a XC-HR50 CCD camera were used to record the moving shapes of the IPMC actuators.
3 2 2 1
1
0
0
-1
-1
4.2. Oscillatory and undulatory motion
-2
Driving Voltage Tip displacement by Method 1 Tip displacement by Method 2
-2
Transvers displacement (mm)
4. Actuation tests for bending and twisting
and exciting frequency of 0.5 Hz was applied to all top and bottom electrode patches with in-phase. The tip transverse displacements of two patterned IPMC actuators by Method 1 and Method 2 are compared in Fig. 11. The tip displacement by Method 1 was much larger than that by Method 2. The maximum transverse displacement obtained by Method 1 was almost two times in comparison with Method 2. The experimental results of the frequency response function between Method 1 and Method 2 are shown in Fig. 12. The fundamental frequencies for the samples fabricated with Method 1 and method 2 are 16.9 and 18.6 Hz, respectively. At the resonance frequencies, the bending response of the specimen by method 1 is larger than that by Method 2. Generally speaking, the bending response of the sample by Method 1 is much larger than that by Method 2. However, beyond the fundamental frequency, the bending response of the sample by Method 2 is much larger than that by Method 1. It means that the stiffness of the sample by Method 2 is stronger than that by Method 1, resulting in the increasing of the fundamental frequency. Therefore Method 2, combining electroplating with the electroless chemical reduction, can be a promising
Voltage (V)
the current density of 0.58 A/dm2 shows larger bending deflections as shown in Fig. 8. Also, surface resistance of the platinum electrodes was measured to compare electrical consumption according to different current densities in electroplating. The surface resistance was determined by using a two-point probe method [14] under the wet condition at room temperature. Keithley sourcemeter series 2400 was used to measure the electric resistance by applying 2.1 V. The distance between the two probes was 1 cm. Surface resistances for different specimens were quite different according to the current densities as shown in Fig. 9 and it means that current densities affect the microstructures of the deposited electrodes. Specimens 2 showed relatively low surface resistance and a small standard deviation.
593
-3 0
1
2
3
4
5
Time (sec)
To generate oscillatory motion of the patterned IPMC actuators, the sine wave with maximum voltage of 1.5 V
Fig. 11. Comparison of tip transverse displacement between Method 1 and Method 2 under driving voltage of 1.5 * sin(2p * 0.5 * t).
Fig. 10. Integrated experimental setup for measurement of transverse displacement and total movement shape of patterned IPMC.
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Method 1 Method 2
60
Magnitude (dB (10-6 m/V))
Transverse displacements (mm)
70
50
40
30
4.0 MAX.
2.0 MAX.
0.0
MIN. MIN.
-2.0 Out of phase : 3, 4 patch In phase : 1,2,,5,6 patch
-4.0 0
20
1
2
3
4
5
x-direction (cm) 10
0 10
20
30
40
50
60
Frequency (Hz)
Fig. 12. Frequency response functions of IPMC actuators made by Method 1 and 2 (1–60 Hz).
Fig. 14. Oscillatory and undulatory wave generation with in-phase and out-of-phase actuation modes under harmonic excitation of 3 * sin(2p * 2 * t).
candidate to pattern multiple electrodes of the IPMC actuator for realization on biomimetic motion, because the bending performance of the specimen by Method 2 is good enough to generate the biomimetic motion of the patterned IPMC actuator. Another main advantage of Method 2 is that we can control the thickness of the local electrodes of the patterned IPMC actuators by using electroplating. By using a CCD camera, the moving shapes of the patterned IPMC actuators fabricated by Method 1 were captured as shown in Fig. 13. Additionally, to generate undulatory motion, the sine wave with maximum voltage of 3 V and exciting frequency of 2 Hz was applied to patches 1, 2, 5, and 6 and the antiphase signal was applied to patches 3 and 4, resulting in an out-of-phase actuation. The oscillatory wave due to inphase actuation and the undulatory wave due to out-ofphase actuation were distinctly generated as shown in Fig. 14. This graph is obtained by using the vision sensing and MROVS techniques [15]. Present result shows that the patterned IPMC actuators fabricated by Method 2 can naturally mimic the higher order propulsive motion of fish. To compare the thrust force between oscillatory and undulatory waves will be a very interesting research topic. 4.3. Twisting motion
Fig. 13. Pure bending by Method 1 under driving voltage of 2.0 * sin(2p * 0.5 * t).
For realization of the twisting motion, an anti-phase signal was applied to patches 2, 4 and 6. The patterned IPMC
Fig. 15. Twisting motion generation using patterned IPMC actuator under harmonic excitation of 3 * sin(2p * 0.1 * t).
J.-H. Jeon et al. / Composites: Part A 39 (2008) 588–596
actuator was twisted as shown in Fig. 15. To quantitatively present the twisting motion, two laser displacement sensors were used as shown in Fig. 16. The following simple equation can give a twisting angle at the tip section of the patterned IPMC actuator. 1 W 1 W 2 h ¼ tan ð1Þ L where W1 and W2 are the transverse displacements at two different points and L is the distance of two measurement points. The time history of twisting angles according to different applied voltages was calculated and plotted in Fig. 17. The twisting angle increased with increasing driving voltages. And the twisting angle by 1.5 V is three times that by 1 V. Present results show the twisting motion by using the patterned IPMC actuator was successfully generated.
Specimen
595
5. Conclusion In this study, the novel patterning methods of multiple electrodes of the IPMC actuators were investigated for realization of bio-mimetic locomotion. Here, two different fabrication methods were tried and compared with respect to the electric conductivity and the mechanical actuation. The conclusions obtained from this work can be summarized as follows: (1) Method 1 based on electroless chemical reduction with the masking tapes can produce relatively large mechanical bending displacement, while it takes a lot of time and labor to fabricate the patterned electrodes. Also, the platinum infiltration between the ionic polymer and the masking tape was a critical problem due to long fabrication time. (2) Method 2 combining electroplating with electroless plating shows precise patterned shapes of the multiple electrodes and saves three days of fabrication time. Also, the electroplating technique has nice advantages to control the stiffness and to make the thickness of the patterned local electrodes different. (3) The patterned IPMC actuators with multiple electrodes can successfully generate oscillatory, undulatory and twisting motions by using in-phase actuation or out-of-phase actuation. Acknowledgement
W1 —W2 W1
θ
W2
L
This work was supported by Grant No. (R01-2005-00010848-0) from the Basic Research Program of the Korea Science and Engineering Foundation.
L
Laser Displacement Sensors
References Fig. 16. Measurement setup and calculation of rotational angle for twisting motion of patterned IPMC actuator.
10 Twisting Angle at 0.5 Volts Twisting Angle at 1.0 Volts Twisting Angle at 1.5 Volts
8
Twisitng Angle (θ ,degree)
6 4 2 0 -2 -4 -6 -8 -10
0
5
10
15
20
Time (s)
Fig. 17. Twisting angles according to different maximum voltages with harmonic excitation of A * sin(2p * 0.1 * t).
[1] Shahinpoor M, Kim KJ. Ionic polymer-metal composites: I. Fundamentals. Smart Mater Struct 2001;10:819–33. [2] Kim JH, Song CS, Yun SR. Cellulose based electro-active papers: performance and environmental effects. Smart Mater Struct 2006;15:719–23. [3] Oh IK, Jeon JH. Dynamic characteristics of novel ionic-polymermetal-composites. Key Eng Mater 2006;321–323:208–11. [4] Salehpoor K, Shahinpoor M, Razani A. Role of ion transport in actuation of IPMC artificial muscles. Proc SPIE Smart Struct Mater 1998;3330:50–8. [5] Sfakiotakis M, Lane DM, Davies JBC. Review of fish swimming modes for aquatic locomotion. IEEE J Ocean Eng 1997;24: 237–52. [6] Tadokoro S, Murakami T, Fuji S, Kanno R, Hattori M, Takamori T, Oguro K. An elliptic friction drive element using an ICPF actuator. IEEE Contr Syst Magaz 1997;17:60–8. [7] Guilly ML, Uchida M, Taya M. Nafion based smart membrane as an actuator array. Proc SPIE Smart Struct Mater 2002;4695: 78–84. [8] Nakano M, Mazzone A, Piffaretti F, Gassert R, Nakao M, Bleuler H. IPMC actuator array as 3-d haptic display. Proc SPIE Smart Struct Mater 2005;5759:331–9. [9] Jeong KM. Research on artificial muscle-like actuator using IPMC. Master thesis. Sung Kyun Kwan University; 2001.
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[10] Sewa S, Onishi K, Asaka K, Fujiwara N, Oguro K. Polymer actuator driven by ion current at low voltage, applied to catheter system. In: IEEE the eleventh annual international workshop on micro electro mechanical systems; 1998. p. 148–53. [11] Nakabo Y, Mukai T, Asaka K. Kinematic modeling and visual sensing of multi-DOF robot manipulator with patterned artificial muscle. In: IEEE international conference on robotics and automation; 2005. p. 4315–20. [12] Oh IK, Jeon JH, Lee YG. Multiple electrode patterning of ionic polymer metal composite actuators. Proc SPIE Smart Struct Mater 2006;6168:286–93.
[13] Lee MK, Hwang YG. A study on the preparation of the platinized expended-titanium electrode. Appl Chem 2004;8:498–501 [in Korean]. [14] Shahinpoor M, Kim KJ. The effect of surface electrode resistance on the performance of ionic polymer metal composite (IPMC) artificial muscles. Smart Mater Struct 2000;9:543–51. [15] Oh I K, Yeom SW, Lee DW. Modal reduced order model for vision sensing of IPMC actuator. Key Eng Mater 2006:326–8, 1523–6. [16] Technical Sheet. 3M UHMW Polyethylene Tape 5423. Foundation Web site: http://www.3m.com/intl/kr/img/single/pdf/5423.pdf. [17] Morrissey RJ. Platinum plating. Met Finish 2001;99:291.
Composites: Part A 39 (2008) 588–596 www.elsevier.com/locate/compositesa
Fabrication and actuation of ionic polymer metal composites patterned by combining electroplating with electroless plating Jin-Han Jeon, Sung-Won Yeom, Il-Kwon Oh
*
School of Mechanical Systems Engineering, Chonnam National University, 300 Yongbong-dong, Buk-gu, Gwang-Ju 500-757, Republic of Korea Received 14 March 2007; received in revised form 21 June 2007; accepted 27 July 2007
Abstract The novel fabrication technique that patterns the multiple electrodes of the ionic polymer metal composite actuators was developed to mimic the swimming and flapping locomotion of a living thing. The developed method is to combine electroplating with the electroless chemical reduction using the patterned mask. The advantages of this fabrication method are that the initial compositing between the polymer and platinum particles can be assured by the chemical reduction method, and the thickness of each electrode can be controlled easily and rapidly by electroplating. By using the fabricated actuator with a multiple degree of freedom, the oscillatory and undulatory waves of the flexible membrane actuator was generated and a twisting motion was also realized to verify the possibility of mimicking the fish-like locomotion. Present results show that this novel method combining electroplating with electroless plating can be a promising technique to easily pattern multiple electrodes and to implement the biomimetic motion of the polymer actuators with good mechanical bending performance. 2007 Elsevier Ltd. All rights reserved. Keywords: A. Smart materials; B. Electrical properties; IPMC; E. Surface treatment
1. Introduction The ionic polymer metal composites (IPMCs) that can be applied to smart structures, bio-medical devices and biomimetic robots have been extensively investigated [1–4]. Those electroactive polymers with high reliability and flexibility can be used as novel sensors and actuators, which are on much demand in several industrial fields. Fig. 1 shows a schematic illustration of the bending principle of the IPMC actuators under the electric fields. As shown in Fig. 2a, there are mobile cations, water molecules and sulfonate side-chains in the ionic polymer membrane. As the electrical current is applied to the electrode surfaces, the metallic cations and water molecules move to the anode. Therefore, one side will swell and the other side will shrink, resulting in the mechanical bending of the cantilevered actuators as shown in Fig. 1. Fig. 2b shows the layer-up *
Corresponding author. Tel.: +82 62 530 1685; fax: +82 62 530 1689. E-mail address: [email protected] (I.-K. Oh).
1359-835X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2007.07.013
structure that is composed of the surface electrodes, the polymer-metal composite layer and the ionic polymer membrane. Actually, the polymer-metal composite layers, which are built up in the primary process of the electroless chemical reduction, play an important role in interfacial bonding, electrical conductivity and mechanical bending performance of the IPMC actuator. So, the electroless chemical reduction method has several advantages in comparison with other deposition techniques such as evaporating and sputtering. Biomimetic engineering, which is biologically inspired by the natural selection mechanism, has become a new and challenging research topic. The fish-like biomimetic locomotion can be artificially mimicked by using flexible polymer actuators. Especially the propulsive and maneuvering abilities are very important and prerequisite to toy robots, bio-medical devices and micro-manipulators. Most fish generate thrust by bending their bodies into a backward-moving propulsive wave that extends to its caudal fin; this type of swimming is called a body and caudal fin
J.-H. Jeon et al. / Composites: Part A 39 (2008) 588–596
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IPMC actuators, in-phase and out-of-phase activation and a twisting motion were generated. 2. Patterning of multiple electrodes of IPMC 2.1. Existing fabrication techniques
Fig. 1. A schematic illustration of actuation principle.
locomotion (BCF) [5]. Fish can also swim by using their median and pectoral fins, thus called a median and paired fin locomotion (MPF). BCF and MPF propulsions are the combination of two motions; undulatory motion involves the passage of a wave along the propulsive structure, while oscillatory motion involves the swivel of the propulsive structure on its base without formation of waves. In the undulatory BCF mode, the propulsive wave traverses the fish’s body in a direction opposite to the overall movement and at a speed greater than the overall swimming speed. In order to smoothly mimic the biological locomotion of crawling and flying insects, swimming fish and walking animals, the patterning technique of multiple electrodes in the electroactive polymers should be developed to control the shape of the actuator surface. In this study, the novel method combining electroplating technique with the electroless chemical reduction was newly developed to pattern the IPMC actuators with a multiple degree of freedom. This method can assure the strong interfacial bonding between the ionic polymer membrane and the electrodes and can control the stiffness of the local area in the process of electroplating. To validate the actuation of the patterned
There are several methods for metal deposition on polymer membranes such as electroless chemical reduction, electroplating, physical deposition, electrochemical deposition and so on. The patterning method based on electroless chemical reduction is simply applied by using a masking technique, which uses a special mask tape, crepe paper [6], and jig. Guilly et al. [7] developed a masking technique using a hydrophobic silicon rubber. And Nakano et al. [8] proposed a similar masking technique, which uses an adhesive tape, 3M Polyethylene Film Tape 480. But, the tapes in all these masking techniques are frequently peeled off because the patterned polymer tapes can shrink and expand due to changes of environmental temperature under the fabrication process. Therefore, it is very difficult to precisely pattern the multiple electrodes by using the previous masking tapes. Jeong [9] fabricated a simple pattern shape of the IPMC actuator by a pressing process using a mechanical jig. But, this method also produced a wrinkling problem of the polymer membrane. Also, a laser cutting method can be used for the electrode patterning of the IPMC fabricated by electroless chemical reduction. In view of preventing damage of the ion exchanging membrane, laser cutting is not proper for patterning. Also, the laser beam has to be precisely controlled by trial and error. Sewa et al. [10] proposed excimer laser processing. And, Nakabo, et al. [11] achieved sufficient insulation at the minimum groove size of 50 lm in width and approximately 20 lm in depth by optimizing the conditions of the bursts of the laser beam. But, this method damaged the ionic polymer membrane and the laser beam cutting required a high fabrication cost. All methods addressed in this section are not adequate enough to pattern the ionic polymer metal
Fig. 2. Ion-exchangeable polymer membrane and layer-up of IPMC: (a) chemical structure of Nafion, and (b) cross-sectional view of IPMC ( , surface electrode; , polymer-metal composite; , membrane).
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bered from 1 to 6 as shown in Fig. 3. This multiple electrodes enable the IPMC actuator to naturally mimic the flexible motion of fish including oscillatory, undulatory and twisting waves. A picture of the expected undulatory wave is shown in Fig. 4. Our goal is to eventually create the motion with a multiple degree of freedom. Details of the fabrication procedures and experimental results are described in the following sections. 3. Fabrication methods of electrode patterning Fig. 3. An improved pattern design of multiple electrodes of IPMC actuator.
Fig. 4. An expected motion of IPMC actuator with multiple DOFs.
composite actuators. Therefore, a novel method to rapidly pattern the multiple electrodes and to minimize the damage of the ionic polymer membrane should be developed. 2.2. Design of multiple electrodes of IPMC In this section, an electrode pattern shape for implementation of a fish-like bio-mimetic motion is addressed. The overall pattern design of the membrane is shown in Fig. 3. All patches have a number from 1 to 6. In several previous fabrication results, some cracks were observed at the sharp corners of the original pattern as shown in Fig. 3. Therefore, the pattern shape was slightly modified with round corners as shown in Fig. 3. The corner of the masking tape was trimmed to 2 mm diameter. The pattern on the membrane consists of two parts; one is the electrical connecting part and the other is the flexible body of the IPMC actuator. The patterned shape for the top and bottom surfaces consists of six isolated electrode patches num-
3.1. Method 1: electroless chemical reduction with masking tapes The simplest patterning method is to stick masking film tapes on both sides of the Nafion film as shown in Fig. 5a and to apply the electroless chemical reduction. Three different tapes were compared and evaluated to find more reliable masking film in Table 1. Although the polyimide film tape 5413 has the best performance for high temperature and chemical resistance among the three tapes, it is too thin to adhere to the Nafion membrane. In many experiments, the tape 5413 was wrinkled and torn in the chemical reduction process. Also, the plastic film tape 472 begins to soften at 107 C and is too sensitive to the change of environmental temperature. However, the UHMW polyethylene tape, 3M 5423, kept proper adhesion between the Nafion membrane and the masking film in the chemical reactions. The patterned shapes by the chemical reduction with the 3M 5423 tape are shown in Fig. 5b. But, there are two problems; the platinum particles permeated into the micro chasm between the Nafion membrane and the masking tape because of long fabrication time, and the edge of the patterned shape was not sharp due to shrinkage and expansion of the tape in the chemical reduction processing. Rough edges with black color in Fig. 5c indicate the infiltration of the platinum. Therefore, the pattern shape of the masking tape was changed as explained in Section 2.2. The width of electrical insulation lines increased slightly and the rectangular edges were changed to round edges. Through trial and error, we got precise and clear
Fig. 5. Patterned IPMCs by electroless chemical reduction with masking tape: (a) bonded tapes to Nafion; (b) infiltration and rough edges; (c) patterning by previous masking tape and (d) patterning by improved masking tape.
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Table 1 Basic characteristics of masking film tapes Product
Thickness (mm)
Temperature range (C)
Adhesion (g/in)
Characteristics
Polyimide film tape 5413
0.07
73 to 260
566
Plastic film tape 472 UHMW polyethylene tape 3M 5423 [16]
0.26 0.28
107 34 to 107
652 737
Stable at high temperature Resistive to the chemical Sensitive to temperature Resistive to the chemical A little trace
Table 2 The process of electroless chemical reduction for platinum layers Formula of reaction
Process
Order
þ ½PtðNH3 Þ4 þ 2Cl þ NHþ 4 þ OH þ H ðinside NafionÞ 2þ ! ½PtðNH3 Þ4 ðinside NafionÞ þ NH4 Cl2 þ H2 O ðlÞ þ NaBH4 þ 8OH ! BO 2 þ Na þ 6H2 O þ 8e 2þ 0 ½PtðNH3 Þ4 þ 2e ! Pt þ 4NH3 NaBH4 þ 2H2 O ! NaBO2 þ 4H2 þ NaBH4 þ 4½PtðNH3 Þ4 2þ þ 8OH ! 4Pt0 ðsÞ þ 16NH3 ðgÞ þ BO 2 þ Na þ 6H2 O ðlÞ
Ion-exchange process and hydrolysis Oxidation response Reduction response Additional response Total response
(1)
patterned electrodes of the IPMC actuators as shown in Fig. 5d. The chemical reduction procedure is separated into two steps; one is the initial platinum compositing process (IPCP) and the other is the surface electroding process (SEP). IPCP reduces the platinum complex to deposit platinum nanoparticles into the ionic polymer whereas SEP grows the platinum on top of the initial platinum surface to reduce surface resistance. In this method, the IPMC was fabricated through 3 times IPCP and 2 times SEP. The electroless chemical reduction procedure is briefly introduced as follows: first, the surfaces of Nafion-117 film are roughened by sandblasting; then a platinum–ammine complex salt is adsorbed onto the membrane. The hydrophilic ion cluster (H+, Nafion) is exchanged for the platinum complex cations ((Pt(NH3)4)2+) using a platinum complex (Pt(NH3)4Cl2) and adding ammonia water as shown in Table 2(1). In the next step, the reduction of the platinum–ammine complex salt deposits metallic nuclei on the surfaces, and then this metal deposition forms thin electrode layers. A proper reducing agent like NaBH4 is used to metalize the polymeric materials by the molecular plating as shown in Table 2(2)– (4). Proper repetition of the absorption-primary plating process, so called IPCP, can make the polymer-platinum composite layer grow with reliable composition in the depth of the membrane. And then, an additional amount of platinum is plated on the deposited platinum layer by the secondary plating process. Then the surface resistance of surface electrodes can be reduced. The final step is to exchange H+ with other counter ions (Li+). The thickness of the platinum electrode layer, formed by the electroless chemical reduction was about 6 lm from SEM pictures. 3.2. Method 2: combining electroplating and electroless plating with masking tape Method 1 requires a long fabrication time of about seven days and has the infiltration problem previously
(2) (3) (4) (5)
described. In this study, a novel method to pattern the multiple electrodes is proposed by combining electroplating with the electroless plating technique. The main advantage of Method 2 is that we can control the thickness of the local electrodes of the patterned IPMC actuators by using electroplating. The electroless chemical reduction, which makes composite layers between the ionic polymer and metallic electrodes, can give better mechanical adhesion and bending performance than other methods like evaporation and sputtering. In Method 2, the electroplating technique follows the electroless chemical reduction via three times IPCP and one time SEP. Electrical currents for electroplating processing are listed in Table 3. The plating bath was prepared with 1 N hydrochloric acid, 2 mM lead (II) nitrate, 20 mM nitric acid and dissolved 5 g Hexachloroplatinate(IV) (H2PtCl6) [13]. The solution composition and operating conditions were carefully controlled to attain the maximum ductility in the deposited platinum electrode layer. First, the proper current density was found to form a consistent and reliable microstructure and to reduce the electrical resistance of the surface electrodes. The recommended electrical operation is that a constant 0.1 A current is applied for 30 min and are repeated seven times [12]. Present results show that current electroplating can save three days worth of time as compared the electroless chemical reduction. Also, the infiltraTable 3 Operating conditions of electroplating Electroplating operating conditions Plating bath Temperature, C Agitation General current density range Anode electrode Proper current density
2.5% Hexachloroplatinic acid plating solution [H2PtCl6, 20 g/L] 30 Mechanical stirring system 0.1–1 A/dm2 [17] Titanium expanded mesh plate coated by platinum Reference to Table 4
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Fig. 6. Patterned IPMC by combining electroplating and electroless plating with masking tapes: (a) specimen by Method 2; (b) SEM cross-section of IPMC sample by Method 2; (c) picture of uneven plating surface; (d) optical microscope picture of plating line disconnected and (e) the direction of electroplating.
Table 4 Current density conditions of electroplating Specimen
1
2
3
4
Unit
Current density Supplied current Operating time (1 time) Supplying quantity (1 time)
0.33 0.04 1382 456
0.58 0.07 786 456
0.83 0.1 549 456
1.08 0.13 422 456
A/dm2 A s C/dm2
Voltage(V) & Displacement (mm)
4 3 2 1 0 -1 -2
Input Voltage Specimen 1 Specimen 2 Specimen 3 Specimen 4
-3 -4 0
2
4
6
8
Time (s)
Fig. 8. Comparison of bending performance according to current density of electroplating; driving voltage: 1.5 * sin(2p * 0.2 * t). 120
100
Surface Resistance (Ohms/cm)
tion problem was solved as shown in Fig. 6a. In Fig. 6b, the thickness of the platinum electrode is about 20 lm. However, a few problems in electroplating were observed. The IPMC made by electroplating was slightly twisted due to residual stresses and showed a reduced bending performance. Above all, the narrow electric insulation line was frequently disconnected during electroplating as shown in Fig. 6c–e. Therefore, insulation lines were widened and the electric connection was separately applied according to patch size. Additionally, four IPMC specimens, which were fabricated by three times IPCP and one time SEP, were prepared to investigate the effect of current density on the bending performance. To find the optimal the current density, the pretest on the electroplating was performed with simple cantilevered beam specimens. The specimens have the same size of 4 mm · 70 mm as shown in Fig. 7. Fig. 7b–c shows the cross-sectional SEM micrographs of the IPMC actuators after the electroplating process according to different current densities listed in Table 4. The platinum layer through the electroless chemical reduction was deposited up to about 5 lm. And the electrode thickness of all specimens increased up to 6 lm through the electroplating process regardless of applied current densities. The thickness growth by electroplating was mainly affected by the supplying quantity rather than the current density. The harmonic excitation of these samples was applied with peak voltage of 1.5 V and exciting frequency of 0.2 Hz. The second specimen fabricated under
80
60
40
20
Fig. 7. IPMC samples used to find proper current density: (a) strips for observing the microstructure; (b) cross-sectional SEM of three times ICPC and one time SEP; (c) cross-sectional SEM after electroplating.
0 Specimen 1
Specimen 2
Specimen 3
Specimen 4
Fig. 9. Surface resistance of specimens according to current density.
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4.1. Experimental setup An integrated experimental setup was used to measure the transverse displacement and to capture the moving shape of the patterned IPMC actuators in aqueous condition. Therefore, in all experiments, the electrical connecting parts of the IPMC actuators are out of water for insulation. However, all IPMC actuators are immersed in water. The overall measurement system is shown in Fig. 10. Input signals were generated by a NI-PXI 6733 board, which was connected to the terminal BNC-2210 output channel and its electric current was amplified by UPM 1503. The NIPXI acquisition board 4472 and a laser displacement sensor, LK 301, were used to measure the tip displacement of the actuators. And the NI-PXI 1409 image acquisition board and a XC-HR50 CCD camera were used to record the moving shapes of the IPMC actuators.
3 2 2 1
1
0
0
-1
-1
4.2. Oscillatory and undulatory motion
-2
Driving Voltage Tip displacement by Method 1 Tip displacement by Method 2
-2
Transvers displacement (mm)
4. Actuation tests for bending and twisting
and exciting frequency of 0.5 Hz was applied to all top and bottom electrode patches with in-phase. The tip transverse displacements of two patterned IPMC actuators by Method 1 and Method 2 are compared in Fig. 11. The tip displacement by Method 1 was much larger than that by Method 2. The maximum transverse displacement obtained by Method 1 was almost two times in comparison with Method 2. The experimental results of the frequency response function between Method 1 and Method 2 are shown in Fig. 12. The fundamental frequencies for the samples fabricated with Method 1 and method 2 are 16.9 and 18.6 Hz, respectively. At the resonance frequencies, the bending response of the specimen by method 1 is larger than that by Method 2. Generally speaking, the bending response of the sample by Method 1 is much larger than that by Method 2. However, beyond the fundamental frequency, the bending response of the sample by Method 2 is much larger than that by Method 1. It means that the stiffness of the sample by Method 2 is stronger than that by Method 1, resulting in the increasing of the fundamental frequency. Therefore Method 2, combining electroplating with the electroless chemical reduction, can be a promising
Voltage (V)
the current density of 0.58 A/dm2 shows larger bending deflections as shown in Fig. 8. Also, surface resistance of the platinum electrodes was measured to compare electrical consumption according to different current densities in electroplating. The surface resistance was determined by using a two-point probe method [14] under the wet condition at room temperature. Keithley sourcemeter series 2400 was used to measure the electric resistance by applying 2.1 V. The distance between the two probes was 1 cm. Surface resistances for different specimens were quite different according to the current densities as shown in Fig. 9 and it means that current densities affect the microstructures of the deposited electrodes. Specimens 2 showed relatively low surface resistance and a small standard deviation.
593
-3 0
1
2
3
4
5
Time (sec)
To generate oscillatory motion of the patterned IPMC actuators, the sine wave with maximum voltage of 1.5 V
Fig. 11. Comparison of tip transverse displacement between Method 1 and Method 2 under driving voltage of 1.5 * sin(2p * 0.5 * t).
Fig. 10. Integrated experimental setup for measurement of transverse displacement and total movement shape of patterned IPMC.
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Method 1 Method 2
60
Magnitude (dB (10-6 m/V))
Transverse displacements (mm)
70
50
40
30
4.0 MAX.
2.0 MAX.
0.0
MIN. MIN.
-2.0 Out of phase : 3, 4 patch In phase : 1,2,,5,6 patch
-4.0 0
20
1
2
3
4
5
x-direction (cm) 10
0 10
20
30
40
50
60
Frequency (Hz)
Fig. 12. Frequency response functions of IPMC actuators made by Method 1 and 2 (1–60 Hz).
Fig. 14. Oscillatory and undulatory wave generation with in-phase and out-of-phase actuation modes under harmonic excitation of 3 * sin(2p * 2 * t).
candidate to pattern multiple electrodes of the IPMC actuator for realization on biomimetic motion, because the bending performance of the specimen by Method 2 is good enough to generate the biomimetic motion of the patterned IPMC actuator. Another main advantage of Method 2 is that we can control the thickness of the local electrodes of the patterned IPMC actuators by using electroplating. By using a CCD camera, the moving shapes of the patterned IPMC actuators fabricated by Method 1 were captured as shown in Fig. 13. Additionally, to generate undulatory motion, the sine wave with maximum voltage of 3 V and exciting frequency of 2 Hz was applied to patches 1, 2, 5, and 6 and the antiphase signal was applied to patches 3 and 4, resulting in an out-of-phase actuation. The oscillatory wave due to inphase actuation and the undulatory wave due to out-ofphase actuation were distinctly generated as shown in Fig. 14. This graph is obtained by using the vision sensing and MROVS techniques [15]. Present result shows that the patterned IPMC actuators fabricated by Method 2 can naturally mimic the higher order propulsive motion of fish. To compare the thrust force between oscillatory and undulatory waves will be a very interesting research topic. 4.3. Twisting motion
Fig. 13. Pure bending by Method 1 under driving voltage of 2.0 * sin(2p * 0.5 * t).
For realization of the twisting motion, an anti-phase signal was applied to patches 2, 4 and 6. The patterned IPMC
Fig. 15. Twisting motion generation using patterned IPMC actuator under harmonic excitation of 3 * sin(2p * 0.1 * t).
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actuator was twisted as shown in Fig. 15. To quantitatively present the twisting motion, two laser displacement sensors were used as shown in Fig. 16. The following simple equation can give a twisting angle at the tip section of the patterned IPMC actuator. 1 W 1 W 2 h ¼ tan ð1Þ L where W1 and W2 are the transverse displacements at two different points and L is the distance of two measurement points. The time history of twisting angles according to different applied voltages was calculated and plotted in Fig. 17. The twisting angle increased with increasing driving voltages. And the twisting angle by 1.5 V is three times that by 1 V. Present results show the twisting motion by using the patterned IPMC actuator was successfully generated.
Specimen
595
5. Conclusion In this study, the novel patterning methods of multiple electrodes of the IPMC actuators were investigated for realization of bio-mimetic locomotion. Here, two different fabrication methods were tried and compared with respect to the electric conductivity and the mechanical actuation. The conclusions obtained from this work can be summarized as follows: (1) Method 1 based on electroless chemical reduction with the masking tapes can produce relatively large mechanical bending displacement, while it takes a lot of time and labor to fabricate the patterned electrodes. Also, the platinum infiltration between the ionic polymer and the masking tape was a critical problem due to long fabrication time. (2) Method 2 combining electroplating with electroless plating shows precise patterned shapes of the multiple electrodes and saves three days of fabrication time. Also, the electroplating technique has nice advantages to control the stiffness and to make the thickness of the patterned local electrodes different. (3) The patterned IPMC actuators with multiple electrodes can successfully generate oscillatory, undulatory and twisting motions by using in-phase actuation or out-of-phase actuation. Acknowledgement
W1 —W2 W1
θ
W2
L
This work was supported by Grant No. (R01-2005-00010848-0) from the Basic Research Program of the Korea Science and Engineering Foundation.
L
Laser Displacement Sensors
References Fig. 16. Measurement setup and calculation of rotational angle for twisting motion of patterned IPMC actuator.
10 Twisting Angle at 0.5 Volts Twisting Angle at 1.0 Volts Twisting Angle at 1.5 Volts
8
Twisitng Angle (θ ,degree)
6 4 2 0 -2 -4 -6 -8 -10
0
5
10
15
20
Time (s)
Fig. 17. Twisting angles according to different maximum voltages with harmonic excitation of A * sin(2p * 0.1 * t).
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