Carbon nanotubes enhanced bimorph effect of U-shaped flexure cantilever beam actuators made from polyethylene terephthalate and polymethyl methacrylate

U-shaped cantilever actuators made from PET and PMMA exhibit a bimorph effect upon radiation heating and beam always moves toward PMMA side with maximum displacement and displacing rate measured to be 2100 μm and 35 μm s−1. This number increases to 3300 μm and 55 μm s−1 while PET surfaces are coated with single-walled carbon nanotubes acting as heat reservoir. Actuations can be further improved by carbon nanotube resistive heating and improvement reaches two-fold (4100 μm and 68.3 μm s−1). Coated beam actuators exhibit an excellent stability over 2 h intermittent operations where the maximum displacement varies only in ±1%.


Introduction
Single-walled carbon nanotubes (SWCNTs) are one-dimension conductor made of rounded graphite sheets. Accordingly, tube strength and conductivity display anisotropy and are mainly contributed by C-C bonds along axial direction [1]. Calculation indicates that thermal conductivity (k) of an ideal SWCNTs is comparable with in-planes of graphite (4000 ∼ 6000 W /m .K) and is best described by three-phonon mechanism [2]. In practice, SWCNTs contain various lattice imperfections where hexagonal symmetry is broken and k decreases to 10 2 W m −1 K −1 [3]. The mean free path of phonons along transverse direction, on the other hand, is limited by intertube junctions so phonon transport is governed by Umklapp process. In this case, intertube junctions behave as heat reservoir and study reveals E ex = E in /E out = 96% where E ex , E in and E out represent heat exchange, heat energy received and irradiated by SWCNTs [4,5].
Soft robotics exhibit a great application potential in micro-surgical technology (MST) and are mostly made from flexible materials, i.e. polymers with low glass transition temperature [6]. Unlike piezoelectric and electrostatic actuators fabricated through complicated procedures the production of thermal actuators is facile and involves combination of two different materials that show differentiated coefficient of thermal expansion (CTE), known as bimorph effect (figure 1(a)) [7]. The bimorph effect driven actuators, however, are severely limited in speed/operating frequency and can barely meet requirement for MST. This study demonstrates a significant improvement on U-shaped flexure cantilever beam actuators made from SWCNTs, polyethylene terephthalate (PET) and polymethyl methacrylate (PMMA).

Experimental
Bipolymer films made from PET and PMMA show an optical transparency and are widely used as protective coats for 3C products (e.g. cell phone, liquid crystal display and personal computers); the former provides strength and chemical stability by the latter. In this work, PET/PMMA films purchased from supplier (Wah Hong Industrial Corp, Taiwan, figure 1(b)) are fabricated into thermal actuators for following reasons, first, PET Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. and PMMA have a comparable CTE (=7 × 10 −5 K −1 for PET and 6 × 10 −5 K −1 for PMMA) so the bimorph effect is expected to be insignificant. In this case, improvements due to SWCNTs coatings become distinguishable. Second, the PET and PMMA have different cross-sections thus facilitating deflection of U-shaped cantilever beam actuators (thickness = 90 μm for PET and 10 μm for PMMA, figure 1(c)-(d)) [8]. Third, PET contains hydrophilic groups capable of interacting with on-tube defects (i.e. oxygenated lattices and dangling edges). Coating is carried out according to procedures below; (i) SWCNTs (20 mg) are ultrasonically dispersed in sodium dodecyl benzene sulfonate (SDBS) solution (20 ml) for 1h, followed by centrifuging treatment at 5000 rpm for 5 min; (ii) the upper layer which contains dispersed SWCNTs and SDBS is extracted and is sprayed onto PET using spin coating at 100 rpm; (iii) a paint roller is used to make coating uniform throughout; (iv) the SDBS is removed by repeated rinsing of coated films in warm deionized water (40°C).   U-shaped cantilever beams and electrical connections are made by gluing copper wires onto coated films using conductive silver paste (figures 2(d)-(e)). An infrared thermal imaging camera (Flir one, 70 mK thermal sensitivity, 160 × 120 thermal resolution, 2°C-20°C range) is used to monitor uniformity of beam heating and SWCNT dispersion on plastic films (figures 2(f)-(g)). Thermal actuators are also characterized by fourier transform infrared spectroscopy (FTIR), x-ray diffraction (XRD) and contact angle (CA) tests in deionized water (DI water) and ethylene glycol. Resistance (R) of coated films is measured by the Van der Pauw method, i.e. fourterminal configuration [9]. where superscript p and d denote polar and non-polar energy. Table 1 lists γ lv , γ lv p and γ lv d for DI water and ethylene glycol and γ sv , γ sv p and γ sv d for PET and PMMA. Clearly, DI water due to H-bonds is governed by γ lv p where γ lv reaches a value as high as 72.8 mN m −1 . Ethylene glycol, on the other hand, contains a greater number of alkyl groups so γ lv d > γ lv p and the γ lv decreases to 48 mN m −1 . A similar trend is observed at solid-vapor interface with γ sv and γ sv p measured to be 30.96 and 40 mN m −1 for PET and 11.36 and 21.5 mN m −1 for PMMA, consistent with figure 3. Figure 4 shows bimorph effect driven actuations of bipolymer films without SWCNTs coating where beam temperature due to light bulb heating (radiation heat) is 36°C. First, the D T proceeds upward as PMMA side faces heating source (a-f & Supplementary material 1). Second, the downward D T occurs as beam is flipped (i.e.  the PET side faces heating source, g-l & Supplementary material 2). Third, D T and D R are similar in both directions (∼1800 μm and 39 ± 5 μm s −1 ). D T driven by heating induced polymer phase transition (i.e. glass transition) however is unlikely according to XRD; (i) characteristic peaks of PET (100) (2θ = 26.4°) and PMMA (110) (2θ = 22.3°) remain unchanged between 25°C-50°C including peak position, intensity and full width at half maximum; (ii) temperature rising does not induce additional reflections (figure 5). Observations above confirm bimorph effect driven actuations and beam always moves toward PMMA side (i.e. thinner crosssection). Figure 6 displays optical and SEM images of PET/PMMA (a-c) and SWCNTs/PET/PMMA (d-e), along with transmittance spectra recorded at visible wavelength (f). SWCNT coating is 1 μm thick and is electrically conductive with R measured to be 5.84 kΩ (d-e). Again, transparency of PET/PMMA film is verified by ∼100% transmittance at 400-700 nm (f). SWCNT coating, however, reduces film transmittance to 28% at 400 nm, 40% at 600 nm and 37% at 700 nm. Homogeneous SWCNTs coating is also evident by infrared thermal camera showing uniform heating images on U-shaped actuators (figures 2(f)-(g)).   ). Apparently, coated beam yields a greater D T at the same T and differentiated D T increases with T rising (figure 8(b)); the profiles slope measured by tangent fit being 0.78 for SWCNTs coated and 0.51 for pristine beams (i.e. a greater bimorph effect). Two factors account for improvements; (i) heat is absorbed by SWCNT coatings; (ii) tube-tube junctions act as heat reservoir thus providing actuators with fast and uniform heating [11].

Results and discussion
The (ii) cited above is further verified by resistive heating driven actuations where D T(max) takes place at t = 60s (figure 9(a)-(f) & Supplementary material 4-7). First, the D T(max) increases with applied voltage (i.e. D T ∝ V) and D T(max) reaches 520 μm at 10V, 1490 μm at 20V, 2900 μm at 30V and 4100 μm at 40V, corresponding to D R = 8.6, 24.8, 48.3 and 68.3 μm s −1 . Second, the D T(resistive) > D T(radiation) . Third, resistive heating produces a higher beam temperature (25°C-Th°C) thus enhancing bimorph effect (profile slope = 0.8, figure 10(a)). It is worth mentioning that non-linearity in D T -T relation is indeed expected because D T does not correlate linearly with thermal energy added to cantilevers [7]. Figure 10(b) shows T-t profiles at various V and can be divided into two regions where the 1st exhibits a T ∝ V relation at t = 40 s. Profiles then level off at the 2nd region with T variation in ±1°C. Apparently, actuations are mainly driven in the 1st region and T rising rate agrees with figures 9 and 10(a).   10(c) displays stability of resistive heating driven D T over 2 h intermittent operations and each charging proceeds at 30V for 30 s (on), then followed by 90 s intervals (off) for heat dissipation. The D T -t profiles recorded at 1st, 15th, 30th, 45th and 60th are selected for a comparison. Clearly, D T(max) is similar (∼3000 μm) and only varies in ±1%. Based on the Joule laws, the power required to drive D T = 3000 μm is calculated to be 5 × 10 −3 W s −1 , much lower than existing MEMS devices (1 × 10 −1 ∼ 10 −2 W s −1 ) [12].

Conclusions
U-shaped PET/PMMA flexure cantilever actuators show a bimorph effect upon radiation heating and beam always displaces toward PMMA side (thinner cross-section). D T(max) and D R are measured to be 2100 μm and 35   μm s −1 ; value which increases to 3300 μm and 55 μm s −1 as PET surfaces are coated with a thin layer of SWCNTs acting as heat reservoir. D T(max) and D R can be further improved by SWCNTs resistive heating and improvement reaches two-fold (i.e. D T(max) = 4100 μm at 40V and D r = 68.3 μm s −1 ). Coated actuators show an excellent stability over 2 h intermittent operations.