pubs.acs.org/NanoLett
Carbon Nanotube Resonator in Liquid Shunichi Sawano,† Takayuki Arie,*,†,‡ and Seiji Akita†,‡ †
Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan, and ‡ CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan ABSTRACT To achieve mass measurement of biological molecules in viscous fluids using carbon nanotube resonators, we investigated the vibration of nanotube cantilevers in water using the optical detection technique. In vacuum, we often found a few resonance modes of nanotube vibrations. However, the nanotube lost its fundamental oscillation once immersed in water, suggesting a great viscous resistance to the nanotube vibration in water. The resonant frequency of the nanotube in water decreased with lowering the water temperature, corresponding to the natural phenomenon by which liquid viscosity tends to increase at lower temperatures. KEYWORDS Carbon nanotube, resonator, liquid, viscosity, viscous resistance
W
liquid.21 We reported the gas damping effect on the CNT vibration by measuring the Q factors of CNT cantilevers in various pressures below 104 Pa.22 However, to achieve ultrasensitive mass measurement using CNT resonators in liquids, it is essential to investigate the vibration of CNTs in water. In this study, we present the vibration of CNT cantilevers in water and investigate the influence of viscous damping to their resonant frequencies and Q factors by changing the water temperature. CNTs used in this study were synthesized by chemical vapor deposition (CVD) followed by postannealing at temperatures higher than 1500 °C to improve their crystallinity. The lengths of the CNTs ranged from 10 to 18 µm, and the diameters from 60 to 270 nm. Subsequently, a CNT cantilever array was produced at the edge of a silicon chip using an ac electrophoresis method.23 The number of protruding CNTs from the edge was controlled and optimized to avoid interference by other CNTs. The typical frequency and voltage we used for the ac electrophoresis were 1 MHz and 1 Vpp, respectively. The measurement of the CNT vibration in vacuum was performed under a SEM. In air and water, on the other hand, the measurements were performed by optical detection under an optical microscope. A schematic representation of our homemade inverted optical microscope is shown in Figure 1a. The individual CNT cantilevers were vibrated by applying ac voltage to a piezoelectric actuator mounted on an SEM stage in vacuum or a glass chamber on the inverted optical microscope in air and water. The CNT vibration in water was measured by pouring water into a glass chamber surrounded by silicone rubber. CNT cantilevers were then irradiated by a 633 nm laser to detect the vibration of CNTs. The detection of the CNT vibration can be achieved with higher sensitivity by inducing the laser into the optical microscope to illuminate only the tip of CNTs. Figure 1b shows the representative example of a cantilevered CNT resonator used in our study. When CNTs vibrate at their resonant frequencies, the scattered light intensity from
ater, one of the most abundant molecules on Earth, is essential for life. Between 50 and 70% of our body consists of water in which all the chemical reactions of life take place. For the elucidation and application of life phenomena, measurement of mass and/ or interactions of biological molecules are to be investigated during reactions in the aqueous medium. Nanomechanical resonators are widely utilized as various sensing applications ranging from ultrasensitive mass1-8 and force9,10 measurements to nanoscale imaging and force mapping using atomic force microscopy.11 However, viscous damping resulting from viscous fluids strongly affects resonance frequency responses of resonators,12-15 making it challenging to perform ultrasensitive measurement of biological molecules in viscous fluids. Carbon nanotubes16 (CNTs) are one of the most potential candidates for various sensing technology applications. Due to their outstanding characteristics such as high aspect ratio, ultrahigh mechanical strength, and extremely light weight, CNT resonators enable ultrasensitive mass measurement and force detection. With cantilevered CNT resonators, mass measurement was performed toward zeptogram sensitivity in a scanning electron microscope (SEM) chamber,17 while the mass of one gold atom was resolved in an ultrahigh vacuum.18 However, since biological materials such as proteins cannot keep their characteristics in vacuum, resolution of small mass changes of biological materials requires that the resonators be vibrated in viscous liquids. Quality factor (Q factor), one of the most important parameters for mechanical resonators, is influenced by energy losses of the vibration system19,20 that are induced by various factors such as clamping and thermoelastic losses or viscous damping. In contrast to the measurements in vacuum, Q factor dramatically reduces due to the damping by surrounding molecules in viscous fluids such as air and * To whom correspondence should be addressed,
[email protected]. Received for review: 04/13/2010 Published on Web: 08/03/2010 © 2010 American Chemical Society
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DOI: 10.1021/nl101292b | Nano Lett. 2010, 10, 3395–3398
FIGURE 2. Molecular dynamics simulation of the CNT vibration. (a) The model indicates a single wall CNT with 0.68 nm in diameter and 8 nm in length, surrounded by water molecules. (b) Calculated frequency response of the CNT vibration in water. From the Lorentzian fitting curve (black line), the Q factor of the oscillation is calculated to be 2.
FIGURE 1. (a) Homemade inverted optical microscope to detect the vibration of CNT cantilevers. (b) Representative scanning electron and (c, d) optical micrographs of a CNT cantilever. Bar in (b) represents 10 µm. Note the marked difference in the scattered light pattern from the (c) nonvibrating and (d) vibrating CNT.
plicable to the vibration of CNTs in viscous fluids, although the Stokes drag calculation is often inapplicable due to the very high frequency range associated with their small size. Figure 3 represents typical frequency spectra of a CNT resonator at the edge of a silicon chip in vacuum. The diameter and length of the CNT used were 60 nm and 13.8 µm, respectively. We often found a few resonance modes of CNT oscillations as shown in the figure. Two resonance peaks were identified in each mode of oscillation: 558 and 577 kHz for the fundamental, and 3165 and 3298 kHz for the second harmonic oscillation. These results may be due to structural defects (crystal imperfections and impurities) of the CNT cantilevers synthesized by CVD or the instable clamping of CNT cantilevers to the Si chips, resulting in the several resonance modes of the CNT oscillation in a very close frequency range. The resonant frequencies of a cantilever with the added mass are approximately expressed by3
vibrating CNTs changes compared to nonvibrating CNTs (Figure 1c,d). The scattered light from cantilevered CNTs was monitored and captured with the various frequencies to obtain the frequency response of the CNT vibration. We then analyzed a series of images recorded with a CCD camera, with which the changes in the scattered light intensity can be calculated at each pixel of images between nonvibrating and vibrating CNTs. As CNTs vibrate, the change in the scattered light increases at their resonant frequencies as noted in Figure 1c,d. Prior to CNT vibration measurement, we first performed molecular dynamics (MD) simulations to explore the size limitation of analyses based on the continuum theory (Figure 2). The CNT used in the calculation was a (5, 5) single wall CNT with 0.68 nm diameter and 8 nm length (30 unit cells). The calculation was performed at the temperature of 300 K with the periodic boundary condition of 2.2 × 2.2 × 10.5 nm3, in which the atomic interactions were modeled by the AMOEBA force field24-26 (atomic multipole optimized energetic for biomolecular applications) for water and MM3 force field27-29 for CNTs. Lennard-Jones-type van der Waals’ potentials were used for intermolecular interactions. A thick line in Figure 2b, a Lorentzian fitting curve based on the continuum theory, is well fitted to our MD result. Furthermore, we had no obvious vortex motion of water molecules. Under the framework of the continuum theory, the viscous damping is strongly influenced by the Reynolds number, which is less than 1.0 for both our MD simulations and experiments for CNTs. In this condition, no specific vortex should appear. Therefore, even for single wall CNTs with a diameter of less than 1 nm, the continuum theory is ap© 2010 American Chemical Society
fn )
βn2 2√3π
k m0 + 4m
(1)
where fn represents the nth mode resonant frequency of a cantilever, k spring constant, m0 the mass of a cantilever, and m the mass attached to the cantilever tip. βn is the solution of
1 + cos βn cosh βn ) 0
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(2)
DOI: 10.1021/nl101292b | Nano Lett. 2010, 10, 3395-–3398
FIGURE 3. Representative frequency spectra of a CNT cantilever in vacuum showing fundamental and second harmonic oscillations. Two peaks are visible at each oscillation mode. Both modes of oscillations were well fitted with the theoretical calculations (blue lines).
From eq 1, the difference in the resonant frequencies of fundamental and second harmonic oscillations is β22/β12 ∼ 6, corresponding to the difference in the frequencies derived from the experiment (Figure 3). By use of the CNT cantilever in vacuum, the resolutions for mass sensing for the fundamental and second harmonic oscillations are estimated to be 12.7 Hz/ag and 72.1 Hz/ag, respectively, which can be unambiguously identified by our method. The CNT cantilever lost its fundamental oscillation mode seen in vacuum when immersed in water. This is inevitable because lower modes of oscillation are more strongly affected by the viscosity of fluids. Higher oscillation modes show the characteristics that have smaller frontal projection areas and lower effective aspect ratios (insets in Figure 3), thereby promoting less viscous damping by fluids. To better understand the influence of the viscous resistance to the CNT vibration, we measured the frequency response of the CNT cantilever in water with changing the water temperature. Figure 4 represents the frequency spectra of the second harmonic oscillation of the CNT cantilever in water at two different temperatures. Note that the two resonance peaks were still visible as seen in Figure 3, which was the evidence that the resonance was explicitly the same oscillation mode between in vacuum and in water. At the temperature of 28.9 °C, the spectra were divided by two theoretical fitting curves with the frequencies and Q factors of 540 kHz and 7.6, and 630 kHz and 21.7, respectively. However, the resonant frequency shifted toward the lower frequency at 18.2 °C (500 kHz, Q ) 7.6), corresponding to the phenomenon by which the viscosity of water increases with lowering the water temperature. It is noted that several artificial spikes are visible, resulting from contaminants in water around the CNT cantilever that can be unambiguously separated from the resonance peak of the CNT by simultaneously recording background noise. We analyzed the CNT vibration in water using viscous model described by Van Eysden and Sader,14 in which the © 2010 American Chemical Society
FIGURE 4. Frequency responses of the CNT vibration in water at two different temperatures. The resonant frequency of 543 kHz at 28.9 °C decreased to 500 kHz at 18.2 °C, corresponding to the natural phenomenon by which the viscosity of water increases at lower temperatures. Inset is the theoretical resonant frequencies14 as a function of Reynolds number with our experimental results.
resonant frequency for the nth mode of vibration is given by
[
πFfluid ωfluid,n ) 1+ Γ (ω , n) ωvac,n 4FCNT r fluid
]
-1/2
(3)
where ωvac,n and ωfluid,n are the nth mode of resonant frequencies of the CNT cantilever in vacuum and fluid, FCNT and Ffluid the densities of the CNT and fluid, respectively, and Γr is the real component of the hydrodynamic function. 3397
DOI: 10.1021/nl101292b | Nano Lett. 2010, 10, 3395-–3398
REFERENCES AND NOTES
When the fluid is inviscid, Γr will be 1. The hydrodynamic function depends on the frequency ω and the mode number n through Re, commonly termed the Reynolds number
(1) (2)
Re )
Ffluidωfluid,nd2 η
(3)
(4) (4) (5)
where η is the fluid viscosity, and d the CNT diameter. Re is the important parameter of inertial forces in the viscous fluid relative to viscous forces. Normally in the case of the CNT cantilever, Re is much smaller than 1, indicating that the fluid viscosity is not negligible. However, as the mode number increases, so does the resonant frequency and the Re number. This results in the less viscous effects from the fluid on higher modes of the oscillation, consistent with the results in Figure 4 in which the second harmonic oscillation of the CNT cantilever was distinctly identified even in water. This implies that using higher oscillation modes the CNT cantilever is more suitable for ultrasensitive mass measurement in viscous liquids. Assuming that the densities of water and a CNT are constant, which is satisfied in this temperature range, the resonant frequencies at 28.9 and 18.2 °C can be estimated from eq 3 to be 583 and 521 kHz, respectively (Figure 4 inset). These data are comparable to those obtained from our experiments, indicating that the resonance of the CNT in water is well fitted with viscous model. In conclusion, we investigated the vibration of CNT cantilevers in water for the future application of ultrasensitive mass measurement in viscous liquids. The fundamental oscillation of the CNT disappeared while the second harmonic oscillation remained, showing the great viscous damping by water. The resonant frequencies at different temperatures were comparable to those derived from viscous model. The higher oscillation mode of the CNT may be more suitable for ultrasensitive mass measurement of biological molecules in viscous liquids.
(6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27)
Acknowledgment. This work was partially supported by Grant-in-Aid for Scientific Research on Priority Area of the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT).
© 2010 American Chemical Society
(28) (29)
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DOI: 10.1021/nl101292b | Nano Lett. 2010, 10, 3395-–3398
