Mechanical characteristics of individual TiO2 nanowire and TiO2 nanowire bundle on micro-manipulator nanoprobe system

Materials Science & Engineering A 641 (2015) 281–289

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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea

Mechanical characteristics of individual TiO2 nanowire and TiO2 nanowire bundle on micro-manipulator nanoprobe system Zhenqiang Ye a, Huijuan Zhu a, Yingying Zheng a,n, Wenjun Dong a, Benyong Chen b a

Center for Optoelectronics Materials and Devices, Department of Physics, Key Laboratory of ATMMT Ministry of Education, Zhejiang Sci-Tech University, Hangzhou 310018, People's Republic of China b Nanometer Measurement Laboratory, Zhejiang Sci-Tech University, Hangzhou 310018, People's Republic of China

art ic l e i nf o

a b s t r a c t

Article history: Received 3 March 2015 Received in revised form 18 June 2015 Accepted 19 June 2015 Available online 21 June 2015

The individual TiO2 nanowire and TiO2 nanowire bundle were prepared through a simple hydrothermal reaction of alkali with the titanium (Ti) metal and with TiO2 powder, respectively. A newly developed test platform which contained the MM3A micro-manipulator nanoprobe system installed in the scanning electron microscope (SEM) chamber was then introduced for the test of the mechanical properties of titanium dioxide nanowires (TiO2 NWs), either an individual or a bundle. The mechanical characteristics of the individual TiO2 NW and the TiO2 NW bundle were determined using a micro-cantilever model and a three-point bending model, respectively. In the tests, a nanoprobe tip was used to apply lateral force and deflect NWs. The load and deflection were measured simultaneously by Spring Table and SEM. And then Young's modulus were calculated based on their respective theoretical formula. The average value of Young's modulus for an individual TiO2 NW and a bundle of TiO2 NWs were found to be 120.39 GPa and 92.01 GPa, respectively. The TiO2 NW Young's modulus exhibits no obvious size effect while the scale of TiO2 NW was in the range of 100 nm
100 μm. The bending method in this new test platform could be widely applied to measure the mechanical properties of all 1D nanostructures under different scale conveniently and accurately, which is helpful for the feasibility of replacing current electrical and optical devices with NWs integrated devices. & 2015 Elsevier B.V. All rights reserved.

Keywords: TiO2 nanowires MM3A micro-manipulator system Bending test Young's modulus

1. Introduction One-dimensional (1D) nanostructures such as nanowires (NWs), nanobelts and nanorods have attracted tremendous attention in recent years due to their exceptional properties and novel potential applications [1–3], such as nanosensors, micro/nano-electromechanical systems (MEMS/NEMS), and so on. These structures exhibit outstanding mechanical, electrical, thermal and optical properties [4], because their size is close to or less than the characteristic length of some important physical phenomena, such as light wavelength, electronic De Broglie wavelength. Especially, mechanical characterization of NWs is necessary to establish the feasibility of replacing current electrical and optical devices with NWs integrated devices based on reliability requirements [5]. However, due to their small size, the manipulation, placement and mechanical characterization of 1D nanostructures in testing still remain as a challenge [6]. Among a large amount of 1D nanomaterials, nanostructured TiO2 plays a leading role in photocatalysis, photoelectrolysis, n

Corresponding author. Fax: þ 86 571 86843587. E-mail address: [email protected] (Y. Zheng).

http://dx.doi.org/10.1016/j.msea.2015.06.057 0921-5093/& 2015 Elsevier B.V. All rights reserved.

sensing, and energy conversion applications due to the exceptional photocatalytic activity, good biocompatibility, chemical and photochemical stabilities and extraordinary size effect. In addition, the nanostructured TiO2 is usually easy to fabricate. Various methods for preparation of the TiO2 nanorods, nanofibers, nanowires and nanotubes, including sol–gel, electrospinning, electrochemical and hydrothermal synthesis methods have been reported [1]. Recently, our research group introduced Ag particles on titanate nanowires and the heteronanostructured Ag/titanate nanowires were assembled into porous, flexible membranes with enhanced photocatalytic properties and bactericidal activities [7] and TiO2 Nanowire were also prepared as multifunctional manowire bioscaffolds and microelectrode for controlled on-site drug release, photocatalytic sterilization and sensors [8–10]. It is important to accurately measure the mechanical properties, which is key to gaining fundamental understanding of surface effects on such properties. Recently, various techniques have been investigated to test the mechanical properties of NWs. Notable experimental methods include resonance [11–16], nanoindentation [17], and bending [18–30]. In the resonance test, amplitude and resonance frequency of NWs can be measured by resonating the free end under the

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thermal or electric field in a scanning electron microscope (SEM) or transmission electron microscope (TEM). Following the resonance characteristic of cantilever beam theory, Young's modulus of NWs can be calculated. But the electrode used in the resonance test need to be customized according to the morphology and size of samples every time, which will cost a lot and limit its application range. Because of the limit of resonance amplitude, the samples only in an extremely small range of scale can be tested by resonance method. Only elastic modulus can be measured, while the strength, toughness and other mechanical properties can't be got by resonance method. The nanoindentation method can measure the load and displacement simultaneously using the tip of an atomic force microscopy (AFM) to deflect the sample, and is more suitable for mechanical characterization of nanofilm not for NWs. However, the uncertainty in boundary condition and base effect usually result in considerable errors in quantitative characterization of Young's modulus. The bending test is the most straightforward and simple method for mechanical characterization. The probe tip of an atomic force microscopy (AFM) is used to deflect samples in quasi-steady, the load and deflection can be measured simultaneously, and then the parameters such as Young's modulus can be calculated. The bending method also wipes out the influence of the base. Here we report newly developed bending methods that enable the mechanical properties of 1D NWs be tested by using the MM3A micro-manipulator nanoprobe system installed in the SEM chamber [31]. With this system, the nano-objects can be observed in real time, so the positioning, manipulation and testing of the nanoobjects can be realized easily and actively. The mechanical characteristics of an individual TiO2 NW and TiO2 NWs bundle which were prepared through a hydrothermal reaction of alkali with titanium source, were measured based on a micro-cantilever/ nanobeam model (single-clamped), and three-point bending model (double-clamped), respectively. The bending defection versus applied lateral force was got, and Young's modulus were calculated. The mechanical characteristic measurement of all the 1D nanostructures under different scale, ranging from nanoscale to microscale, can be realized conveniently and quickly using the bending method in this new testing platform.

2. Materials and methods 2.1. Preparation of individual TiO2 nanowire The titanate nanowire was prepared based on previously described method [7–9]. Before the synthesis, titanium plates 20 mm  10 mm were inserted in 10 mL of acetone at room temperature, ultrasonicated for 15 min, then ultrasonicated for 10 min in 10 mL of absolute ethylalcohol, and rinsed with deionized water thereafter. The Ti plate was then placed in a Teflon-lined vessel containing 10 mL of 1.2 mol/L NaOH solution. Afterward, the vessel was sealed and then hydrothermally heated at 240 °C for 8 h. Thus-treated Ti plate, covered by the titanate nanowire matrix, were finally collected, rinsed with deionized water, and dried in air. 2.2. Preparation of self-assembled TiO2 nanowire bundle The titanate nanowire bundle was provided by Dr. Wenjun Dong [10]. In a typical synthesis, 10 mg of TiO2 powder (Degussa P25) was introduced into 10 mL of 2 mol/L NaOH solution in a 30 mL Teflon-lined autoclave container. A cylindrical Teflon rod (3 cm in diameter and 2 cm in height) was set in the liner as the template. After 60 min sonication, the hydrothermal reaction was placed in an oven for 10 days at temperatures above 180 °C. The

white, paper-like nanowire bundle product was collected, washed with water, dried in air, and then separated with tweezers. 2.3. Characterizations The SEM image investigation was completed on a Hitachi S4800 microscope. X-ray photoelectron spectroscopy (XPS) was used as element analysis on a VGESCALABMKII X-ray photoelectron spectrometer using non-monochromatized Al-Kα X-ray (hγ ¼ 1486.6 eV) as the excitation source. The binding energies obtained in the XPS analysis were corrected for specimen charging by referencing the C1s to 284.60 eV. XRD patterns were collected on a Bruker AXS X-ray diffractometer (D8 Discover) with CuKα (λ ¼1.5405 Å) at room temperature at a scanning rate of 0.02 deg s
1 and 2θ ranges from 10° to 80°. 2.4. The new test platform In this experiment, a MM3A nanoprobe system with four arms manufactured by Kleindiek Company was used for the mechanical characteristic measurement [30], which had been installed inside the Hitachi-S4800 scanning electron microscope (SEM) chamber. It combined the advantages of the probe system with that of the electron microscope. With this system, not only the nano-objects can be observed in real time by the fine electron beam of SEM, but also the positioning, manipulation and testing of the nanoobjects can be realized actively. A Quickstart Spring Table and Force Measurement Analysis software package are specifically designed for MM3A mechanical measurement, which is an ingenious and low-tech way of in-situ measuring forces and deflections. The sample to be tested is mounted on a Spring Table with a defined spring constant k0 (8.66 N/m or 347 N/m). The W probe tip is used to apply a lateral force on the sample's surface. As shown in Fig. 1, x1 is the displacement of the Spring Table after the W tip applies the force, and x2 is the tracking displacement of the sample. Then x2–x1 is the real deflection (d) of sample. 2.5. Model of micro-cantilever test for individual TiO2 nanowire Lateral forces were applied to bend the nanobeam using MM3A nanoprobe tip for Force–deflection (F–d) characteristics measurement. Fig. 2 showed the process of nanobeam bended by a probe tip. The tip bended the nanobeam with a linear increase lateral force and the beam had the corresponding linear increase deflection. While the tip went back to its equilibrium position, there were a linear decrease lateral force and a corresponding linear decrease deflection of the nanobeam. During the whole bending process, the tip should be always perpendicular to the axis of the nanobeam. In this process, a series of SEM images can be snapshot to record the position of the tip and the position of reference object. Thus, the corresponding deflections (d) of the nanobeam can be obtained. And the Force (F) can be calculated according to the displacement (x1) and spring constant of Spring table. The F–d data acquired in this way were used to determine Young's modulus (E) of the nanobeam [19]. For our experimental geometry (Fig. 2), the general response of a nanobeam to a force F applied at the distance L (along the x axis) from the fixed pinning point (x ¼0) is given by [7]

d2y M = EI dx2

(1-1)

where y is the deflection, I is the moment of inertia of the beam and M is the bending moment (M = F (L − x )). This equation can be integrated and rearranged to express the applied force in terms of

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over the entire bending range. In this model, a probe tip was used to bend the sample at the middle along its suspended length, offering a direct approach to measure the F–d characteristics [1]. This configure has been used to determine the mechanical properties of polymeric nanofibers and carbon nanotubes, and make the direct determination of the applied force as a function of deflection become possible. From the measured F–d curve, a comprehensive analysis in order to extract linear material constants such as Young's modulus (E) was performed. But to account for the linear material constants, the linear elastic beam bending theory should be considered. Young's modulus is normally obtained from a measurement of the beam deflection as a function of the applied force. For a clamped–clamped beam used here, the resulting curve is described by the following well-known equation [7]:

F= Fig. 1. Schematic of the deformation while the sample was bended by the W tip (CA:conductive adhesive) (1) before bended and (2) after bended.

Young's modulus and deflection d:

y=

F (L − x)3 + C1x + C2 6EI

(1-2)

where C1 and C2 are both integral constants. At the fixed pinning point (x ¼0), both displacement and angle are zero, so C1 ¼FL2/2EI, C2 ¼
FL3/6EI, according to the boundary conditions y(0) ¼y'(0) ¼ 0. So the deflection equations at the distance L (along the x axis) from the fixed pinning point (x ¼0) can be displayed as (y is equal to d):

d=

FL3 3EI

(1-3)

where I is πD /64 for a solid cylinder of diameter D. At last, the formula of Young's modulus in cantilever nanobeam model can be expressed as

192EI L3

d

(1-5)

where F is the load applied to the center of the beam, d is the deflection at the load point, E is Young's modulus, I¼ πD4/64 is the moment of inertia of a cylindrical beam, D is the diameter, and L is the length of the suspended nanowire. Importantly, this equation predicts a linear relationship between the applied load and the deflection. So that, Young's modulus was obtained from the threepoint bending of a beam with two ends fixed [6]:

E=

FL3 192dI

(1-6)

At last, the formula of Young's modulus in double-clamped beam model can be expressed as

E=

1 F L3 ⋅ ⋅ 3π d D 4

(1-7)

4

64 F L3 E= ⋅ ⋅ 3π d D 4

(1-4)

2.6. Model of three-bending test for TiO2 nanowire bundle For a bundle of nanowire, a new test model configure was introduced (Fig. 3). Sample was set in a double-clamped beam case

3. Results and discussion 3.1. Formation of individual TiO2 nanowire and TiO2 nanowire bundle The individual TiO2 nanowires were prepared on the Ti foil directly after a hydrothermal reaction for 8 h at 240 °C in a 1.2 mol/L NaOH solution [8,9]. SEM photomicrographs demonstrates that dense long nanowires (about 250–950 nm in width and 2–30 μm in

Fig. 2. Schematic of the experimental setup for nanobeam bended by an MM3A probe tip. The tip (aciculiform) moves in the direction of the arrow, and the lateral force is indicated by the trace at the bottom. (a) No lateral force and no deflection before the tip contacts the beam. (b) The tip is bending the beam with a linear increase lateral force and the beam has the corresponding linear increase deflection. (c) A linear decrease lateral force and a corresponding linear decrease deflection during the tip is going back to its equilibrium position. (d) The lateral force drops to zero, and the beam snaps back to its equilibrium position.

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Fig. 3. Schematic of the experimental setup for lateral NWs manipulation in three-point bending test. The NWs under investigation is suspended over a trench in the substrate and fixed by conductive adhesive (CA) at the trench edges. (a) The tip is far from the sample and there's no interaction and deflection. (b) The tip contacts the surface and the sample's deflection appears in the curve as a straight line vs applied load. (c) The tip moves along the opposite direction and the deflection decreases. (d) The tip detaches from the sample and the NWs comes back to its equilibrium position.

length) have grown on the Ti foil. The SEM photographs in high magnification from a tilted sample reveal details about the nanofibers which self organized into the macroporous scaffolds (Fig. 4 (a)). The XRD shows clear diffraction peaks of the titanate on the Ti foil, suggesting that titanate nanowires are formed (Fig. 4(b)). The XRD pattern resembles that of the layered hydrogen titanates H2Tin O2n þ 1  xH2O. It was also observed that after being calcined at 400 °C, the TiO2 NWs were transformed to the TiO2-B phase (a¼12.1787, b¼3.7412, c¼6.5249, β ¼107.0548), and then the TiO2-B can change to the anatase structure at 800 °C (data not shown). XPS was also used to characterize the composition of the TiO2 nanowires. The peaks observed at 464.55 and 458.75 eV can be attributed to Ti2p1/2 and Ti2p3/2 of the Ti oxidation state. TiO2 nanowire bundle was prepared through a hydrothermal reaction of alkali with TiO2 powder [10]. The white, paper-like nanowire bundle product were got because of the pressure induced by the cylindrical Teflon rod. SEM showed that the nanowire bundles have a diameter of 20–100 mm (approximately 100– 1000 nanowires in each bundle), and the single nanowire's diameter is between 20 and 80 nm. The length of the nanowire bundle varies from 1 mm to several millimeter (Fig. 4(c)). EDX analysis showed that titanium and oxygen were the dominant elements present. 3.2. Mechanical characteristics of an individual TiO2 NW in microcantilever case To determine the F–d curve of the individual TiO2 NW in microcantilever case, two connections were made. One connection is to fix one end of the TiO2 NW on sample stage, and the other is to permit the measurement of F and d. Making this two connections on such a small scale is inherently difficult. In this study, a flexible

method was devised to solve this problems. One end of the TiO2 NW was pinned on the sample stage by the conductive adhesive (CA), a W tip was used to apply lateral forces to bend NW, and the Force Measurement Analysis software (FMA) was used to analyze the F–d data. Firstly, TiO2 NWs were dispersed randomly on a small piece of CA, which had been pasted on the sample stage. The sample stage with the sample were then fixed on the Spring Table (the constant of the Spring Table is 8.66 N/m ). And then the whole MM3A nanoprobe workstation was put into SEM. Secondly, the individual NW of which one end was on the CA and the other end was free was selected under SEM. Lastly, the W tip was used to adjust the position of this individual NW to make sure the growth direction of which was perpendicular to the tensile direction of the standard Spring Table, and then pressed the fixed end of NWs to make sure the NWs has been firmly fixed on the CA. Considering that the W tip of the nanoprobe might slip away from the surface of NW while it was applying the lateral force on the free end of NW, and the force might cause a nonlinear effect, a high vacuum compatible SEM glue (SEMGLU) was adapted to eliminate this effect. In the experiment, another W tip on another arm was dipped into SEMGLU quickly. Once the electron beam was focused on the glue, the polymerization and solidification began which fastened the NW to the W tip after a few minutes. Fig. 5 showed this series of snapshot SEM images which displayed the process when lateral forces were loaded on the free end of an individual TiO2 NW by the MM3A nanoprobe tip. Fig. 5 (a) showed the W tip just came into contact with the TiO2 NW at the free end, set as the initial point (F¼0 μN, d ¼0 nm). Fig. 5bc-d-e showed increasing deflection after the lateral force was loaded increasely. Image (e) showed the point that the W tip was bending TiO2 NW at the maximum of deflection. The maximum of lateral force was 0.4819 μN and the maximum of deflection was

Fig. 4. (a) SEM micrographs of TiO2 NW on Ti, (b) XRD patterns of (A) the Ti foil and (B) the TiO2 NW on Ti foil (all asterisk-denoted peaks are for titanate, and other peaks for Ti), and (c) SEM micrographs of TiO2 nannowire bundle.

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Fig. 5. A series of SEM snapshots of an individual TiO2 NW after continuously applying lateral forces, a-b-c-d-e showed the force load process for the F–d characteristics measurement, while e-f-g-h were the unloading force process (the green smaller rectangular box tracks the position of NW, and the red bigger rectangular box trackes the position of reference point (RP)). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

491.84 nm, which is just about 10% of its suspended length and thus will prevent excessive bending from failure of its elastic deformation of the individual TiO2 NW. Then, the W tip left the NW at the opposite direction to unload the force and the deflection decreased (shown in Fig. 5e-f-g-h). At last, the free end of NW could go back to its equilibrium position and the NW restored to its original shape. Table 1 showed the data of the forces and deflections got by the Force Measurement Analysis software (FMA) which based on all the SEM snapshot in force load and unload process. The red bigger box showed in Fig. 5 was used to track the reference position of the Spring Table. The displacement of the Spring table was named as x1. According to Hooke's law, the lateral force can be calculated as Fsample ¼k0  x1. k0 is the defined constant of the Spring Table. Whereas the green smaller box was used to track an edge of the deformed NW. The tracking displacement was x2. The tracking displacement (x2) was not the real deflection of the free end. The real deflection was the relative displacement xsample ¼x2
x1, named as deflection d.

F–d curve and linear fitting curve for the F–d curve were shown in Fig. 6. The slopes of the F–d curve for force load process and unload process were K1 ¼ 0.975 N/m and K2 ¼0.979 N/m, respectively. Young's modulus (E) of individual TiO2 NW were E¼ 110.77 GPa calculated according to the formula (1-4), as the length of the individual TiO2 NW was L¼5.6 μm, and the diameter was D ¼320 nm, which were shown in Fig. 5(a). The deformation restorability of the individual TiO2 NW exhibited a bit hysteresis in the process of unloading. While the slopes of F–d curve in loading and unloading process were consistent, which indicated that the TiO2 NW is deformed within the strain that elastic deformation persists.

Table 1 The data of F and d of the individual TiO2 NW got by FMA. Load process F (μN)

a

0 0.0692 0.1448 0.1957 0.2495 0.3095 0.3562 0.4376 0.4819 a

Unload process

Error ( 7μN)

d (nm)

F (μN)a

Error ( 7μN)

d (nm)

0 0.0182 0.0253 0.0335 0.0413 0.0476 0.0452 0.0468 0.0425

0 73.45 135.72 203.48 259.96 322.25 378.72 435.2 491.84

0.4819 0.4376 0.3182 0.2553 0.1688 0.1068 0.0514 0

0.0425 0.0472 0.0521 0.0553 0.0512 0.0563 0.0475 0.0342

491.84 480.78 401.31 310.96 226.28 141.36 96.05 19.07

F ¼k0  x1, k0(Spring constant) ¼ 8.66 N/m

Fig. 6. F–d curve of the individual TiO2 NW for load process and unload process.

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Fig. 7. A series of SEM snapshots of a bundle of TiO2 NWs after continuously applying lateral forces, a-b-c-d-e showed the force load process for the F–d characteristics measurement, while e-f-g-h were the unloading force process (the green smaller rectangular box tracks the position of NW, and the red bigger rectangular box tracks the position of reference point (RP)). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.3. Mechanical characteristics of a bundle of TiO2 NWs in doubleclamped case While the length-diameter ratio of 1D nanomaterials became larger, the system error due to the own gravity became larger when the micro-cantilever configuration was adopted. The TiO2 NWs bundle has the large scale and great length-diameter ratio, so three-point bending test was proposed to measure the mechanical properties. Before the test, two strips of rectangular CA were stuck on the sample stage which was fixed on the Spring Table. These two parallel CA strips were parallel to the tensile direction of Spring Table. The space between these two CA was approximately 1 mm. The suspended TiO2 NWs bundle is 1.38 mm in length and 25.6 μm in diameter approximately. A W tip was used to apply lateral force and bend the NWs bundle at the middle of the TiO2 NW along its suspended length. Fig. 7 a-b-c-d-e showed the force load process and the corresponding deflection. Fig. 7e-fg-h were the unloading process. Fig. 7(a) illustrated that the W tip had just come into contact with the middle of a bundle of nanowires along its suspended length, set as the initial point (d ¼0 nm, F¼ 0 μN). The W tip was then moved in direction perpendicular to the NWs to apply lateral force to the NWs step by step. At the same time the corresponding deflection occurred at the load point. Fig. 7(e) showed the maximum of deflection bended by W tip. Then, the tip moved in the opposite direction in the same way to unload the force bit by bit, the deflection decreased gradually and the NW almost restored to its undeflected shape. All the data of forces and deflections were obtained using the same method as above by the FMA software, shown in Table 2. Fig. 8 showed the F–d curve and the linear fitting curve (straight line) in load process of the TiO2 NWs bundle. The slop was

Table 2 The data of F and d for load process and unload process of the TiO2 NW bundle got by FMA. Load process F (μN)

a

0 9.060 20.980 36.419 46.569 55.749 69.988 84.253 97.459 113.695 a

Unload process

Error ( 7μN)

d (nm)

F (μN)a

Error ( 7 μN)

d (nm)

0 2.831 3.462 3.943 4.066 3.982 4.326 2.167 3.452 3.847

0 105.3 193.05 310.05 397.8 468 555.75 614.25 684.45 737.1

113.695 93.547 77.223 52.990 36.705 21.467 11.348 2.371 0.539

3.847 4.528 5.673 4.463 4.872 6.228 5.941 3.826 2.455

737.1 705.4 664.45 563.61 473.33 373.89 274.45 134.07 44.12

F¼ k0  x1, k0(Spring constant) ¼ 347 N/m.

K¼ 149.8 N/m. There was not a good linearity between the F and d in unload process. There were two aspects to cause this phenomenon. Firstly, while the two ends of the NWs bundle were fixed, there was an apparent axial tension under the bending deformation. Bending together with stretching at the same time led to the nonlinear F–d curve in unload process; Secondly, sliding maybe occurred at the two fixed ends of the bundle due to the excessive bending. So, only the data of the load process were taken into consideration. The length of TiO2 NWs bundle was L¼1.38 mm, the average diameter tested 6 times at different locations was D¼25.6 μm and the length– diameter ratio was L/D¼53.9. Young's modulus of the TiO2 NWs bundle can be calculate as E¼101 GPa following the formula (1-7).

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Fig. 8. F–d curve of the TiO2 NW bundle for load process and unload process. Table 3 Young's modulus for 12 individual TiO2 NWs. No.

Cantilever length L (μm)

Diameters D (nm)

Length–Diameter ratio L/D

F–d ratio K (N/m)

Young's modulus E (GPa)

1 2 3 4 5 6 7 8 9 10 11 12 Average7 r

3.8 7.6 6.6 5.6 9.2 16.2 12 20 6.8 15 24 27 12.827 7.65

270 520 400 320 490 850 560 900 300 650 920 880 588.3 7 247.1

14.07 14.62 16.5 17.5 18.77 19.06 21.43 22.22 22.67 23.08 26.09 30.68 20.55 7 4.82

2.49 2.41 1.88 0.974 1.21 1.34 0.68 0.889 0.627 0.78 1.35 0.608 1.2707 0.664

174.58 98.26 143.37 110.77 110.99 74.11 81.14 73.61 165.28 100.14 176.9 135.51 120.39 7 37.96

Table 4 Young's modulus (E) for 10 bundles of TiO2 NWs. No.

Cantilever length L (mm)

Diameters D (μm)

Length–Diameter ratio L/D

F–d ratio K (N/m)

Young's modulus E (GPa)

1 2 3 4 5 6 7 8 9 10 Average7 r

2.28 2.57 2.04 3.85 1.38 2.85 2.55 3.13 3.87 2.47 2.707 0.77

52 56 38 71.6 25.6 52 45 42.6 51.6 29 46.34 713.50

43.85 45.89 53.68 53.77 53.91 54.81 56.67 73.47 75 85.2 59.63 7 13.56

310.14 541.7 125.82 424.3 155.57 177.1 234.8 101.78 152.26 52.89 227.64 7154.32

53.34 99.2 54.35 99.761 101 59.5 100.74 100.55 132.09 119.57 92.017 27.24

3.4. Analysis of the size effect for young's modulus Young's modulus for 12 individual TiO2 NWs and 10 bundles of TiO2 NWs were tested respectively (shown in Tables 3 and 4, respectively). The average values of Young's modulus for the individual TiO2 NW and that for the TiO2 NWs bundle were 120.39 GPa and 92.01 GPa, respectively. The E value for the TiO2 NWs bundle is a bit lower than that for the individual TiO2 NW. Firstly, the relative motion of the single TiO2 NWs among the TiO2NWs bundle in the bending process may reduce the accuracy of the test; Secondly, there may be a sliding occurred at the two fixed ends of the bundle due to the excessive bending, which leads to a lower result. The E values for TiO2 NW sample prepared by hydrothermal synthesis method in this article is considerably

lower than that for bulk TiO2[1] because the shear deformation was neglected in this article. And it is higher than that for the electrospun TiO2 nanofibers [1] and that for titanate nanowires synthesized by the microwave hydrothermal process [2], whose Young's modulus were 75.6 GPa and 14–17 GPa, respectively. The crystal orientations of these NWs synthesized by these three different methods were the main cause. The hydrothermal synthesis method optimized the crystal orientation of TiO2 nanowires, so the TiO2 NW prepared by hydrothermal synthesis has the highest Young's modulus. The scatter diagram of Young's modulus (E) values in different diameters D for an individual TiO2 NW and TiO2 NWs bundle were shown in Fig. 9(A) and (C), respectively. There were no obvious size dependence of Young's modulus for both the individual TiO2

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Fig. 9. (A) and (C) The scatter diagram of Young's modulus (E) vs. Diameter (D) for an individual TiO2 NW, and for a bundle of TiO2 NWs; (B) and (D) The scatter diagram of Young's modulus (E) vs. L-D ratio for an individual TiO2 NW, and for a bundle of TiO2 NWs.

NW and TiO2 NWs bundle. Moreover, Fig.9(B) and (D) showed the scatter diagram of Young's modulus (E) vs. the radio of length and diameter (L/D). There was also no significant relationship between them.

Acknowledgements

4. Conclusions

References

In conclusion, the individual TiO2 NW and TiO2 NW bundle were synthesized through a hydrothermal reaction of alkali with different titanium source, respectively and the mechanical properties of individual TiO2 NW and TiO2 NW bundle were characterized by the MM3A micromanipulator system through a quantitative measurement of the lateral force-deflection characteristics. The individual TiO2 NW was tested in the micro-cantilever case and Young's modulus was 120.39 GPa, while the TiO2 NWs bundle was set as double-clamped model and its Young's modulus was 92.01 GPa. There was no obvious size dependence of Young's modulus, for both the individual TiO2 NW and TiO2 NWs bundle. The mechanical characteristic measurement of all the 1D nanostructure under the different size in a range from several nanometers to hundreds of millimeters, can be realized conveniently, accurately and quickly by using the bending method in this new test platform which contain the MM3A micro-manipulator nanoprobe system installed in the scanning electron microscope (SEM) chamber. It provides a comprehensive methodology for the mechanical analysis and measurement of nanowire systems in high precision and in broad range.

This work was partially supported by Natural Science Foundation of China (No. 51172209).

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