Mechanical Properties of TiO2 nanotubes investigated by AFM and FEM


 The mechanical measurements of nanostructures are crucial to the development and processing of novel nanodevices. Herein, TiO2 nanotubes were synthesized from an electrospun method combined with subsequent heat-treatment. The elastic modulus and fracture strength of a single TiO2 nanotube were measured by atomic force microscopy (AFM). The effect of elastic modulus and dimensional size on the mechanical behaviors of the nanotubes was simulated by the finite element method (FEM).


Introduction
The design and construction of nanodevices such as microbatteries, quantum cascade lasers, eld-effect transistors, light-emitting diodes, gas nanosensors, etc. rely critically on our ability to fabricate functional heterostructures and interfaces with desirable characteristics [1][2][3]. Fortunately, the development of nanomaterials has created great excitement and expectations in the eld of nanodevices.
Much progress in the synthesis, fabrication and assembly of nanomaterials has already been gained in the past decades. Especially, nanostructured semiconducting oxides have attracted much attention due to their tunable physical properties and wide applications. Various kinds of semiconducting oxides, such as TiO 2 [4], ZnO [5], SiO 2 [6], In 2 O 3 [7], Ga 2 O 3 [8], GeO 2 [9], SnO 2 [10], CdO [11], and PbO 2 [12] with different morphology have been successfully prepared. Among them, TiO 2 has been investigated mainly owing to its widespread applications in lithium ion batteries [13], solar cells [14], photocatalysts [15], and sensors [16]. Most of the previous researches focused on the morphological controlling and property modulation of TiO 2 . The mechanical behavior of materials at the nanoscale is often different from that at the macroscopic scale. Thus, the mechanical properties of nanomaterials are crucial to the development and processing of novel nanodevices [17,18].
The challenge of research on nanomechanical properties is not only due to the lack of nanoscale experimental techniques, but also the lack of multiscale theories to describe the size effects [19]. In recent years, in-situ transmission electron microscopy (TEM) and scanning electron microscopy (SEM) nanomechanical testing have been developed to image and measure the deformation inside the instruments [20][21][22]. Besides, atomic force microscopy (AFM) was employed to image and measure the deformation and applied force of the object simultaneously at the nanoscale [23][24][25][26]. As an open platform, AFM provides multiple possibilities for the mechanical characterization of nanomaterials. For example, the three-point bending test and nanoindentation were widely performed on AFM to measure Young's modulus and hardness of nanostructures [24,27,28]. However, due to the lack of basic data and related experimental equipment, the nite element method (FEM) was widely employed to simulate and predict the mechanical properties of nanomaterials under complicated conditions [10,25,26,29]. Herein, TiO 2 nanotubes were synthesized from an electrospun method combined with subsequent heat-treatment. A series of destructive and nondestructive tests were carried out to characterize the mechanical properties of a single TiO 2 nanotube.
The fracture strength of a single TiO 2 nanotube was measured by the AFM technology. The effect of elastic modulus and dimensional size on the mechanical behaviors of the nanotubes was simulated by the FEM.

Preparation of materials
TiO 2 nanotubes were synthesized from an electrospun method combined with subsequent heat-treatment [30]. In a typical procedure, a certain amount of polyvinyl Pyrrolidone (PVP, M W 1300000), acetic acid and titanium tetraisopropanolate were dissolved in ethanol. The as-prepared solution and mineral oil were used as external and internal uid in coaxial electrospinning. The distance (from the tip of the pinhead to the collector: 20 cm) and the electrospun voltage (applied to the tip: 15kV) were xed. The obtained electrospun membrane was soaked in n-octane to remove the mineral oil. After being heat-treated at 500°C for 3h, TiO 2 nanotubes were fabricated from the electrospun membrane.

Characterization of materials
Morphology of TiO 2 nanotubes was observed by eld emission scanning electron microscope (FEI Nova NanoSEM450), transmission electron microscope (FEI Tecnai G2 F30) and atomic force microscopy  with various diameters was observed. The diameter of the TiO 2 nanotubes was in the range of 30~200nm. The tube-like structure was con rmed by the fractured surface. The detailed structure of the synthesized TiO 2 nanotubes was studied by TEM. The clear tube wall can be recognized in Fig.2b. The HRTEM image (Fig.1c) indicates that TiO 2 nanotube apparently consists of tiny nanocrystallites, indicating a polycrystalline nature of the nanotubes. XRD patterns (Fig.1d) reveal that the presence of the crystallographic structure of anatase was observed for the sample calcined at 500°C [31].

Results And Discussion
Morphology of a single TiO 2 nanotube before and after nanoindentation was presented in Fig.2. The size of the TiO 2 tube tested by AFM was presented in S1. A well-shaped TiO 2 nanotube with a diameter of 220 nm was picked as a target (Fig.2a). The AFM nanoindentation test was performed after surface scanning. The AFM tip was carefully moved to the top of the nanotube by repeatedly zooming in [32]. Then a controllable force was exerting to the AFM tip until the nanotube was broken (Fig.2b). Apparently, the TiO 2 nanotube shows brittle fracture behavior at nanoscale. At the fracture location, the wall thickness of the nanotube can be measured. After the nanoindentation test, the mechanical properties of the nanotube were calculated from the force-distance curve collected by the AFM.
A typical force-displacement curve obtained from the nanoindentation test is shown in Fig.3. The forcedisplacement curve can be divided into three stages: in the rst stage, the indentation force linearly increased with the displacement, indicating the elastic deformation region of the nanotube. In the second stage, the indenter impaled the wall of the nanotube. No apparent plastic deformation was observed, indicating a brittle fracture of the nanotubes. In the third stage, with the further increase of the indentation force, the destruction continued until the complete collapse of the nanotube. The fracture strength of the single TiO 2 nanotube measured by AFM is ~ 35GPa. Based on the AFM experiments, the FEM model was established as shown in S2. The effect of elastic modulus and dimensional size on the mechanical behaviors of the nanotubes can be predicted by FEM simulation. A typical deformation nephogram from FEM simulation is shown in S3. Obviously, the maximal value of the deformation can be found under the indenter. Furthermore, most of the deformation appears at the top surface of the tube.
The effect of the equivalent radius of the indenter on the deformation of the TiO 2 nanotubes over the linearly elastic range was simulated by FEM as shown in Fig.4a. Undoubtedly, with the decrease of the equivalent radius of the indenter, the deformation of the TiO 2 nanotubes under the same force increases.
It should be noticed that this phenomenon becomes increasingly obvious with the decrease in the equivalent radius. Besides, with the indent force increases, the deformation increases linearly. Slight difference in the slopes is found, indicating the effect of different equivalent radius on the deformation of TiO 2 nanotubes is exhibited in different ways.
With a xed indented force, smaller the equivalent radius, larger the nanotube's deformation due to the remarkably increasing pressure under the indenter. As shown in Fig.4b, with the radius is in the range of 0.02 -0.03 μm, the effect of the radius on the deformation can be neglected.

Conclusions
In summary, the mechanical behavior of a single TiO 2 nanotube was successfully characterized by AFM and FEM method. The ultimate strength of the TiO 2 nanotube measured from AFM is around 35 GPa.
FEM results indicate that the mechanical behavior of the nanotubes is greatly affected by the indenter's equivalent radius, material's elastic modulus and nanotube's dimensional size. Based on the FEM simulation, the mechanical behavior of the nanotubes can be effectively predicted.

Con icts of interest
The authors declare no competing nancial interest      Relationship between nanotube's deformation and indented force (a) and elastic modulus (b) simulated by FEM.