Frictional shear stress of ZnO nanowires on natural and pyrolytic graphite substrates

The friction behaviour of ZnO nanowires on natural graphite (NG) and highly oriented pyrolytic graphite (HOPG) substrates was tested in ambient conditions by use of optical microscopy based nanomanipulation. Nanowires on the step-free and waviness-free NG substrate exhibit a diameter-independent nominal frictional shear stress of 0.48 MPa, and this provides a benchmark for studying how the surface topography of graphite influences nanowire friction. Nanowires on the HOPG substrate present a significant diameter-dependent frictional shear stress, increasing from 0.25 to 2.78 MPa with the decrease of nanowire diameter from 485 to 142 nm. The waviness of HOPG has a limited effect on the nanowire friction, as a nanowire can fully conform to the substrate. The surface steps on the HOPG can significantly enhance the nanowire friction and lead to a much higher frictional shear stress than that on NG due to mechanical blocking and the presence of a Schwoebel barrier at step edges. The surface steps, however, can also generate small wedge-shaped gaps between a nanowire and substrate, and thus reduce the nanowire friction. With the decrease in nanowire diameter, the capacity for the nanowire to better conform to the substrate reduces the length of the wedge-shaped gaps, leading to the observed increase in nanowire friction. The results have improved our understanding of the unique friction behaviour of nanowires. Such an improved understanding is expected to benefit the design and operation of nanowire-friction-based devices, including bio-inspired fibrillar adhesives, soft grippers, rotary nanomotors, and triboelectric nanogenerators.

Numerous nanowire friction tests carried out on smooth substrates have shown that the friction force between a nanowire and substrate is proportional to their contact area. This relationship is similar to that exhibited by atomic force microscopy (AFM) tips and nanoparticles on smooth substrates [12,[17][18][19][20][21][22][23][24][25]. Nanowires on substrates containing surface features, however, exhibit a more complex friction behavior. Segments of a nanowire may bridge over a region of a substrate containing surface features due to the mechanical constraint enforced by its contact with surface steps or asperities, leading to a significant decrease in its real contact area. As a result, the friction force, which is proportional to the real contact area, would decrease on substrates with uneven surface topography [26,27]. On the other hand, a nanowire may conform to the topography of a substrate and thus exhibit significantly enhanced friction as compared to its bulk counterpart. The later mechanism is generally accepted as being primarily responsible for the high friction/adhesion of gecko-like fiber-based adhesives [3,28], which was demonstrated experimentally in our recent study [29]. According to the theory of solid mechanics, the lateral flexibility of a nanowire is highly sensitive to its diameter, and so is its frictional shear stress. Such a dependence has not yet been validated experimentally [26,27,29]. Moreover, AFM tips and nanoparticles sliding over a rough substrate typically exhibit enhanced friction forces due to mechanical interlocking and the presence of a Schwoebel barrier at steps or asperities [30][31][32][33][34][35]. Nevertheless, due to the significant experimental challenges associated with testing nanowires, it is not yet known whether they exhibit similar behaviour.
This study seeks to understand the effect of surface topography on the frictional behavior of a nanowire. With this goal, we comparatively examine the frictional shear stress of ZnO nanowires on both a natural graphite (NG) substrate and a highly oriented pyrolytic graphite (HOPG) substrate under the ambient atmosphere. It is generally accepted that both NG and HOPG substrates are free of sharp asperities and have the same surface chemistry. Meanwhile, NG substrates are free of surface steps, and have insignificant waviness, while HOPG substrates typically exhibit atomic surface steps and microscale waviness. The selection of NG and HOPG substrates for examination in this comparative study therefore eliminates the possible effect induced by the surface asperity and surface chemistry, and also enable us to clarify how atomic surface steps and microscale waviness influence the friction between nanowires and substrates. This will not only improve our fundamental understanding of the friction behavior of nanowires, but also benefit the design of nanowire-friction-based nanodevices.

Experimental details
The ZnO nanowires were synthesized on a Si wafer via chemical vapor deposition (CVD), and the wires exhibit a hexagonal cross-sectional profile with atomically smooth surfaces and a Young's modulus of  140 E GPa [36,37]. The NG and HOPG substrates were cleaved with the aid of a scotch tape immediately prior to the friction tests and their surface topographies were characterized using an Agilent 5500 AFM.
The friction between a nanowire and substrate was measured using the midpoint push test in an ambient environment (temperature: ~ 25 °C; relative humidity: ~ 50%) [19]. In the test, a nanowire was directly transferred from the Si wafer (i.e. growth substrate) onto the HOPG substrate using an optical microscopy (OM) nanomanipulation technique [19,38]. The transfer did not use any additional liquids or adhesives, which therefore avoided the absorption of contaminants onto the surface from nanowires or substrates [39,40]. The nanowire on the HOPG substrate was pushed at its midpoint by using an electrochemically etched W tip with a diameter of ~ 400 nm, to generate a sliding that has a constant speed of ~ 200 nm/s. A W tip with a relatively large tip diameter was used to ensure it was sufficiently robust to apply the required pushing force as well as to avoid damaging the nanowire through contact-induced stress concentrations. In addition, graphite surfaces are generally considered hydrophobic, and therefore capillary necks are not expected to appear when the testing environment is maintained with a moderate humidity of 50% [41,42]. Capillary forces are therefore considered to have a negligible effect on the friction behavior of the nanowires in this study. The entire testing process was monitored in real time by an OM (Objective lens: Mitutoyo M Plan APO 100× with a resolution of 0.4 μm). The nanowire was formed into an arc shape, sliding on the substrate surface. The sliding remained stable due to a balance between the pushing force of the W www.Springer.com/journal/40544 | Friction tip at the nanowire's midpoint and the friction force distributed uniformly along the entire length of the nanowire. During sliding, if the W tip was not in contact at the midpoint of a nanowire, or if the moments about its contact point generated by the frictional forces on each side of the nanowire were not balanced, the nanowire began to rotate. In such cases, the contact point between the tip and nanowire must be adjusted according to the sliding status of the nanowire. Immediately after friction testing on the HOPG substrate, the same nanowire was transferred onto the NG substrate under OM. The midpoint push test was subsequently repeated using the same W tip. The nanowire remained on the NG substrate after testing and was examined using field-emission scanning electron microscopy (SEM, JEOL JSM-7800F and FEI Nova NanoSEM 450, operated at 10 kV). and 0.01 nm, respectively. The NG substrate had an atomically smooth surface without atomic steps over the scale of several tens of μm, and only very shallow waviness could be identified on the surface. The waviness can be approximately described by use of a sinusoidal function,

Results and discussion
nm and   10 μm can be considered as the amplitude and wavelength, respectively. The very small amplitudeto-wavelength ratio, , indicates that the waviness is very shallow, and should not affect the contact behavior between the nanowire and substrate [27,29]. In contrast, the HOPG substrate, shown in Figs. 1(d)-1(f), exhibits waviness, and also contains many steps with heights corresponding to that of a single or few-layer graphite. For comparison, the values for a , R a , Consequently, any features with amplitudes below 100 pm is the 2 µm × 2 µm micrographs are expected to constitute noise. For ease of use, the piezo-scanner of the AFM was set at a lower sensitivity during the larger area 50 µm × 50 µm scans, and therefore features with amplitudes below 1 nm may also constitute noise. 29.97 L 0.05 μm. The friction forces exerted on the nanowire are assumed to be distributed uniformly along its length, and are balanced by the elastic restoring force of the nanowire, as illustarted in Fig. 2(f). According to the non-linear beam model, the kinetic friction force per unit length on the nanowire, f, can be written as [43]: where x  and s are the vertical distance and length of an arbitrary point measured on the nanowire  In this work, 12 ZnO nanowires were tested on both substrates, and their measured frictional shear stress values are plotted in Fig. 3. The frictional shear stress values measured on the NG substrate,  NG , ranged from 0.31 to 0.74 MPa, showing no diameter dependence, providing an average value of 0.48 MPa with a standard deviation of 0.09 MPa. The surface of the NG substrate as well as the nanowire facets are atomically smooth, so that a full contact over the entire facet area of a nanowire can be assumed. The fact that the obtained frictional shear stress values are diameter-independent further supports full conformation of the nanowires occurred [45]. The average frictional shear stress value of 0.48 MPa measured on the 'smooth' NG substrate can therefore be used as a benchmark against which the friction behaviour of nanowires on rough or textured substrates can be compared. In contrast, the frictional shear stress value measured on the HOPG substrate,  HOPG , drastically increases from 0.25 to 2.78 MPa with the nanowire diameter decreasing from 485 to 142 nm. Theoretically, the frictional shear stress of a nanowire can be affected by the presence of surface steps as well as by the waviness of the HOPG substrate. The effect of steps of a substrate surface on the frictional shear stress is complex, due to the existence of competing mechanisms. First, the sliding of a nanowire maybe blocked by the steps on the surface. As a result, a greater force must be applied to the nanowire to overcome the blocking than that on the NG substrate [33]. The contact angle formed between the surface of nanowire and an atomic step can be evaluated by D/h, where D is the nanowire diameter and h is the step height. The contact angle will therefore increase for nanowires with smaller diameters. The increase in friction force exhibited by a nanowire due to atomic step-induced mechanical blocking is therefore expected to be more pronounced for nanowires with smaller diameters. Such friction behavior would be considered analogues to that exhibited previously by the micro/ nanoscale contact of spherical balls on stepped surfaces [31,35]; however, the exact relationship is yet to be explored. Meanwhile, a Schwoebel barrier is present at the steps, and this will further increase the force for the nanowire to pass the steps [34]. Both mechanisms can lead to a significant increase of the friction force exhibited by a nanowire. Second, the 2064 Friction 10(12): 2059-2068 (2022) | https://mc03.manuscriptcentral.com/friction surface steps can induce the formation of atomic-scale wedges at the nanowire/substrate interface, as shown in Fig. 4. This in turn may reduce the frictional shear stress exhibited by a nanowire.
When a nanowire lies across a step, the length of the nanowire segment that remains suspended (forming the wedge) is governed by the balance between the adhesion energy of the nanowire-substrate interface and the elastic energy stored in the conforming nanowire. Using the elastic beam theory, the length of a wedge can be estimated by [46]: where h is the step height which typically corresponds to one or several graphite layers, and   ZnO G is the ideal adhesion energy between ZnO and graphite, defined as the energy required to separate a smooth ZnO slab from a graphite surface [47]. A   ZnO G of 0.261 J/m 2 is used in this study, and this value was previously measured between a ZnO coated flat AFM nanotip and a HOPG substrate [47]. By evaluating the length of the wedge formed by a nanowire that lies over a step, and then comparing it to the distance between the steps observed on the HOPG substrate, we can estimate what portion of a nanowire's length remains in contact with the substrate and what portion is suspended. Nanowires with  100 D , 200, 300, and 400 nm were selected for evaluation as these diameters are within the range of the nanowires tested. We estimate that a step edge has a height corresponding to a single graphite layer (h = 0.34 nm [33,34]), and this corresponds to wedge lengths of  w s 93, 157, 212, and 263 nm, obtained from Eq. (2). In Fig. 1(f),   Fig. 4 Sketches of a nanowire conforming to a wavy substrate surface and the step-induced gap between the nanowire and substrate surface. the distance between steps, or rather, the width of the step terraces, ter w , typically ranges from 100-500 nm. The estimated wedge length values should range from ter / 4 w to ter w . This indicates that a large portion of the length of a nanowire is actually suspended above the HOPG substrate. Moreover, Eq. (2) indicates that the real contact length of a nanowire,   c t e r w s w s , should decrease linearly with the 3/ 4 D . In our nanowire-HOPG system, the friction force is proportional to the real contact area [48,49]. Therefore, we can express the friction force as a function of the real contact length of a nanowire, written as   where  max is the maximum measured  value. In other words,  HOPG exhibits a reciprocal dependence with 3/ 4 D . To validate this relationship, a curve of the form   (where C 1 and C 2 are constants) was fitted to the measured values of  HOPG of all the nanowires, and is plotted in Fig. 3. The R squared value of 0.8739 indicates that the proposed relationship between  HOPG and D is in good agreement with the data.
The surface waviness of the substrate can potentially influence the friction behavior of a nanowire by constraining in it in a way that prevents contact at wave valleys or trapping/blocking it at the wave valleys/crests via interlocking [50]. In this study, the nanowires were observed to slide in stable manner along the substrate surface. This indicates that the friction force is uniformly distributed along the length of the nanowires during sliding. Therefore, it is reasonable to derive that the friction behavior is independent on the waviness of the substrate in our cases. Otherwise, if the friction force was dependent on the substrate waviness, then the nanowire should lose its stability during sliding. In fact, the lack of dependence on waviness observed in our test can be understood by considering how a nanowire conforms to a substrate. For a nanowire that has elastically conformed to a wavy substrate, its bending and tensile energies, associated with confirmation to each characteristic wavelength should be less than or equal to the corresponding adhesion energy, where k is the curvature function of the wavy surface,    ZnO G is the actual adhesion energy between the ZnO nanowires and the HOPG substrate with surface steps and www.Springer.com/journal/40544 | Friction waviness, and  and S are the tensile stress and crosssectional area of the nanowire, respectively [51,52].
U , the critical diameter c D for the conformed nanowire can be estimated by Here    ZnO G can be estimated by [49]: , and the typically values measured here range from 0.1% to 1.0%. Also, no surface asperities could be detected (R a = 0.01 nm). Consequently, a waviness-induced interlock effect is expected to insignificantly influence the friction behavior of a nanowire. This is also supported by a previous investigation on the friction behavior of a sharp AFM tip, which found that buried steps had a much smaller contribution on the friction of the tip compared to that of exposed steps. The study also found that the profile of a buried single graphite layer step was equivalent to a surface waviness with a maximum slope of  / H ≈ 0.17 [53], within the same range of substrate waviness observed in this study.
The largest diameter of the nanowires investigated here was limited to below 500 nm due the CVD growth process. The shear stress for nanowires with diameters greater than 500 nm is expected to continually decrease with increasing diameter. This can be explained by considering that as the diameter of a nanowire increases, the length of the wedge w S formed at a step edge on the substrate increases according to Eq. (2), this in turn would lead to a decrease in the real contact length (area) of the nanowire, as hence decrease the frictional force (shear stress). Larger diameter nanowires may also no longer be able to conform to the waviness profile of the substrates, according to the above-estimated c D values by Eq. (3). Such a non-full conformation would further decrease the contact area and frictional shear stress.

Conclusions
In summary, the averaged frictional shear stress of ZnO nanowires on a NG substrate was 0.48 MPa, irrelevant of the nanowire diameter. In contrast, the frictional shear stress generated on the HOPG substrate increased from 0.25 to 2.78 MPa when the nanowire diameter decreased from 485 to 142 nm. The surface waviness of the HOPG substrate showed insignificant influence on the friction behaviour of ZnO nanowires because the nanowires can conform to the substrate surface. In contrast, the surface steps present on the HOPG substrate can significantly influence the frictional shear stress via competing mechanisms. Surface steps can increase the force required by a nanowire to overcome blocking as well as the associated Schwoebel barrier when sliding over the step edges. This mechanism can therefore act to increase the frictional shear stress. Meanwhile, surface steps can generate small wedge-shaped gaps between nanowire and substrate. The length of a gap is dependent on the diameter of the conforming nanowires and dictates the real contact area. This mechanism can therefore act to decrease the frictional shear stress, particularly for larger diameter nanowires. Consequently, the friction shear stress of nanowires on HOPG increases with decreasing nanowire diameter, i.e.  