Some aspects of formation and tribological properties of silver nanodumbbells
© Polyakov et al.; licensee Springer. 2014
Received: 12 December 2013
Accepted: 2 April 2014
Published: 21 April 2014
In this paper, metal nanodumbbells (NDs) formed by laser-induced melting of Ag nanowires (NWs) on an oxidized silicon substrate and their tribological properties are investigated. The mechanism of ND formation is proposed and illustrated with finite element method simulations. Tribological measurements consist in controllable real-time manipulation of NDs inside a scanning electron microscope (SEM) with simultaneous force registration. The geometry of NDs enables to distinguish between different types of motion, i.e. rolling, sliding and rotation. Real contact areas are calculated from the traces left after the displacement of NDs and compared to the contact areas predicted by the contact mechanics and frozen droplet models.
81.07.-b; 62.25.-g; 62.23.Hj
KeywordsSilver nanowires Nanomanipulation Tribology
Metal nanoparticles (NPs) are well-known objects for tribological studies and nanomanipulation experiments . The majority of studies had been performed on NPs assumed to be spherically shaped, while significantly less number of works was dedicated to nonspherical NPs [2–5]. Taking into account the fact that the friction force at the nanoscale is proportional to the contact area , it is important to know the exact geometry of NPs for correct calculation of their contact area. However, in the case of spherical NPs, it is difficult to distinguish between sliding, rolling and rotating motions. Therefore, an elongated object (e.g. nanowire or nanorod) could be more suitable for revealing different regimes of motion in tribological tests. However, due to increased contact area (and static friction), the manipulation of elongated structures can be problematic. For example, the displacement of CuO nanowires (NWs) on a smooth silicon substrate is almost impossible without damaging and breaking of NWs .
Metal NWs (especially Ag NWs) are a perspective class of materials for transparent conductive electrodes, intensively investigated during the last few years [8, 9]. Optical welding of NW percolating networks is a fast and cost-effective method of improving the conductivity of an electrode by improving wire-to-wire contact resistance . NW-to-substrate adhesion after optical or laser processing is a key parameter of NW-based electrode operation.
Laser-induced melting of metal nanostructures is an intriguing phenomenon studied by several research groups. Habenicht et al. described laser-induced melting, dewetting and ejection (‘jumping’) of Au nanoparticles formed from triangular nanostructures on HOPG substrate . The driving mechanism of NP ejection was minimization of surface energy of the liquid droplet, and the NP ejection velocity was proportional to the energy of laser pulse. In spite of the small time span of melting, ejection and solidification processes (ns), some NPs were frozen in different stages of dewetting and ejection. This phenomenon was analysed and numerically simulated by Afkhami and Kondic . Laser-induced melting of Ag NWs was recently investigated by Liu et al. . They analysed the distribution of electric field and melting patterns along the length of a NW. Maximal field is concentrated on the ends of a NW, promoting melting of the ends of the NW. At relatively small laser pulse energy, spheroid-like structures are formed on the ends of NWs. The resulting nanostructure resembles a ‘dumbbell’ that hereafter will be referred as a nanodumbbell (ND). At higher pulse energy, spherical particles can detach from the NW, or even the whole NW can be melted into the separated spherical NPs due to Rayleigh-Plateau instability .
A ND can be roughly considered as two spheroidal NPs connected by a NW. A ND is a novel and attractive object for nanotribological studies. If the distance between the rounded ends of a NW is short enough, the dumbbell might rest on the rounded ends mainly. Thus, the end bulbs of a ND ensure a relatively small contact area, reduced adhesion and static friction compared to those of intact NWs. Therefore, NDs can be easily manipulated, and different types of motion can be distinguished (sliding, rolling, rotation). However, subsequent analysis and interpretation of experimental data can be complicated. In particular, correct determination of the contact area of NDs is a nontrivial problem. Conventional contact mechanics models developed for solid spherical particles cannot be applied for calculation of the ND contact area. This is due to the physics of ND formation that involves melting and solidifying of NPs on their ends, and this is needed to be taken into account.
In this work, we studied formation and tribological properties of Ag NDs produced by laser processing of corresponding metal NWs on an oxidized silicon surface. Detachment of the ND central part was discussed and analysed using finite element method simulations. Contact areas and static friction of end bulbs of NDs were investigated experimentally and analysed theoretically. NDs were manipulated on oxidized silicon wafers inside a scanning electron microscope (SEM) with simultaneous force recording. Different motion types of NDs were observed during the experiment. To the best of our knowledge, metal NDs were used for nanomanipulations for the first time.
Ag NWs of 120 nm in diameter were purchased from Blue Nano (Charlotte, NC, USA). The nanowires were deposited on an oxidized silicon wafer substrate (cut from a 3-in. wafer, 10-3 Ω cm, 50 nm thermal SiO2, Semiconductor Wafer, Inc., Hsinchu, Taiwan) from solution. For laser treatment of the samples, the second harmonic (532 nm) of Nd:YAG laser (Ekspla NL-200, Vilnius, Lithuania) with a pulse duration of 9 ns and a repetition rate of 500 Hz was used. The beam diameter was 0.6 mm, and the laser pulse energy was approximately 0.9 mJ. After laser treatment, Au and Ag NDs were examined in a transmission electron microscope (Tecnai GF20, FEI, Hillsboro, OR, USA).
The experimental set-up comprised of a 3D nanopositioner (SLC-1720-S, SmarAct, Oldenburg, Germany) equipped with a self-made force sensor installed inside a SEM (Vega-II SBU, TESCAN, Brno, Czech Republic; typical chamber vacuum 3 × 10-4 mbar). High-resolution images of NDs and traces left after displacement of NDs were taken inside FEI Helios Nanolab SEM. The force sensor was made by gluing a commercial atomic force microscope (AFM) cantilever with a sharp tip (Nanosensor ATEC-CONT cantilevers, Neuchatel, Switzerland, C = 0.2 N/m) to one of the prongs of a commercially available quartz tuning fork (QTF). The signal from the QTF was amplified by a lock-in amplifier (SR830, Stanford Research Systems, Sunnyvale, CA, USA) and recorded through the ADC-DAC card (NI PCI-6036E, National Instruments, Austin, TX, USA). The typical values of the driving voltage were 20 to 50 mV, and the corresponding tip oscillation amplitude was in the order of 100 nm. The tip oscillated parallel to the sample surface, i.e. in the shear mode.
During the experiments, the tip was positioned at about the half height of a ND above the substrate surface. Each manipulation experiment started with a displacement of the ND from its initial position by an abrupt tip motion to reduce the initial adhesion. Initial displacement was followed by controlled manipulation of the ND by pushing it with the AFM tip with simultaneous force recording. During the manipulation, the tip moved parallel to the surface along a straight line without feedback loop. The point of the tip contact with ND was varied to investigate different scenarios of ND behaviour. More details about the nanomanipulation technique can be found in .
The Solid Mechanics module in COMSOL Multiphysics (version 4.3b) was used to build a stationary physics model of a deflected dumbbell resting on a flat substrate. The material properties of Ag were taken from the COMSOL material library; only Young's modulus was added manually, with the value 83 GPa.
Results and discussion
ND formation process
SEM observations show that some NWs were completely removed from the substrate by laser processing, where former positions of NWs can be identified as dark ‘shadows’ on the surface of the substrate (Additional file 1: Figure S3). Examination at 45° sample tilt reveals that a number of NDs contact the substrate by one end only (Figure 1f). Complete detachment is likely connected to the ejection of the liquid droplets described by Habenicht et al. . The exact mechanism of melting and complete detachment of NWs is rather complex and requires advanced computer simulations [17, 18].
In order to support the proposed mechanism of ND formation, let us consider a rough estimation of the balance of forces involved on the stages of separation of ND from the substrate: adhesion of the NW, elastic force of the bent NW pulled by the bulbs and thermally induced stress in the NW.
where A is the Hamaker constant for the Ag/SiO2 system and D is the cutoff distance . The Hamaker constant for the system can be approximated as , where AAg is the Hamaker constant of silver and ASiO2 is the same for SiO2, with values 3.72 × 10-19 and 0.62 × 10-19 J, respectively, and the cutoff distance is approximately D ≈ 0.2 nm . Using Equation 1, the calculated contact pressure for the system is approximately 1 GPa, which is the minimal pressure necessary to separate the contacting bodies.
where αAg is the thermal expansion coefficient of silver and ΔT is the difference of the initial and final temperatures. The thermal expansion coefficient of bulk silver is 19.7 × 10-6/K , and considering the temperature difference of 680 K, the strain for such a process is approximately 1.34%. Calculating the thermal stress by σth = EAg th, where E is Young's modulus for silver (EAg ≈ 83 GPa), one yields σth ≈ 1.1 GPa. As the result of superposition of the elastic stress of bent NW and thermal stress, interface separation takes place similarly to crack propagation.
Contact area and static friction
The contact area, as well as friction between the end bulbs and the substrate, will strongly depend on the shape of the bulbs. According to the experimental observations, the end bulbs of the NDs have an ellipsoidal shape that is close to prolate spheroid with the semi-axes R1 and R2. For purposes of simplicity, we will use spherical ball approximation, justified by the ratio R1/R2 ~ 1. Thus, the effective radius will only be used.
where Θ is the contact angle for the Ag/SiO2 interface.
In another scenario, the molten structure detaches from the substrate, as was shown in several works [11, 17], and solidifies before contacting the substrate again (Figure 1f). The bulb shape will be close to the sphere or ellipsoid, and the contact will be governed by adhesion and elastic forces. Such situation can also occur when ND with frozen droplet-shaped bulbs is displaced from its initial position and rolled to the ‘rounded’ side of the bulbs.
where τ is the interfacial shear stress/strength and A is the contact area . The shear strength is defined as an ultimate shear stress τ before the object is displaced and can be estimated using the relation τtheo = G* / Z, where ν is Poisson's ratio and G* = [(2 - ν1) / G1 + (2 - ν2) / G2]-1[25, 26]. Z is an empirical material-dependent coefficient ranging from 5 to 30 . Taking Z = 15 as the typical value for most metals , theoretical shear strength for Ag equals τ ≈ 0.59 GPa.
Nanomanipulation technique inside SEM with simultaneous force registration was used to control the applicability of FDM and DMT-M models for description of ND contact with the substrate surface experimentally. The experiment has shown that in most cases, the end bulbs of NDs ensure a relatively small contact area and therefore reduced adhesion and friction force. For comparison, displacement of untreated uniform Ag NWs on a flat silicon substrate was almost impossible without severe damage and plastic deformation of NW (Additional file 1: Figure S5).
NDs exhibited several regimes of motion in manipulation experiments. The most common scenario was rotation of the ND around one of its ends. Long-range rolling of Ag NDs was rarely observed, while rolling up to approximately 90° was registered frequently. In some cases, one end of ND was losing contact with the substrate surface, and ND rotated around the adhered end out of the substrate plane. In a few cases, static friction was high enough to keep one of the ends fixed, which led to plastic deformation of the ND during manipulation (Additional file 1: Figure S6).
Experimentally observed trace areas remained after ND displacement; contact areas calculated for the same NDs according to the FDM (Equation 3) and DMT (Equation 6) approaches using radii of ND end bulbs, measured in SEM, are shown in Figure 6. It is evident that experimental results obtained by trace observations are closer to values of contact area calculated by FDM than to those by the DMT-M model (Figure 6). It means that the end bulbs of these NDs are not perfect spheroids, but truncated ones solidified in the contact with the substrate. However, the obtained experimental values are still lower than FDM predicts. The possible reasons for FDM to overestimate the contact area are as follows: (1) the equilibrium shape of the droplet may differ significantly from the truncated spheroid, (2) the droplet solidifies before reaching the equilibrium shape, (3) it is possible that the contact angle of the substrate surface with liquid metal nanodroplets is larger than the contact angle of that with macroscopic droplets (135° to 150° instead of 123.8°).
A phenomenon directly related to variations in friction force and contact area is a temporal dependence of contact area or aging [15, 30]. The force required to displace NDs was inversely proportional to the time intervals between the manipulation events. Figure 5c demonstrates the traces left after the first and the second displacement of the same ND (time interval of a few minutes). The area of the first pair of traces is approximately 9.03 × 103 and 10.82 × 103 nm2 and only approximately 2.63 × 103 and 2.62 × 103 nm2 for the second pair of traces. Analysis of the shape of this ND before and after displacement provides evidence that ND was displaced by sliding and rotation only. Therefore, the decrease of the contact area in this case cannot be explained by rolling of the ND onto the more spherical side of the end bulbs. Possible explanation of contact aging is diffusion of metal atoms, which can be accelerated by local heating or migration of electrons caused by the electron beam of SEM. However, detailed analysis of the contact aging phenomenon is out of the scope of this article.
It was demonstrated that metal NDs are attractive objects for nanomanipulation and nanotribology. Formation of metal ND on the substrate from a NW under laser beam radiation is a complex process. The final configuration of a ND is a result of the interplay between the intrinsic effects (i.e. melting, crystallization, effect of thermal stress, elastic forces) and adhesion during the separation of the NW from the substrate. The experimental study showed reduced contact area and adhesion of NDs in comparison to intact NWs. The geometry of NDs enabled to study different regimes of motions in manipulation experiments, i.e. sliding, rolling and rotation. Contact areas and static friction forces of NDs were measured and compared to the DMT-M and FDM contact models.
frozen droplet model
finite element method
scanning electron microscope.
This work was supported by the ESF project Nr. 2013/0015/1DP/126.96.36.199.0/13/APIA/VIAA/010, the ESF FANAS programme ‘Nanoparma’ and EU through the ERDF (Centre of Excellence ‘Mesosystems: Theory and Applications’, TK114). The work was also partly supported by ETF grants 8420 and 9007, the Estonian Nanotechnology Competence Centre (EU29996), ERDF ‘TRIBOFILM’ 3.2.1101.12-0028, ‘IRGLASS’ 3.2.1101.12-0027 and ‘Nano-Com’ 3.2.1101.12-0010. The authors are grateful to Alexey Kuzmin for the fruitful discussions and to Krisjanis Smits for the help in TEM measurements.
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