The estimation of the contact area A

is obtained from geometrical consideration for a spheroid of radius R e and a cutting plane of the contact: (3) where Θ is the contact angle for the Ag/SiO2 interface. In another scenario, the molten structure Staurosporine 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. The contact area of the sphere-on-plane can be calculated on the Selleckchem BIBW2992 basis of continuum elasticity models for deformable spheres such as JKR [21] or DMT-M model [22], which also gives a good approximation for ellipsoids providing R 1/R 2 ~ 1 [19]. Ricolinostat mw According to Tabor [23], the choice of the most suitable model is determined by the parameter (4) where γ is the work of adhesion and z 0 is the equilibrium spacing for the Lennard-Jones potential of the surfaces. K is the combined elastic modulus of the sphere

and substrate, defined as (5) in which ν 1,2 and E 1,2 are the Poisson ratios and Young moduli of the substrate and sphere, respectively. For small η, the DMT-M theory is more appropriate [24] and will be used below. According to the DMT-M model, the contact area A DMT of

the sphere on a flat surface is (6) Friction force can be expressed as the following simple form: (7) where τ is the interfacial shear stress/strength and A is the contact area [25]. The shear strength is defined as an ultimate shear stress τ before the object is displaced and can be estimated using the relation τ theo = G* / Z, where ν is Poisson’s ratio and G* = [(2 - ν 1) / G 1 + (2 - ν 2) / G 2]-1[25, 26]. Z is an empirical material-dependent coefficient ranging from 5 to 30 [27]. Taking Z = 15 as the typical value for most metals [27], theoretical shear strength for Ag equals τ ≈ 0.59 GPa. Real-time manipulations 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 Mannose-binding protein-associated serine protease 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.