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2.2 Electrically charged nanocontacts 19 and the upper integration limit Ecut → ∞. Eq. (2.12) reduces to Eq. (2.5) when T → 0. A plot of Eq. (2.12) for different temperatures is shown in Figure 2.2. Due to thefinitetemperature,morestatesbecomesavailablefortheelectronsfromEF upto aboutEF +kBT;decreasingthenumberofoccupiedstatesbetweenEF andabout EF − kB T . Figure 2.2 demonstrates that at room temperature the curve follows the zero temperature curve well, except around the minima where a new state is added due to bending. Here the room temperature curves are smoothed. In this section we have found that the spring constant oscillates with the bending – an effect that, however, is slightly reduced due to thermal effects. For small bend- ing the spring softens or hardens as the amplitudes increases. If we have softening or hardening is dependent on the proximity of electron states to the Fermi level at the actual nanowire diameter. This softening or hardening of the spring has an influence on the resonance frequency, which becomes amplitude dependent. 2.2 Electrically charged nanocontacts We want to increase the fundamental understanding of the triboelectric effect. A phenomenon related to this contact electrification is the formation of mounds under a charged nanosized tip. Under a charged nanosized metallic tip, mounds can be formed by electrostatic forces and van der Waals forces acting on the adsorbed atoms on the surface. This can then contribute to making a contact. If we have a nanosized charged tip over a conducting surface we can model the electric field at the surface as the field from a point charge located inside the volume of the tip and its charge mirror located under the surface. We obtain [Paper II] close to the surface q 2d 15d3z2 Ez ≈ −4πε (d2 + r2)3/2 + (d2 + r2)7/2 , Er ≈ 6qdr z. 4πε(d2 + r2)5/2 (2.15) (2.16) Here the charge q can be expressed in terms of the voltage between the conducting tip and the surface: q = U R2+2DR. (2.17) 4πε 2D The dipole moment p for an adatom in an electric field E is given by Tsong and Kellogg [1]: p = μ+αE+61γE3+···, (2.18) where μ is the surface-induced dipole moment of the adatom, α is its polarizability and γ is its hyperpolarizability. μ always points away from the surface that it sits on, see ref. [32, 33], so μ is always positive in our calculations regardless of the polarityPDF Image | Nanomechanics Quantum Size Effects, Contacts, and Triboelectricity
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