Unconventional two-dimensional vibrations of a decorated carbon nanotube under electric field: linking actuation to advanced sensing ability

Abstract

We show that a carbon nanotube decorated with different types of charged metallic nanoparticles exhibits unusual two-dimensional vibrations when actuated by applied electric field. Such vibrations and diverse possible trajectories are not only fundamentally important but also have minimum two characteristic frequencies that can be directly linked back to the properties of the constituents in the considered nanoresonator. Namely, those frequencies and the maximal deflection during vibrations are very distinctively dependent on the geometry of the nanotube, the shape, element, mass and charge of the nanoparticle, and are vastly tunable by the applied electric field, revealing the unique sensing ability of devices made of molecular filaments and metallic nanoparticles.

Figure 1

(a) The clamped CNT with a charged NP attached, bent under applied electric field. (b) A CNT decorated with a ring-shaped NP (100 atoms), and (c) with a dot-shaped NP (50 atoms) (zoomed in). (d) The variation of the maximal deflection of CNTs midpoint (u ₀) relative to the CNT length (L) with electric field (E), and (e) the NP charge q. The inset in (e) shows variations of u ₀/L with E for q = 10 e, while q = 1 e in (d). The lines plotted in (d,e) are the best fits obtained using Eq. (1).

Figure 2

Cross-sectional view (55% of the CNT length) of the two-dimensional motion of the (3,3) CNT (L = 50 nm) decorated with a dot-shaped Ag NP (N = 50, q = 1 e), subjected to E = 4 V nm⁻¹ (direction indicated by the arrow). The colour bar represents the simulation time in nanoseconds.

Figure 3

(a) Cross-sectional view of a decorated CNT, with indicated typical force components on the right and left side of the NP (F _R and F _L respectively), and the resulting torque τ. The path of vibrational motion in the (x, y) plane of the midpoint of a (5,0) CNT with L = 50 nm decorated with a ring-shaped Ag NP of 100 atoms and q = 1 e, subjected to electric field E = 3 V nm⁻¹ (b), 5 V nm⁻¹ (c), and 12 V nm⁻¹ (d). The corresponding relative deflections u _x/L and u _y/L as a function of time are shown in panels (e–g), respectively. The envelope frequencies Ω_x and Ω_y are indicated in panel (f).

Figure 4

The path of vibrational motion in the (x, y) plane of the midpoint of a (5,0) CNT with L = 50 nm, subjected to the electric field E = 2 V nm⁻¹ and decorated with a Na (a), Pd (b) and Ag (c) ring-shaped NP of 100 atoms and q = 1 e. The corresponding relative deflection u _x/L as a function of time is shown in panels (d–f), respectively.

Figure 5

The variation with time of the relative deflections (a) u _x/L and (b) u _y/L, and the corresponding path of vibrational motion in the (x, y) plane of the midpoint of a pristine (5,0) CNT with L = 50 nm, q = 1 e, and subjected to the electric field E = 5 V nm⁻¹, for a simulation time (c) under 3.5 ns and (d) in the period 17 ns–20 ns.

Figure 6

The variations of resonance frequency f _x with (a) length (L) of three different CNTs, (b) number of atoms in the NP (N) and (c) applied electric field (E). All CNTs were decorated with a dot-shaped Ag NP (q = 1 e). In (a,b) E = 0 while for the inset of panel (a) E = 2 V nm⁻¹. In (b,c), L = 50 nm and in (a,c), N = 50. The lines plotted in (a,b) are fits using Eq. (3). The dashed and dotted lines in (c) are the fits obtained using empirical dependencies [see text].

Figure 7

The variations of f _x and f _y with (a) L, for a ring-shaped NP and E = 2 V nm⁻¹, (b) N, for a dot-shaped NP and E = 0, and (c) E, for a ring-shaped NP and N = 100. In all the panels a (5,0) CNT and a Ag NP (q = 1 e) are considered. The lines plotted in (a,b) are fits using Eq. (3). The dashed and dotted lines in (c) are the fits obtained using empirical dependencies [see text].