Revealing Subsurface Vibrational Modes by Atom-Resolved Damping Force Spectroscopy

Abstract

We propose to use the damping signal of an oscillating cantilever in dynamic atomic force microscopy as a noninvasive tool to study the vibrational structure of the substrate. We present atomically resolved maps of damping in carbon nanotube peapods, capable of identifying the location and packing of enclosed Dy@C82 molecules as well as local excitations of vibrational modes inside nanotubes of different diameter. We elucidate the physical origin of damping in a microscopic model and provide quantitative interpretation of the observations by calculating the vibrational spectrum and damping of Dy@C82 inside nanotubes with different diameters using ab initio total energy and molecular dynamics calculations. [2,3] can be performed on electrically insulating systems, but yield subsurface images with nanoscale resolution at best. Building on the high spatial resolution and sensitivity of dynamic non-contact AFM [4, 5], we introduce Damping Force Spectroscopy (DFS) as a non-invasive tool to study subsurface structure and vibrational modes in complex molecular systems at the atomic scale. We have chosen carbon nanotube peapods [6,7,8] consisting of linear chains of fullerenes enclosed in single-wall carbon nanotubes (SWNTs) [9] as a prominent example of supramolecular compounds. Of particular interest are (M@C n )@SWNT peapods containing M@C n metallofullerenes, hollow cages of n carbon atoms surrounding the metal atom M, known for their unusual electronic transport behavior [10].Here, we demonstrate that monitoring the damping of an oscillating AFM tip provides invaluable information not only about topography, but also the subsurface vibrational modes that have not been observed before with atomic-scale spatial resolution. Our DFS studies of (Dy@C 82 )@SWNT indicate that the observed damping of the tip oscillation depends sensitively on its position and host tube diameter of (Dy@C 82 )@SWNT, in agreement with extensive molecular dynamics (MD) studies reported here. Results of our predictive calculations trace back the observed damping to the excitation of local vibrational modes by transferring energy from the oscillating AFM tip. This truly mechanical oscillator couples to the enclosing nanotube first and subsequently to the enclosed molecules, revealing their packing structure.(Dy@C 82 )@SWNT peapods were prepared by encapsulating Dy@C 82 metallofullerenes in open-ended SWNTs at a filling rate of ≈60%, as confirmed by high-resolution transmission electron microscopy and DFS [11]. The peapods were deposited at low coverage onto an insulating flat SiO 2 surface of a Si substrate and observed by a home-built dynamic AFM [11], shown schematically in Fig. 1(a). The AFM, equipped with a commercial Si cantilever (spring constant of 34.3 N/m, eigenfrequency of 159 kHz) and Si tip (nominal tip radius of 20Å), was operated at constant oscillation amplitude of 21 − 23Å under ultra-high vacuum (p < 1×10 −8 Pa) at low temperature (T < 13 K).High-resolution AFM topography observations of SWNTs and peapods, illustrated in Fig. 1(...

Revealing Subsurface Vibrational Modes by Atomic-Resolution Damping Force Spectroscopy

“…8.7 [28]. In that case the AFM tip was reported to have an "atomically sharp" apex, whose radius R was estimated to be less than 0.5 nm [5]. The sharpness and the effective shape of the tip apex were deduced by deconvoluting AFM images of empty SWNTs, used for calibration.…”

“…These hybrid structures have been investigated predominantly using electrons as a probe in electronic transport measurements [10,21], transmission electron microscopy (TEM) [22,23], and scanning tunnelling microscopy/spectroscopy (STM/STS) [24,25] studies. Figure 8.5 shows TEM images of the (Dy@C 82 )@SWNT sample used in [5], in which the fullerene cages are imaged as circles and the enclosed Dy atoms as dark spots positioned off the center, clearly representing the "quasi" one-dimensional crystal formation [26] of encapsulated Dy@C 82 endohedral metallofullerene molecules. In the process of sample preparation, the Dy@C 82 molecules were encapsulated into open-ended SWNTs with different diameters by heating their mixture in a platinum crucible under 10 −6 Torr at 440 • C for 5 days [27].…”

“…The technique based on the nonlinear detection of ultrasonic oscillation in elastically "indented" samples, however, yields subsurface images with nanometer-scale resolution at best. Building on the high spatial resolution and sensitivity of dynamic non-contact AFM, Damping Force Spectroscopy (DFS) [5] has been introduced as a non-invasive tool to study subsurface structure and vibrational modes in complex molecular systems at the atomic scale. Carbon nanotube peapods [6][7][8] consisting of linear chains of fullerenes enclosed in single-walled carbon nanotubes (SWNTs) [9] have been chosen as a prominent example of supramolecular compounds.…”

Energy Dissipation of AFM Studied by MD/Continuum Coupling Model

“…In the non-contact AFM operation, a cantilever with the sharp tip is oscillated at resonant frequency above the surface and its frequency provides an atomic resolution image of the surface. In addition to the frequency, information of damped amplitude of the oscillation also offers a structural atomic image and an insight into atomic dynamics such as phonon local density of states on the surface [2][3][4][5][6][7][8][9]. The origin of energy dissipation of the damped oscillation, however, has been the subject of debate over the past decade.…”

Analysis of Tip Stability in Adhesion Process in AFM Using Potential Energy Surface: Stability Versus Dissipation

“…Dissipation has been observed in noncontact atomic force microscopy (AFM), and a map of the dissipation shows atomic-scale features for several surfaces [1][2][3][4][5][6][7][8][9]. The origin of dissipation in AFM has been intensively discussed by theoretical and computational methods [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”