Quantifying Molecular Stiffness and Interaction with Lateral Force Microscopy

Abstract

True atomic resolution was demonstrated for AFM more than 15 years ago, but only recently has it been possible to atomically engineer the tip apex (1-4), a technique pioneered in the STM community (5,6). Tip termination with a CO molecule has made studies of inter-and intramolecular bonding possible (7-11). The CO-terminated tip itself, however, has proven to be difficult to characterize, despite experimental and theoretical approaches (12, 13), in part because it is challenging to characterize lateral forces and stiffnesses with AFM. With any study of shortrange interactions, AFM requires that the long-range background interaction of the macroscopic tip and surface be subtracted (14). Although a full three-dimensional (3D) dataset can reconstruct the potential energy, lateral forces and stiffnesses are only accessible by taking a numerical derivative of experimentally determined energies (15), which results in substantial noise in the data.In LFM, the tip is oscillated parallel to the surface (16,17), and the recorded frequency shift (Δf) is a direct measure of the lateral stiffness (18). The subtraction of long-range contributions, necessary in normalforce AFM (where the tip oscillates normal to the surface) to identify the short-range force components, is obsolete in LFM, rendering LFM particularly appealing for measurements in which the short-range interaction is the signal of interest (e.g., Ref. (19)). We have used both normalforce AFM and LFM to characterize a CO terminated tip and quantify parameters of a model incorporating torsional springs to account for the response of the CO molecules to lateral forces.When the CO tip was first used to image pentacene, it was remarked that the image seemed to be distorted due to CO relaxation (7). Further experiments showed that the relaxation of the CO molecule on the tip was an important part of the tip-surface interaction (13). This relaxation is usually characterized as a torsional spring, with the CO bending around the metal atom to which it is bound (12).We used a CO-terminated tip to probe a single CO molecule on Cu(111). CO on Cu(111) has been well-studied and the system offers a high degree of symmetry. The asymmetry in a normal-force AFM image of a CO with a CO-terminated tip (Fig. 1A) is the result of the slight asymmetry of the tip with respect to the surface, amplified by the bending of both tip and surface CO molecules. Images collected at further distances [e.g., those shown in Fig. S1 (20)] do not show this degree of asymmetry.We acquired a 3D dataset by collecting constant-height normal-force AFM images at various distances from the surface (21). To isolate the shortrange interaction, we subtracted the raw Δf data from the Δf signal above the bare Cu surface (14). The data were then deconvoluted and integrated twice along the z-direction (where z denotes the distance to the surface) to yield the potential energy (21-23). The potential energy map of the short-range interaction at closest approach is shown in Fig. 1B.A plot of the energy as a functio...

Image correction for atomic force microscopy images with functionalized tips

“…The vertical force resulting from the latter was previously determined to be up to 80 pN [1] for similar imaging conditions. If we use the same moment arm as Weymouth et al of 3.02Å [33], this vertical force alone results in a stiffness of the CO molecule of 0.26 N/m, even if there are no other restoring forces. This stiffness is a factor of 3 larger than the value of 1/α, underscoring that the two quantities are not at all the same.…”

Identifying the absolute orientation of a low-symmetry surface in real space

“…However, relaxation of the surface carbonate group or secondary interactions with the neighboring surface or tip species could lead to an amplification of the observed tilt, especially giving a plausible explanation for the tail observed in the vertical interaction at tip-sample distances z 3 and closer. The relaxation of single molecules has very recently been measured for the case of two CO molecules [50], which bend towards each other in the attractive interaction regime. The observation of strikingly similar features in our lateral force data leads us to the conclusion that a relaxation of the carbonate group in the surface might amplify the interaction transition, especially at small tip-sample distances.…”

Subatomic resolution force microscopy reveals internal structure and adsorption sites of small iron clusters

“…Pauli repulsion allows for a descriptive interpretation where the AFM image represents the charge density that is maximal on top of atoms-in contrast to STM, which maps the charge density at the Fermi level. However, the CO molecule bonded to the metal tip easily bends laterally (13,19), and artifacts such as lateral distortions, apparent bond lengthening, bond sharpening, and cusplike maxima within aromatic rings must be anticipated [see figure 1 in (15)]. Thus, we first checked the imaging characteristics of CO tips for adatoms using silicon, with its well-known structure.…”