Van der Waals interactions and the limits of isolated atom models at interfaces

Abstract

Van der Waals forces are among the weakest, yet most decisive interactions governing condensation and aggregation processes and the phase behaviour of atomic and molecular matter. Understanding the resulting structural motifs and patterns has become increasingly important in studies of the nanoscale regime. Here we measure the paradigmatic van der Waals interactions represented by the noble gas atom pairs Ar-Xe, Kr-Xe and Xe-Xe with a Xe-functionalized tip of an atomic force microscope at low temperature. Individual rare gas atoms were fixed at node sites of a surface-confined two-dimensional metal-organic framework. We found that the magnitude of the measured force increased with the atomic radius, yet detailed simulation by density functional theory revealed that the adsorption induced charge redistribution strengthened the van der Waals forces by a factor of up to two, thus demonstrating the limits of a purely atomic description of the interaction in these representative systems.

Figure 1. Rare gas atom stabilized by 2D MOF.

(a) Schematic drawing of the AFM measurement set-up. (b) Chemical structure of Cu-coordinated molecular network on Cu(111); the two symmetry-inequivalent nodal sites are indicated as i and ii. (c) STM topographies before and after the vertical manipulation of a Xe atom. (d) Distance-dependent curve of the tunnelling current in the process. Measurement parameters: I=2 pA and V=200 mV in c, and V=2 mV in d. Scale bar, 1 nm.

Figure 2. Atomic scale observation.

(a) STM topography and (b) AFM images taken with a Xe-functionalized tip and (c) a CO-functionalized tip. The two symmetry-inequivalent nodal sites are indicated as i and ii; the five-membered C₃N₂ of the 3deh-DPDI exo-ligands are indicated by a white arrow. Measurement parameters: I=2 pA and V=−200 mV in a, and A=60 pm and V=0 mV in b,c. Scale bar, 1 nm.

Figure 3. van der Waals force detection.

(a) STM topography of the Cu-coordinated 3deh-DPDI network after measuring interaction curves above Ar, Kr and Xe atoms. (b) Frequency shift curves taken at the equivalent node sites with and without a Xe atom, measured with a Xe-functionalized tip. (c) Subtracted distance-dependence curves of the frequency shift for Ar–Xe, Kr–Xe and Xe–Xe junctions. (d) F₄ interaction forces and Lennard-Jones fits for each system, extracted from the frequency shift signal and (e) the equivalent potential energy curves. Measurement parameters: V_tip=500 mV and I=4 pA in a, and A=38 pm, f=23,063 Hz and Q=52,044, and V=1 mV in b,c. Scale bar, 2 nm.

Figure 4. Theoretical calculation.

Comparison of simulated tip–surface and dimer potential energy curves with experimentally derived curves (the same experimental data as in Fig. 3e) for each rare gas atom pair. The z-position of the experimental curves has been normalized with respect to the simulated Xe–Kr tip–surface curve. The curves were fitted with polynomial functions. Inset: atomic snapshot of the simulated tip–surface system.