Abstract
Van der Waals (vdW) forces act ubiquitously in condensed matter. Despite being weak on an atomic level, they substantially influence molecular and biological systems due to their long range and system-size scaling. The difficulty to isolate and measure vdW forces on a single-molecule level causes our present understanding to be strongly theory based. Here we show measurements of the attractive potential between differently sized organic molecules and a metal surface using an atomic force microscope. Our choice of molecules and the large molecule-surface separation cause this attraction to be purely of vdW type. The experiment allows testing the asymptotic vdW force law and its validity range. We find a superlinear growth of the vdW attraction with molecular size, originating from the increased deconfinement of electrons in the molecules. Because such non-additive vdW contributions are not accounted for in most first-principles or empirical calculations, we suggest further development in that direction.
Highlights
Van der Waals forces act ubiquitously in condensed matter
Even for two electrically neutral objects devoid of any static multipole moments, quantum mechanical fluctuations lead to the attractive dispersion or van der Waals interaction[1]
Semi-empirical correction schemes for density functional theory (DFT) are often used that simplify the Van der Waals (vdW) interaction to a sum over atompair potentials[9,10,11]. Those dispersion correction schemes employ drastic simplifications: The vdW interaction is obtained by a pairwise summation over atom–atom potentials and, related, the polarizability of complex objects such as multiatomic molecules is decomposed into a sum of atomic, possibly volume-scaled, polarizabilities
Summary
Van der Waals (vdW) forces act ubiquitously in condensed matter. Despite being weak on an atomic level, they substantially influence molecular and biological systems due to their long range and system-size scaling. The analytically derived asymptotic relation for the atom–atom potential Vav-daWðrÞ 1⁄4 À C6r À 6 (refs 9,10) is attenuated by a purely empirical damping function and used at short distances. In this situation, it is all the more unfortunate that a gap, similar to the one in theory, exists between successful measurements of vdW and Casimir forces for single atoms on the one hand[12,13,14,15,16] and macroscopic bodies on the other[17,18], as comparable experiments for molecules are absent. It was recently demonstrated that qPlus sensors yield very precise force gradient spectra and images[20,21,22]
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