Limits...
Non-additivity of molecule-surface van der Waals potentials from force measurements.

Wagner C, Fournier N, Ruiz VG, Li C, Müllen K, Rohlfing M, Tkatchenko A, Temirov R, Tautz FS - Nat Commun (2014)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: 1] Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425 Jülich, Germany [2] Jülich Aachen Research Alliance (JARA)-Fundamentals of Future Information Technology, 52425 Jülich, Germany.

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.

No MeSH data available.


Related in: MedlinePlus

Determination of the force law.(a) Averaged frequency shift Δf curves from individual contacting experiments. The Δf on tip approach has been subtracted from the curves (see Supplementary Fig. 4). All curves are z-aligned at large ztip where molecule and surface are well separated. The absolute z-scale is obtained by comparison to simulations24 (see Supplementary Fig. 5). The arrows indicate where each molecule is detached from the surface with cartoons at the top showing the respective geometries. The inset exemplifies reproducibility and noise level for TTCDA. The grey background marks the part of each curve that is used in the fit. (b) Fit quality s and fit parameter z0 for different force law exponents α. The best fit is obtained for z0=1.3 Å at α=2.85 (dotted lines). The corridor of physically reasonable z0 values (and of the respective exponents α) is shaded grey. (c) Fixing the exponent to α=3, we obtain a sharp minimum in s at z0=dAu(111)/2 (dotted line).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4263323&req=5

f2: Determination of the force law.(a) Averaged frequency shift Δf curves from individual contacting experiments. The Δf on tip approach has been subtracted from the curves (see Supplementary Fig. 4). All curves are z-aligned at large ztip where molecule and surface are well separated. The absolute z-scale is obtained by comparison to simulations24 (see Supplementary Fig. 5). The arrows indicate where each molecule is detached from the surface with cartoons at the top showing the respective geometries. The inset exemplifies reproducibility and noise level for TTCDA. The grey background marks the part of each curve that is used in the fit. (b) Fit quality s and fit parameter z0 for different force law exponents α. The best fit is obtained for z0=1.3 Å at α=2.85 (dotted lines). The corridor of physically reasonable z0 values (and of the respective exponents α) is shaded grey. (c) Fixing the exponent to α=3, we obtain a sharp minimum in s at z0=dAu(111)/2 (dotted line).

Mentions: Regarding the accuracy of the force gradient measurements, a peak-to-peak noise in Δf below 0.05 Hz is required, more than one order of magnitude lower than in the seminal experiment in ref. 20. This is achieved by averaging over several hundred carefully aligned individual Δf curves (each with ~0.4 Hz noise level), obtained in 11 NTCDA, 7 PTCDA and 7 TTCDA contacting experiments (see Methods section). These global averages exhibit a noise level as low as 0.02 Hz and form the basis of our analysis. The averaged curves from each individual contacting experiment are shown in Fig. 2a. We note that while the curves scatter considerably as long as the molecules are under the influence of the surface corrugation, they become perfectly reproducible (exemplified for TTCDA in the inset of Fig. 2a) in the region of interest where the molecules and the surface are well separated and the asymptotic vdW force law is expected to apply. It is this reproducibility that allows us to average over several contacting experiments.


Non-additivity of molecule-surface van der Waals potentials from force measurements.

Wagner C, Fournier N, Ruiz VG, Li C, Müllen K, Rohlfing M, Tkatchenko A, Temirov R, Tautz FS - Nat Commun (2014)

Determination of the force law.(a) Averaged frequency shift Δf curves from individual contacting experiments. The Δf on tip approach has been subtracted from the curves (see Supplementary Fig. 4). All curves are z-aligned at large ztip where molecule and surface are well separated. The absolute z-scale is obtained by comparison to simulations24 (see Supplementary Fig. 5). The arrows indicate where each molecule is detached from the surface with cartoons at the top showing the respective geometries. The inset exemplifies reproducibility and noise level for TTCDA. The grey background marks the part of each curve that is used in the fit. (b) Fit quality s and fit parameter z0 for different force law exponents α. The best fit is obtained for z0=1.3 Å at α=2.85 (dotted lines). The corridor of physically reasonable z0 values (and of the respective exponents α) is shaded grey. (c) Fixing the exponent to α=3, we obtain a sharp minimum in s at z0=dAu(111)/2 (dotted line).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4263323&req=5

f2: Determination of the force law.(a) Averaged frequency shift Δf curves from individual contacting experiments. The Δf on tip approach has been subtracted from the curves (see Supplementary Fig. 4). All curves are z-aligned at large ztip where molecule and surface are well separated. The absolute z-scale is obtained by comparison to simulations24 (see Supplementary Fig. 5). The arrows indicate where each molecule is detached from the surface with cartoons at the top showing the respective geometries. The inset exemplifies reproducibility and noise level for TTCDA. The grey background marks the part of each curve that is used in the fit. (b) Fit quality s and fit parameter z0 for different force law exponents α. The best fit is obtained for z0=1.3 Å at α=2.85 (dotted lines). The corridor of physically reasonable z0 values (and of the respective exponents α) is shaded grey. (c) Fixing the exponent to α=3, we obtain a sharp minimum in s at z0=dAu(111)/2 (dotted line).
Mentions: Regarding the accuracy of the force gradient measurements, a peak-to-peak noise in Δf below 0.05 Hz is required, more than one order of magnitude lower than in the seminal experiment in ref. 20. This is achieved by averaging over several hundred carefully aligned individual Δf curves (each with ~0.4 Hz noise level), obtained in 11 NTCDA, 7 PTCDA and 7 TTCDA contacting experiments (see Methods section). These global averages exhibit a noise level as low as 0.02 Hz and form the basis of our analysis. The averaged curves from each individual contacting experiment are shown in Fig. 2a. We note that while the curves scatter considerably as long as the molecules are under the influence of the surface corrugation, they become perfectly reproducible (exemplified for TTCDA in the inset of Fig. 2a) in the region of interest where the molecules and the surface are well separated and the asymptotic vdW force law is expected to apply. It is this reproducibility that allows us to average over several contacting experiments.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: 1] Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425 Jülich, Germany [2] Jülich Aachen Research Alliance (JARA)-Fundamentals of Future Information Technology, 52425 Jülich, Germany.

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.

No MeSH data available.


Related in: MedlinePlus