Diffusion Coefficients from Signal Fluctuations: Influence of Molecular Shape and Rotational Diffusion

Abstract

Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to molecules with circle-like shapes. Here we extend these treatments to molecules with rectangle-like shapes, for which also rotational diffusion needs to be taken into account. Focusing on the distribution of peak widths in the signal, we show how translational as well as rotational diffusion coefficients can be determined. We address also the question, how the distribution of interpeak time intervals and autocorrelation function can be employed for determining diffusion coefficients. Our approach is validated against kinetic Monte Carlo simulations.

Complex Surface Diffusion Mechanisms of Cobalt Phthalocyanine Molecules on Ag(100)

“…The authors, however, did not take into account the unequal input of different atoms of the tip into the tunneling current during motion of large molecule. The noise fluctuation method can detect also the uncoupled rotational motion of molecules with rectangular shape as for example PTCDA . Only two above studies combine the experimental work with DFT calculations of the diffusive paths in order to reveal the full complexity of the motion of the organic molecule, and thus the underlying reason for the observed behavior remains to be understood.…”

On the Possibility of Exploring Tip-Molecule Interactions with STM Experiments

“…Here we focus on a specific technique of determining the diffusion coefficient from the analysis of current fluctuations in scanning tunneling microscopy (STM). These fluctuations are caused by molecules entering and leaving the detection area under an STM tip at a fixed spatial position [3][4][5][6]. Thus, this method is particularly well suited for molecules with high mobility since the tunneling current can be measured at a high time resolution.…”

“…In previous studies, different techniques have been developed and investigated to evaluate the times series of the tunneling current [5,6]. These studies include molecules of different shapes, as well as effects of additional rotational diffusion.…”

“…These fluctuations are caused by molecules entering and leaving the detection area under an STM tip at a fixed spatial position. [3][4][5][6] Thus, this method is particularly well suited for molecules with high mobility since the tunneling current can be measured at a high time resolution. For studies of diffusion of molecules on surfaces, a time resolution in the microsecond regime should be sufficient in general, while it is possible to monitor STM current fluctuations even in the picosecond time regime.…”

Determination of diffusion tensors from oscillating and circulating scanning probe tips

“…For molecules with strongly anisotropic shape, as, e.g., rod-like molecules [26], adjustments of the methods are possible, following the concepts outlined above. More elaborate extensions are necessary when rotational diffusion of the molecules needs to be taken into account [27]. Although being more complex at the experimental stage, the ROP method has the advantage to require only a single experimental measurement followed by simple decompositions of the quasi-continuous signal.…”