Determining molecule diffusion coefficients on surfaces from a locally fixed probe: Analysis of signal fluctuations

Abstract

Methods of determining surface diffusion coefficients of molecules from signal fluctuations of a locally fixed probe are revisited and refined. Particular emphasis is put on the influence of the molecule's extent. In addition to the formerly introduced autocorrelation method and residence time method, we develop a further method based on the distribution of intervals between successive peaks in the signal. The theoretical findings are applied to STM measurements of copper phthalocyanine (CuPc) molecules on the Ag(100) surface. We discuss advantages and disadvantages of each method and suggest a combination to obtain accurate results for diffusion coefficients.

Occupation times on a comb with ramified teeth

“…Obviously, a cutoff will follow as the comb is fully explored and we shall obtain the ergodic phase. Such cutoffs have been observed in experiments of fluorescence statistics of nanoparticles [24], surface diffusion on an Ag(100) substrate [19] and analytical models [25]. Our work shows the relation between the statistics of the first passage time (FPT) on a single tooth, a cluster of teeth and the occupation time.…”

“…( 60), for short times t L 2 t , The system behaves as an infinite comb with Eqs. (18)(19)(20)(21) being valid. The occupation fraction's statistics is given by Eq.…”

“…Occupation * barkaie@biu.ac.il time analysis on combs is relevant to the analysis of the reaction time or rate in a subspace of a comb-like system [17]. Single particle tracking allows to measure the statistics with high precision [18,19]. For a short time the dynamics of a finite comb should resemble that of an infinite comb (see details below).…”

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

“…For the ACF, the consideration of shapes different from circular ones can be readily accounted for by defining corresponding detection functions, see Ref. 10.…”

“…For atomic diffusion, the ACF method yields relative changes of diffusion coefficients D. Recently, this method has been extended to molecules with sizes larger than the step length of translational moves. 10 This way absolute values of D become accessible. Furthermore, the residence time-distribution 11 (RTD) has been discussed and another new method, the interpeak-time distribution (ITD), has been introduced.…”