Surface Diffusion

Single-molecular diffusivity and long jumps of large organic molecules: CoPc on Ag(100)

“…The dependence of α (Δ K ) on the momentum Δ K = |Δ K | for the diffusion of CoPc on Ag(100) ( T S = 350 K) is shown in Figure 2 for the two high-symmetry directions of the crystal. For the case that the diffusion of the adsorbate is governed by the interaction of the molecule with a corrugated surface, its motion can be well described by the Chudley-Elliott (CE) model of jump-diffusion ( Chudley and Elliott, 1961 ; Barth, 2000 ; Jardine et al, 2009 ; Ferrando and Jardine, 2020 ). The CE model provides an analytic solution for I (Δ K , t ) with the dephasing rate α vanishing when the momentum transfer Δ K matches a reciprocal surface lattice vector and varying sinusoidally in between.…”

“…Finally, the diffusion coefficient D for two-dimensional motion, i.e., tracer-diffusion can be calculated from the hopping rate as determined from the CE model using: where Γ is the hopping rate and ⟨ l ⟩ the mean jump length ( Barth, 2000 ; Jardine et al, 2009 ; Ferrando and Jardine, 2020 ). For a hopping rate of 1.9 ⋅ 10 10 s −1 and a mean jump length of 4.52 Å we obtain a diffusion coefficient of: at 350 K. D measured at 350 K corresponds to a prefactor for the diffusivity with D 0 = 2.7 ⋅ 10 –8 m 2 /s and is thus much smaller than D 0 ≈ 1 ⋅ 10 –5 m 2 /s as reported in STM works by Antczak et al (2015a) .…”

“…Moreover, for aromatic organic molecules, the interaction with the substrate often occurs via weak van der Waals (vdW) forces and friction may become so low that the molecule exhibits a diffusive motion in the ballistic regime ( Calvo-Almazán et al, 2016 ). The variety of these processes and possible correlation between those makes the study of surface diffusion challenging ( Ferrando and Jardine, 2020 ). In the traditional view of atomistic surface diffusion, the motion is realised by a random walk of the adatom by crossing a barrier between two neighbouring potential wells: Particles move by hopping from one favourable adsorption site to one of the nearest adjacent sites, following the energetically most favourable route across the potential energy surface (PES).…”