Diffusion mechanisms at the Pb solid–liquid interface: Atomic level point of view

Non-Brownian Interfacial Diffusion: Flying, Hopping, and Crawling

“…Specifically, molecules execute intermittent trajectories, with periods of slow and/or confined surface diffusion alternating with long “flights” in a generalized continuous time random walk process. These observations were confirmed for various small-molecule and macromolecular species at diverse interfaces, ,,,,,,− in thin films, , as well as for adsorbed nanoparticles, ,, for swimming bacteria, − and even for individual atoms . A connection was made between intermittent trajectories and theoretical models that predicted molecular flights through an adjacent liquid phase, each of which comprising a series of hops , with potential readsorption determined by a probabilistic sticking coefficient .…”

“…These observations were confirmed for various small-molecule and m a c r o m o l e c u l a r s p e c i e s a t d i v e r s e i n t e r f aces, 27,30,35,36,38,50,79−85 in thin films, 86,87 nanoparticles, 80,88,89 for swimming bacteria, 90−92 and even for individual atoms. 93 A connection was made between intermittent trajectories and theoretical models that predicted molecular f lights through an adjacent liquid phase, each of which comprising a series of hops, with potential readsorption determined by a probabilistic sticking coef f icient. During the waiting times between flights, adsorbates may undergo crawling motion.…”

Three-Dimensional Tracking of Interfacial Hopping Diffusion

“…While interfacial diffusion is nominally two-dimensional (2D) and conventionally described in terms of 2D Brownian motion, longstanding theoretical models [7][8][9][10][11][12][13][14][15][16] have predicted that interfacial mass transport could actually be dominated by "flights" through an adjacent liquid phase, which would dramatically alter the nature of interfacial molecular motion; an understanding of this process is necessary in order to rationally control mass transport at surfaces. Recent experimental results indirectly support these predictions, by measuring the 2D projection of trajectories for atoms, molecules, polymers, and nanoparticles, in thin films, at solid/liquid interface, and on lipid bilayers, which can be represented as an intermittent process, with periods of apparent immobility alternating with long "flights" comprising a heavy-tailed distribution [17][18][19][20][21][22][23][24][25][26]. However, the evidence for the presence of three-dimensional (3D) hops remains indirect, and critical aspects of the proposed "hopping" process remain a mystery.…”

3D Imaging of Hopping Molecules

“…While interfacial diffusion is nominally two dimensional (2D) and conventionally described in terms of 2D Brownian motion, longstanding theoretical models [7][8][9][10][11][12][13][14][15][16] have predicted that interfacial mass transport could actually be dominated by "flights" through an adjacent liquid phase, which would dramatically alter the nature of interfacial molecular motion; an understanding of this process is necessary in order to rationally control mass transport at surfaces. Recent experimental results indirectly support these predictions by measuring the 2D projection of trajectories for atoms, molecules, polymers, and nanoparticles, in thin films, at solid-liquid interface, and on lipid bilayers, which can be represented as an intermittent process with periods of apparent immobility alternating with long flights comprising a heavy-tailed distribution [17][18][19][20][21][22][23][24][25][26]. However, the evidence for the presence of three-dimensional (3D) hops remains indirect, and critical aspects of the proposed "hopping" process remain a mystery.…”