Schematic representations of a structured crystallite. Raised steps bifurcate the surface into two topologically distinct sites. Terrace sites immediately adjacent to a step edge are denoted in the text, while those one terrace site removed (at a corner) are labeled . In general, the steps will not necessarily be of uniform height, and delineated regions on the surface need not have the same area.
Idealized lattice representation of a structured protein crystallite (a) and a zeolite nanoparticle (b). In a surface free of imperfections, the crystallite would be a Euclidean cube, with all terrace sites of equal area. For a structured surface, only sites and are accessible to a diffusing platelet (see text).
Lattice characterization of the first overlayer of an expanded diffusion space. The Cartesian scaffolding surrounding the crystallite introduces 150 additional locations; the second and third overlayers (not shown) introduce, respectively, additional 343 and 486 locations.
(a) Average walklength for a diffusing species averaged over all trajectories initiated from sites which are nearest neighbors to a corner docking site in a surface-only process. (b) Average walklength for a diffusing species averaged over all trajectories initiated from sites which are nearest neighbors to an edge/ledge docking site in a surface-only process.
(a) Average walklength for a diffusing species having access to an expanded diffusion space of ambient overlayers. The docking site is positioned at a corner site . The crystallite is assumed to have either an undifferentiated, terrace-only surface , or a structured surface with imperfections . Results are shown assuming two different barriers to surface diffusion (see text), and confining boundary conditions are imposed. (b) Same as the caption for (a) except that the docking location is at an edge/ledge site .
Docking efficiency in surface-only diffusion processes; average walklength from nearest-neighbor sites.
Influence of ambient layers on docking efficiency; average walklength for different constraints
Influence of barriers to surface diffusion on the docking efficiency; confined diffusion. See text for definitions of and .
Influence of barriers to surface diffusion on the docking efficiency; fluxional diffusion, see text for definitions of and .
Influence of ambient layers on docking efficiency; three smallest eigenvalues .
Rate constant ratios (bulk vs surface diffusion).
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