E1 Dimensionality and Classification

Topic

The dimensionality of the nanostructure—whether it is a quantum dot with virtually no extension in any direction (0D), a nanowire or nanotube extended in a single direction (1D), a sheet extended in two directions (2D), or a nanoparticle extended comparably in all three directions (3D)—determines how its surface-to-volume ratio scales as the nanostructure grows or shrinks: the fewer dimensions the nanostructure has, the faster this surface-to-volume ratio increases as its characteristic size decreases. Being 0D, rather than 1D, 2D, or 3D, causes the nanostructure's surface-to-volume ratio to scale most dramatically in response to a reduction in its characteristic size.

A high surface-to-volume ratio—determined by the nanostructure's dimensionality and characteristic size—increases the fraction of surface atoms: the proportion of total atoms located specifically on the exposed surface, rather than being completely surrounded by other atoms within the interior volume. A larger surface-to-volume ratio results in a larger fraction of surface atoms; in the limit of an extremely small nanostructure, this approaches a state where virtually all its atoms are surface atoms.

Consequently, within this model—defined by its dimensionality and surface-to-volume ratio—the fraction of surface atoms ultimately determines when the nanostructure's surface effects dominate over the behavior the material would exhibit in bulk form: when this fraction of surface atoms is high, the nanostructure's behavior is governed by surface phenomena rather than by the average behavior of a comparatively small interior volume. The fact that this fraction of surface atoms—determined here based on the dimensionality and size of this nanostructure—serves as the dimensional basis for two other models in this set means that both depend directly on it: the model describing the nanostructure's surface energy, which is proportional to this same fraction of surface atoms, and the model describing its surface functionalization, which utilizes this same surface area as the available space for anchoring any functional coating.

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