A notable phenomenon is described involving the polarization of valence electrons that operates in the edge regions of graphene materials, including compact polyaromatic hydrocarbon (PAH) molecules, because of the mismatch between interior and perimeter chemical bonds. The topology of hexagonal-shaped zigzag-edged systems, with alternating perimeter CC bond lengths, enhances the effect, making recognition easier, compared to graphene ribbons where it is weak. The phenomenon is delineated in ab initio density-functional theory calculations of the electronic structure of a 4 nm diameter hexagonal zigzag-edged molecule C486 H54, chosen because it is a representative of larger ones. Using CC bond length as a surrogate measure, we map the polarization of valence electrons from the perimeter to the center. In a pattern that mimics the bonding, the polarization of the two outermost sets of edge bonds (transverse along rows and radial connecting nested rows of carbon atoms) is impressed on the graphene interior bonds with amplitude that decreases rapidly from the perimeter to the center. All bonds display a decaying oscillation with radial bonds longer than transverse bonds at the same location. This difference leads to a characteristic quinoidal pattern of CC bonds linking the zigzag hexagonal edges joined at each apex. The phenomenon and its analysis are applicable to geometries periodic or not, substituent modified edges and interior.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - 2009 Jun 8|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics