An enduring puzzle: the width variations of the 2175 Angstrom extinction
  band
  Graphene, a single infinite, planar, sheet of graphite, has the same
dielectric resonances as bulk graphite, but solid state theory indicates that
its features are about half as wide. Based on this theory, the dielectric
functions of mono- and multi-layer graphenes are deduced and compared with
those of terrestrial graphite. The resonance width of an ordered stack of
graphenes is found to increase with the number of layers while the central
frequency stays constant. This is the basis of the polycrystalline model of the
carrier of the 2175 Angstrom interstellar extinction band. In this model, the
carrier dust grains derive from parent hydrocarbon grains. As a grain ages in
the IS medium, the light atoms are expelled, hexagonal carbon rings lump
together into compact planar clusters, which then assemble into stacks of
parallel, equidistant, graphene-like layers. This so-called graphitization is
well known to occur in the earth or under strong heating. As the number of
layers in each stack increases and their relative orientational order improves,
the pi resonance width increases asymptotically towards that of terrestrial
graphite. Because of the initial random structure of the parent grains, many
randomly oriented stacks may coexist in the same grain. Calculations of the
dielectric response of this composite medium show that, for such a grain, the
width of the extinction efficiency peak follows the same trend as the pi
resonance of the average stack, and thus covers the observed range of IS
feature widths, at very nearly constant peak frequency.
