Effects of structural and chemical disorders on the visible/UV spectra of carbonaceous interstellar grains

The recent spectacular progress in the experimental and theoretical understanding of graphene, the basic constituent of graphite, is applied here to compute, from first principles, the UV extinction of nano-particles made of stacks of graphene layers. The theory also covers cases where graphene is affected by structural, chemical or orientation disorder, each disorder type being quantitatively defined by a single parameter. The extinction bumps carried by such model materials are found to have positions and widths falling in the same range as the known astronomical 2175 \AA features: as the disorder parameter increases, the bump width increases from 0.85 to 2.5 $\mu$m$^{-1}$, while its peak position shifts from 4.65 to 4.75 $\mu$m$^{-1}$. Moderate degrees of disorder are enough to cover the range of widths of the vast majority of observed bumps (0.75 to 1.3 $\mu$m$^{-1}$). Higher degrees account for outliers, also observed in the sky. The introduction of structural or chemical disorder amounts to changing the initial $sp^{2}$ bondings into $sp^{3}$ or $sp^{1}$, so the optical properties of the model material become similar to those of the more or less amorphous carbon-rich materials studied in the laboratory: a-C, a-C:H, HAC, ACH, coals etc. The present treatment thus bridges gaps between physically different model materials.