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Small graphite grains are assumed to produce the 2175 \AA\ interstellar extinction bump. The principal observational characteristic of the bump is the invariance of its central wavelength (2174 $\pm$ 9 \AA) among almost all lines of sight through diverse environments. On the other hand, its FWHM varies from about 0.80 \pmi{} to 1.2 \pmi{} among the same lines of sight. Variations in bump width among different sight lines are attributed to coatings on the graphite grains. The necessary properties of the coating material are determined.
If the mantle material has a bulk resonance in the wavenumber range 4.4 - 5.0 \pmi{} (5.4 - 6.2 eV), mantles can explain: (a) the constancy of $\lambda_0$, the wavelength of maximum extinction, for all sight lines except those with the broadest bumps; (b) the shift of $\lambda_0$ to smaller wavelength for the broadest bumps; (c) the fact that the bumps in the regions of highest radiation density (bright nebulosities) are narrow, while those in dark, quiescent clouds are broad; (d) the lack of correlation of the bump width with R (the total-to-selective extinction ratio), and, consequently, with the underlying UV extinction and particle size distribution; and (e) the behavior of the deviations of the bumps seen in individual sight lines from the mean.
Simple neutral polycyclic aromatic hydrocarbons (PAHs) have measured laboratory absorptions remarkably similar to those required to explain the broadening of the bump. Only 1.5\% of cosmic carbon in PAHs is required to produce very broad bumps; this is $\approx$ 8\% of the PAHs believed to be in the gas phase. Coatings of amorphous carbon, hydrogenated or not, diamond-like bonded carbon, or water ice do not have published optical constants that vary rapidly enough in wavenumber to produce the variations.
