  Fullerenes have been observed in several astronomical objects since the
discovery of C$_{60}$ in the mid-infrared (mid-IR) spectrum of the planetary
nebula (PN) Tc 1. It has been suggested that the carriers of the broad
unidentified infrared (UIR) plateau features, such as the 9$-$13$\mu$m emission
feature (12$\mu$m hereafter), may be related to the formation of fullerenes. In
particular, their carriers have been suggested to be mixed aromatic or
aliphatic hydrocarbons such as hydrogenated amorphous carbon (HAC-like
hereafter) grains. For this study, we modeled the mid-IR emission of the
C$_{60}$-PN Tc 1 with a photoionization code, including for the first time the
laboratory optical constants ($n$ and $k$ indices) of HAC-like dust at 300 K.
Interestingly, we find that the broad 12$\mu$m plateau feature in Tc 1 is well
reproduced by using a distribution of canonical HAC grains, while at the same
time they provide an important fraction of the IR dust continuum emission and
are consistent with the other UIR features observed (e.g., the broad
6$-$9$\mu$m plateau feature). This finding suggests that HAC-like grains may be
possible carriers of the 12$\mu$m plateau feature, being likely related to the
fullerene formation mechanism in PNe. More laboratory experiments, to obtain
the optical constants of HAC-like dust with several structures or a composition
at different physical conditions, are strongly encouraged -- that is, in order
to extend this pilot study to more fullerene PNe, and to unveil the details of
fullerene formation and of the potential carriers of the elusive UIR plateau
features.
