Variations on a theme - the evolution of hydrocarbon solids: III. Size-dependent properties - the optEC(s)(a) model

Context. The properties of hydrogenated amorphous carbon (a-C:H) dust evolve in response to the local radiation field in the interstellar medium and the evolution of these properties is particularly dependent upon the particle size. Aims. A model for finite-sized, low-temperature amorphous hydrocarbon particles, based on the microphysical properties of random and defected networks of carbon and hydrogen atoms, with surfaces passivated by hydrogen atoms, has been developed. Methods. The eRCN/DG and the optEC(s) models have been combined, adapted and extended into a new optEC(s)(a) model that is used to calculate the optical properties of hydrocarbon grain materials down into the sub-nanometre size regime, where the particles contain only a few tens of carbon atoms. Results. The optEC(s)(a) model predicts a continuity in properties from large to small (sub-nm) carbonaceous grains. Tabulated data of the size-dependent optical constants (from EUV to cm wavelengths) for a-C:H (nano-)particles as a function of the bulk material band gap [Eg(bulk)], or equivalently the hydrogen content, are provided. The effective band gap [Eg(eff.)] is found to be significantly larger than Eg(bulk) for hydrogen-poor a-C(:H) nano-particles and their predicted long-wavelength ({\lambda} > 30{\mu}m) optical properties differ from those derived for interstellar polycyclic aromatic hydrocarbons (PAHs). Conclusions. The optEC(s)(a) model is used to investigate the size-dependent structural and spectral evolution of a-C(:H) materials under ISM conditions, including: the IR-FUV extinction, the 217 nm bump and the infrared emission bands. The model makes several predictions that can be tested against observations.