λ²Q_abs/a for 0.33 nm (short-dashed), 0.5 nm (solid), 1 nm (dashed-dotted) and 3 nm (long-dashed) radius particles: for a-C(:H) with E_g(bulk) = 0.5, 0.25 and 0.1 eV (black lines, from lower to upper at 100   μm) and neutral and cation PAHs with the same number of C atoms (dark and light grey solid lines, respectively, Desert et al. 1990; Draine & Li 2001, 2007; Compiègne et al. 2011). The dashed, vertical, grey line shows the peak position of the UV bump and the solid, vertical, grey line shows the upper wavelength limit for the well-constrained a-C(:H) IR features.