The interband optical properties of polystyrene in the vacuum ultraviolet (VUV) region have been investigated using combined spectroscopic ellipsometry and VUV spectroscopy. Over the range 1.5–32 eV, the optical properties exhibit electronic transitions we assign to three groupings, E1, E2, and E3, corresponding to a hierarchy of interband transitions of aromatic (π → π*), non-bonding (n → π*, n → σ*), and saturated (σ → σ*) orbitals. In polystyrene there are strong features in the interband transitions arising from the side-chain π bonding of the aromatic ring consisting of a shoulder at 5.8 eV (E1′) and a peak at 6.3 eV (E1), and from the σ bonding of the C–C backbone at 12 eV (E3′) and 17.1 eV (E3). These E3 transitions have characteristic critical point line shapes associated with one-dimensionally delocalized electron states in the polymer backbone. A small shoulder at 9.9 eV (E2) is associated with excitations possibly from residual monomer or impurities. Knowledge of the valence electronic excitations of a material provides the necessary optical properties to calculate the van der Waals–London dispersion interactions using Lifshitz quantum electrodynamics theory and full spectral optical properties. Hamaker constants and the van der Waals–London dispersion component of the surface free energy for polystyrene were determined. These Lifshitz results were compared to the total surface free energy of polystyrene, polarity, and dispersive component of the surface free energy as determined from contact angle measurements with two liquids, and with literature values. The Lifshitz approach, using full spectral Hamaker constants, is a more direct determination of the van der Waals–London dispersion component of the surface free energy of polystyrene than other methods.
Spectral mixing formulations for van der Waals–London dispersion interactions between multicomponent carbon nanotubes
