Calculations of van der Waals forces in 2-dimensionally anisotropic materials and its application to carbon black

We present calculations of the van der Waals force for carbon black dispersions in both aqueous and nonaqueous media using Lifshitz theory. The microstructure and composition of carbon black are complex, but an initial approximation to the shell-like microstructure of carbon black allows the local interaction of carbon black particles to be approximated as oriented domains of graphite. The dielectric spectra for graphite, which has a 2-dimensional anisotropy due to its the layered microstructure, is required for the Lifshitz theory van der Waals force calculations. The anisotropic dielectric spectra of graphite (which behaves as a semiconductor) was constructed by modeling the conduction or free charge response separately from the polarization or bound charge response. The free charge response was modeled using the Drude model, while the dielectric spectra for the bound charge response was constructed from the spectroscopic data directly according to the Kramers-Kronig relation for the dielectric function, epsilon(omega). The expressions for calculating the fully retarded van der Waals force for half spaces with 2-dimensional dielectric anisotropy were derived as well as. The construction for the dielectric spectra of polystyrene from recent spectroscopic data from the literature according to the method outlined in (Dagastine, R. R., Prieve, D. C., and White, L. R., J. Colloid Interface Sci.231, 351 (2000)) is also presented.