Fluids of rodlike particles near curved surfaces

We study fluids of hard rods in the vicinity of hard spherical and cylindrical surfaces at densities below the isotropic-nematic transition. The Onsager second virial approximation is applied, which is known to yield exact results for the bulk properties in the limit of infinitely thin rods. This approach requires the computation of the one-particle distribution function and of the Mayer function, which is greatly facilitated by an appropriate expansion in terms of spherical harmonics. We determine density and orientational profiles as well as the surface tension $\gamma$ as a function of the surface curvature radius R. Already in the low-density limit of noninteracting rods $\gamma \mathrm{}\left(R\right)\mathrm{}$ turns out to be nonanalytic at $1/R=0,$ which prohibits the application of the commonly used Helfrich expansion. The interparticle interaction modifies the behavior of $\gamma \mathrm{}\left(R\right)\mathrm{}$ as compared to the low-density limit quantitatively and qualitatively.