Length segregation in mixtures of spherocylinders induced by imposed topological defects

We explore length segregation in binary mixtures of spherocylinders of lengths L₁ and L₂ which are tangentially confined on a spherical surface of radius R. The orientation of spherocylinders is constrained along an externally imposed direction field which is either along the longitude or the latitude lines of the sphere. We show that the integer orientational defects at the poles induce a complex segregation picture also depending on the length ratio factor γ=L₂/L₁ and the total packing fraction η of the spherocylinders. In longitude preoriented cases shorter rods tend to accumulate at the poles whereas longer rods occupy central equatorial area of the spherical surface. In lattitude preoriented cases longer rods are predominantly both in the cap and in the equatorial areas and shorter rods are localized in between. A reference situation with a defect-free flat plane does not show any length segregation at similar γ and η. We also develop an Onsager-like density functional theory which is capable to predict length segregation in ordered mixtures. At low density, the results of this theory are in good agreement with the simulation data.