The effective torque on patchy spheres nearby a flat substrate induced by infinitely thin rods with adsorptive ends

The system studied here is the mixture of infinitely thin rods and a patchy sphere nearby a flat substrate. The adsorption between the rod ends and the patch can induce an effective torque on the sphere, which are studied by the Monte Carlo method. At the proper patch angle, the effective torque makes the patchy surface face away from the substrate, and the effective interaction between the bare surface and the substrate is attractive at the same time. The effective torque strengthens with the approach between the sphere and the substrate, while first strengthens and then weakens with the increase of the included angle between the axis of the patch and the normal of the substrate. The relationships between the effective torque and the adsorptive strength, the patch angle and the diameter of the sphere have also been studied. The effective torque discussed here may play a role in the biological lock-and-key mechanism and be used to adjust the two-dimensional self-assembly of the colloidal particles with the anisotropic surface.