A mean field theory for the orientation ordering of tethered rods on patterned surfaces

A mean field theory has been developed to elucidate the orientational behavior of rodlike molecules, with two distinct orientations in the model, tethered onto a patterned surface. The binodal phase diagram of grafted rods can be symmetric and asymmetric, depending on the interactions between rods. By applying an external field to responsive grafted rods, the asymmetric phase diagram can be transformed into a symmetric one. The critical point of the field-induced phase diagram is relevant to the rod-rod interactions.

Phase diagrams of orientation transition (reduced temperature t vs. composition of rods aligned on surface x) can be symmetric or asymmetric depending on the rod-rod interaction Δ. Below the transition points (dash-dotted line), the asymmetric phase diagrams consist of one stable state (solid lines) and one metastable state (dotted lines).