A density functional theory of chiral block copolymer melts

A density functional theory is developed for the diblock copolymer melt, where one block contains the segment orientation dependent chiral interaction. In addition to the standard (scalar) pair interaction between the two types of monomers, the chiral block has the additional pairwise interaction, which is linear in the tangent vectors of the segments. We construct a density functional, which contains both the scalar density field and the vector chain alignment field. The quadratic part of the density functional comes from the mean field theory of the microscopic model, whereas the fourth order terms are introduced phenomenologically in the spatially local form. From the stability analysis of this model, we find that the additional chiral interaction shifts the order-disorder transition, which is consistent with the behavior of experimental system. Further numerical calculation reveals a new metastable chiral helical cylinder structure, which is similar to the one found experimentally. Another similar metastable structure but with zigzag modulation is also observed. As the helical and zigzag structures disappear when the chiral interaction is switched off, we understand that the chiral effect is the driving force for the formation of these exotic metastable structures.