Self-assembly of semiflexible block copolymers: 2D numerical implementation of self-consistent field theory

Abstract

The phase behavior of rod-coil diblock copolymers is investigated in a two-dimensional positional space by using self-consistent field theory (SCFT) based on wormlike chain model. The segment orientation is defined on a unit spherical surface in three-dimensional space with an icosahedron triangular mesh and a finite volume algorithm is borrowed to numerically solve the Laplacian on the sphere. By taking advantage of 2D space calculation, the phase diagram including isotropic, nematic, smectic-A, smectic-C and further appended non-lamellar structures is constructed for the rod-coil diblock copolymers within the framework of Onsager excluded-volume interactions, in which microphase separation and liquid crystalline behavior are driven only by the entropy. Similar to our previous 1D space calculations, although smectic structures occupy large region in the phase diagram, tetragonal packed arrays of ellipse like domains in our 2D space simulations is observed at relatively high coil fractions and strong orientational interactions. We also reexamine the stability of zigzag and confirm it as a thermodynamically metastable structure of rod-coil copolymers in terms of the SCFT free energy.