Self-Consistent Field Theory for Smectic Ordering of Semiflexible Homo-polymers
A model of liquid crystalline homopolymers using self-consistent field theory (SCFT) for semiflexible spherocylinder-shaped particles is developed that can form the isotropic (I) phase, nematic (N) phase and smectic-A phase (SmA). As in previous works by Chen and Du ̈chs et al. the excluded volume interaction based on a second virial approximation (SVA) due to Onsager is employed, which is able to stabilize the N phase for wormlike chains. To stabilize the SmA phase, the excluded volume interaction between cylindrical segments and the terminal end segments is included, as in Hidalgo et al. However Hidalgo et al. contains two limitations, which are addressed in this study: Their numerical algorithm cannot obtain solutions for strongly ordered states, which occur for molecular length to diameter ratio L/D > 10. Also, the phase boundaries occur for packing fractions that are too high, due to their use of SVA. A Crank-Nicolson type method applied to the orientations is developed, having better convergence for strongly ordered states, and obtains solutions for L/D as high as ⇠ 55 for the N-SmA transition. A technique based on the method of Parsons and Lee is also implemented which goes beyond the SVA, successfully predicting the N-SmA boundary very close to that predicted by the computer simulations by Bohuis and Frenkel. N ordering and SmA ordering are looked at in some detail and comparison to Monte Carlo simulations and measurements on virus particles are made. The stability of rigid chains in the SmA phase is predicted to increase with increasing L/D. However, the SmA phase loses its stability for only a small amount of flexibility due to the relative contributions of the segment-segment and end-segment intermolecular interactions.