Advancing the computational methodology of rigid rod and semiflexible polymer systems: A new solution to the wormlike chain model with rod-coil copolymer calculations

Abstract

A wormlike chain model for rod type blocks in a rod-coil diblock copolymer is implemented in the self-consistent field theory (SCFT) formalism. A pseudo-spectral method is used to solve for the single-chain partition function of this copolymer system. Orientation degrees of freedom are discretized using Lebedev sphere rules such that orientation integrations are carried out through a Lebedev quadrature, an approach not used previously in tandem with the pseudo-spectral method. Phase behavior in the rigid-rod limit as a function of rod segment volume fraction, Flory–Huggins interaction parameter χ, degree of polymerization N, and rod contour length ratio β are examined in detail in one and two dimensions. Examples extending to three dimensions are included. Semiflexible behavior via the rod bending rigidity κ is explored. An approximation is used for rigid-rods that do not need spherical harmonics leading to increased speed in finding equilibrium morphologies. The results show that standing vertical structures may be more easily produced with rigid-rod blocks compared to coil-coil lamellae, an important feature in nanolithographic applications. Suggestions are made for using the model in future molecular orientation studies where the model can be used with inverse search methods to measure the values of the model parameters for the real systems. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 29–39.