Modeling conjugated polymers as ribbon-like chains

The conformational statistics of conjugated polymers (CP) and ladder polymers are often described using the worm-like chain (WLC) statistics. The WLC model captures the bending stiffness but neglects the anisotropy of CP monomers. Here, we develop a ribbon-like chain (RLC) model that generalizes the WLC model by explicitly incorporating the anisotropic bending stiffness and the finite twist stiffness. The free-chain conformational statistics are fully solved, that predict the correlations of monomeric orientations along the CP backbone, the raidus of gyrations, the end-to-end distance etc. Three persistence lengths are introduced, accouting for the relaxation of the orientations along the two normal directions and the tangent direction, respectively. The regimes of the conformational statistics are discussed that include the 2D WLC and 3D WLC model as limiting cases. A simple method for parameterizing the model using molecular simulations is proposed and demonstrated for a few representative polymers. The framework may serve as a starting point for systematically building coarse-grained models of CPs.