Conformation statistics of ideal ribbon-like chains

The conformation statistics of polymers with stiff backbones, such as ladder polymers and conjugated polymers, can not be adequately captured by the worm-like chain model. These molecules have anisotropic bending stiffness and their conformations depend on how easily they can be twisted. By developing and solving the Fokker-Planck equation for the ribbon-like chain (RLC) model, we show that three independent persistence lengths can be identified, corresponding to the relaxation of tantent, normal, and binormal directions of "ribbon-like" monomers. Furthermore, as contour length grows, the chain conformation is shown to progresses from being rod-like, to deflected 2-d random walk, and finally to 3-d random walk, the crossovers determined by the relative values of bending and twist stiffness. The parametrization of real polymers against the RLC model is also presented.