Understanding the stiffness of macromolecules: From linear chains to bottle-brushes

The intrinsic local stiffness of a polymer is characterized by its persistence length. However, its traditional definition in terms of the exponential decay of bond orientational correlations along the chain backbone is accurate only for Gaussian phantom-chain-like polymers. Also care is needed to clarify the conditions when the Kratky-Porod wormlike chain model is applicable. These problems are elucidated by Monte Carlo simulations of simple lattice models for polymers in both d = 2 and d = 3 dimensions. While the asymptotic decay of the bond orientational correlations for real polymers always is of power law form, the Kratky-Porod model is found to be applicable for rather stiff (but not too long) thin polymers in d = 3 (but not in d = 2). However, it does not describe thick chains, e.g., bottle-brush polymers, where stiffness is due to grafted flexible side-chains, and the persistence length grows proportional to the effective thickness of the bottle-brush. A scaling description of bottle-brushes is validated by simulations using the bond fluctuation model