Static and dynamic scaling of semiflexible polymer chains—a molecular dynamics simulation study of single chains and melts

Abstract

A molecular dynamics study of the effect of increasing molecular chain stiffness on the dynamic properties of single linear chains and polymer melts is presented. The chain stiffness is controlled by a bending potential. By means of a normal mode analysis the systematic crossover behavior of coarse-grained linear polymer systems from Rouse modes to bending modes with increasing mode number p is presented systematically for the first time via simulation data. The magnitude and the onset of the region where crossover behavior occurs is investigated in dependence of a systematic variation of the chains’ persistence lengths. For long wavelength modes the well-known p−2 behavior is observed which represents the Rouse scaling, whereas for the bending modes one observes a distinct p−4 scaling of the mean square mode amplitudes and the relaxation times. Additionally, the effect of this crossover behavior on the monomer dynamics given by their mean square displacements is investigated. The findings are contrasted with previous simulation studies of semiflexible chain behavior and it is shown that those studies—due to too small persistence lengths Lp—were actually limited to the crossover regime where both, Rouse and bending modes contribute to the chain dynamics, and no distinct p−4 scaling can be observed. Using an expansion of the monomer position vector, a simple theory of the observed scaling behavior is proposed which allows for deriving analytic expressions that describe the presented simulation data very well.