Dynamics of semiflexible recursive small-world polymer networks

One of the fundamental issues in polymer physics is to reveal the relation between the structures of macromolecules and their various properties. In this report, we study the dynamical properties of a family of deterministically growing semiflexible treelike polymer networks, which are built in an iterative method. From the analysis of the corresponding dynamical matrix we derive the solution for its eigenvalues and their multiplicities, making use of a combined numerical and analytical approach. The eigenvalue spectra allow us to investigate the mechanical relaxation forms in depth for different values of the stiffness parameter. We observe that the dynamics of semiflexible networks is sensitive to the stiffness parameter. Our work paves a way to explore the structures of the highly symmetric polymers and provides a comprehensive understanding of the role of semiflexibility for the regular treelike networks which possess a small-world feature.