Dynamics of end-linked star polymer structures

TL;DR

This paper analyzes the eigenvalue spectrum of end-linked star polymer networks using an exact real-space renormalization approach, revealing insights into their dynamics and mechanical properties across various topologies.

Contribution

It provides an exact analytical method to determine the eigenvalue spectrum of star polymer networks, including complex topologies like dendrimers, using a generalized Gaussian model.

Findings

Eigenvalue spectrum comprises two parts: one from the renormalized network, one from spacer motion.

Analytical spectra for copolymeric dendrimers are calculated.

Results include storage and loss moduli for specific polymer structures.

Abstract

In this work we focus on the dynamics of macromolecular networks formed by end-linking identical polymer stars. The resulting macromolecular network can then be viewed as consisting of spacers which connect branching points (the cores of the stars). We succeed in analyzing exactly, in the framework of the generalized Gaussian model, the eigenvalue spectrum of such networks. As applications we focus on several topologies, such as regular networks and dendrimers; furthermore, we compare the results to those found for regular hyperbranched structures. In so doing, we also consider situations in which the beads of the cores differ from the beads of the spacers. The analytical procedure which we use involves an exact real-space renormalization, which allows to relate the star-network to a (much simpler) network, in which each star is reduced to its core. It turns out that the eigenvalue spectrum of the star-polymer structure consists of two parts: One follows in terms of polynomial equations from the relaxation spectrum of the corresponding renormalized structure, while the second part involves the motion of the spacer chains themselves. Finally, we show exemplarily the situation for copolymeric dendrimers, calculate their spectra, and from them their storage and the loss moduli.