Local orientational mobility in regular hyperbranched polymers

Abstract

We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes.

NMR relaxation in semiflexible Vicsek fractals

“…Vicsek fractals [45] (VF) are regular structures that enjoy a growing popularity for the last few decades [44,. In Figure 1 93, respectively, and the VF can be embedded into the three-dimensional space.…”

“…(7). Here, as in our previous work [44] dedicated to the dielectric relaxation of flexible VF (FVF), we consider the relaxation of reorientation of the core segments belonging to different shells, see Fig. 1.…”

“…3) of the relaxation times τ λ . The relaxation spectrum of a VF can be distributed in two groups [44,65]. The first group, the inner spectrum, is related to the local-scale motion and it depends weakly on the macromolecular size.…”

“…The second group of the spectrum can be interpreted as the pulsation (or overall branch relaxation) spectrum of a dendrimer [34][35][36]. However, for FVF the pulsating modes are exited not only for the subbranches but also for the inner parts of the macromolecule [44,52].…”

Dynamics of networks in a viscoelastic and active environment

“…The ensuing set is supplemented at generation g by the eigenvalues 1 with degeneracy ( f − 2)( f + 1) g−1 + 1, f + 1 with degeneracy 1, and 0 with degeneracy 1. 25 Based on eqn (25) one can readily find the behavior of low eigenvalues, 25,48 leading to the respective spectral dimension d VF s = 2 ln( f + 1)/ ln(3 f + 3). 25 As can be readily seen, a huge advantage of VFs is that their spectral dimension can be easily modified by using different values of functionality f .…”