Trapping in dendrimers and regular hyperbranched polymers

TL;DR

This study analyzes how the structure of dendrimers and hyperbranched polymers affects trapping efficiency by deriving exact formulas for average trapping time in their models, revealing structural impacts on trapping dynamics.

Contribution

The paper provides the first exact analytical formulas for average trapping time in Cayley trees and Vicsek fractals, highlighting structural effects on trapping efficiency.

Findings

ATT scales differently in Cayley trees and Vicsek fractals

Structural differences influence trapping efficiency

Formulas enable differentiation between polymer types

Abstract

Dendrimers and regular hyperbranched polymers are two classic families of macromolecules, which can be modeled by Cayley trees and Vicsek fractals, respectively. In this paper, we study the trapping problem in Cayley trees and Vicsek fractals with different underlying geometries, focusing on a particular case with a perfect trap located at the central node. For both networks, we derive the exact analytic formulas in terms of the network size for the average trapping time (ATT)---the average of node-to-trap mean first-passage time over the whole networks. The obtained closed-form solutions show that for both Cayley trees and Vicsek fractals, the ATT display quite different scalings with various system sizes, which implies that the underlying structure plays a key role on the efficiency of trapping in polymer networks. Moreover, the dissimilar scalings of ATT may allow to differentiate readily between dendrimers and hyperbranched polymers.