Hyperbranched polymer stars with Gaussian chain statistics revisited

TL;DR

This paper revisits the conformational properties of hyperbranched polymer stars with Gaussian chain statistics, analyzing their scaling behavior and effects of interactions through numerical methods.

Contribution

It provides a numerical analysis of hyperbranched polymer stars with Gaussian statistics, comparing different star architectures and discussing the validity of the Gaussian approximation.

Findings

Scaling laws for fractal dimensions $d_f=3$ and $d_f=2.5$ are characterized.

Power-law and self-similar stars exhibit different conformational properties.

Weak excluded volume interactions influence the Gaussian regime in dense solutions.

Abstract

Conformational properties of regular dendrimers and more general hyperbranched polymer stars with Gaussian statistics for the spacer chains between branching points are revisited numerically. We investigate the scaling for asymptotically long chains especially for fractal dimensions $d_f = 3$ (marginally compact) and $d_f = 2.5$ (diffusion limited aggregation). Power-law stars obtained by imposing the number of additional arms per generation are compared to truly self-similar stars. We discuss effects of weak excluded volume interactions and sketch the regime where the Gaussian approximation should hold in dense solutions and melts for sufficiently large spacer chains.