# Universal size and shape ratios for arms in star-branched polymers: theory and mesoscopic simulations

## TL;DR

This paper combines theoretical models and mesoscopic simulations to analyze how the size and shape of arms in star-branched polymers change with the number of arms, revealing universal ratios and behaviors.

## Contribution

It introduces a theoretical framework and simulation validation for size and shape ratios of star polymer arms across different arm numbers.

## Key findings

- Qualitative agreement between theory and simulations on arm size and shape trends.
- Higher-order theoretical approximations needed for quantitative accuracy.
- Universal size and shape ratios identified for star polymer arms.

## Abstract

Star polymer undergoes a transformation from a group of loosely coupled chains at low number of arms to a dense hairy colloid at their high number. This change affects solubility, aggregation and rheological behavior and is of much practical interest. We study the range of size and shape properties of the star molecule and of its individual arms upon this transformation. Theoretical calculations are based on a continuous chain model and are performed in the first order in $\epsilon=4-d$. Computer simulations are done by the dissipative particle dynamics and in part by Monte Carlo method and the results demonstrate very good agreement with the selected set of properties known from the previous simulations. Theory and simulations provide qualitatively similar trends upon increase of the number of arms, but higher order of approximation is required in a theory to achieve a good quantitative agreement.