# Universality of Osmotic Equation of State in Star Polymer Solutions

## TL;DR

This study demonstrates that the osmotic equation of state for star polymer solutions is universal across different arm numbers, by experimentally measuring osmotic pressures and analyzing their scaling behavior.

## Contribution

It provides experimental evidence that star polymers follow a universal osmotic equation of state similar to linear polymers, accounting for arm number effects.

## Key findings

- Universal scaling function describes osmotic pressure in star polymers
- Arm number influences overlap concentration and osmotic pressure
- Gyration radius and interpenetration factor dependencies clarified

## Abstract

We experimentally measure the osmotic pressures of linear polymers and three-, four-, and eight-arm star polymers in a good solvent via membrane osmometry. These results reveal that the osmotic equations of state in the star polymer solutions are universally described by the same scaling function that describes linear polymer solutions. This universality is achieved by canceling increasing overlap concentrations and decreasing osmotic pressure, owing to the increased arm number. We further clarify the molar mass and arm number dependencies of the gyration radius and interpenetration factor, ensuring universality in star polymer solutions.