Scaling of Star Polymers with one to 80 Arms

TL;DR

This paper presents large-scale simulations of star polymers with up to 80 arms, analyzing their scaling behavior and critical exponents using an efficient algorithm on a lattice model.

Contribution

It introduces a novel simulation approach for large star polymers and provides precise estimates of critical exponents for various arm numbers.

Findings

Critical exponents $b3_f$ accurately estimated for up to 80 arms.

Swelling behavior characterized through center-to-end distances.

Efficient chain growth algorithm enables large-scale polymer simulations.

Abstract

We present large statistics simulations of 3-dimensional star polymers with up to $f=80$ arms, and with up to 4000 monomers per arm for small values of $f$. They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor $v<1$. We use this to allow all arms to be attached at the central site, and we use the `magic' value $v=0.6$ to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances), but also the partition sum. The latter gives very precise estimates of the critical exponents $\gamma_f$. For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent $\gamma$.