Star Polymers Confined in a Nanoslit: A Simulation Test of Scaling and Self-Consistent Field Theories

TL;DR

This study uses simulations and theoretical models to analyze the behavior of star polymers confined in nanoslit geometries, comparing predictions from Flory and self-consistent field theories with numerical and molecular dynamics results.

Contribution

It evaluates the accuracy of Flory and SCF theories in predicting star polymer behavior under confinement, highlighting their limitations in free energy estimation.

Findings

Flory and SCF theories correctly predict the scaling of the star's size.

These theories do not reliably estimate the free energy cost of confinement.

The confinement behavior differs between a star in a slit and one interacting with a single wall.

Abstract

The free energy cost of confining a star polymer where $f$ flexible polymer chains containing $N$ monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance $D$ apart is considered, for good solvent conditions. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens-Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent field (SCF) theory yield the correct scaling of the parallel linear dimension of the star with $N$, $f$ and $D$, but cannot be used for estimating the free energy cost reliably. We demonstrate that the same problem occurs already for the confinement of chains in cylindrical tubes. We also briefly discuss the problem of a free or grafted star polymer interacting with a single wall, and show that the dependence of confining force on the functionality of the star is different for a star confined in a nanoslit and a star interacting with a single wall, which is due to the absence of a symmetry plane in the latter case.