Universal properties of a single polymer chain in slit: Scaling versus MD simulations

TL;DR

This study uses Molecular Dynamics simulations to validate and analyze the static and dynamic properties of a confined polymer chain in a slit, confirming scaling laws and revealing mode coupling effects.

Contribution

It provides comprehensive simulation data that confirm scaling predictions and introduces new insights into the dynamic mode coupling of confined polymers.

Findings

Static properties match analytic models quantitatively.

Bond orientation profiles agree with theoretical predictions.

Normal and lateral relaxation modes are coupled with distinct timescales.

Abstract

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyse their range of validity by means of comprehensive Molecular Dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width $D$ = $4 \div 10$ (in units of the bead radius) and for chain lengths $N=50 \div 300$. We demonstrate that a wide range of static chain properties in normal direction can be described {\em quantitatively} by analytic model - independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation, is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.