Entropic force of cone-tethered polymers interacting with a planar surface

TL;DR

This study uses Monte Carlo simulations to analyze the entropic force of cone-tethered polymers near a flat surface, testing theoretical predictions and exploring effects of multiple polymers on force behavior.

Contribution

It provides the first detailed simulation-based validation of the entropic force predictions for cone-tethered polymers interacting with a surface, including multiple polymer cases.

Findings

Simulation results largely agree with theoretical predictions.

Multiple tethered polymers exert roughly constant entropic force per polymer.

Small quantitative discrepancies highlight limitations of current theoretical approximations.

Abstract

Computer simulations are used to characterize the entropic force of one or more polymers tethered to the tip of a hard conical object that interact with a nearby hard flat surface. Pruned-enriched-Rosenbluth-method (PERM) Monte Carlo simulations are used to calculate the variation of the conformational free energy, $F$, of a hard-sphere polymer with respect to cone-tip-to-surface distance, $h$, from which the variation of the entropic force, $f\equiv |dF/dh|$, with $h$ is determined. We consider the following cases: (1) a single freely-jointed tethered chain, (2) a single semiflexible tethered chain, and (3) several freely-jointed chains of equal length each tethered to the cone tip. The simulation results are used to test the validity of a prediction by Maghrebi et al. (EPL, 96, 66002(2011); Phys. Rev. E 86, 061801 (2012)) that $f\propto (\gamma_\infty-\gamma_0) h^{-1}$, where $\gamma_0$ and $\gamma_\infty$ are universal scaling exponents for the partition function of the tethered polymer for $h=0$ and $h=\infty$, respectively. The measured functions $f(h)$ are generally consistent with the predictions, with small quantitative discrepancies arising from the approximations employed in the theory. In the case of multiple tethered polymers, the entropic force per polymer is roughly constant, which is qualitatively inconsistent with the predictions.