Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections.

Ming Li,Jizeng Wang

doi:10.3390/polym11122050

Abstract

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

Highlights

The statistical behaviors of semiflexible polymers confined in nano- and micro-tubes are fundamental problems in polymer physics and have been investigated both experimentally and theoretically for decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
We theoretically investigated the conformations of wormlike chain (WLC) confined in narrow tubes with arbitrary cross-sections and established a unique force-confinement-extension relation which is quantitatively applicable to nanotubes with any cross-sections
We studied the statistical mechanics behavior of WLCs confined in narrow tubes with arbitrary

Summary

Introduction

The statistical behaviors of semiflexible polymers confined in nano- and micro-tubes are fundamental problems in polymer physics and have been investigated both experimentally and theoretically for decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The conformational behavior of a polymer in a tube is determined by the competition of three interactions: bending, excluded volume interacting, and confining [1]. The polymer is highly extended and lies in the Odijk regime [20,21,22]. At the opposite extreme of large tubes, the polymer falls into the classic de Gennes regime [23]. Between these limits, rich physical regimes have been gradually revealed, which include the extended de Gennes [24,25,26] and the backfolded Odijk regimes, in which the latter was first predicted by Odijk [27,28]

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Results

Conclusion