Abstract
How the statistical behavior of semiflexible polymer chains may be affected by force stretching and tube confinement is a classical unsolved problem in polymer physics. Based on the Odijk deflection theory and normal mode decomposition in terms of Fourier expansion, we have derived a new compact formula for the extension of a wormlike chain of finite length strongly confined in a tube and simultaneously stretched by an external force. We have also suggested a new deflection length, which together with the force-extension relation is valid for a very extended range of the tube-diameter/persistence-length ratio comparing to the classic Odijk theory. The newly derived formula has no adjustable fitting parameters for the whole deflection regime; in contrast, the classic Odijk length needs different prefactors to fit the free energy and average extension, respectively. Brownian dynamics simulations based on the Generalized Bead-Rod (GBR) model were extensively performed, which justified the theoretical predictions.
Highlights
A variety of theoretical and technical applications [1,2,3,4,5,6,7] are subject to confinement and manipulation of macromolecules, which motivates researchers to explore physical interpretations of how the statistical behavior of polymer chains is affected when they are geometrically confined [8,9,10,11]and mechanically stretched [12,13]
For a sufficiently long polymer chain trapped in a cylindrical tube, studies based on wormlike chain (WLC) theory [14] have revealed various well-known regimes in terms of the ratio between tube diameter (D) and chain persistence length (L p )
We length have which theoretically numerically studied average extensions of tube-confined unified theand concept of Odijk length in freethe energy and geometry understandings, semiflexible polymerand chains under we stretch in the deflection regime
Summary
A variety of theoretical and technical applications [1,2,3,4,5,6,7] are subject to confinement and manipulation of macromolecules, which motivates researchers to explore physical interpretations of how the statistical behavior of polymer chains is affected when they are geometrically confined [8,9,10,11]. In spite of the above progress in the understanding of statistical behavior of confined polymers in the deflection regime, there are still open questions on how the Odijk length can be uniquely and precisely defined, so that this length scale can be valid for a very extended range of the ratio D/Lp , and for the behavior of a polymer chain with finite length and under the combined actions of tube confinement and force stretch, an accurate force-confinement-extension relation without adjustable parameters can be established. In this study, based on the Odijk deflection theory and an accurate expression on the confinement free energy for the chains with finite length by Yang et al [21], we propose a modification to the classic deflection length scale In terms of this modification, we derive the force-confinement-extension relation for the chain with finite length confined in a tube and stretched by an external force. Brownian dynamics simulations based on the Generalized Bead Rod (GBR) model [19] will be extensively performed to justify theoretical predictions
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