Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy F is measured as a function of λ, the end-to-end distance of the polymer. In the case of a flexible linear polymer, F(λ) is a linear function in the folded regime with a gradient that scales as f ≡ |dF/dλ| ∼ N⁰D^{–1.20±0.01} for a tube of diameter D and a polymer of length N. This is close to the prediction f ∼ N⁰D^–1 obtained from simple scaling arguments. The discrepancy is due in part to finite-size effects associated with the de Gennes blob model. A similar discrepancy was observed for the folding of a single arm of a three-arm star polymer. We also examine backfolding of a semiflexible polymer of persistence length P in the classic Odijk regime. In the overlap regime, the derivative scales f ∼ N⁰D^{–1.72±0.02}P^{–0.35±0.01}, which is close to the prediction f ∼ N⁰D^–5/3P^–1/3 obtained from a scaling argument that treats interactions between deflection segments at the second virial level. In addition, the measured free energy cost of forming a hairpin turn is quantitatively consistent with a recent theoretical calculation. Finally, we examine the scaling of F(λ) for a confined semiflexible chain in the presence of an S-loop composed of two hairpins. While the predicted scaling of the free energy gradient is the same as that for a single hairpin, we observe a scaling of f ∼ D^{–1.91±0.03}P^{–0.36±0.01}. Thus, the quantitative discrepancy between this measurement and the predicted scaling is somewhat greater for S-loops than for single hairpins.

中文翻译：

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圆柱约束下折叠聚合物的自由能

蒙特卡洛计算机模拟用于研究局限在长圆柱管中的折叠聚合物的构象自由能。将该聚合物建模为硬球链。它的构象自由能F是λ的函数，它是聚合物的端到端距离。以灵活的线性聚合物的情况下，˚F（λ）处于折叠制度的线性函数的梯度即秤作为˚F ≡| d ˚F /Dλ| 〜Ñ ⁰ d ^-1.20±0.01对直径的管d和长度的聚合物Ñ。这是接近预测˚F〜Ñ ⁰ d ^-1从简单的缩放参数获得。差异部分归因于与de Gennes blob模型相关的有限大小效应。对于三臂星形聚合物的单臂折叠，观察到相似的差异。我们还研究了经典Odijk体制中持久性长度为P的半柔性聚合物的反折。在重叠体制，该衍生物秤˚F〜Ñ ⁰ d ^-1.72±0.02 P ^-0.35±0.01，这是接近预测˚F〜Ñ ⁰ d ^-5/3 P ^-1/3从缩放参数获得，该缩放参数在第二维里尔水平上处理偏转段之间的相互作用。另外，测得的形成发夹匝的自由能成本在数量上与最近的理论计算是一致的。最后，我们检查在存在由两个发夹组成的S形环的情况下，约束半柔性链的F（λ）的缩放比例。虽然自由能梯度的预测定标是相同的，对于一个单一的发夹，我们观察到的缩放˚F〜d ^-1.91±0.03 P ^-0.36±0.01。因此，对于S环，此测量结果与预测缩放比例之间的定量差异要比单个发夹要大一些。