将polymer链拖到纳米管中并随后释放
Dragging a polymer chain into a nanotube and subsequent release
摘要：
我们提出了一个标度理论和Monte Carlo（MC）模拟结果的柔性聚合物链缓慢拖动一端进入纳米管。我们还描述了当完全限制的链被释放并逐渐离开管时的情况。采用有偏链增长算法--剪枝-富集Rosenbluth方法对自回避格点模型进行了MC模拟。纳米管是一端开口的长通道，其直径$D$远小于溶液中聚合物线圈的尺寸。我们分析了以下特性作为管内链末端位置$x$的函数：限制的自由能，平均端到端距离，被囚禁的单体的平均数量，以及对于$D$的各种值和链中单体的数量，$N$的限制部分的链的平均拉伸。我们表明，当链端被拖到管中的一定的临界距离$x^*$，聚合物进行一阶相变，从而剩余的自由尾部突然吸入管。这是伴随着跳跃的平均大小，被囚禁的片段的数量，并在平均拉伸参数。临界距离的尺度为$x^*\sim ND^{1-1/ν}$。当大约3/4的链条单元被拖进管中时，发生过渡。提出的理论是基于构建的朗道自由能作为一个功能的序参量，提供了一个完整的描述平衡和亚稳态。我们认为，如果被困的链被释放与所有单体允许波动，反向过程中，链离开禁闭顺利发生，没有任何跳跃。最后，我们应用该理论估算了纳米管中处于亚稳态的DNA的寿命。
英文摘要：
We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/ν}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes.
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