Polymers confined to a narrow channel are subject to strong entropic forces that tend to drive the molecules apart. In this study, we use Monte Carlo computer simulations to study the segregation behavior of two flexible hard-sphere polymers under confinement in a cylindrical channel. We focus on the effects of using polymers of different lengths. We measure the variation of the conformational free energy, $F$, with the center-of-mass separation distance, $\lambda$. The simulations reveal four different separation regimes, characterized by different scaling properties of the free energy with respect to the polymer lengths and the channel diameter, $D$. We propose a regime map in which the state of the system is determined by the values of the quantities $N_2/N_1$ and $\lambda /(N_1+N_2)D^{-\beta }$, where $N_1$ and $N_2$ are the polymer lengths, and where $\beta \approx 0.64$. The observed scaling behavior of $F\left(\lambda \right)$ in each regime is in reasonable agreement with predictions using a simple theoretical model. In addition, we use MC dynamics simulations to study the segregation dynamics of initially overlapping polymers by measurement of the incremental mean first-passage time with respect to $\lambda$. For systems characterized by a wide range of $\lambda$ in which a short polymer is nested within a longer one, the segregation dynamics are close to that expected for two noninteracting one-dimensional random walkers undergoing unbiased diffusion. When the free-energy gradient is large, segregation is rapid and characterized by out-of-equilibrium effects.

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两种不同长度的通道受限聚合物的自由能和偏析动力学

限制在狭窄通道内的聚合物会受到强大的熵力的作用，这往往会使分子分开。在这项研究中，我们使用蒙特卡洛计算机模拟来研究两种弹性硬球聚合物在圆柱状通道内的偏析行为。我们专注于使用不同长度的聚合物的效果。我们测量构象自由能的变化，$F$，以质心分离距离 $\lambda$。模拟显示了四种不同的分离方式，其特征在于自由能相对于聚合物长度和通道直径的不同缩放特性，$d$。我们提出一个状态图，其中系统的状态由数量的值确定${ñ}_2/{ñ}_{\mathrm{1个}}$ 和 $\lambda /（{ñ}_{\mathrm{1个}}+{ñ}_2）d^{-\beta }$，在哪里 ${ñ}_{\mathrm{1个}}$ 和 ${ñ}_2$ 是聚合物的长度，以及 $\beta \approx 0.64$。观察到的结垢行为$F（\lambda ）$在每个方案中，使用简单的理论模型与预测合理地吻合。此外，我们使用MC动力学模拟通过测量相对于的增量平均首次通过时间来研究初始重叠聚合物的偏析动力学。$\lambda$。对于具有以下特点的系统$\lambda$其中一种较短的聚合物嵌套在一个较长的聚合物中，其分离动力学接近于两个无干扰的一维随机游走器进行无偏扩散的预期。当自由能梯度大时，分离迅速并且具有不平衡效应的特征。