Anomalous polymer dynamics is non-Markovian: memory effects and the generalized Langevin equation formulation
Anomalous polymer dynamics is non-Markovian: memory effects and the generalized Langevin equation formulation
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异常聚合物动力学是非马尔可夫的：记忆效应和广义朗之万方程公式
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发表时间：
2010
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通讯作者：
D. Panja
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作者：
D. Panja
任何一门关于聚合物物理的第一门课程都会告诉我们，聚合物的标记单体的动力学是反常的次扩散，即标记单体的均方位移随着tα的增加而增加，直到聚合物的末端松弛时间α。在Timeτ之后，标记单体的运动变得扩散。聚合物物理中反常动力学的经典例子是单聚合物系统，如幻影Rouse、自回避Rouse、自回避Zimm、旋转、通过膜上狭窄的孔的转移，以及多聚合物系统，如聚合物熔体。在这篇教学论文中，我报告了聚合物系统中所有这些反常动力学的例子都是由统一的广义朗之万方程(GLE)方案中的幂定律记忆核来稳健地刻画的，因此是非马尔可夫的。幂记忆核的指数与聚合物对局部应变的松弛响应有关，由聚合物的平衡统计物理推导而来。然后，通过涨落耗散定理(FDT)从GLE的幂定律存储核中再现了这些体系中标记的聚合物单体的反常动力学。利用这一GLE公式，我进一步证明了由(弱)外加电场对这些聚合物体系造成的漂移的特征也可以从相应的记忆核中得到。
Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as tα for some α < 1 until the terminal relaxation time τ of the polymer. Beyond time τ the motion of the tagged monomer becomes diffusive. Classical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts. In this pedagogical paper I report that all these instances of anomalous dynamics in polymeric systems are robustly characterized by power-law memory kernels within a unified generalized Langevin equation (GLE) scheme, and therefore are non-Markovian. The exponents of the power-law memory kernels are related to the relaxation response of the polymers to local strains, and are derived from the equilibrium statistical physics of polymers. The anomalous dynamics of a tagged monomer of a polymer in these systems is then reproduced from the power-law memory kernels of the GLE via the fluctuation-dissipation theorem (FDT). Using this GLE formulation I further show that the characteristics of the drifts caused by a (weak) applied field on these polymeric systems are also obtained from the corresponding memory kernels.