Institute for Theoretical Physics, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.
J Chem Phys. 2009 Oct 21;131(15):154903. doi: 10.1063/1.3244678.
Using a lattice-based Monte Carlo code for simulating self-avoiding flexible polymers in three dimensions in the absence of explicit hydrodynamics, we study their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected to be statistically independent; nevertheless, we demonstrate that numerically these modes maintain a high degree of statistical independence. Based on high-precision simulation data we put forward an approximate analytical expression for the mode amplitude correlation functions for long polymers. From this, we derive analytically and confirm numerically several scaling properties for self-avoiding flexible polymers, such as (i) the real-space end-to-end distance, (ii) the end-to-end vector correlation function, (iii) the correlation function of the small spatial vector connecting two nearby monomers at the middle of a polymer, and (iv) the anomalous dynamics of the middle monomer. Importantly, expanding on our recent work on the theory of polymer translocation, we also demonstrate that the anomalous dynamics of the middle monomer can be obtained from the forces it experiences, by the use of the fluctuation-dissipation theorem.
使用基于格子的蒙特卡罗代码在不存在显式流体力学的情况下模拟三维无规行走柔性聚合物，我们研究了它们的罗瑟（Rouse）模式。对于无规行走聚合物，罗瑟模式预计不会具有统计独立性；然而，我们证明，在数值上这些模式保持高度的统计独立性。基于高精度模拟数据，我们提出了一个长聚合物模式振幅相关函数的近似解析表达式。由此，我们推导出了无规行走柔性聚合物的几个标度性质的解析结果，并通过数值方法进行了验证，例如（i）实空间末端到末端的距离，（ii）末端到末端向量相关函数，（iii）连接聚合物中间两个相邻单体的小空间向量的相关函数，以及（iv）中间单体的异常动力学。重要的是，在我们最近关于聚合物易位理论的工作的基础上，我们还证明了通过使用涨落耗散定理，中间单体的异常动力学可以通过它所经历的力来获得。
