Kim Ji-Hyun, Lee Woojin, Sung Jaeyoung, Lee Sangyoub
Department of Chemistry, Seoul National University, Seoul 151-747, South Korea.
J Phys Chem B. 2008 May 15;112(19):6250-8. doi: 10.1021/jp076426i. Epub 2008 Apr 18.
On the basis of the recently developed optimized Rouse-Zimm theory of chain polymers with excluded volume interactions, we calculate the long-time first-order rate constant k(1) for end-to-end cyclization of linear chain polymers. We first find that the optimized Rouse-Zimm theory provides the longest chain relaxation times tau(1) of excluded volume chains that are in excellent agreement with the available Brownian dynamics simulation results. In the free-draining limit, the cyclization rate is diffusion-controlled and k(1) is inversely proportional to tau(1), and the k(1) values calculated using the Wilemski-Fixman rate theory are in good agreement with Brownian dynamics simulation results. However, when hydrodynamic interactions are included, noticeable deviations are found. The main sources of errors are fluctuating hydrodynamic interaction and correlation hole effects as well as the non-Markovian reaction dynamic effect. The physical natures of these factors are discussed, and estimates for the magnitudes of required corrections are given. When the corrections are included, the present theory allows the prediction of accurate k(1) values for the cyclization of finite-length chains in good solvents as well as the correct scaling exponent in the long-chain limit.
基于最近发展的具有排除体积相互作用的链状聚合物的优化Rouse-Zimm理论，我们计算了线性链状聚合物端到端环化的长时间一级速率常数k(1)。我们首先发现，优化的Rouse-Zimm理论给出了排除体积链最长的链松弛时间τ(1)，这与现有的布朗动力学模拟结果非常吻合。在自由排水极限下，环化速率受扩散控制，k(1)与τ(1)成反比，并且使用Wilemski-Fixman速率理论计算的k(1)值与布朗动力学模拟结果吻合良好。然而，当考虑流体动力学相互作用时，会发现明显的偏差。误差的主要来源是波动的流体动力学相互作用和相关空穴效应以及非马尔可夫反应动力学效应。讨论了这些因素的物理本质，并给出了所需校正量的估计。当包含这些校正时，本理论能够预测良溶剂中有限长度链环化的准确k(1)值以及长链极限下正确的标度指数。
