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- The Journal of Physical Chemistry B, 112 (19), 2008, pp 6250–6258
Ji-Hyun Kim ,‡ Woojin Lee ,‡ Jaeyoung Sung ,*§ and Sangyoub Lee *‡
Department of Chemistry, Seoul National University, Seoul 151-747, South Korea, and Department of Chemistry, Chung-Ang University, Seoul 156-756, South Korea
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 k1 for end-to-end cyclization of linear chain polymers. We first find that the optimized Rouse-Zimm theory provides the longest chain relaxation times τ1 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 k1 is inversely proportional to τ1, and the k1 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 k1 values for the cyclization of finite-length chains in good solvents as well as the correct scaling exponent in the long-chain limit.