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首页> 外文期刊>The European physical journal, E. Soft matter >Renormalization group analysis of polymer cyclization with non-equilibrium initial conditions
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Renormalization group analysis of polymer cyclization with non-equilibrium initial conditions

机译：具有非平衡初始条件的聚合物环化的重整化组分析

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We develop a renormalization group approach for cyclizing polymers for the case when chain ends are initially close together (ring initial conditions). We analyze the behavior at times much shorter than the longest polymer relaxation time. In agreement with our previous work (Europhys. Lett. 73, 621 (2006)) we find that the leading time dependence of the reaction rate k(t) for ring initial conditions and equilibrium initial conditions are related, namely k (ring)(t) proportional to t(-delta) and k (eq)(t) proportional to t(1-delta) for times less than the longest polymer relaxation time. Here delta is an effective exponent which approaches delta = 5/4 for very long Rouse chains. Our present analysis also suggests a "sub-leading" term proportional to (ln t)/t which should be particularly significant for smaller values of the renormalized reaction rate and early times. For Zimm dynamics, our RG analysis indicates that the leading time dependence for the reaction rate is k(t) similar to 1/t for very long chains. The leading term is again consistent with the expected relation between ring and equilibrium initial conditions. We also find a logarithmic correction term which we "exponentiate" to a logarithmic form with a Landau pole. The presence of the logarithm is particularly important for smaller chains and, in the Zimm case, large values of the reaction rate.
机译：对于链端最初彼此靠近（环初始条件）的情况，我们开发了一种将环化聚合物的规整化组方法。我们分析的行为有时比最长的聚合物弛豫时间短得多。与我们之前的工作（Europhys.Lett.73，621（2006））一致，我们发现反应速率k（t）对环初始条件和平衡初始条件的超前时间依赖性是相关的，即k（ring）（ t）与t（-delta）成正比，k（eq）（t）与t（1-delta）成正比，其时间小于最长的聚合物弛豫时间。在此，delta是有效的指数，对于很长的Rouse链，其接近delta = 5/4。我们目前的分析还提出了一个正比于（ln t）/ t的“次领先”术语，对于较小的重新归一化反应速率和早期时间值，该术语尤其重要。对于Zimm动力学，我们的RG分析表明，对于非常长的链，反应速率的提前时间依赖性为k（t）类似于1 / t。前导项再次与环和平衡初始条件之间的预期关系一致。我们还找到一个对数校正项，我们用Landau极点“对数”对数形式。对数的存在对于较小的链尤其重要，在Zimm情况下，对反应速率的值较大。

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