树枝状大分子和规则超支化聚合物中的陷阱
Trapping in dendrimers and regular hyperbranched polymers
摘要：
树枝状聚合物和规则超支化聚合物是两类经典的大分子，它们分别可以用Cayley树和Vicsek分形来描述。在本文中，我们研究了Cayley树和Vicsek分形与不同的底层几何的陷阱问题，专注于一个特殊的情况下，一个完美的陷阱位于中心节点。对于这两个网络，我们推导出精确的解析公式的平均捕获时间（ATT）的网络规模-平均节点到陷阱的平均首次通过时间在整个网络。所得的封闭解表明，对于Cayley树和Vicsek分形，ATT随体系尺寸的不同表现出不同的标度，这意味着底层结构对聚合物网络的捕获效率起着关键作用.此外，ATT的不同缩放可以允许容易地区分树枝状聚合物和超支化聚合物。
英文摘要：
Dendrimers and regular hyperbranched polymers are two classic families of macromolecules, which can be modeled by Cayley trees and Vicsek fractals, respectively. In this paper, we study the trapping problem in Cayley trees and Vicsek fractals with different underlying geometries, focusing on a particular case with a perfect trap located at the central node. For both networks, we derive the exact analytic formulas in terms of the network size for the average trapping time (ATT)---the average of node-to-trap mean first-passage time over the whole networks. The obtained closed-form solutions show that for both Cayley trees and Vicsek fractals, the ATT display quite different scalings with various system sizes, which implies that the underlying structure plays a key role on the efficiency of trapping in polymer networks. Moreover, the dissimilar scalings of ATT may allow to differentiate readily between dendrimers and hyperbranched polymers.
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