半刚性规则超支化聚合物的动力学。

Dynamics of semiflexible regular hyperbranched polymers.

机构信息

Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany.

出版信息

J Chem Phys. 2013 Jan 21;138(3):034904. doi: 10.1063/1.4775584.

Abstract

We study the dynamics of semiflexible Vicsek fractals (SVF) following the framework established by Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)], a scheme which allows to model semiflexible treelike polymers of arbitrary architecture. We show, extending the methods used in the treatment of semiflexible dendrimers by Fürstenberg et al. [J. Chem. Phys. 136, 154904 (2012)], that in this way the Langevin-dynamics of SVF can be treated to a large part analytically. For this we show for arbitrary Vicsek fractals (VF) how to construct complete sets of eigenvectors; these reduce considerably the diagonalization problem of the corresponding equations of motion. In fact, such eigenvector sets arise naturally from a hierarchical procedure which follows the iterative construction of the VF. We use the obtained eigenvalues to calculate the loss moduli G(")(ω) of SVF for different degrees of stiffness of the junctions. Finally, we compare the results for SVF to those found for semiflexible dendrimers.

摘要

我们研究了 Dolgushev 和 Blumen 所建立的框架下的半刚性 Vicsek 分形（SVF）的动力学，该方案允许对任意结构的半刚性树状聚合物进行建模。我们通过扩展 Fürstenberg 等人在处理半刚性树状聚合物时使用的方法，展示了这种方法可以在很大程度上对 SVF 的朗之万动力学进行分析。为此，我们为任意 Vicsek 分形（VF）展示了如何构建完整的本征向量集；这些向量集极大地简化了相应运动方程的对角化问题。事实上，这样的本征向量集自然地源于一种层次化的过程，该过程遵循 VF 的迭代构造。我们利用得到的本征值来计算不同连接刚度下 SVF 的损耗模量 G(")(ω)。最后，我们将 SVF 的结果与半刚性树状聚合物的结果进行了比较。