Werner Marco, Sommer Jens-Uwe
Leibniz-Institut für Polymerforschung Dresden eV, Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051802. doi: 10.1103/PhysRevE.83.051802. Epub 2011 May 16.
We investigated membrane-like polymer structures of fractal connectivity such as Sierpinski gaskets and Sierpinski carpets applying the bond fluctuation model in three dimensions. Without excluded volume (phantom), both polymeric fractals obey Gaussian elasticity on larger scales determined by their spectral dimension. On the other hand, the swelling effect due to excluded volume is rather distinct between the two polymeric fractals: Self-avoiding Sierpinski gaskets can be described using a Flory-type mean-field argument. Sierpinski carpets having a spectral dimension closer to perfect membranes are significantly more strongly swollen than predicted. Based on our simulation results it cannot be excluded that Sierpinski carpets in athermal solvent show a flat phase on larger scales. We tested the self-consistency of Flory predictions using a virial expansion to higher orders. From this we conclude that the third virial coefficient contributes marginally to Sierpinski gaskets, but higher order virial coefficients are relevant for Sierpinski carpets.
我们在三维空间中应用键涨落模型研究了具有分形连通性的膜状聚合物结构，如谢尔宾斯基垫圈和谢尔宾斯基地毯。在没有排除体积（理想状态）的情况下，两种聚合物分形在由其谱维决定的较大尺度上均服从高斯弹性。另一方面，两种聚合物分形之间由于排除体积引起的溶胀效应相当不同：自回避谢尔宾斯基垫圈可以用弗洛里型平均场理论来描述。谱维更接近完美膜的谢尔宾斯基地毯的溶胀程度明显比预测的要强得多。基于我们的模拟结果，不能排除在无热溶剂中的谢尔宾斯基地毯在较大尺度上呈现平坦相的可能性。我们使用维里展开到更高阶来检验弗洛里预测的自洽性。由此我们得出结论，第三维里系数对谢尔宾斯基垫圈的贡献很小，但高阶维里系数与谢尔宾斯基地毯相关。
