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Self-organized stiffness in regular fractal polymer structures

Marco Werner and Jens-Uwe Sommer

  • Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Strasse 6, 01069 Dresden, Germany and Technische Universität Dresden, Institute of Theoretical Physics, 01069 Dresden, Germany

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Phys. Rev. E 83, 051802 – Published 16 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.051802

Abstract

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.

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      Phys. Rev. E 83, 051802– Published 16 May, 2011
      • Received 28 January 2011

      ©2011 American Physical Society

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