Statistical and Biological Physics
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Polymer Networks

Fibrous and cellular materials are ubiquitious in nature. Prominent examples are found in biology such as bone, wood and the cytoskeleton of cells. The elastic properties of these biomaterials result from a subtle interplay between the architecture of the network and the elastic properties of its building blocks.

In these networks highly non-affine deformations as well as inhomogeneous distribution of stresses have been found. Few is known, however, about the actual nature of the deformations present. The expression "non-affine" is exclusively used to signal the absence of affine deformations that are used for example in the theory of rubber elasticity. This work tries to fill this gap by characterizing in detail the non-affine deformation field present in fibrous networks. By relating non-affinity to the low-energy excitations we can, starting from a microscopic picture, calculate the macroscopic elastic moduli both in a scaling theory and a self-consistent effective medium theory.

In a second study [2] we highlight the very special properties of networks of thermally fluctuating stiff polymers. As compared to their purely mechanical counterparts, it is shown that these thermal networks have a qualitatively different elastic response. By accounting for the entropic origin of the single-polymer elasticity, the networks acquire a strong susceptibility to polydispersity and structural randomness that is completely absent in athermal models.

In extensive numerical studies we systematically vary the architecture of the networks and identify a wealth of phenomena that clearly show the strong dependence of the emergent macroscopic moduli on the underlying mesoscopic network structure. In particular, we highlight the importance of the full polymer length that to a large extent controls the elastic response of the network, surprisingly, even in parameter regions where it does not enter the macroscopic moduli explicitly. We provide theoretical scaling arguments to relate the observed macroscopic elasticity to the physical mechanisms on the microscopic and the mesoscopic scale.

Literature:

  1. C. Heussinger and E. Frey,
    Floppy Modes and Nonaffine Deformations in Random Fiber Networks,
    Phys. Rev. Lett. 97, 105501 (2006)
  2. C. Heussinger and E. Frey,
    Stiff Polymers, Foams and Fiber Networks,
    Phys. Rev. Lett. 96, 017802 (2006) [arXiv:cond-mat/0503359]
  3. C. Heussinger and E. Frey,
    The Role of Architecture in the Elastic Response of Semiflexible Polymer and Fiber Networks,
    [arXiv:cond-mat/0512557]