Role of architecture in the elastic response of semiflexible polymer and fiber networks

We study the elasticity of cross-linked 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 polymer length, which 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. Understanding these subtle effects is only
possible by going beyond the conventional approach that considers
the response of typical polymer segments only. Instead, we propose
to describe the elasticity in terms of a typical polymer filament
and the spatial distribution of cross-links along its backbone. We
provide theoretical scaling arguments to relate the observed
macroscopic elasticity to the physical mechanisms on the
microscopic and mesoscopic scales.