Nonaffine rubber elasticity for stiff polymer networks

We present a theory for the elasticity of cross-linked stiff
polymer networks. Stiff polymers, unlike their flexible
counterparts, are highly anisotropic elastic objects. Similar to
mechanical beams, stiff polymers easily deform in bending, while
they are much stiffer with respect to tensile forces
("stretching"). Unlike in previous approaches, where network
elasticity is derived from the stretching mode, our theory properly
accounts for the soft bending response. A self-consistent effective
medium approach is used to calculate the macroscopic elastic moduli
starting from a microscopic characterization of the deformation
field in terms of "floppy modes"-low-energy bending excitations
that retain a high degree of nonaffinity. The length scale
characterizing the emergent nonaffinity is given by the "fiber
length" l(f), defined as the scale over which the polymers remain
straight. The calculated scaling properties for the shear modulus
are in excellent agreement with the results of recent simulations
obtained in two-dimensional model networks. Furthermore, our theory
can be applied to rationalize bulk rheological data in
reconstituted actin networks.