Nonaffine rubber elasticity for stiff polymer networks

Abstract

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.

Stiffest elastic networks

“…beams must be collinear in pairs. In agreement with Maxwell's criterion [9,[25][26][27], it is known that twodimensional stiff networks must have a node connectivity more than or equal to 4. But in addition, our analysis specifies what must be the geometry of the junctions ( figure 5).…”

Actin Mechanics and Fragmentation

“…by myosin motors) (74). Strain stiffening in networks composed of linearly elastic filaments/bundles can also arise from geometric effects (75,76).…”

Nonlinear effective-medium theory of disordered spring networks

“…One characteristic these varied systems share is their particular sensitivity to external stress; in densely jammed systems, for instance, the external pressure can cause the system to transition between rigid and floppy states [1,2,[6][7][8][9], while reconstituted biological filamentous networks exhibit dramatic strain stiffening under shear [10][11][12][13]. This remarkable nonlinear elastic behavior of fiber networks has attracted much attention in the last decade; in addition to the physiological relevance of this nonlinear elastic response for cells and many biological tissues [14,15], these systems are also interesting from a fundamental perspective, owing to their unusual nonlinear materials properties [11][12][13][16][17][18][19][20][21][22][23][24], including negative normal stresses [25]. Understanding how their intrinsic disordered nature affects the elastic deformations is required for a complete theoretical description of their nonlinear mechanical behavior.…”

“…Understanding how their intrinsic disordered nature affects the elastic deformations is required for a complete theoretical description of their nonlinear mechanical behavior. Although structural disorder and inhomogeneous deformations clearly play a central role in jamming systems [2,7,26], their precise role in the nonlinear behavior of fibrous networks remains unclear [7,16,19,20,24,27,28].…”