Abstract
We briefly review the recent developments in the theory of individual semiflexible filaments, and of a crosslinked network of such filaments, both permanent and transient. Starting from the free energy of an individual semiflexible chain, models on its force-extension relation and other mechanical properties such as Euler buckling are discussed. For a permanently crosslinked network of filaments, theories on how the network responds to deformation are provided, with a focus on continuum approaches. Characteristic features of filament networks, such as nonlinear stress-strain relation, negative normal stress, tensegrity, and marginal stability are discussed. In the new area of transient filament network, where the crosslinks can be dynamically broken and re-formed, we show some recent attempts for understanding the dynamics of the crosslinks, and the related rheological properties, such as stress relaxation, yield stress and plasticity.
Highlights
What is today routinely called “semiflexible filaments”, 30 years ago was more frequently referred to as polymer chains with high bending modulus
When a semiflexible filament is highly stretched, its end-to-end factor will be close to unity, and an approximation can be implemented in Equation (8): 1 − x2 ' 2(1 − x ), making the force-extension relation at x > x0 : f (x)
Parameters used here are a = 10−3 L, c = 0.4 and x0 = 0.8. This is a brief overview of the current state of theoretical understanding of physical properties of semiflexible filaments and their crosslinked networks, permanent or transient
Summary
What is today routinely called “semiflexible filaments”, 30 years ago was more frequently referred to as polymer chains with high bending modulus. Very soon people realized that adding the bending rigidity to this ideal chain would lead to many interesting theoretical results and analogies, and would better describe many actual polymer chains and filaments. Our aim is to examine the properties of an isolated filament (subject to various external forces and extensions), and proceed to the crosslinked networks of such filaments, in all cases remaining in the regime of low total volume fraction This is closely corresponding to many biological scaffolding systems, which underpins the current active interest in this class of materials
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