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Register a new userNonaffine rubber elasticity for stiff polymer networks
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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 non-affinity. The length-scale characterizing the emergent non-affinity 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.
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Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.
Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.
The cytoskeleton of eukaryotic cells provides mechanical support and governs intracellular transport. These functions rely on the complex mechanical properties of networks of semiflexible protein filaments. Recent theoretical interest has focused on mesoscopic properties of such networks and especially on the effect of local, non-affine bending deformations on mechanics. Here, we study the impact of local network deformations on the scale-dependent mobility of probe particles in entangled networks of semiflexible actin filaments by high-bandwidth microrheology. We find that micron-sized particles in these networks experience two opposing non-continuum elastic effects: entropic depletion reduces the effective network rigidity, while local non-affine deformations of the network substantially enhance the rigidity at low frequencies. We show that a simple model of lateral bending of filaments embedded in a viscoelastic background leads to a scaling regime for the apparent elastic modulus G(omega) sim omega^{9/16}, closely matching the experiments. These results provide quantitative evidence for how different a semiflexible polymer network can feel for small objects, and they demonstrate how non-affine bending deformations can be dominant for the mobility of vesicles and organelles in the cell.
Due to their unique structural and mechanical properties, randomly-crosslinked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (textit{e.g.} chain-length and end-to-end distributions), we generate disordered phantom networks with different crosslinker concentrations $C$ and initial density $rho_{rm init}$ and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same $C$, which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by $rho_{rm init}$. We rationalise this dependence by employing a generic stress-strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a non-monotonic function of the density of elastically-active strands, and that this behaviour has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly-crosslinked polymer networks, the knowledge of the exact chain conformation distribution is essential for predicting correctly the elastic properties. Finally, we apply our theoretical approach to published experimental data, qualitatively confirming our interpretations.
This paper discusses the elastic behavior of polyelectrolyte networks. The deformation behavior of single polyelectrolyte chains is discussed. It is shown that a strong coupling between interactions and chain elasticity exists. The theory of the complete crosslinked networks shows that the Flory - Rehner - Hypothesis (FRH) does not hold. The modulus contains contributions from the classical rubber elasticity and from the electrostatic interactions. The equilibrium degree of swelling is estimated by the assumption of a $c^{*}$-network.
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