Fluidization of Transient Filament Networks

Abstract

Stiff or semiflexible filaments can be crosslinked to form a network structure with unusual mechanical properties, if the crosslinks at network junctions have the ability to dynamically break and reform. The characteristic rheology, arising from the competition of plasticity from the transient crosslinks and nonlinear elasticity from the filament network, has been widely tested in experiments. Though the responses of a transient filament network under small deformations are relatively well understood by analyzing its linear viscoelasticity, a continuum theory adaptable for finite or large deformations is still absent. Here we develop a model for transient filament networks under arbitrary deformations, which is based on the crosslink dynamics and the macroscopic system tracking the continuously reshaping reference state. We apply the theory to explain the stress relaxation, the shape recovery after instant deformation, and the necking instability under a ramp deformation. We also examine the role of polydispersity in the mesh size of the network, which leads to a stretched exponential stress relaxation and a diffuse elastic-plastic transition under a ramp deformation. Although dynamic crosslinks are taken as the source of the transient network response, the model can be easily adjusted to incorporating other factors inducing fluidization, such as filament

Origin of Slow Stress Relaxation in the Cytoskeleton

“…[15] and a large body of follow-up work on cell rheology [20][21][22][23][24][25], the shear modulus of cells is characterized by a shear modulus that increases as a weak power-law of frequency, with exponents as low as 0.1, for which the term soft glassy rheology has been used. Interestingly, in contrast with prior models of soft glassy rheology of cytoskeletal networks [16][17][18], here we show that exponents below 0.5 are only observed in the nonlinear regime. We show that the time-and stress-dependent response of actin networks is consistent with a model that accounts for both the nonlinear stiffening [7,8] and transient crosslinking [13] of semi-flexible polymers.…”

“…Recently, Ref. [18] proposed a model for the nonlinear response of transient semiflexible networks, but no specific relationship between the stress and the exponent governing the time dependence was predicted.…”

Elasticity and Relaxation in Full and Partial Vitrimer Networks

“…23,24 Physically-bonded transient networks are well understood theoretically. [25][26][27][28][29][30][31] Here the crosslink number is not constant, and so the breakage and the re-forming of the crosslinks are treated as two independent processes. The characteristic property of vitrimers, that the number of covalent bonds remains constant at all times, not only helps to maintain the integrity of the material at a high temperature, but also keeps the effect of non-affine deformation almost unchanging during deformation, as the non-affine effects are usually local and only depend on the networks connectivity, which is strictly conserved in vitrimers.…”

A review on recent development of theoretical modeling of hydrogel phase behavior subject to mechanics and multiphysics coupled effects

“…Recently, Meng et al developed a continuum theory to model the rheology of hydrogels containing reversible network junctions [51][52][53], by which three regimes of the polymeric network, elastic, plastic flow, and a necking instability region separating the two, were illustrated to respond to a ramp extension with a constant strain rate. Zhao et al proposed a Maxwell model to simulate the viscoelastic behavior ideal reversible polymer networks [54] with a single Maxwell element of a spring and a dashpot in series, which was applied to measure and control the network behaviors associated with viscoelasticity, such as kinetics of crosslinks, instantaneous shear modulus, and relaxation time.…”