Critical behaviour in the nonlinear elastic response of hydrogels

Abstract

In this paper we study the elastic response of synthetic hydrogels to an applied shear stress. The hydrogels studied here have previously been shown to mimic the behaviour of biopolymer networks when they are sufficiently far above the gel point. We show that near the gel point they exhibit an elastic response that is consistent with the predicted critical behaviour of networks near or below the isostatic point of marginal stability. This point separates rigid and floppy states, distinguished by the presence or absence of finite linear elastic moduli. Recent theoretical work has also focused on the response of such networks to finite or large deformations, both near and below the isostatic point. Despite this interest, experimental evidence for the existence of criticality in such networks has been lacking. Using computer simulations, we identify critical signatures in the mechanical response of sub-isostatic networks as a function of applied shear stress. We also present experimental evidence consistent with these predictions. Furthermore, our results show the existence of two distinct critical regimes, one of which arises from the nonlinear stretch response of semi-flexible polymers.

Viscoelastic properties of marginal networks in a solvent

“…The semiflexible synthetic networks of Ref. [49], which have been shown to exhibit critical behavior in their response to stress [50,51], have a value of X ∼ 10 −4 -10 −3 in water, well below the peak value and close to where we expect stiffer networks with low α c . For biopolymer networks consisting of neurofilaments, for example, we estimate X ∼ 10 −2 -10 −1 in water [49], which should show some of the effects of hydrodynamic interactions [see Fig.…”

“…While we have used Hookean springs as model filament's in this work, semiflexible polymers, which make up such real networks, exhibit a more complex response to stress: Hookean springs show only a linear force-extension response, while semiflexible polymers show an initial force extension, followed by a nonlinear stiffening as it is stretched towards its contour length. This effect has been shown to give rise to increasingly complex critical behavior in the stress response of marginal networks [50,51], and an open question we aim to address in future work is how using more realistic model filaments will effect the critical response found here.…”

“…In an experimental system, c f , M f , and M n are typically fixed, while the network concentration c n (i.e., the concentration of polymers in the fluid) can be varied, as in the experimental studies of Refs. [49][50][51]. In these systems, the ratio c n /c f can be in the range ∼10 −3 -10 −1 , while M n /M f can be in the range ∼10 3 -10 5 .…”

Ultra-responsive soft matter from strain-stiffening hydrogels

“…So far, marginal materials have been described only in theory and by simulations 17 and no experimental (bio)polymer network has validated these predictions yet. The PIC gels are the first materials that display some of the predicted characteristics 25 . An additional prediction is a vanishing σ c (also experimentally observed in the PIC hydrogel, Fig.…”

Structural Insights into the Mechanism of Heat‐Set Gel Formation of Polyisocyanopeptide Polymers

“…In our previous research, we described a synthetic ECM‐mimicking system based on a helical ethylene‐glycol‐functionalized polyisocyanopeptide (PIC, Figure S3, Supporting Information) and found that this gel closely resembles the mechanical properties of naturally occurring polymer networks. [ 20–22 ] This synthetic PIC polymer forms soft thermoresponsive heat‐set gels with rheological properties that closely mimic the strain‐stiffening behavior of biogels, [ 23–25 ] such as actin, [ 26 ] collagen, and intermediate filaments. [ 27 ] The benefit of PIC, as a well‐defined synthetic material, is that complex rheological and functional properties of the PIC gels can be easily controlled and tuned to specific needs and applications.…”