Strain Stiffening and Negative Normal Force of Agarose Hydrogels.

Lahja Martikainen,Kia Bertula,Olli Ikkala,Matti Turunen

doi:10.1021/acs.macromol.0c00601

Abstract

Inspired by the specific strain stiffening and negative normal force phenomena in several biological networks, herein, we show strain stiffening and negative normal force in agarose hydrogels. We use both pre-strain and strain amplitude sweep protocols in dynamic rheological measurements where the gel slip was suppressed by the in situ gelation in the cross-hatched parallel plate rheometer geometry. Within the stiffening region, we show the scaling relation for the differential modulus K ∝ σ1, where σ is stress. The strain at the onset of stiffening is almost constant throughout the concentration range. The gels show negative apparent normal stress difference when sheared as a result of the gel contraction. The pore size of the hydrogel is large enough to allow water to move with respect to the network to balance the pressure difference caused by the hoop stress. The rheological analysis together with scanning electron microscopy suggests that the agarose gels can be described using subisostatic athermal network models where the connectivity dictates the stiffening behavior. Therefore, the simple agarose gels appear to capture several of the viscoelastic properties, which were previously thought to be characteristic to biological protein macromolecules.

Highlights

Fibrillar hydrogels derived from biological tissues show two interesting nonlinear mechanical behaviors: strain stiffening and negative normal stress difference when shear is applied.[1]Models and simulations have suggested that both phenomena arise either from the specific mechanical properties of the individual fibrils or from the network topology.[2]
We investigated strain stiffening and negative normal force in agarose hydrogels using pre-strain and strain amplitude sweep protocols where the slip was suppressed by in situ gelation in the cross-hatched parallel plate rheometer geometry
Our main findings suggest that the agarose hydrogels can be described as subisostatic athermal networks

Summary

Introduction

Fibrillar hydrogels derived from biological tissues show two interesting nonlinear mechanical behaviors: strain stiffening and negative normal stress difference when shear is applied.[1]Models and simulations have suggested that both phenomena arise either from the specific mechanical properties of the individual fibrils or from the network topology.[2]. The neo-Hookean model can already explain the stiffening of the elastic fibrils in tension, yet it cannot capture the strain stiffening in shear deformation at rather small strains or the negative normal force.[18] In shear deformation, part of the fibrils are stretched and the others are contracted. The overall strain stiffening can be observed only if the effects of the fibrils, which are contracting and stretching, do not cancel each other out and the fibrils resist more extension than compression. Another main reason for stiffening is the topology of the network, i.e., the connectivity of the junctions. If the connectivity is below the central force isostatic point (CFIP, 6 in 3D), the structure is considered as floppy, but for ≥6, it will be rigid.[21−23] Sharma et al showed that this is a mechanical phase transition and CFIP is a critical point.[23,24]

Methods

Results

Conclusion