Simultaneous determination of Young's modulus, shear modulus, and Poisson's ratio of soft hydrogels

Abstract

Besides biological and chemical cues, cellular behavior has been found to be affected by mechanical cues such as traction forces, surface topology, and in particular the mechanical properties of the substrate. The present study focuses on completely characterizing the bulk linear mechanical properties of such soft substrates, a good example of which are hydrogels. The complete characterization involves the measurement of Young's modulus, shear modulus, and Poisson's ratio of these hydrogels, which is achieved by manipulating nonspherical magnetic microneedles embedded inside them. Translating and rotating these microneedles under the influence of a known force or torque, respectively, allows us to determine the local mechanical properties of the hydrogels. Two specific hydrogels, namely bis-cross-linked polyacrylamide gels and DNA cross-linked polyacrylamide gels were used, and their properties were measured as a function of gel concentration. The bis-cross-linked gels were found to have a Poisson's ratio that varied between 0.38 and 0.49, while for the DNA-cross-linked gels, Poisson's ratio varied between 0.36 and 0.49. The local shear moduli, measured on the 10 μm scale, of these gels were in good agreement with the global shear modulus obtained from a rheology study. Also the local Young's modulus of the hydrogels was compared with the global modulus obtained using bead experiments, and it was observed that the inhomogeneities in the hydrogel increases with increasing cross-linker concentration. This study helps us fully characterize the properties of the substrate, which helps us to better understand the behavior of cells on these substrates.

Fibroblast Morphology on Dynamic Softening of Hydrogels

“…Most importantly, DNA gel design parameters can be controlled to mimic the stiffness of biological tissues. 6 This stringent control over design parameters and stiffness makes DNA gels a promising tool for applications in tissue engineering and cell-ECM modeling.…”

Cytoskeletal Mechanics Regulating Amoeboid Cell Locomotion

“…The range of Poisson ratios, σ, that has been reported for polyacrylamide gels is between 0.3 and 0.49 [59] [60] [61]. The Young's modulus obtained in our experiments, assuming the Poisson ratio to be 0.3, has an average of E = 910 Pa and a standard deviation of 360 Pa.…”

Rheology of soft particle suspensions

“…ν is a measure of how a material contracts in the lateral dimension (lateral compressive strain) when stretched longitudinally (longitudinal extensional strain). The maximum ratio of 0.5 is found for some rubbers, which are termed incompressible, metals have a Poisson's ratio around 0.25 -0.35 (Pilkey, 2005) and hydrogels fall in an intermediate range of 0.38 to 0.49 (Chippada et al, 2010, Chen et al, 2013 Micromanipulation and Atomic Force Microscopy (AFM), shown schematically in Figure 2.6, are techniques that probe particle elasticity at a particular point on the particle surface.…”

“…; and the number of nearest neighbours, n = 10 as determined by Rognon et al (2011) through discrete element simulation of packed suspensions of non-colloidal elastic spheres. Poisson's ratio is estimated based on the literature suggesting ν of hydrogels is dependent on cross-link density and falls in the range 0.38 to 0.49 (Chippada et al, 2010, Chen et al, 2013. Viscoelastic fluid behaviour is observed at φ rcp ≤ φ 0 ≤ φ j .…”