(A-34) Facile determination of Poisson’s ratio and Young’s modulus of polyacrylamide gels and polydimethylsiloxane

Introduction:: Hydrogels and elastomers are popular substrates used for mechanobiology and cell mechanics studies to mimic the mechanical properties of native extracellular matrices (ECM). This is partly due to the ability to tune the elastic properties within the range relevant to soft tissues (Young's modulus of 1 – 40 kPa) by adjusting their chemical compositions. Biomaterials are often characterized mechanically on smaller scales using atomic force microscopy (AFM), on larger scales using bulk shear and normal rheology or dynamically using indentation or tensile testing. Within these mechanical characterizations, there are several discrepancies due to length scales and testing conditions. These discrepancies highlight the importance of systematically characterizing the mechanical response of PAH and the need for direct measurement of Poisson’s ratio. This is particularly important in quantitative studies, like traction force microscopy (TFM) where cell-induced substrate deformations are directly visualized, quantified, and then used with appropriate constitutive models for the gel to estimate focal adhesion-related stress fields. We directly characterized the Poisson ratio and Young’s modulus, two elastic constants, of both PAH and PDMS using static tension test (from which E and ν are directly obtained) and shear rheology (to obtain the bulk shear modulus, G). We find a high degree of agreement between shear rheology and macroscopic tension tests for PAH but not PDMS. Our study emphasizes the importance of accurately characterizing E and ν of gels and elastomers, rather than assuming the incompressible value, especially for use in mechanobiology studies.


Materials and Methods:: Fully swollen PAH and PDMS rods were prepared and hydrated in water. These were then mounted on the stretcher device. Two stains were made (inked) using a permanent marker and used as fiducial markers. These were made far from the clamps and close to the center of the rods. Inked gels were then subjected to static tensile forces by applying dead weights on the lower end of the rods. Using a digital single-lens reflex camera (Nikon, D750) with a macro lens (Nikon, AF-S Micro Nikkor 105) mounted on a tripod, pictures were taken via a wireless intervalometer to prevent mechanical drift. The rods were imaged once with each incremental step of dead weights added, ensuring that the fiducial markers were within the field of view. Images were subsequently post-processed in FIJI (NIH). Our first goal was to directly measure the Poisson ratio of the PAH and PDMS formulations. Our second goal was to cross-evaluate and compare E obtained from the static tension test, with that estimated from shear rheology by using G. We convert from the shear modulus to Young’s modulus by assuming the continuum relationship valid for a linear isotropic elastic material and using the appropriate value of the Poisson’s ratio, equation 1: G = E/ 2(1 + ν). We use equation 1 to calculate Young’s modulus by i) assuming incompressibility, and ii) by using the actual (measured) value of the Poisson ratio. This allows us to quantify variations in the predicted value of E, resulting from the approximation.


Results, Conclusions, and Discussions:: We observe small deviations (within experimental error) in the cross-correlation agreement between E and G estimated using both an idealized incompressible value of Ε and G exactly measured value. This, however, does not imply that it is a valid assumption to always consider ν as incompressible. This is especially important when we consider dynamic effects, specific to mechanobiology studies on cell motility on biomimetic hydrogel surfaces. For instance, the deformation fields induced in the substrate due to the contractile and time-dependent stresses in focal adhesion regions depend crucially on the Poisson ratio. A second instance where the Poisson ratio may play an important role is in the rate-dependent deformation of initially planar hydrogels of finite stiffness. Here, axial and normal deformations here are coupled via the Poisson ratio and together determine the time-dependent forces felt by the indenter. Such rate-dependent deformations are not static and involve significant poroelastic effects.

Many experimental studies that interpret data obtained using these gels and elastomers as substrates, as well as other computational studies assume that the PAH is incompressible and thus ν = 0.5. Here, we corroborate that this assumption is not correct and that ν of PAHs increases with increasing polymer volume fraction and crosslinking degree, as previously reported and as predicted by scaling concepts of polymer physics. The static tensile test describes herein obtains bulk properties. However, these can be scale-dependent. For instance, approaches such as embedded microneedles actuated with external magnetic fields yield different values, emphasizing the importance of the scale of the characterization. Our ν values for PAH and others are summarized in Figure 1(a). We observe a similar behavior for PDMS, that is, ν increased with increasing degrees of crosslinks. Our ν values for PDMS and others are summarized in Figure 1 (b).


Acknowledgements (Optional): : A.M.S., A.G., and R.C.A.E. acknowledge funding from the NSF- CREST: Center for Cellular and Biomolecular Machines through the support of the National Science Foundation (NSF) Grant.


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