Facile Determination of the Poisson's Ratio and Young's Modulus of Polyacrylamide Gels and Polydimethylsiloxane.

Polyacrylamide hydrogels (PAH gel) and polydimethylsiloxane (PDMS, an elastomer) are two soft materials often used in cell mechanics and mechanobiology, in manufacturing lab-on-a-chip applications, among others. This is partly due to the ability to tune their elasticity with ease in addition to various chemical modifications. For affine polymeric networks, two (of three) elastic constants, Young's modulus ( E ), the shear modulus ( G ), and Poisson's ratio (ν), describe the purely elastic response to external forces. However, the literature addressing the experimental determination of ν for PAH (sometimes called PAA gels in the literature) and the PDMS elastomer is surprisingly limited when compared to the literature that reports values of the elastic moduli, E and G . Here, we present a facile method to obtain the Poisson's ratio and Young's modulus for PAH gel and PDMS elastomer based on static tensile tests. The value of ν obtained from the deformation of the sample is compared to the value determined by comparing E and G via a second independent method that utilizes small amplitude shear rheology. We show that the Poisson's ratio may vary significantly from the value for incompressible materials (ν = 0.5), often assumed in the literature even for soft compressible hydrogels. Surprisingly, we find a high degree of agreement between elastic constants obtained by shear rheology and macroscopic static tension test data for polyacrylamide hydrogels but not for elastomeric PDMS.