Elastic moduli and strain-dependent lateral strain to axial strain ratio in semi-dilute polyacrylamide hydrogels

Regulating elastic modulus of basic synthetic hydrogels, such as polyacrylamide, is crucial for their application in various fields of biotechnology. However, the measurement of elastic modulus and stress-strain response under different deformation modes is challenging in soft and fragile hydrogels. In this study, a non-contact, 2-dimensional digital image correlation (2D-DIC) technique is used to measure tensile and simple shear stress-strain responses of fully swelled polyacrylamide hydrogels at semi-dilute concentrations, over strain rates ranging between 10^-3-10^-1/s. The measured strain fields exhibit uniformity across all the deformation modes up to threshold strain levels. The elastic moduli were found to be strain-rate insensitive, except at small strains for 10^-1/s due to strain acceleration and inertia of the specimen. The E and G determined from the initial slopes of stress-strain responses of lower strain-rate experiments followed De Genne's c^9/4 power law scaling with equilibrium gel concentrations. The Poisson's ratio determined from the measured axial and lateral strains at small strains was found to closely match with the Poisson's ratio determined from E/G, indicating that the gels follow linear elasticity for nearly incompressible solids at small strains, but deviate from linear elasticity and becoming compressible at higher tensile strains leading to nonlinearity in tensile stress-strain response marked by reduction in instantaneous tensile modulus. The simple shear stress-strain response remains linear throughout. Finally, a polymer physics-based explanation connecting hydrogel concentration, mesh size and elastic moduli is proposed to explain strain-dependent evolution of stresses in semi-dilute polyacrylamide hydrogels for different deformation modes. Therefore, design of technologies using hydrogels must consider active deformation mode.