Non-affine deformations in flexible and semi-flexible polymer gels

We test the validity of affine deformation assumption in flexible and semi-flexible polymer networks by embedding different-sized fluorescent tracer beads within model polymer networks and quantifying their displacements under shear. A conventional rheometer is used with a confocal microscope for this purpose. Non-affinity is quantified as a function of applied strain, polymer chain density, cross-link concentration, network morphology, reaction kinetics and size of probe particles used. ~Non-affinity measurements in flexible polymer gels are in qualitative agreement with current theories in rubber elasticity. ~For semi-flexible bio-polymer gels, measurements indicate that non-affine deformations are small for networks of thinner, relatively flexible filaments and get smaller as strain increases into non-linear elastic regime. These small measures are consistent with the entropic model for non-linear elasticity of semi-flexible gels. However, as filament stiffness and mesh size increase, the deformations become more non-affine, as predicted by the enthalpic bending and stretching models of non-linear elasticity.