Linear elasticity of polymer gels: Fundamental differences from rubbers

We recently found that the energy contribution to the linear elasticity of polymer gels in the as-prepared state can be a significant negative value; the shear modulus is not proportional to the temperature. Our finding prompts a paradigm shift in the understanding of polymer-gel elasticity, challenging the conventional notion that the polymer-gel elasticity is mainly determined by entropy contribution. Existing molecular models of classical rubber elasticity theories, including the affine, phantom, or junction affine network model, cannot be used to estimate the structural parameters of polymer gels. In this focus review, we summarize the experimental studies on the linear elasticity of polymer gels in the as-prepared state using tetra gels with a homogenous polymer network. We also provide a unified formula for the linear elasticity of polymer gels with various network topologies and densities. Using the unified formula, we resolve the past experimental results that seem to be inconsistent with each other. Finally, we mention that there are still fundamental unresolved problems with the linear elasticity of polymer gels.