  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.
