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We recently found that the energy contribution to the linear elasticity ofpolymer gels in the as-prepared state can be a significant negative value; theshear modulus is not proportional to the absolute temperature [Y. Yoshikawa etal., Phys. Rev. X 11, 011045 (2021) (arXiv:1912.13191)]. Our finding challengesthe conventional notion that the polymer-gel elasticity is mainly determined bythe entropy contribution. Existing molecular models of classical rubberelasticity theories, including the affine, phantom, and junction affine networkmodels, cannot be used to estimate the structural parameters of polymer gels.In this focus review, we summarize the experimental studies on the linearelasticity of polymer gels in the as-prepared state using tetra-armpoly(ethylene glycol) (PEG) hydrogels with a homogenous polymer network. Wealso provide a unified formula for the linear elasticity of polymer gels withvarious network topologies and densities. Using the unified formula, wereconcile the past experimental results that seemed to be inconsistent witheach other. Finally, we mention that there are still fundamental unresolvedproblems involving the linear elasticity of polymer gels.

Linear elasticity of polymer gels in terms of negative energy elasticity