Fig. 3

Representative experimental results before the discovery of negative energy elasticity. a Normalized shear modulus (G/G_affine) as a function of the overlap parameter (c/c*). The open gray symbols represent the data from the original paper [16], which are inaccurate due to the samples and measurement method. The filled black symbols represent the data from ref.  [1] that are more accurate in terms of the samples and measurement method (see main text). Rhombuses, circles, squares, and triangles represent M = 5, 10, 20, and 40 kg/mol, respectively. The blue and red dashed lines show G/G_affine = 0.5 (the prediction of the phantom network model) and 1 (the prediction of the affine network model), respectively. The overlap parameter in the horizontal axis is converted from the polymer volume fraction ϕ/ϕ* (in the original paper [16]) to concentration c/c*. b Normalized shear modulus (G(p)/G(1)) as a function of the connectivity of the polymer network (p). The polymer concentrations are c = 40, 60, 80, 100, and 120 g/L. The molar mass of the precursors is M = 20 kg/mol, and the corresponding overlap concentration is 40 g/L. We calculate the dashed lines from the affine and phantom network models with the Bethe approximation. The data are taken from ref.  [17]. c Shear modulus (G) as a function of the connectivity of the polymer network (p) in the dynamic gelation process (DP) and the static replica (SR). The polymer concentrations are c = 30, 60, and 120 g/L, and the molar mass of the precursors is M = 20 kg/mol. The data are taken from ref.  [18]. We note that the data in b and c were measured accurately in the same way as ref. [1]