Probing the cross-effect of strains in non-linear elasticity of nearly regular polymer networks by pure shear deformation

Abstract

The pure shear deformation of the Tetra-polyethylene glycol gels reveals the presence of an explicit cross-effect of strains in the strain energy density function even for the polymer networks with nearly regular structure including no appreciable amount of structural defect such as trapped entanglement. This result is in contrast to the expectation of the classical Gaussian network model (Neo Hookean model), i.e., the vanishing of the cross effect in regular networks with no trapped entanglement. The results show that (1) the cross effect of strains is not dependent on the network-strand length; (2) the cross effect is not affected by the presence of non-network strands; (3) the cross effect is proportional to the network polymer concentration including both elastically effective and ineffective strands; (4) no cross effect is expected exclusively in zero limit of network concentration in real polymer networks. These features indicate that the real polymer networks with regular network structures have an explicit cross-effect of strains, which originates from some interaction between network strands (other than entanglement effect) such as nematic interaction, topological interaction, and excluded volume interaction.

Nonlinear Elasticity of Ultrasoft Near-Critical Gels with Extremely Sparse Network Structures Revealed by Biaxial Stretching

“…As observed in Figure c, the cross-effect vanishes at Φ el < 0.11, whereas it is finite at Φ el > 0.19, suggesting that Φ el is a governing parameter for the strain cross-effect. The IR-T-PEG gel is the sparsest network in ref , but it is considerably distant from the gel point, which is evident from the large value of Φ el (0.42) calculated from the p value.…”

“…In the figures, the value of A 2 at λ x = 1.4 in planar stretching for each gel is used for comparison and reduced by the shear modulus to exclude the difference in rigidity among gels. The figures include the corresponding data for the two types of tetra-PEG gels, , i.e., a near-ideal PEG network with almost no structural defect comprising uniform network strands (designated as a T-PEG gel) and an irregular PEG network with a finite amount of dangling chain made by reducing the reaction extent ( p ) (designated as an IR-T-PEG gel). In Figure a, the T-PEG gel and IR-T-PEG gel have a finite strain cross-effect, although their values of w net (<0.2) are considerably smaller than those of near-critical PTHF and PDMS gels with A 2 ≈ 0, indicating that w net is not a governing parameter for the strain cross-effect.…”

New aspects of nonlinear elasticity of polymer gels and elastomers revealed by stretching experiments in various geometries

“…Figure shows the ϕ dependence of r for the Tetra‐PEG gels with precursor chains of various molecular weights . Most importantly, r remains finite at small values of ϕ and tends to diminish only in the zero limit of ϕ .…”

“…The biaxial stress − strain relations of the Tetra‐PEG gels with various volume fractions of the network ( ϕ ) were investigated . In Fig.…”

“…Volume conservation ( λ x λ y λ z = 1) is also a kind of cross‐effect of strains ( λ x λ y = λ z −1 ), and this is implicitly considered in I 1 ‐only models such as the NH and Gent models. The following model, which is a simple sum of Eqn and a linear I 2 term, is considered as the minimal extension of the Gent model: …”