Unlike hard materials such as metals and ceramics, rubbery materials can endure large deformations due to the large conformational degree of freedom of the cross-linked polymer network. However, the effect of the network’s branching factor on the ultimate mechanical properties has not yet been clarified. This study shows that tri-branching, which entails the lowest branching factor, results in a large elastic deformation near the theoretical upper bound. This ideal elastic limit is realized by reversible strain-induced crystallization, providing on-demand reinforcement. The enhanced reversible strain-induced crystallization is observed in the tri-branched and not in the tetra-branched network. A mathematical theory of structural rigidity is used to explain the difference in the chain orientation. Although tetra-branched polymers have been preferred since the development of vulcanization, these findings highlighting the merits of tri-branching will prompt a paradigm shift in the development of rubbery materials.

Diffusion behavior of particles in hydrogels is important both for the fundamental understanding of mass transport and for practical applications and has been investigated for a long time. There are three major theories describing the diffusion behavior of small particles in a polymer network: obstruction, hydrodynamic, and free volume theories. Although many researchers have examined these three theories, their applicability is still unclear due to ambiguity stemming from the heterogeneity of conventional hydrogels. Recently, we have developed a near-ideal hydrogel called Tetra-PEG gel that provides a unique possibility to correlate gel structure with properties. In this study, we measured the diffusion coefficient of water molecules (D) in Tetra-PEG gels by pulsed field gradient spin-echo 1 H NMR. By comparing D and the correlation length of a polymer network (ξ) measured by small-angle neutron scattering, we observed an identity formula similar to the hydrodynamic theory (D/D 0 = exp(−d/ξ), where D 0 is the diffusion coefficient of particles in the absence of polymers and d is the diameter of a particle). This result suggests that the diffusion behavior of small particles in hydrogels is determined by the characteristic sizes of a particle (d) and a polymer network (ξ).

Dynamics of a polymer gel network is described by the theory proposed by Tanaka, Hocker, and Benedek (THB) that gives the diffusion coefficient of a polymer network D K G f 4 3

Friction between polymer chains and water is considered to govern the water retention and permeation in hydrogels. This concept has been examined by means of water permeation measurements through hydrogels. Previous studies used hydrogels in the equilibrium swollen state and supported the scaling relationship between the friction coefficient (f) and the blob size (ξ) proposed by Tanaka and de Gennes (f ∼ ξ–2). However, the experiments on equilibrium-swollen hydrogels are not enough, and those on as-prepared hydrogels are needed to fully examine the validity of the scaling relationship. In this study, we established a novel water permeation apparatus, which well prevented the swelling of gels and enabled the water permeation experiments on gels in the as-prepared state. Using this novel apparatus, we measured f of a model polymer network system, i.e., Tetra-PEG gels. By comparing f measured by the water permeation experiment and ξ measured by a small-angle neutron scattering experiment, we confirmed the scaling relationship f ∼ ξ–2 even in the as-prepared state. This result strongly supports the availability of the current model in the equilibrium swollen state and thus strengthens the validity of the model.

For the application of polymer gels, it is necessary to control independently and precisely their various physical properties. However, the heterogeneity of polymer gels hinders the precise control over the structure, as well as the verification of theories. To understand the structure-property relationship of polymer gels, many researchers have tried to develop a homogeneous model network. Most of the model networks were made from polymer melts that did not have a solvent and had many entanglements in the structure. Because the contribution of entanglements is much larger than that of chemical crosslinking, it was difficult to focus on the crosslinking structure, which is the structure considered in conventional theories. To overcome such a situation, we have developed a new model network system that contains much solvent. Specifically, we fabricated the polymer gel (Tetra-PEG gel) by mixing two types of solutions of tetra-armed poly(ethylene glycol) (Tetra-PEG) with mutually reactive end groups (amine (-PA) and activated ester (-HS)). Because the existence of a solvent strongly reduces the effect of entanglements, the effect of the crosslinking structure on the physical properties can be extracted. In this review, we present the structure-property relationship of Tetra-PEG gel. First, we show the structural homogeneity of Tetra-PEG gels. Then, we explain gelation reaction, elastic modulus, fracture energy and kinetics of swelling and shrinking of Tetra-PEG gels by comparing the theories and experimental results.