Percolation-induced gel-gel phase separation in a dilute polymer network.

Cosmic large-scale structures, animal flocks and living tissues can be considered non-equilibrium organized systems created by dissipative processes. Replicating such properties in artificial systems is still difficult. Herein we report a dissipative network formation process in a dilute polymer-water mixture that leads to percolation-induced gel-gel phase separation. The dilute system, which forms a monophase structure at the percolation threshold, spontaneously separates into two co-continuous gel phases with a submillimetre scale (a dilute-percolated gel) during the deswelling process after the completion of the gelation reaction. The dilute-percolated gel, which contains 99% water, exhibits unexpected hydrophobicity and induces the development of adipose-like tissues in subcutaneous tissues. These findings support the development of dissipative structures with advanced functionalities for distinct applications, ranging from physical chemistry to tissue engineering.

Solvent-Induced Negative Energetic Elasticity in a Lattice Polymer Chain.

The negative internal energetic contribution to the elastic modulus (negative energetic elasticity) has been recently observed in polymer gels. This finding challenges the conventional notion that the elastic moduli of rubberlike materials are determined mainly by entropic elasticity. However, the microscopic origin of negative energetic elasticity has not yet been clarified. Here, we consider the n-step interacting self-avoiding walk on a cubic lattice as a model of a single polymer chain (a subchain of a network in a polymer gel) in a solvent. We theoretically demonstrate the emergence of negative energetic elasticity based on an exact enumeration up to n=20 and analytic expressions for arbitrary n in special cases. Furthermore, we demonstrate that the negative energetic elasticity of this model originates from the attractive polymer-solvent interaction, which locally stiffens the chain and conversely softens the stiffness of the entire chain. This model qualitatively reproduces the temperature dependence of negative energetic elasticity observed in the polymer-gel experiments, indicating that the analysis of a single chain can explain the properties of negative energetic elasticity in polymer gels.

Brownian simulations for tetra-gel-type phantom networks composed of prepolymers with bidisperse arm length.

We studied the effect of arm length contrast of prepolymers on the mechanical properties of tetra-branched networks via Brownian dynamics simulations. We employed a bead-spring model without the excluded volume interactions, and we did not consider the solvent explicitly. Each examined 4-arm star branch prepolymer has uneven arm lengths to attain two-against-two (2a2) or one-against-three (1a3) configurations. The arm length contrast was varied from 38-2 to 20-20 for 2a2, and from 5-25 to 65-5 for 1a3, with the fixed total bead number of 81, including the single bead located at the branch point for prepolymers. We distributed 400 molecules in the simulation box with periodic boundary conditions, and the bead number density was fixed at 4. We created polymer networks by cross-end-coupling of equilibrated tetra-branched prepolymers. To mimic the experiments of tetra gels, we discriminated the molecules into two types and allowed the reaction only between different types of molecules at their end beads. The final conversion ratio was more than 99%, at which unreacted dangling ends are negligible. We found that the fraction of double linkage, in which two of the four arms connect a pair of branch points, increases from 3% to 15% by increasing the arm length contrast. We stretched the resultant tetra-type networks to obtain the ratio of mechanically effective strands. We found that the ratio is 96% for the monodisperse system, decreasing to 90% for high arm length contrast. We introduced bond scission according to the bond stretching to observe the network fracture under sufficiently slow elongation. The fracture behavior was not correlated with the fraction of double linkage because the scission occurs at single linkages.

Tri-branched gels: Rubbery materials with the lowest branching factor approach the ideal elastic limit.

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.

Temperature Dependence of Polymer Network Diffusion.

The swelling dynamics of polymer gels are characterized by the (collective) diffusion coefficient D of the polymer network. Here, we measure the temperature dependence of D of polymer gels with controlled homogeneous network structures using dynamic light scattering. An evaluation of the diffusion coefficient at the gelation point D_{gel} and the increase therein as the gelation proceeds ΔD≡D-D_{gel} indicates that ΔD is a linear function of the absolute temperature with a significantly large negative constant term. This feature is formally identical to the recently discovered "negative energy elasticity" [Y. Yoshikawa et al. Phys. Rev. X 11, 011045 (2021)PRXHAE2160-330810.1103/PhysRevX.11.011045], demonstrating a nontrivial similarity between the statics and dynamics of polymer networks.

Universal Equation of State Describes Osmotic Pressure throughout Gelation Process.

The equation of state of the osmotic pressure for linear-polymer solutions in good solvents is universally described by a scaling function. We experimentally measure the osmotic pressure of the gelation process via osmotic deswelling. We find that the same scaling function for linear-polymer solutions also describes the osmotic pressure throughout the gelation process involving both the sol and gel states. Furthermore, we reveal that the osmotic pressure of polymer gels is universally governed by the semidilute scaling law of linear-polymer solutions.

Connectivity dependence of gelation and elasticity in AB-type polymerization: an experimental comparison of the dynamic process and stoichiometrically imbalanced mixing.

To control various physical properties of polymer gels, it is important to control the connection probability between functional groups of network structures (connectivity). In this study, we compare two methodologies tuning the connectivity in AB-type polymerization: one is stopping the reaction intentionally at a certain conversion, and the other is mixing two prepolymers in a stoichiometrically imbalanced ratio. By experimentally examining the relationships between elastic modulus and connectivity, we find that the relationships are almost the same for these two methodologies. However, the critical connectivity for gelation is different. These results are well reproduced by a kind of phantom network model whose structural parameters are estimated by using a mean-field approximation.

Exactly solvable model for a velocity jump observed in crack propagation in viscoelastic solids.

Needs to impart appropriate elasticity and high toughness to viscoelastic polymer materials are ubiquitous in industries such as concerning automobiles and medical devices. One of the major problems to overcome for toughening is catastrophic failure linked to a velocity jump, i.e., a sharp transition in the velocity of crack propagation occurred in a narrow range of the applied load. However, its physical origin has remained an enigma despite previous studies over 60 years. Here, we propose an exactly solvable model that exhibits the velocity jump incorporating linear viscoelasticity with a cutoff length for a continuum description. With the exact solution, we elucidate the physical origin of the velocity jump: it emerges from a dynamic glass transition in the vicinity of the propagating crack tip. We further quantify the velocity jump together with slow- and fast-velocity regimes of crack propagation, which would stimulate the development of tough polymer materials.

Semiquantal analysis of adiabatic hydrogen transfer rate.

The reaction rate of adiabatic proton/hydrogen/hydride (H) transfers in condensed phase is examined by combining the semiquantal time-dependent Hartree theory and the multidimensional transition state theory, which takes into account the zero-point effect and the dynamical modulation of the wavepacket width in the adiabatic transfer regime. By applying the theory to a model potential consisting of a quartic double well coupled linearly and quadratically (symmetrically) to external degrees of freedom, a set of compact analytical formulas was derived for the adiabatic H transfer rate. The analysis suggests that the kinetic isotope effect on the H transfer rate may exhibit a maximum as a function of the coupling strength to the external degrees of freedom measured by the reorganization energy.