Molecular-Level Elucidation of a Fracture Process in Slide-Ring Gels via Coarse-Grained Molecular Dynamics Simulations

Abstract

Slide-ring (SR) gels with slidable cross-linked cyclic molecules exhibit considerably higher fracture toughness than conventional fixed cross-link (FC) gels. However, the mechanical properties of SR gels are still unsatisfactory, and thus, these gels cannot be practically applied. Therefore, molecular scale insights into the fracture mechanism of SR gels are required to improve their mechanical properties. This study conducted tensile strain simulations of FC and SR gels using a coarse-grained molecular dynamics (CGMD) method to elucidate the fracture mechanism of SR gels. The CGMD simulations showed that the SR gels exhibited higher fracture toughness than the FC gels. In the FC gels, the axis chains easily broke under a low strain because fixed cross-links constrain the polymer chain, resulting in stress concentration on the axis chains. On the contrary, in the SR gels, the axis chains did not break until a high strain was applied because the cross-linked cyclic molecules slide not to accumulate stress concentration. The analysis of the fracture mechanism of the SR gels revealed that the chain-ends are the origin of the fracture in the SR gels. The cross-linked and un-cross-linked cyclic molecules slide on the axis chains and are stacked around the chain-ends. The stacked cross-linked cyclic molecules induced stress concentrations around the chain-ends. Next, we investigated the effect of coverage on the SR gels. We found that low-coverage SR gels exhibited higher fracture toughness and ultimate strength than highcoverage SR gels because the stacked un-cross-linked cyclic molecules prevent cross-linked cyclic molecules from sliding, leading to a low fracture toughness caused by the stress concentration at the chain-ends. The axis chains of the low-coverage SR gels with a high fracture toughness deformed to the strain direction until a high strain. Thus, the low-coverage SR gels showed a high orientation toward the strain direction. A high orientation contributes to the uniform distribution of mechanical stress on the chains, leading to a high ultimate strength. Although the SR gels generally exhibit a low ultimate strength, SR gels with a low coverage ratio of 5% showed a higher ultimate strength than FC gels. Finally, we propose that, compared with the high-coverage SR gels, the low-coverage SR gels exhibit both higher fracture toughness and ultimate strength, based on the atomistic insight pertaining to the mechanism by which the low-coverage SR gels possess free space for cross-linked cyclic molecules to move to the chain-ends until a high strain is applied.

Effect of Pore Size of Carbon Support on Electrode Reaction Activity of Catalyst Layer in Polymer Electrolyte Fuel Cell: Reactive Molecular Dynamics Simulations

“…To investigate distributions of the Nafion chains and water molecules around Pt nanoparticles in the CL, we used our developed molecular dynamics simulator "Laich" [3].…”

Elasticity of Slide-Ring Gels

“…The elastic modulus of slide-ring gels is lower than that of chemical gels with the same density of cross-links, − and the equilibrium swelling ratio is greater than that of equivalent cross-linked gels . Slide-ring gels are capable of stretching by a much higher extension factor before failure in comparison to the typical conventional chemically cross-linked gels ,− with the same modulus (λ = 13 was reported for slide-ring gels in ref , while cross-linked networks with the same modulus fail at around λ = 3). The high extensibility results in a remarkably high fracture energy of ∼60 J/m 3 reported in ref in comparison to the equivalent cross-linked network with fracture energy ∼10 J/m 3 .…”

Excluded Volume of Slide Rings in Single-Chain Polyrotaxane

“…E bend is solely employed for ring beads to preserve the shape of the rings and is described as follows: E bend = 1 2 k ring ( θ − θ ring ) 2 where k ring = 1000.0 ε/ rad 2 is the angle strength and θ ring = 5π/7 is the equilibrium angle for three consecutive beads in one ring. The choice of parameters ensures that the diameter of the ring is large enough to enable unimpeded sliding along the polymer backbone. , …”