Molecular Simulation and Theoretical Analysis of Slide-Ring Gels under Biaxial Deformation

Abstract

Slide-ring (SR) gels, a new type of gels that have cross-links moving along the chains, are known to have unique mechanical characteristics. In the case of biaxial deformations, it has been experimentally shown that the stress–strain (S–S) relationships of SR gels can be well described by the neo-Hookean (NH) model. This behavior is quite different from that of conventional chemical gels, where the S–S curves deviate from the NH model. To understand the molecular mechanism of such peculiar elastic properties of SR gels, we studied the effects of movable cross-links by using molecular simulations and theoretical analysis. We calculate the S–S relationships in biaxial deformation for two types of models: slip model, where the cross-links can slide along chains representing SR gels, and non-slip model, which corresponds to conventional chemical gels. In the theoretical analysis, we calculate the S–S relationships by using the models with the Gaussian and the Langevin chains to investigate the nonlinear stretching effect of the chain in the slip and non-slip models. As a result, we found that the peculiar elastic behaviors of SR gels in biaxial deformations are well explained by the effect of movable cross-links suppressing the nonlinear stretching of the chain.

A constitutive theory for large stretch behaviors of slide-ring gels by considering molecular frictions

“…27 With the introduction of the alignment entropy of uncross-linked rings between crosslinks, a finite Young's modulus of slide-ring gels was predicted, 27 which, unfortunately, did not quantitatively agree with the value reported in experiments. Molecular dynamics simulations for relatively small stretch under different loading conditions were also performed, 28,29 based on which a simple equation for the Young's modulus as a function of degree of sliding of crosslinks was developed. 29 It was suggested that movable crosslinks could explain the elasticity of slide-ring gels by suppressing the nonlinear stretch of polymer chains 28 and also overcome the trade-off relationship between the stiffness and toughness of polymer network within slide-ring gels.…”

“…Molecular dynamics simulations for relatively small stretch under different loading conditions were also performed, 28,29 based on which a simple equation for the Young's modulus as a function of degree of sliding of crosslinks was developed. 29 It was suggested that movable crosslinks could explain the elasticity of slide-ring gels by suppressing the nonlinear stretch of polymer chains 28 and also overcome the trade-off relationship between the stiffness and toughness of polymer network within slide-ring gels. 30 As revealed in experiments, the crack resistance of slide-ring gels was sensitive to the strain rate and the measured fracture energy of slide-ring gels decreased dramatically around a strain rate of 0.2/s.…”