Abstract
Two-dimensional triangulated surface models for membranes and their three-dimensional (3D) extensions are proposed and studied to understand the strain-induced crystallization (SIC) of rubbers. It is well known that SIC is an origin of stress relaxation, which appears as a plateau in the intermediate strain region of stress–strain curves. However, this SIC is very hard to implement in models because SIC is directly connected to a solid state, which is mechanically very different from the amorphous state. In this paper, we show that the crystalline state can be quite simply implemented in the Gaussian elastic bond model, which is a straightforward extension of the Gaussian chain model for polymers, by replacing bonds with rigid bodies or eliminating bonds. We find that the results of Monte Carlo simulations for stress–strain curves are in good agreement with the reported experimental data of large strains of up to 1200%. This approach allows us to intuitively understand the stress relaxation caused by SIC.
Highlights
Natural rubbers undergo strain-induced crystallization (SIC), which attracts a lot of attention and has been studied extensively [1,2,3,4]
The strain of the carboxylated nitrile rubber (XNBR) with layered double hydroxide (LDH) is reported to be very large (∼1000% or more), and the stress–strain data are influenced by SIC; XNBR/LDH is similar to natural rubber
Note that the convergence speed of the 3D model is relatively faster than that of the 2D models. We consider that this result comes from the fact that the surface or lattice fluctuation of the 3D models is relatively smaller than that of the 2D model, or, in other words, the phase space volume for the Monte Carlo (MC) update of the polymer position ri is expected to be relatively smaller in the 3D model than in the 2D models
Summary
Natural rubbers undergo strain-induced crystallization (SIC), which attracts a lot of attention and has been studied extensively [1,2,3,4]. 2D and 3D versions of the Gaussian bond potential are assumed for our new SIC modeling For these potential energies, the crystalline state can be implemented by replacing elastic bonds with rigid bonds or empty bonds, where the rigid bond is a three-dimensional rigid body of fixed length and has no tensile energy, and the empty bond has no tensile energy; these models are called the “rigid bond model” and “empty bond model”, respectively, in this paper. The crystalline state can be implemented by replacing elastic bonds with rigid bonds or empty bonds, where the rigid bond is a three-dimensional rigid body of fixed length and has no tensile energy, and the empty bond has no tensile energy; these models are called the “rigid bond model” and “empty bond model”, respectively, in this paper These two models are close to each other in the sense that no tensile energy is defined on the bond corresponding to the crystalline state. We study rubber elasticity by statistical mechanical models in which two different microscopic variables are assumed, and we will not go into the details of thermodynamic theory
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