The Microscopic Effect of Filler on Rubber Reinforcement: A Coarse-grained Molecular Dynamics Study
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The Microscopic Effect of Filler on Rubber Reinforcement: A Coarse-grained Molecular Dynamics Study Yosuke Kimura and Masatoshi Sato Toyota Technical Development Corporation, 2-28-23, Izumi, Higashi-ku, Nagoya, Aichi, 4610001, Japan.
ABSTRACT In this paper, we developed a microscopic approach to understand rubber reinforcement using coarse-grained molecular dynamics simulations. We investigated static uniaxial tensile behavior of filled and unfilled rubber models, and found two reinforcement mechanisms. One of these is the same as the mechanism predicted by Guth, which depends only on the volume content of fillers. We have confirmed this mechanism at small strain region. The other is caused by filler-filler network created by the advantage of chemical bond at large strain. In this region, some polymers linked fillers and were stretched, that is, these polymers generated tension. Additionally, we investigated the effect of filler distribution on rubber reinforcement.
INTRODUCTION Finite Element Method (FEM) is widely employed in automobile development with the aim of shortening the development time and improving the efficiency. On the other hand, although new polymeric materials that have different properties and functionalities are being widely developed, it is not easy to identify the properties of these new materials for numerical analysis of a continuum model such as using FEM. Therefore, it is important to identify the properties of materials and to reveal mechanisms of reinforcement. In this paper, we present a study of the microscopic effect of filler on rubber reinforcement to reveal these mechanisms. Adding filler particles such as carbon black to cross-linked rubber raises the stiffness, increases the hysteresis loss due to internal friction and causes stress softening in cyclic deformation (referred to as Mullins effect1). However, the mechanisms by which these macroscopic changes occur are areas in active research. A microscopic filler-rubber and fillerfiller interactions are considered to play important role in the occurrence of these phenomena. We developed a microscopic approach to understand rubber reinforcement using coarse-grained molecular dynamics simulations. MODELS Kremer-Grest model Polymers are described by the well known Kremer-Grest chain and cross-linked each other. The model has polymer chains where monomers are represented by repulsive LennardJones beads,
V (r ) 4
LJ
0,
LJ r r 2
1/6
12
LJ r LJ
6
1 , 4
r 2
1/6
LJ
,
.
The beads are connected together along the chain by a FENE (finitely extensible nonlinear elastic) potential. V FENE ( r )
kF
,
R 0 ln 1 r / R 0 2
2
2
,
r R0 ,
r R0 ,
Here, LJ and LJ are LJ parameters (simulation unit energy and length) , where R0=1.5LJ, kF=30LJ/LJ2. We have simulated an NVT ensemble by using Langevin dynamics at kBT=LJ, where kB is Boltzmann constant.2 This method has parameters by which the polymers do not slip through each other. Therefore, it is
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