Cross-Linked Rubber
Rubber materials are mostly applied in their cross-linked states, and also majority of them are used under large cyclic deformation. Therefore, understanding the effect of cross-links under deformation is very important for developing new rubber materials
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Cross-Linked Rubber Hiroshi Shima
15.1 Introduction Typical rubber materials are usually used in a cross-linked state. It is therefore important to understand the effect of cross-linking when developing rubber materials. In particular, considering that rubber materials are often used in a deformed state, it is important to grasp the effect of cross-linking under deformation. For usual non-cross-linked polymers, there are various theoretical models and calculation methods based on such models, and viscoelasticity can be predicted from the molecular weight, structure (e.g., branches), molecular weight between entanglement points, and relaxation time of entanglement using simulators such as PASTA or NAPLES. For cross-linked materials, among theoretical models, the results of Edwards– Vilgis slip-link model [1] have been shown to agree with those of experiments conducted by Urayama [2]. Among simulators, PASTA cannot handle cross-linked materials whereas NAPLES can; however, because NAPLES simulation involves a large degree of coarse graining, it has a limited range of applications. A calculation based on coarse-grained molecular dynamics, the Kremer–Grest model [3], has the following merits: • Physical properties can be predicted with a model of arbitrarily defined molecular weight between cross-linking points and its distribution. • The observation of behaviors of molecular chains under large deformation is possible. Furthermore, the calculation is considered to have a wide range of application despite its large calculation load.
H. Shima () BRIDGESTONE Corporation, Tokyo, Japan e-mail: [email protected] © Springer Science+Business Media Singapore 2016 Japan Association for Chemical Innovation, Computer Simulation of Polymeric Materials, DOI 10.1007/978-981-10-0815-3_15
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H. Shima
COGNAC can easily handle deformation and cross-linking reactions in addition to the basic functions of the calculation made in the coarse-grained molecular dynamics method; therefore, COGNAC is suitable for the analysis of cross-linked materials. The following describes the formation of cross-linked structures and elongational physical properties in the analysis of cross-linked materials using COGNAC.
15.2 Formation of Cross-Linked Structures 15.2.1 Formation Method The main methods of forming cross-linked structures include a method for random cross-linking and a method for end cross-linking. The following outlines these two methods (Fig. 15.1): 1. Method for random cross-linking Random cross-linking is conducted according to the following procedure, as described in the literature [4]: • A system containing a plurality of polymers is prepared. • The desired number of cross-linking points is placed randomly in the system. • A polymer particle at the position closest to the cross-linking points is considered to be an activated particle. • A particle that is within a distance of 1.3 ¢ from the activated particle is randomly selected, and a bond is created between the selected particle and the activated particle. In
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