Abstract
The rubber elasticity of four types of defectless crystalline-like networks has been investigated by coarse-grained molecular dynamics simulations to test the validity of Kuhn’s affine network theory of rubber elasticity. The shear moduli of the realizable ideal networks are obtained through their uniaxial deformation. The relation between the shear modulus and the partial chain density reveals that the elasticity of the phantom ideal networks with no excluded volume interactions can be explained by a generalized Kuhn’s theory. In addition, the shear moduli of the real networks with excluded volume interactions are usually lower than those of the corresponding phantom networks, which is because of a decrease in the conformational entropy of each partial chain. Coarse-grained molecular dynamics simulations of phantom networks is a promising approach to deeply understand cross-linked rubbers.
Highlights
Cross-linked rubbers have been valuable materials from an industrial point of view since the discovery of vulcanization of uncross-linked natural rubber with sulphur by Goodyear in 1839.1 They are used in a wide range of areas, such as tires, paints, and oil seals.[2]
The entropic elasticity is qualitatively different from the energetic elasticity that is usually observed in non-rubber materials such as metals and glasses and it is one of the most important properties on which a group of soft materials is based
The solid lines correspond to the phantom networks without excluded volume (EV) interactions, while the dashed lines correspond to the real networks with EV interactions
Summary
Cross-linked rubbers have been valuable materials from an industrial point of view since the discovery of vulcanization of uncross-linked natural rubber with sulphur by Goodyear in 1839.1 They are used in a wide range of areas, such as tires, paints, and oil seals.[2]. In terms of fundamental science, it is important to understand the properties of rubber materials, such as their entropic elasticity. To more effectively utilize cross-linked rubbers in industrial areas and further develop soft material science, it is crucial to deeply understand the properties of cross-linked rubbers. The affine network theory proposed by Kuhn is still one of the most basic and useful molecular models. He assumed that the rubber networks are composed of only elastically effective bridged chains and have no structural defects, such as dangling chains, loops, and trapped entanglements,[1,7,8] which are contained in actual cross-linked rubbers.
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