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The origin of theC2term in rubber elasticitya)

 

作者: M. H. Wagner,  

 

期刊: Journal of Rheology  (AIP Available online 1994)
卷期: Volume 38, issue 3  

页码: 655-679

 

ISSN:0148-6055

 

年代: 1994

 

DOI:10.1122/1.550480

 

出版商: The Society of Rheology

 

关键词: RUBBERS;RHEOLOGY;ELASTICITY;STRESS−STRAIN RELATION;MELTS;DEFORMATION;NETWORK STRUCTURE;CROSS−LINKING;POLYMER NETWORKS

 

数据来源: AIP

 

摘要:

A unifying stress–strain model for physical networks (polymer melts) and for permanent networks (rubbers) is presented. It is based on three assumptions: (1) the uncrossability condition of real chains can be modeled by the tube concept; (2) the tube diameter is a function of the average stretch; and (3) the tube volume is invariant with respect to deformation. The model predicts that stress–strain behavior of dry and swollen rubber networks is completely determined by four material constants: the equilibrium modulusG∞of the bulk network; the critical entanglement modulusG*e, which is equivalent to the plateau modulusGNof the un‐crosslinked parent melt; a finite extensibility parameter α; and a solvent‐polymer interaction exponent β. Predictions are compared with experimental data in elongation, and agreement is excellent. The Mooney–Rivlin constantC2of unswollen networks with high crosslink densities is limited to roughlyGN/2, and the origin of theC2term is shown to be due to nonaffine deformation of the entanglement network. Nonaffine deformation of network strands is caused by an increasing lateral restriction due to neighboring chains, while upon swelling, the nonaffine reduction of the microscopic length scale leads to the vanishingC2value of highly swollen rubbers.

 

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