Strain-dependent dynamic properties of filled rubber network systems, 2: The physical meaning of parameters in the L-N-B model and their applicability
✍ Scribed by Chen-Ron Lin; Yu-Der Lee
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 563 KB
- Volume
- 6
- Category
- Article
- ISSN
- 1022-1344
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✦ Synopsis
Abstract
In Part 1 of this series, the strain‐dependent dynamic properties of filler loaded rubber systems were modelled with a newly derived L‐N‐B (links‐nodes‐blobs) model. In this paper, the physical meaning and significance of parameters of the L‐N‐B model are described and compared with experimental results. Furthermore, with the combination of a van der Waals force model, these parameters can be described in terms of basic physical material properties of filler and rubber matrix. The temperature dependence of dynamic properties of filled rubbers is successfully described in terms of the series combination of the angular deformation element \documentclass{article}\pagestyle{empty}\begin{document}$\frac{{2d\bar G}}{{mL_1 a^2 }}$\end{document} in series with the tension element \documentclass{article}\pagestyle{empty}\begin{document}$\frac{{dQ}}{{L_1 a^2 }}$\end{document}. Moreover, the normalized storage modulus can be expressed as a master curve \documentclass{article}\pagestyle{empty}\begin{document}$Z_{L - N - B} = {\rm Ei}\left[ {\frac{{ - a_2 mQ\varepsilon _b }}{{2d\bar G}} \bullet L_1 } \right]/{\rm Ei}\left[ {\frac{{ - a_2 mQ\varepsilon _b }}{{2d\bar G}}} \right]$\end{document}. The parameter \documentclass{article}\pagestyle{empty}\begin{document}$\frac{{ - a_2 mQ\varepsilon _b }}{{2d\bar G}}$\end{document} is almost a constant for different carbon black filled systems. The distributions of blob and link in a L‐N‐B model are similar for carbon black filled rubber systems. The applicability and the limitation of the L‐N‐B model are also discussed and illustrated with experimental results. Beside carbon black filled rubber systems, silica filled rubber and filler‐in‐oil systems are discussed.