An entanglement model for the dependence of fracture surface energy on molecular weight
作者:
P. C. Moon,
R. E. Barker,
期刊:
Journal of Polymer Science: Polymer Physics Edition
(WILEY Available online 1973)
卷期:
Volume 11,
issue 5
页码: 909-917
ISSN:0098-1273
年代: 1973
DOI:10.1002/pol.1973.180110508
出版商: John Wiley&Sons, Inc.
数据来源: WILEY
摘要:
AbstractOver the last decade, empirical evidence has indicated that the effective surface energy γ associated with the fracture of noncrystalline is a linear function of the reciprocal of the viscosity–average molecular weight:\documentclass{article}\pagestyle{empty}\begin{document}$ \gamma = \gamma _\infty - b\bar M_v ^{ - 1} $\end{document}. For poly(methyl methacrylate), data of J. P. Berry, G. C. Berry and Fox show that gamma; ∼ 0 at about the same value ofM̄vthat corresponds to the polymer chain‐entanglement length. From this fact, we have developed an entanglement network model for fracture, that bears a resemblance to F. Bueche's entanglement model for the melt viscosity of bulk polymers. Our model allows for the expression of the previously empirical constants, γ∞andb, in terms of molecular parameters:\documentclass{article}\pagestyle{empty}\begin{document}$ {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } \mathord{\left/ {\vphantom {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } {\bar M_{\rm s} }}} \right. \kern-\nulldelimiterspace} {\bar M_{\rm s} }} $\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$ b = 2({{\bar M_v } \mathord{\left/ {\vphantom {{\bar M_v } {\bar M_n }}} \right. \kern-\nulldelimiterspace} {\bar M_n }})\gamma _\infty M_{\rm f} $\end{document}whereM̄nandM̄fare the number‐average molecular weights of the polymer and of the free chain ends,M̄vis the viscosity‐average molecular weight, γsis the average fracture‐energy per entanglement in the craze volume,Asis the average cross‐sectional area of the polymer chain,Zcand ρcare the thickness and density of crazed material on the fracture surface, respectively;M̄sis the average strand molecular weight between entanglements, a
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