Abstract: | Over 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} $\end{document}. For poly(methyl methacrylate), data of J. P. Berry, G. C. Berry and Fox show that gamma; ~ 0 at about the same value of M?v that corresponds to the polymer chain-entanglement length. From this fact, we have developed an entanglement network model for fracture, that bears a resemblance to F. Bueche's entanglement model for the melt viscosity of bulk polymers. Our model allows for the expression of the previously empirical constants, γ∞ and b, in terms of molecular parameters: \documentclass{article}\pagestyle{empty}\begin{document}$ {{\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} where M?n and M?f are the number-average molecular weights of the polymer and of the free chain ends, M?v is the viscosity-average molecular weight, γs is the average fracture-energy per entanglement in the craze volume, As is the average cross-sectional area of the polymer chain, Zc and ρc are the thickness and density of crazed material on the fracture surface, respectively; M?s is the average strand molecular weight between entanglements, and NA is AvogadrO's number. |