An entanglement model for the dependence of fracture surface energy on molecular weight

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: {article}{empty}{document}γ = γ _∞ - b Mᵥ - 1{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 M̄ 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: {article}{empty}{document}$ {{γ _∞ = γ ₛ Aₛ Zc ρ c N_A } {/ { {{γ _∞ = γ ₛ Aₛ Zc ρ c N_A } { Mₛ }}} . -} { Mₛ }} document and articleemptydocument b = 2({{ M_v } {/ { {{ M_v } { M_n }}} . -} { M_n }})γ _∞ Mf ${document} where M̄ n and M̄ f are the number‐average molecular weights of the polymer and of the free chain ends, M̄ v is the viscosity‐average molecular weight, γ s is the average fracture‐energy per entanglement in the craze volume, A s is the average cross‐sectional area of the polymer chain, Z c and ρ c are the thickness and density of crazed material on the fracture surface, respectively; M̄ s is the average strand molecular weight between entanglements, and N A is AvogadrO's number.