Deformation and toughness of polymeric systems: 3. Influence of crosslink density

In part 1 of this series the phenomenon of a critical ligament thickness (ID_c) below which brittle polymers become ductile was investigated for polystyrene (PS). Using the thermoplastic polystyrene-poly(2,6-dimethyl-1,4-phenylene ether) (PS-PPE) model system, it was demonstrated in part 2 of this series that the absolute value of ID_c as well as the maximum toughness (i.e. maximum strain to break) was dependent on the network density of the polymer used. In this study the toughness and ID_c of crosslinked thermosetting polymers were investigated using epoxides based on the diglycidyl ether of bisphenol A as a model system. The crosslink density (v_c) is varied between values comparable with (v_c = 9 × 10²⁵ chains m⁻³), up to values much higher than (v_c = 235 × 10²⁵ chains m⁻³), the entanglement density in the thermoplastic PS-PPE system. The maximum macroscopic toughness proportional to the strain to break (λ_macr) or given by the slow-speed fracture toughness (G_Ic) and the notched high-speed tensile toughness (G_h) of core-shell rubber-modified epoxides uniquely increases with an increasing molecular weight between crosslinks (M_c). Only by using extreme testing conditions (notched high-speed impact testing), could the ID_c of a limited range of epoxides be determined: 0.21 μm (v_c = 9 × 10²⁵ chains m⁻³) ≤ ID_c ≤ 0.29 μm (v_c = 14 × 10²⁵ chains m⁻³). Both the experimentally determined values of ID_c and the toughness of the epoxides compare well with the values determined for the entangled thermoplastic PS-PPE model system in the same range of network densities, elucidating the principal similarity of the influence of entanglements and crosslinks on the deformation processes. Good agreement was observed between the experimentally determined values of ID_c of the epoxides and the values predicted by the simple model introduced in part 2 of this series.