Entanglement networks of 1,2-polybutadiene cross-linked in states of strain. V. Relaxation phenomena and calculations of entanglement trapping

Linear 1,2-polybutadiene is cross-linked near its glass transition temperature by γ-irradiation while strained in simple extension with a stretch ratio λ_o. After release, the sample retracts to a state of ease (λ_s). From λ_o, λ_s, and stress-strain measurements in extension from the state of ease, the concentrations of network strands terminated by trapped entanglements (v_N) and by cross-links (v_x) can be calculated. For v_x/v_N ≡ R′_o > 1, retraction to the state of ease is rapid. For R ? 0.3 or less, retraction is slow and extends over many logarithmic decades of time scale. When an eased sample is stretched to λ_o where the cross-links do not contribute to stress, the subsequent stress relaxation of the entanglement network toward equilibrium is also very slow if R′_o is small. The slow timedependent processes are attributed to a high proportion of untrapped entanglements on dangling branched structures. The concentration of trapped entanglement strands, v_N, can also be calculated from the equilibrium stress at λ_o. The fraction of trapped entanglements agrees rather well with the predictions of the theory of Langley.