Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. VII. Stress-birefringence relations

Crosslinks are introduced by γ irradiation into 1,2-polybutadiene while strained in uniaxial extension near T_g with stretch ratio λ₀, thereby trapping a proportion of the entanglements originally present. The stress at any subsequent strain λ is accurately given by the sum σ_N + σ_x, where σ_N is the stress contributed by a trapped entanglement network with λ = 1 as reference and a Mooney–Rivlin stress-strain relation, and σ_x is that contributed by a crosslink network with λ = λ₀ as reference and neo-Hookean stress-strain relation. The birefringence is accurately given as δn = ?_Nσ_N + ?_xσ_x, where the ?'s are the respective stress-optical coefficients. From measurements at λ = λ₀ where σ_x = 0, ?_N can be determined separately. For polymer with 88% 1,2 microstructure, ?_N and ?_x are nearly equal and independent of irradiation dose, though strongly dependent on temperature. For polymer with (95–96)% 1,2, ?_N and ?_x are different (even opposite in sign) and dependent on dose. This behavior is associated with a side reaction of cyclization by the γ irradiation, which is inhibited by the 1,4 moiety in the polymer with lesser 1,2 content. It is responsible for residual birefringence in the state of ease (λ = λ_s) where σ_N = –σ_x and the stress is zero.