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Entanglement networks of 1,2‐polybutadiene crosslinked in states of strain. IV. States of ease and stress–strain behavior
Author(s) -
Carpenter Rick L.,
Kramer Ole,
Ferry John D.
Publication year - 1978
Publication title -
journal of applied polymer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.575
H-Index - 166
eISSN - 1097-4628
pISSN - 0021-8995
DOI - 10.1002/app.1978.070220202
Subject(s) - polybutadiene , viscoelasticity , stress relaxation , materials science , glass transition , quantum entanglement , relaxation (psychology) , stress (linguistics) , polymer , thermodynamics , polymer chemistry , strain (injury) , analytical chemistry (journal) , composite material , chemistry , physics , organic chemistry , copolymer , quantum mechanics , medicine , psychology , social psychology , linguistics , creep , philosophy , quantum
Linear 1,2‐polybutadiene, glass transition temperature ( T g ) −18°C, is crosslinked at −10°C, to −20°C by γ irradiation while strained in simple extension, with extension, ratios (λ 0 ) from 1.2 to 2.7. After release, the sample retracts to a state of ease (λ s ) at room temperature. From equilibrium stress–strain measurements up to a stretch ratio relative to the state of ease (Λ) of 1.2, together with λ 0 and λ s , the concentration of network strands terminated by trapped entanglements (ν N ) is calculated. For this purpose, a three‐constant Mooney–Rivlin formulation is used, in which the entanglement network is described by Mooney–Rivlin coefficients C 1 N and C 2 N , whereas the crosslink networks is described by the coefficient C 1 x only. The ratio ψ N = C 2 N /( C 1 N + C 2 N ) is estimated from parallel studies of nonlinear stress relaxation of the uncrosslinked polymer, taking into account the thermal history before and during irradiation. For substantial degrees of crosslinking, i.e., for R 0′ = ν x /ν N > 0.4 (where ν N is the concentration of network strands terminated by crosslinks), and for λ 0 < 1.8, C 2 N agrees rather well with the value obtained from stress relaxation of the uncrosslinked polymer in the range of time scale where it is nearly independent of time (1.87 X 10 5 pascals). The corresponding value of ν N is 2.3 × 10 −4 moles/cm 3 , in good agreement with that obtained from viscoelastic measurements of the uncrosslinked polymer in the plateau zone (2.5 × 10 −4 ). However, for R 0′ ≅ 0.2, smaller values of C 2 N and ν N are obtained, indicating that for low degrees of crosslinking the entanglements are not completely trapped. Also, for higher values of λ 0 , C 2 N and ν N turn out to be somewhat smaller. Similar, less extensive results were obtained previously on a 1,2‐polybutadiene with somewhat higher vinyl content and a higher T g . Crosslinked samples of both these polymers were subjected to equilibrium stress–strain measurements in simple elongation from the state of ease at higher strains up to Λ = 1.7. The results agreed closely with calculations from the three‐constant Mooney–Rivlin theory.