Premium
Entanglement networks of 1,2‐polybutadiene cross‐linked in states of strain. V. Relaxation phenomena and calculations of entanglement trapping
Author(s) -
Carpenter Rick L.,
Kan HsinChia,
Ferry John D.
Publication year - 1979
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760190408
Subject(s) - quantum entanglement , polybutadiene , trapping , stress relaxation , relaxation (psychology) , materials science , stress (linguistics) , logarithmic growth , strain (injury) , thermodynamics , condensed matter physics , physics , polymer , quantum mechanics , composite material , quantum , copolymer , philosophy , creep , mathematics , ecology , mathematical analysis , linguistics , biology , social psychology , medicine , psychology
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 o≃ 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.