Entanglement Networks of 1, 2-Polybutadiene Cross-Linked in States of Strain: XV. Simple Extension Special Case Comparison of the CKF Theory to Swelling Equilibrium Data

Abstract

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 network strand concentrations terminated by trapped entanglements (ν_N) and by cross-links (ν_X) can be calculated. In this type of configuration the resulting cross-link networks traps the entanglements originally present. In addition the forces associated with the crosslinks and the trapped entanglements act in opposite directions in the equilibrium state of ease. The CKF Strain Energy Function for simple extension, previously denoted as the Three Constant Two Network Mooney-Rivlin Model, produced consistent results if the stress-strain relations for the trapped entanglement network are described by the CKF coefficients C_1N and C_2N while those for the cross-link network are neo-Hookean in character and described by the CKF coefficient C_1X only. Young’s modulus was calculated indirectly from swelling measurements in n-heptane and found to be similar in magnitude to that derived from stress-strain measurements in extension from the state of ease for two such networks, although the deviations from neo-Hookean elasticity were not taken into account at that time. Also, it was noted that the swelling was anisotropic, being greater in the direction of original stretch than in the other two directions.