Viscoelastic properties of physically crosslinked networks: Part 2. Dynamic mechanical moduli

Abstract

Linear response to oscillatory deformations is studied for a model transient network made up of uniform polymer chains reversibly crosslinked by associating end groups. In the unentangled regime, where the molecular weight M of a chain is smaller than the entanglement molecular weight M e, the dynamic mechanical moduli are obtained as functions of the frequency ω and the chain breakage rate β( r). By the consideration of the activation process for chain dissociation, the latter is related to the temperature T, molecular weight M, and the life time τ x of the bond duration. It is found that the storage modulus G'(ω) increases with the temperature, markedly differing from the uncrosslinked melts, and also that the plateau of the modulus is extended to the lower ω region with increasing τ x. The temperature shift factor a T., which is necessary to carry out the frequency-temperature superposition, is proportional to τ x, and, hence, depends exponentially on the temperature. It is also found that the frequency-dependent viscosity η(ω) = G(ω)/ω derived from the loss modulus G(ω) is generally smaller than the stationary viscosity η st(γ) (γ being the shear rate) when compared at ω = γ, thus indicating the breakdown of the Cox-Merz rule in physically crosslinked networks.