VISCOELASTIC PROPERTIES OF PHYSICALLY CROSS-LINKED NETWORKS .2. DYNAMIC MECHANICAL MODULI

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-omega and the chain breakage rate beta(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 tau(x) of the bond duration. It is found that the storage modulus G'(omega) increases with the temperature, markedly differing from the uncrosslinked melts, and also that the plateau of the modulus is extended to the lower omega-region with increasing tau(x). The temperature shift factor a(T), which is necessary to carry out the frequency-temperature superposition, is proportional to tau(x), and, hence, depends exponentially on the temperature. It is also found that the frequency-dependent viscosity eta(omega) = G"(omega)/omega-derived from the loss modulus G"(omega) is generally smaller than the stationary viscosity eta(st)(gamma) (gamma-being the shear rate) when compared at omega = gamma, thus indicating the breakdown of the Cox-Merz rule in physically crosslinked networks.