Viscoelastic properties of physically crosslinked networks

TLDR: The stationary solution for the transient network model of reversibly crosslinked gels is found under arbitrary macrodeformation in this paper, where the number of active chains, stationary viscosity, first and second normal stress differences are calculated as functions of γ.

Abstract: The stationary solution for the transient network model of reversibly crosslinked gels is found under arbitrary macrodeformation. For shear flow with constant shear rate γ, the number of active chains, stationary viscosity, first and second normal stress differences are calculated as functions of γ. Elongational flow with constant elongational rate ϵ is also studied. It is found that these stationary properties depend rather sensitively on the chain breakage function β(r) and the recombination probability p of the sticky dangling ends. On the basis of the polymer statistics, a specific form of β(r) = βo exp kr is proposed, where βo and k are functions of the temperature T and the molecular weight M of the polymer chain. Stationary viscoelastic properties are shown to exhibit an exponential dependence on T due to the activation process for the junction dissociation, differing markedly from an uncrosslinked polymer melt whose viscosity varies as a power of the temperature. Thickening and thinning conditions for both types of flow are examined. It is shown that limiting behaviour of the shear viscosity under high shear rate obeys the scaling law η(γ) ≈ γ −2 n ( n +1) if β(r) is proportional to rn at high stretching.