Primitive chain network simulations for elongational viscosity of bidisperse polystyrene melts
In spite of the industrial significance, molecular mechanism of the strain hardening saliently observed in bidisperse polymeric liquids has not been elucidated yet. In this study, the multi-chain slip-link simulation (called primitive chain network simulation) was performed for the bidisperse polystyrene blends for which experimental data for elongational viscosity have been reported earlier. The simulation reasonably reproduced linear viscoelasticity and transient and steady uniaxial elongational viscosities. It has been confirmed that the long chain stretch dominates the stress at the strain hardening as already demonstrated earlier via the tube model. The molecular analysis employing the decoupling approximation revealed for the first time that there exist two molecular mechanisms to induce strain hardening in bidisperse blends. The mechanism switches depending on the Weissenberg number with respect to the Rouse relaxation time of the long chain, WiRL. At WiRL < 1, the simultaneous increase of the long chain orientation and stretch with increasing WiRL lifts the viscosity beyond the Trouton’s viscosity. At WiRL ≥ 1, the isotropic short chain suppresses the stretch/orientation-induced reduction of friction to enhance the stretch of long chain.
Wall slip in primitive chain network simulations of shear startup of entangled polymers and its effect on the shear stress undershoot
In some recent experiments on entangled polymers of stress growth in startup of fast shear flows an undershoot in the shear stress is observed following the overshoot, i.e., before approaching the steady state. Whereas tumbling of the entangled chain was proposed to be at its origin, here we investigate another possible cause for the stress undershoot, i.e., slippage at the interface between polymer and solid wall. To this end, we extend the primitive chain network model to include slip at the interface between entangled polymeric liquids and solid walls with grafted polymers. We determine the slip velocity at the wall, and the shear rate in the bulk, by imposing that the shear stress in the bulk polymers is equal to that resulting from the polymers grafted at the wall. After confirming that the predicted results for the steady state are reasonable, we examine the transient behavior. The simulations confirm that slippage weakens the magnitude of the stress overshoot, as reported earlier. The undershoot is also weakened, or even disappears, because of a reduced coherence in molecular tumbling. In other words, the disentanglement between grafted and bulk chains, occurring throughout the stress overshoot region, does not contribute to the stress undershoot.
The tube model theory of rubber elasticity
Rubbers are highly elastic solids formed by the random permanent linkages between long chain polymers. Their elasticity is largely entropic in origin, so that the molecular theory is largely a matter of counting the configurations available to the polymers and how this number changes under deformation. To do this one needs to know the way in which the crosslinks are formed, which need not be related to any equilibrium process, and to know the restriction placed on the chains by one another's presence, i.e. their entanglements. Recent theoretical developments suggest that the problem is by no means as intractable as it might at first sight appear, and simple models of tube confinement seem to give very good agreement with experiment.