NUMERICAL SIMULATION OF MORPHOLOGY OF POLYMER CHAIN COILS IN COMPLEX FLOWS

A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.

DIGITAL ANALYSIS TECHNOLOGY FOR MORPHOLOGY OF POLYMER CHAIN COILS IN FLOW FIELDS

Polymer chain coils with entanglement is a crucial scale of structures in polymer materials since their relaxationtimes are matching practical processing times.Based on the phenomenological model of polymer chain coils and a new finiteelement approach,we have designed a computer software including solver,pre-and post-processing modules,and developeda digital analysis technology for the morphology of polymer chain coils in flow fields(DAMPC).Using this technology wemay simulate the morphology development of chain coils in various flow fields,such as simple shear flow,elongational flow,and any complex flow at transient or steady state.The applications made up to now show that the software predictions arecomparable with experimental results.

OVERSHOOTS IN STRESS AND FREE ENERGY CHANGE DURING THE FLOWINDUCED CRYSTALLIZATION OF POLYMERIC MELT IN SHEAR FLOW

The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization （FIC） model based on the conformation tensor incorporating the pre-shear effect was proposed. The model is capable of predicting the overshoot phenomena of the stress and the flow-induced free energy change of the polymeric system at high pre-shear rates. Under the condition of flow, the increase in the activated nuclei number was contributed by the flow-induced free energy change, which showed an overwhelming effect on the nuclei formation during the pre-shear process at high shear rates. The half crystallization time （t1/2） of polypropylene （PP） as functions of pre-shear rate and pre-shear time at different crystallization temperatures was predicted and compared with the experiment data. Both numerical and experimental results showed that t1/2 of PP decreased dramatically when the flow started but leveled off at long times. It was found that two transformation stages in t1/2 existed within a wide range of shear rates. For the first stage where the melting polymer experienced a relatively weak shear flow, the acceleration of crystallization kinetics was mainly contributed by the steady value of free energy change while in the second stage for high shear rates, strong overshoot in flow-induced free energy change occurred and the crystallization kinetics was thus significantly enhanced. The overshoots in stress and flow-induced free energy change reflected an important role of flow on the primary nucleation especially when the flow was strong enough.

Rigidity Theorems of Riemannian Manifold with 2Ric=0

Ricci curvature tensor is denoted by Ric. We study when the manifold which satisfy 2Ric=0 become a Einstein manifold or a space form.