Application of a tie molecule model to the postyielding deformation of crystalline polymers

Our past paper reported that the postyielding deformation of crystalline polymers such as polyethylene (PE), poly(oxymethylene) (POM), poly(propylene) (PP) and nylon 6 (Ny 6) was expressed by master curves with a characteristic constant for each polymer when normalized true stress and true strain are plotted in both logarithmic graphs and suitably shifted. For a molecular understanding of the postyielding process, we present a tie molecule model which assumes that the tie molecules are pulled out from the lamellar fragment at a constant number of tie molecules. The limit in applicability of the model is in the final stage of fiber formation. Fundamental equations of the model are solved to give a critical point at which all the molecular parameters can be uniquely determined from the characteristic constant for each polymer. At the critical point, the tie molecule length monotonously increases at a fixed number of tie molecules. The limit of the tie molecule length increases in the order of PE, POM, PP and Ny 6. By using an empirical relationship between the area fraction of tie molecules and the degree of crystallinity of these polymers, it is found that the order of area fraction of the tie molecules in Ny 6, PP, POM and PE is entirely reversed to the order of weight fraction of the tie molecules of the above polymers.