Theoretical prediction of tie-chain concentration and its characterization using postyield response

Abstract

In the past, relative tie-chain concentration has been semiquantitatively characterized by infrared dichroism on a stretched sample and from brittle fracture strenght. The probability of tie-molecule formation has also been theoretically estimated from chain dimensions and the semicrystalline morphology of the polymers. In this article the probability of tie-chain formation of monodisperse and homogeneous single-site ethylene copolymers has been estimated over a range of densities and molecular weights using the model proposed by Huang and Brown. The relative tie-chain concentration is obtained by multiplying tie-chain probability with the volume fraction crystallinity of polymer. A modified rubber elasticity theory is applied to calculate the concentration of chain links between junction points (crystallites) of the INSITE technology polymers (ITPs) from measured rubber modulus. It is expected that the chain-link concentration should relate to the tie-chain concentration. The calculated rubber modulus, or the chain-links concentration, of the ITPs increases with an increase in density in the 0.865 to 0.910 g/cc range and did not change significantly in the density range of about 0.91 g/cc to 0.954 g/cc. Normalized rubber modulus and relative tie-chain concentration data shows that the relative tie-chain concentration predicated by Huang and Brown model and measured using the modified rubber elasticity theory are quantitatively similar below 0.01 g/cc density. However, above 0.91 g/cc density, the measured rubber modulus is influenced by additional tie-chain formation during deformation due to breakdown of crystallities and, hence, the discrepancy exists between the two methods of estimating relative tie-chain concentration. © 1996 John Wiley & Sons, Inc.