Nonlinear strain measures for general biaxial extension of polymer melts

Abstract

Starting from the idea of equilibration, i.e., assuming that all molecular tensions are evenly distributed onto short and long chains in polydisperse polymer melts, we derive a general strain measure from a slip‐link model. By specifying disentanglement and slip of polymer chains, the strain measures of Lodge, Wagner, Doi, and Marrucci are shown to be special cases of this general strain measure. Predictions are compared to experimental data of uniaxial, planar, ellipsoidal, and equibiaxial extensions of a well‐characterized polydisperse polyisobutylene melt. The data do not support Doi’s assumption that the tube diameter remains unchanged by deformation. The relative tube diameter and its inverse, the molecular stress function, can be extracted directly from the data. The tension of the average polymer chain increases with increasing deformation, i.e., the polymer chain is stretched. At small strains, the relative cross section of the tube is inversely proportional to the average stretch of the tube.