Constitutive equations from molecular network theories for polymer solutions

Abstract

In this mainly expository paper, constitutive equations based on the network models ofYamamoto,Lodge, andKaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum. The derivations are thereby simplified in some respects and the differences of detail between the models are clarified. InLodges theory, the sub-network superposition assumption is replaced by alternative assumptions concerning the creation and loss of network segments, and the theory is extended to non-Gaussian networks.Kayes theory is extended to allow for the presence of entanglement junctions of different complexities.