Investigations on several empirical rules for entangled polymers based on a self-consistent full-chain reptation theory

摘要

Empirical rules, including the stress-optical rule, the Cox-Merz rule, the Gleissle's mirror relation, and the Laun's rule, that provide important alternatives in obtaining rheological data for concentrated polymer liquids are investigated via stochastic simulations of a recently proposed full-chain reptation theory [Hua and Schieber, J. Chem. Phys. 109, 10018 (1998)] capable of treating rigorously all fundamental effects for concentrated polymer systems. Theoretical investigations of these rules are important, for they provide strict consistency checks on the predictions of existing molecular theories; at the same time, the limitations of these rules may also be explored. The current simulation implies that deviations from these empirical rules are likely to be observed when polymer chain stretching becomes significant. The effects of molecular weight and molecular weight distribution on the applicability of these rules are inferred; accordingly, we are able to explain the essential feature of the experimental finding when deviations from the Cox-Merz rule were observed. On the other hand, the theory is slightly modified to account for the proper stress-optical relation so that it can be used to simulate directly the birefringence fields of complex flows without being restricted by the validity of the stress-optical rule. Despite its remarkable success in explaining many experimental findings, the theory is found to be unable to predict satisfactorily the Cox-Merz rule and other similar empirical relationships in the power-law region. The discrepancies seem to imply that certain important effects might still be missing in existing reptation theories, and we discuss this issue within the reptation picture. (C) 2000 American Institute of Physics. [S0021-9606(00)50218-9]. [References: 35]