(An) analysis of the nonlinear stress relaxation of highly concentrated linear monodisperse polymer solutions in short-time region

Abstract

As a purpose to develop a molecular theory for linear flexible polymer concentrated solutions and melts, Doi and Edwards suggested in 1978 a good manageable constitutive equation called reptation theory, which would represent the stress-strain relationship. It covered only a long-time scale corresponding to the region of linear (small strain) viscoelasticity. But, in 1980 Doi proposed the short-time relaxation process in terms of the time and strain, associated with that of nonlinear (large strain) relaxation behaviors. Based upon Doi``s theory, a sequence of modified short-time relaxation process was deduced for the nonlinear viscoelasticity of monodisperse polymer system. There might be four possible modes of relaxation mechanisms:(A) Rouse segmental motion between two fixed slip-links, (X) chain slippage motion to recover the equivalent monomer density, (B) equilibration of primitive segment along the chain contour, and (C) reptational motion with disengagement corrected for contour length fluctuation. In this study, the constitutive equation for the process (X) was derived by considering the slippage motion across the slip-links and compared with the earlier relaxation theories. As a result, the proposed process (X) was proved to reinforce the existence of the relaxation step (X) analytically between processes (A) and (B), and was capable to combine the theory of linear viscoelasticity with the nonlinear viscoelasticity.