Significance of the longest rouse relaxation time in the stress relaxation process at large deformation of entangled polymer solutions

The significance of linear density equilibration time, 2tau(R), of a polymer chain in Doi-Edwards (DE) tube model theory was investigated for the relaxation modulus, G(t,gamma), at various magnitudes of shear, gamma, for polystyrene solutions. The longest Rouse relaxation time, TR, was defined by assuming that the Rouse model is applicable to the dynamic modulus, G'(omega), provided that G' infinity omega(1/2) over a range of angular frequency, omega. The time-dependent damping function, h(t,gamma) = G(t,gamma)/G(t,0), as a function of gamma and reduced time, t/2TR, was common to solutions with a low number of entanglements per molecule, N = 5-18. h(t,gamma) leveled off at t/2tau(R) = 10-20 to a limiting value, h(gamma), approximately equal to the DE theoretical value. It was inferred that the diffusion of chain coil and the retraction of extended chain proceeded independently. For systems with high N, h(t,gamma) was not that simple. A reduced modulus, G(t,gamma)/G(N) at high gamma (3 and 5), as a function of t/2TR was common to samples with N = 14-59 at times t/2tau(R) < 10. Here Qv is the entanglement modulus. In the same range, G(t,0)/G(N) was a universal function of t/tau(1), where tau(1), is the longest stress relaxation time. The result may imply that stress relaxation at high gamma is due mostly to chain retraction in contrast with that at low gamma. At t/2tau(R) > 10, h(t,gamma) as well as G(t,gamma)/G(N) varied in a complicated manner, which may be affected not only by 2TR but also by tau(1).