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, 2τ R, of a polymer chain in Doi−Edwards (DE) tube model theory was investigated for the relaxation modulus, G ( t,γ), at various magnitudes of shear, γ, for polystyrene solutions. The longest Rouse relaxation time, τ R, was defined by assuming that the Rouse model is applicable to the dynamic modulus, G ‘(ω), provided that G ‘ ∝ ω 1/2 over a range of angular frequency, ω. The time-dependent damping function, h ( t,γ) = G ( t,γ)/ G ( t,0), as a function of γ and reduced time, t /2τ R, was common to solutions with a low number of entanglements per molecule, N = 5−18. h ( t,γ) leveled off at t /2τ R = 10−20 to a limiting value, h (γ), 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,γ) was not that simple. A reduced modulus, G ( t,γ)/ G N at high γ (3 and 5), as a function of t /2τ R was common to samples with N = 14−59 at times t /2τ R < 10. Here G N is the entanglement modulus. In the same range, G ( t,0)/ G N was a universal function of t /τ 1, where τ 1 is the longest stress relaxation time. The result may imply that stress relaxation at high γ is due mostly to chain retraction in contrast with that at low γ. At t /2τ R > 10, h ( t,γ) as well as G ( t,γ)/ G N varied in a complicated manner, which may be affected not only by 2τ R but also by τ 1 .