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, 2τR, 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, τR, was defined by assuming that the Rouse model is applicable to the dynamic modulus, G‘(ω), provided that G‘ ∝ ω1/2over 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/2τR, was common to solutions with a low number of entanglements per molecule, N = 5−18. h(t,γ) leveled off at t/2τR = 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/2τR was common to samples with N = 14−59 at times t/2τR < 10. Here G N is the entanglement modulus. In the same range, G(t,0)/G N was a universal function of t/τ1, where τ1 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/2τR > 10, h(t,γ) as well as G(t,γ)/G N varied in a complicated manner, which may be affected not only by 2τR but also by τ1.