Rouse Analysis of Nonlinear Rheology of Unentangled Polymer Melts under Fast Shear: Viscoelastic Response to Superposed Oscillatory Strain

Abstract

Nonlinear rheological behavior of unentangled polymer melts can be described by the Rouse model given that its parameters, spring strength κ, bead friction coefficient ζ, and mean-square Brownian force intensity B, are allowed to change under fast flow/large strain (and to take anisotropic tensorial forms when necessary). Within this model, analytic expressions in terms of those parameters have been obtained for measurable quantities that include viscosity η, the first normal stress difference coefficient Ψ 1, and complex dielectric permittivity ε*. Those expressions in turn enable us to extract κ, ζ, and B from experimental data of unentangled melts. In particular, the rheo-dielectric ε* data under shear, recently obtained for unentangled low- M poly(butylene oxide) melt having type-A dipoles (PBO-16k; M = 16 × 10 3 ), suggest that the tensorial ζ and B have negligibly small off-diagonal components in a range of Weissenberg number Wi up to 1.2. On the basis of that study, we here focus on the complex shear moduli G ∥ * and G ⊥ * of the Rouse chain defined as responses to a small oscillatory strain superposed on the steady shear flow, with ∥ and ⊥ representing parallel and perpendicular superposition, respectively. In the case of negligible off-diagonal components of ζ and B, the Rouse analysis gave a very simple expression of those moduli, G X * (ω) = b X [ G ] G eq * (ω a X [ G ] ) with X = ∥ and ⊥, where G eq * (ω) is the linear viscoelastic (LVE) complex modulus at an angular frequency ω. Namely, in that case, the relaxation time of G X * decreases by a factor of a X [ G ] (<1) and its terminal relaxation intensity is enhanced by a factor of b X [ G ] (>1), but a relative distribution of the relaxation modes exhibits no change. Furthermore, the Rouse parameters obtained from the η, Ψ 1, and ε* data of PBO-16k were found to satisfy a specific empirical relationship, { b ∥ [ G ] } 2 ≅ 1/ a ∥ [ G ] . Because G eq ′ (ω) ≅ G eq ″ (ω) ∝ ω 1/2 at high ω where the LVE Rouse relaxation has not completed, this relationship suggests G ∥ ′′ (ω) = G eq ″ (ω) at ω > 1/τ ∥ [ G ] and G ∥ ″ (ω) < G eq ″ (ω) at ω < 1/τ ∥ [ G ], where τ ∥ [ G ] is the terminal viscoelastic relaxation time defined for G ∥ * (ω). This behavior of G ∥ ″ (ω) is superficially equivalent to that expected for a case of disappearance of viscous contributions of low-order Rouse eigenmodes under fast shear discussed in the literature on the basis of the concept of Pincus blob. However, the current Rouse analysis clearly indicated that all eigenmodes keep their viscous contributions with a magnitude determined by ζ and κ under flow, confirming the importance of nonequilibrium changes of ζ and κ in the nonlinear flow behavior of unentangled melts.

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