Relaxation of Spherical Micellar Systems of Styrene−Isoprene Diblock Copolymers. 2. Nonlinear Stress Relaxation Behavior

Abstract

Nonlinear stress relaxation after imposition of step strain γ (≤2) was examined for blends of styrene−isoprene (SI) diblock copolymers in a homopolyisoprene (hI) matrix. The blends contained spherical micelles with S cores and I corona. For most cases, the blends had no plasticity and exhibited complete relaxation. Fast and slow relaxation processes characterizing the linear viscoelastic behavior of the micelles (part 1) were observed also for nonlinear relaxation moduli G(t,γ). For sufficiently small γ, G(t,γ) agreed with the linear relaxation moduli evaluated from the G* data of part 1. However, G(t,γ) decreased for larger γ (mostly for γ > 0.1). This nonlinear damping was much more significant for the slow process than for the fast process. For quantitative analysis of the damping behavior, the linear viscoelastic relaxation time τ* of the fast process was utilized to successfully separate the G(t,γ) data into contributions from the fast and slow processes, Gf(t,γ) and Gs(t,γ), in the following way: At t > 6τ* where the fast process had negligible contribution to G(t,γ), Gs(t,γ) were taken to be identical to G(t,γ). By extrapolating those Gs(t,γ) data to shorter time scales, Gs(t,γ) were evaluated at t < 6τ*. Gf(t,γ) were evaluated as G(t,γ) − Gs(t,γ). For both Gf(t,γ) and Gs(t,γ), the terminal relaxation times were insensitive to γ and the time−strain separability held in respective terminal regions. This separability enabled us to define damping functions in those regions, hx(γ) = Gx(t,γ)/Gx(t) (x = f, s). For the fast process of the SI micelles, hf(γ) exhibited only modest γ dependence that was in good agreement with the dependence for homopolymer chains. This result indicated that the fast process corresponded to relaxation of individual corona I blocks, giving a strong support for the discussion of part 1. On the other hand, hs(γ) of concentrated micelles exhibited very strong γ dependence that was comparable, in both magnitudes and sensitivities to the I block concentration and molecular weight, with the dependence of the damping function hC14(γ) obtained for solutions of SI in an I-selective solvent, n-tetradecane (C14). Those solutions exhibited plasticity due to macrolattices of the micelles, and their nonlinearity was attributed to strain-induced changes in the micelle position. Thus, the similarity of hs(γ) and hC14(γ) suggested that the slow process of the concentrated micelles in the SI/hI blends was related to the changes in the micelle position and the subsequent micelle diffusion, again supporting the discussion of part 1.