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, G f(t,γ) and G s(t,γ), in the following way: At t > 6τ* where the fast process had negligible contribution to G(t,γ), G s(t,γ) were taken to be identical to G(t,γ). By extrapolating those G s(t,γ) data to shorter time scales, G s(t,γ) were evaluated at t < 6τ*. G f(t,γ) were evaluated as G(t,γ) − G s(t,γ). For both G f(t,γ) and G s(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, h x(γ) = G x(t,γ)/G x(t) (x = f, s). For the fast process of the SI micelles, h f(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, h s(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 h C 14 (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 h s(γ) and h C 14 (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.

Nonlinear stress relaxation in palladium(II) complexes with triblock copolymers of styrene and butadiene

“…Relaxation moduli were calculated via division of the time-dependent engineering stress by the magnitude of the jump strain in each experiment. This procedure to calculate the stress relaxation modulus is consistent with the methodology of Watanabe et al 29 Chen et al 41 suggest that true stress is more accurate than engineering stress, particularly in the nonlinear regime.…”

“…Osaki et al 30 conclude that time-dependent reptation based on the tube model and time-and strain-dependent retraction along the tube axis are uncoupled below 700% strain, but the factorability of time and strain is not possible at higher strains. Watanabe et al 29 conclude that time-strain separability can be applied to styrene-isoprene diblock copolymers in the terminal relaxation regime, where terminal relaxation times are strain-independent below 200% strain. Ionic interactions in molten ionomers 28 do not invalidate the separability of time and strain.…”

Large amplitude oscillatory microrheology

“…9 does not pass through the origin, the Brownian response is given explicitly by the value of the curve there. This is much the same as with cessation experiments performed in a macroscopic rheometer [Watanabe et al (1996a[Watanabe et al ( , 1996b]. While it can be quite difficult to extract the Brownian microstructural response by direct imaging of particles, in this approach one need only make observations of the Lissajous-Bowditch curves.…”

“…A thorough review of traditional rheology techniques may be found in the work of Barnes et al (1989). Transient flows also give insight into the micromechanics of rate-dependent processes in steady-state flow behavior: Sudden removal of external forcing demonstrates that the microstructure relaxes over multiple time scales, each associated with distinct physical processes [Mackay and Kaffashi (1995); Watanabe et al (1996aWatanabe et al ( , 1996b; Kaffashi et al (1997); Foss (1999); Zia and Brady (2013)]. Such temporal response reveals the underlying connection between structure and rheology.…”

Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology

“…For example Mackay and Kaffashi (1995) and Kaffashi et al (1997) studied the decay of stress immediately after the cessation of imposed strain-rate on a sheared suspension; they found that the hydrodynamic stress decays instantaneously, as it must-the hydrodynamic stress is proportional to the imposed strain-rate, and thus must vanish in the absence of flow. Watanabe et al (1996b) and Watanabe et al (1996a) analyzed stress development and relaxation in sudden startup and cessation of shearing flow and found both short-and long-time relaxation modes. These studies show that the macroscopic stress relaxes via distinct transport processes, but the microstructural evolution that accompanies this relaxation is not as thoroughly studied.…”