Viscoelasticity, Nonlinear Shear Start-up, and Relaxation of Entangled Star Polymers

Abstract

We report on a detailed rheological investigation of well-defined symmetric entangled polymer stars of low functionality with varying number of arms, molar mass of the arms, and solvent content. Emphasis is placed on the response of the stars in simple shear, during start-up, and for relaxation upon flow cessation. To reduce experimental artifacts associated with edge fracture (primarily) and wall slip, we employ a homemade cone-partitioned plate fixture which was successfully implemented in recent studies. Reliable data for these highly entangled stars could be obtained for Weissenberg numbers below 300. The appearance of a stress overshoot during start-up with a corresponding strain approaching a value of 2 suggests that in the investigated shear regime the stars orient but do not stretch. This is corroborated by the fact that the empirical Cox–Merx rule appears to be validated, within experimental error. On the other hand, the (shear) rate dependent steady shear viscosity data exhibit a slope smaller than the convective constraint release slope of −1 (for linear polymers) for the investigated range of rates. The broadness of the stress overshoot reflects the broad linear relaxation spectrum of the stars. The initial stress relaxation rate, reflecting the initial loss of entanglements due to the action of convective constraint release in steady shear flow, increases with Weissenberg number. More importantly, when compared against the relevant rates for comb polymers with relatively short arms, the latter are slower at larger Weissenberg numbers. At long times, the relaxation data are consistent with the linear viscoelastic data on these systems.

Stochastic and preaveraged nonlinear rheology models for entangled telechelic star polymers

“…It is a "non-sticky" region. Indeed, our predictions of the shear stress growth coefficient, η + , in this regime are consistent with shear experiments on non-telechelic entangled star polymers [41].…”

“…(i) When the shear rate is smaller than the inverse of the effective stretch relaxation time, τ sφ = τ s /(1 − φ), for regions A 1 and A 2 , or smaller than the stretch relaxation time τ s for region B, the viscosity shows a mild overshoot before reaching the steady state. This mild overshoot under the LVE has been observed experimentally for non-telechelic entangled stars [41]. Indeed, at low shear rates, the system is not aware of the stickers.…”

“…During this detachment and retraction process, it contributes significantly to CCR, and we capture this through Equation (41).…”

A computational and experimental study of the linear and nonlinear response of a star polymer melt with a moderate number of unentangled arms

“…The slope of η max /η steady fromγ = 10 s −1 for the experimental data is very close to that observed for low functionality highly entangled polyisoprene (PI) star polymer melts. 27 The difference in the simulation data can be attributed as above for the steeper shear thinning to the absence of polymer deformation. We also calculated γ max which is the strain where η max for the shear thinning regimes.…”

“…The data and WLF fits are consistent with other PS architectures and molar masses referred to the same temperature. 27,32 At low frequencies in the FS measurements, large errors in the storage modulus G can develop at high phase angles (approaching 90 • ) where the loss modulus G far exceeds G . In this regime, only a small amount of the response signal is associated with G and as such a slope characteristic of terminal relaxation for G may be absent.…”