Stress Buildup under Start-Up Shear Flows in Self-Assembled Transient Networks of Telechelic Associating Polymers

Abstract

The nonaffine transient network theory is used to study the time development of the shear and normal stresses under start-up shear flows in networks formed by self-assembled telechelic, hydrophobically modified water-soluble polymers. The initial slope, strain hardening, and overshoot of the shear stress are studied in detail in relation to the nonlinear tension-elongation curve of the elastically active chains in the network. The condition for the occurrence of strain hardening (upward deviation of the stress from the reference curve defined by the linear moduli) is found to be gamma > gammac(A), where gamma is the shear rate, gamma(c) is its critical value for strain hardening, and A is the amplitude of the nonlinear term in the tension of a chain. The critical shear rate gamma(c) is calculated as a function of A. It is approximately 6.3 (in the time unit of the reciprocal thermal dissociation rate) for a nonlinear chain with A = 10. The overshoot time t(max) when the stress reaches a maximum and the total deformation gamma(max) = gamma(t max) accumulated before the peak time are obtained in terms of the molecular parameters of the polymer chain. The maximum deformation gamma(max) turns out to depend weakly upon the shear rate gamma. The first and second normal stress differences are also studied on the basis of the exact numerical integration of the theoretical model by paying special attention to their overshoot, undershoot, and sign change as a function of the shear rate. These theoretical results are compared with recent rheological experiments of the solutions of telechelic hydrophobically modified poly(ethylene oxide)s carrying short branched alkyl chains (2-decyl-tetradecyl) at both ends.

Rate-Dependent Stiffening and Strain Localization in Physically Associating Solutions

“…This is consistent with the fluid fracture experiments of Berret et al 9 and with more recent theoretical results and start-up experiments of non-linear stress growth in telechelic polymer solutions 27 and more complex transient networks. 4 At lower reduced rates (Γ < 1), the maxima in the stress-strain curves persisted, although the feature shifts to greater values of strain.…”

Rheology of associative polymer solutions

“…Some time ago Tanaka and Edward [9,77] proposed a theory, based on the transient network model that successfully explained some typical rheological behaviors observed for telechelic associating polymers, but they did not consider non-linear rheology. In recent years their theory was refined and extended to describe also the shear-thickening phenomena observed with associating polymers [11,[78][79][80][81][82][83][84]. In the modified theory it was assumed that overstretching of the bridging chains leads to thickening, while a reduced bond life time of stretched chains leads to shear-thinning.…”

Rheology of Aqueous Solution of Hydrophobically Modified Ethoxylated Urethane (HEUR) with Fluorescent Probes at Chain Ends: Thinning Mechanism

“…Specifically, the thickening often noted at shear rates g 4 just above the equilibrium relaxation frequency 1/t has been attributed to the finite extensible nonlinear elasticity (FENE) of the HEUR strands under fast shear, 3,[14][15][16]24,25) or, the shear-induced increase of the number density n of effective bridge chains. [17][18][19] However, recently, both h and …”