Stress relaxation in living polymers: Results from a Poisson renewal model

Abstract

The problem of stress relaxation in entangled, reversibly breakable polymers (e.g., wormlike micelles) is considered. In the case where the dominant diffusive mode for the polymers is reptation, this problem has been treated in earlier numerical work by coupling the full reaction kinetics of scissions and recombinations to the dynamics of reptation (represented by a one-dimensional stochastic process). Here we study a simplified renewal model, which replaces the exact reaction kinetics by a Poisson jump process that neglects temporal correlations in the chain length experienced by a particular monomer or tube segment. Between jumps in chain length, the stress relaxation is presumed to follow that of an equivalent unbreakable chain. We apply the solution to the case of reptating flexible polymers and compare the resulting complex modulus with the earlier numerical treatments. It is found that agreement is very good. The renewal model is then used to analyze in detail, for the first time, the crossover to a rapid-scission regime in which chain diffusion between scission events is dominated by breathing modes. A third regime, in which the motion between scission events is Rouse-like, remains unsuitable for study with this model, for reasons that we explain. Various implications of the renewal model for the interpretation of experimental results are discussed. We also provide explicit estimates for chain lengths in CTAC/NaSal/NaCl systems using experimental Cole–Cole plots.

Effect of Screening of Intermicellar Interactions on the Linear and Nonlinear Rheology of a Viscoelastic Gel

“…The Cole-Cole plots for the CTAT samples with low salt content (≤ 5mM) are found to deviate considerably from the semicircular behavior characteristic of a Maxwellian fluid. We note that these deviations at high frequencies (ω ≥ ω b ) and the subsequent upturn (ω ≥ ω e ) in the Cole-Cole plots are due to the reversible breaking of the wormlike chains at a characteristic time τ break and the contribution of the localized dynamics between entanglements (the Rouse modes), respectively [19]. The absence of a well-defined plateau in the elastic modulus G ′ (ω) of the samples with low salt content at high angular frequencies ω, is possibly due to long breaking times or the occurrence of Rouse modes at relatively low frequencies.…”

Effect of ionic strength on rheological behavior of polymer-like cetyltrimethylammonium tosylate micellar solutions

“…30,31 At even higher normalized frequencies (us C > 30), an upturn in G 00 is detected, i.e., G 00 departs from the Maxwell model, goes through a minimum and then it increases linearly with frequency. 28,31 This upturn in G 00 is related to the occurrence of the Rouse and the breathing relaxation modes at high frequencies. Notice that the minimum value of G 00 at the upturn (G CTAT concentration increases and so, the dynamical response moves to higher frequencies.…”

“…Moreover, the Maxwell model with a single relaxation time predicts remarkably well the data except for the normalized viscous modulus at moderate normalized frequencies (us C > 1), as expected from Cates' model. 28 The departures from Maxwell behavior of G 00 at higher frequencies can be associated to the breaking time (s break ) of the micelles. 30,31 At even higher normalized frequencies (us C > 30), an upturn in G 00 is detected, i.e., G 00 departs from the Maxwell model, goes through a minimum and then it increases linearly with frequency.…”

“…The linear viscoelastic data are analyzed with the GranekCates model to determine whether the dynamics of the micelles are kinetically controlled (fast breaking regime) or diffusioncontrolled (slow breaking regime) 28 and the nonlinear shear data are compared with the predictions of the BMP model. 29 The relationship between these regimes with the formation of shear banding in steady shear flow as well as the roles of electrostatic and ion-specific interactions are further examined.…”

Viscoelastic properties of new mixed wormlike micelles formed by a fatty acid salt and alkylpyridinium surfactant

“…5a presents the frequency dependences G (ω) and G (ω) at different temperatures for the molar ratio [C 8 Pyr]/[potassium oleate] = 0.6. From these dependences the values of the plateau modulus G 0 and the loss modulus at high-frequency minimum G min were determined, which are related to the average contour length L of micelles by equation [25]:…”