Determining threadlike micelle lengths from rheometry

Abstract

We show that the average length ⟨L⟩ of threadlike micelles in surfactant solutions predicted by fitting results of a mesoscopic simulation, the “pointer algorithm,” to experimental G′(ω), G″(ω) data, is longer than, and more accurate than, that from a scaling law that equates ⟨L⟩/le to the modulus ratio G0/Gmin′′. Here, G0 is the plateau modulus, Gmin′′ is obtained at the local minimum in G″, and le is the entanglement length. The accuracy of the pointer algorithm is supported by the agreement of its predictions with results from a recent application of the slip-spring simulation method to threadlike micelles. Improved fits of the pointer algorithm to the slip-spring results are obtained for weakly entangled micelles (with an average number of entanglements of Z < 15) if the full spectrum of Rouse modes is included in the description rather than just the high-frequency modes included in an earlier version. For sodium laureth-1 sulfate and cocamidopropyl betaine in NaCl solutions, we find scaling relations for micelle length, the plateau modulus, and the persistence length that are in rough agreement with the predictions of mean field theory and with the modified scaling relation in which ⟨L⟩/le is raised to the 0.82 power, rather than unity, that we recommend as an improvement to the original scaling law.

Complete Dynamic Phase Diagram of a Supramolecular Polymer

“…It coincides the cross-over between G′ and G″, as expected for Maxwellian response with one terminal time and observed in living wormlike micelles. 19,20,29 In this situation, G′ exhibits an unambiguous plateau, which extends to over more than 2 decades in frequency. As the temperature increases, the low-frequency modulus crossover is still detected, along with a G′ plateau (at higher frequencies), where G′ > G″.…”

Modeling Techniques for the Rheology of Wormlike Micellar Solutions

“…Based on Cates' model, one of the most sophisticated models is the pointer algorithm originally developed by Zou and Larson. [13][14][15][16] The pointer algorithm is a mesoscopic simulation method that tracks relaxed/unrelaxed parts of an ensemble of micelles to calculate the stress relaxation modulus. In this model, the reptation, chain-length fluctuation, constraint release, Rouse modes, and bending modes are addressed for an accurate linear rheology prediction.…”

“…Recently, using this model, Tan and coworkers established a sophisticated relation to estimate a micelle length from linear rheological data. 16) Despite the success of the pointer algorithm in linear rheology, nonlinear rheology cannot be addressed by the current pointer algorithm.…”

Dynamics and Rheology of Supramolecular Assemblies at Elevated Pressures

“…In the absence of humidity, the scaling for the modulus was confirmed, but not that for the terminal relaxation time (where a lower exponent, by about half, was reported) . Recently, Larson and co-workers combined rheology, scattering, and simulations and provided quantitative estimates for the characteristic lengths of supramolecular polymer solutions. − These assemblies are characterized by a length distribution which affects the rheological properties . Using efficient chain stoppers or increasing temperature, we can induce changes in their length (which in general follows Arrhenius behavior, ⟨ L ⟩ ≈ e ( E / k B T ) , where E is the activation energy associated with bonding, k B is the Boltzmann constant, and T is the absolute temperature). − In this study, we report that pressure can also induce changes in the average length, ⟨ L ⟩, as illustrated schematically in Figure .…”