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.