(742d) Determining Micelle Lengths and Persistence Lengths from Rheometry

Using a mesoscopic simulation, "the pointer algorithm," we are able to extract surfactant micelle parameters, such as the average micelle length and relaxation time, from experimental rheological data. Our overall goal is to relate microscopic micelle parameters to macroscopic flow behavior (rheology) and salt and surfactant concentration (solution composition). Here, we focus on determining the micelle persistence length from high frequency rheology data, obtained from diffusing-wave spectroscopy (DWS). We consider several methods for extracting the persistence length from rheology - 1) using the pointer algorithm to fit the rheology curves across the entire frequency range, where the persistence length is an output from the simulation, 2) calculating the persistence length from the magnitude of the G" curve at high frequency, and 3) calculating the persistence length from the frequency where the Rouse-Zimm regime transitions to bending modes, which occurs when the slope of the G" curve transitions from a 5/9 to 3/4 power law scaling. Methods 1 and 2 are based on treating the micelles as semiflexible chains that can bend under stress[1]. We can then compare the results from each of these methods to other results from literature, and we consider both persistence lengths extracted from rheology[2,3] and from other techniques, including small-angle neutron scattering (SANS)[4], flow-birefringence[5], and coarse-grained molecular dynamics (CGMD)[6].

Once the persistence length is known, we are able to predict the remainder of the micelle parameters required for our simulation from a combination of experimental data and correlations. We find that for some solutions, the micelle lengths present can approach 100 μm, which is much longer than reported in literature, but appears consistent with electron micrographs. Our results for the average micelle length and persistence length expand on the range of systems studied using the pointer algorithm and indicate the presence of extremely long wormlike micelles that are an order of magnitude longer than previously reported.

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[3] Galvan-Miyoshi, J.; Delgado, J.; Castillo, R. Diffusing wave spectroscopy in Maxwellian fluids. Eur. Phys. J. E 2008, 26, 369-377.
[4] Vogtt, K.; Jiang, H.; Beaucage, G.; Weaver, M. Free Energy of Scission for Sodium Laureth-1-Sulfate Wormlike Micelles. Langmuir 2017, 33, 1872-1880.
[5] Helgeson, M. E.; Hodgdon, T. K.; Kaler, E. W.; Wagner, N. J. A systematic study of equilibrium structure, thermodynamics, and rheology of aqueous CTAB/NaNO₃ wormlike micelles. Journal of Colloid and Interface Science 2010, 349, 1-12.
[6] Mandal, T.; Koenig, P. H.; Larson, R. G. Nonmonotonic Scission and Branching Free Energies as Functions of Hydrotrope Concentration for Charged Micelles. Phys. Rev. Lett. 2018, 121, 038001.