Microrheology and characteristic lengths in wormlike micelles made of a zwitterionic surfactant and SDS in brine.

We study the Brownian motion of probe particles embedded in a wormlike micellar fluid made of a zwitterionic surfactant N-tetradecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (TDPS), sodium dodecyl sulfate (SDS), and salty water to get structural and dynamical information of the micellar network. The motion of the probe particles was tracked with diffusing wave spectroscopy, and the mean square displacement as a function of time for the particles was obtained. This allowed us to obtain the long-time diffusion coefficient for microspheres moving in the micellar network and the cage size where each particle is harmonically bound at short times in that network. The bulk mechanical susceptibility of the fluid determines the response of the probe particles excited by the thermal stochastic forces. As a consequence, the mean square displacement curves allowed us to calculate the elastic (storage) and the viscous (loss) moduli as a function of the frequency. From these curves, spanning a wide frequency range, we estimated the characteristic lengths as the mesh size, the entanglement length, the persistence length, and the contour length for micellar solutions of different zwitterionic surfactant concentration, surfactant ratio ([SDS]/[TDPS]), salt concentration, and temperature. Mesh size, entanglement length, and persistence length are almost insensitive to the change of these variables. In contrast, the contour length changes in an important way. The contour length becomes shorter as the temperature increases, and it presents a peak at a surfactant ratio of ∼0.50-0.55. When salt is added to the solution, the contour length presents a peak at a salt concentration of ∼0.225 M, and in some solutions, this length can reach values of ∼12 μm. Scission energies help us to understand why the contour length first increases and then decreases when salt is added.