Slow dynamics of wormlike micelles

We present an extensive rheology study of the wormlike micelle system lecithin-water-cyclohexane. In this system the micelles are really wormlike, meaning that there are no signs of micellar branching, as it has previously been demonstrated by NMR self-diffusion experiments (R. Angelico, U. Olsson, G. Palazzo and A. Ceglie, Phys. Rev. Lett., 1998, 81, 2823). Wormlike micelles break and recombine, processes that are important for the stress relaxation. When branching is highly unfavorable, micelle recombination reactions only involve micelle ends, the concentration of which are very low when the micelles are very long. Hence, the break and recombination kinetics is very slow for true wormlike micelles. In the present system, the stress relaxation times are of the order of an hour. This is about three to four orders of magnitude longer than what commonly is observed in systems claimed to contain wormlike micelles. We conclude that systems with true wormlike micelles are very rare. An exponential stress relaxation is observed except at lower concentrations, where the micellar breaking time appears to exceed the reptation time. Because of the slow dynamics, the linear elastic modulus can be obtained from small rapid shear deformations, for which the system obeys Hooke's law. Larger deformations result in a fracture of the micellar network at a critical strain gamma* similar to phi(-1), where phi is the micelle volume fraction. For gamma < gamma* we may still obtain fracture, although with a lag time, tau*, that decreases with increasing gamma, and vanishes when gamma = gamma*. Extrapolating tau* to zero deformation we obtain the estimate approximate to 250 s at the highest concentration phi = 0.29. We interpret this time as the equilibrium micellar breaking time at rest, a quantity not previously measured.