Transient network theory of wormlike micelles: topological force accelerates relaxation

A new transient network theory is developed to study the rheological properties of entangled wormlike micelles. The dynamic mechanical moduli are calculated on the basis of the model network in which local structure of the wormlike micelles is represented by the entangled loops. These loops interact with each other by statistical force due to the topological constraints. They are assumed to pass through each other within a finite time to release the internal stress (phantom chain-crossing model). The high frequency plateau modulus G(infinity) and the relaxation time tau as functions of the micellar concentration are calculated and compared with the experimental data on the aqueous solutions of cetyltrimethylammonium bromide (CTAB) mixed with ionic aromatic compound sodium salicylate (NaSal). It turns out that creation and annihilation of the entanglements are strongly coupled to the topological force. The rheological relaxation time decreases with the concentration of the micelles because the average radius (correlation length xi) of the entangled loops, and their contour length L decrease with the CTAB concentration. Hence, the topological force is amplified by the increase in the concentration and, as a result, accelerates the stress relaxation by chain-crossing.