Entanglement networks of rod-like micelles

Surfactant solutions with rod-like micelles can have notable viscosities up to six times higher than the water viscosity [37]. This can be explained by the presence of entangled rodlike micelles (often also called worm-like micelles or thread-like micelles) which arrange themselves in a supramolecular transient network [38-41 ]. Such solutions often have elastic properties but they do not show a yield stress. This means that even high viscous solutions flow under the influence of very small shear stress. In this situation they show a zero shear viscosity which is given by  

In other cases, several discrete relaxation times or distributions of relaxation times can be found [39]. This is typically the case if the stress relaxation is dominated by reptation processes [42 ]. The stress relaxation model can explain why surfactant solutions with wormlike micelles never show a yield stress Even the smallest applied stress can relax either by reptation or by breakage of micelles. For higher shear rates those solutions typically show shear thinning behaviour and this can be understood by the disentanglement and the orientation of the rod-like micelles in the shear field. 

While the network density v is more or less given by the concentration of the surfactant, the relaxation time can depend on many parameters such as surfactant concentration, temperature, type of counterions or ionic strength. 

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