Entangled wormlike micelles

J. F. Berret, J. Appell, G. Porte. Linear rheology of entangled wormlike micelles. Langmuir 9 2851-2854, 1993. 

A decisive step towards the description of the micellar dynamics was taken with the first quantitative measurements of the linear viscoelastic response of these solutions. The pioneering works were those of Rehage, Hoffmann, Shikata, and Candau and their coworkers [14,19-33], The most fascinating result was that the viscoelasticity of entangled wormlike micelles was characterized by a single exponential in the response function. The stress relaxation function G t) was found of the form G t) = Goexp(-f/Ti ) over a broad temporal range, where Go denotes the elastic modulus and Xr is the relaxation time. Since then, this property was found repeatedly... 

The steady-state mechanical behavior described in this paragraph is representative for entangled wormlike micelles solutions. In the semidilute concentration range, however, a few exceptions to this standard behavior have been reported, as briefly discussed below. 

In combination with Equation 9.9 it is now possible to calculate the dimensions of the rod-shaped micelles from the minimum of G Tco). Kern et al. performed systematic studies of the average micellar lengths of wormlike aggregates. Typical values are of the order of several micrometers, but extreme values of more than 0.1 mm were also sometimes observed. These data are in fairly good agreement with results of cryo-TEM, which also show the presence of entangled wormlike micelles with dimensions as long as several micrometers. 

If the ideas of Marrucci [69] are correct and the non-monotonic predictions of the simple Doi-Edwards theory need to be modified in the case of polymer melts (for a recent development see [78]), then an explanation will be required for the apparent difference at high shear rates between melts and wormlike micelle solutions. There is also evidence that ordinary entangled polymer solutions do exhibit non-monotonic shear-stress behaviour [79]. As in the field of linear deformations, it may be that a study of the apparently more complex branched polymers in strong flows may shed light on their deceptively simple linear cous-... 

Some ionic surfactants form long, wormlike micelles in aqueous media, especially in the presence of electrolyte or other additives that decrease the repulsion between the ionic head groups (Raghavan, 2001). These giant, wormlike micelles give rise to unusually strong viscoelasticity because of the entanglement of these structures. 

Very large micelles may also form in binary surfactant systems. These are long wormlike micelles that become entangled at higher concentrations, giving rise to rheological properties similar to those in polymer solutions. Such systems have been examined by H band shape analysis [52,53]. The protons of the surfactant hydrocarbon chain form a very large dipolar coupled spin system with an essentially continuous distribution of transverse relaxation rates. The distribution of relaxation rates is related to the distribution of order... 

Khatory A, Kern F, Lequeux F, Appell J, Porte G, Motie N, Ott A, Urbach W (1993a) Entangled versus multiconnected network of wormlike micelles. Langmuir 9(4) 933-939... 

Wormlike micellar solutions exhibit a rich and complex rheological behavior because of their dynamical nature (continuous breaking and re-formation) and their ability to form entanglements similar to those of polymer solutions [1-8]. A crucial parameter in understanding the dynamics of wormlike micelles is the ratio of the breaking and the reptation times, (=Tbreak/Trep)... 

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