Wormlike micelles

A numerical study of the MMEP kinetics, as described by the system of nonlinear differential equations (26), subject to mass conservation (Eq. (27)), has been carried out [64] for a total number of 1000 monomers and different initial MWDs. As expected, and in contrast to the case of wormlike micelles, it has been found that during relaxation to a new equilibrium state the temporal MWD does not preserve its exponential form. 

While these model predictions have been confirmed experimentally [11] in a number of cases, significant deviations have been observed [73] in both limits of very low and high salt concentrations in systems of wormlike micelles. 

Living polymers and wormlike micelles suggest an interesting field for basic research in which the constant process of scission and recombination of the... 

In contrast to statics, the relaxational kinetics of living polymers and of giant wormlike micelles is unique (and different in both cases). It is entirely determined by the processes of scission/recombination and results in a nonlinear approach to equilibrium. A comparison of simulational results and laboratory observations in this respect is still missing and would be highly desirable. 

M. Kroger, R. Makhloufi. Wormlike micelles under shear flow A microscopic model studied by nonequihbrium molecular dynamics computer simulations. Phys Rev E 55 2531-2536, 1996. 

A. Khatory, F. Lequeux, F. Kern, S. J. Candau. Linear and nonlinear viscoelasticity of semidilute solutions of wormlike micelles at high-salt content. Langmuir 9 1456-1464, 1993. 

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

E. Faetibold, G. Waton. Dynamical properties of wormlike micelles in the vicinity of the crossover between dilute and semidilute regimes. Langmuir 77 1972-1979, 1995. 

FIG. 1 Self-assembled structures in amphiphilic systems micellar structures (a) and (b) exist in aqueous solution as well as in ternary oil/water/amphiphile mixtures. In the latter case, they are swollen by the oil on the hydrophobic (tail) side. Monolayers (c) separate water from oil domains in ternary systems. Lipids in water tend to form bilayers (d) rather than micelles, since their hydrophobic block (two chains) is so compact and bulky, compared to the head group, that they cannot easily pack into a sphere [4]. At small concentrations, bilayers often close up to form vesicles (e). Some surfactants also form cyhndrical (wormlike) micelles (not shown). 

In order to illustrate the potential applications of rheo-NMR five examples have been chosen. The first example deals with wormlike micelles [22] in which NMR velocim-etry is used to profile anomalous deformational flow and deuterium NMR spectroscopy is used to determine micellar ordering in the flow. The second example concerns flow in a soft glassy material comprising a solution of intermittently jammed star polymers [23], a system in which flow fluctuations are apparent. The third... 

Shear-banded Flow in Wormlike Micelle Solutions... 

Banding effects have also been seen in these wormlike micelle materials via optical birefringence [31, 32], although it is not clear that birefringence banding necessarily corresponds to shear banding [33], Of course, the anisotropy of bi-... 

Fig. 2.8.10 (a) Grey scale map of shear taken across gap of 7° cone-and-plate device, for the semi-dilute wormlike micelle system 60 mM cetylpyridinium chloride—100 mM sodium... 

Fig. 2.8.11 Schematic constitutive relationship (shear stress versus shear rate) for a wormlike micelle system exhibiting constitutive instability. When the average shear rate exceeds yc the fluid subdivides into two coexisting shear bands residing on stable branches of the constitutive relationship.

Instead of the familiar sequence of morphologies, a broad multiphase window centred at relatively high concentrations (ca. 50-70% block copolymer) truncates the ordered lamellar regime. At higher epoxy concentrations wormlike micelles and eventually vesicles at the lowest compositions are observed. Worm-like micelles are found over a broad composition range (Fig. 67). This morphology is rare in block copolymer/homopolymer blends [202] but is commonly encountered in the case of surfactant solutions [203] and mixtures of block copolymers with water and other low molecular weight diluents [204,205]. 

Nieh MP, Raghunathan VA, Glinka CJ, Harroun TA, Pabst G, Katsaras J (2004) Magnetically alignable phase of phospholipid bicelle mixtures is a chiral nematic made up of wormlike micelles. Langmuir 20 7893-7897... 

Regioselective crosslinking of the core domain of cylindrically shaped, wormlike micelles composed of poly[(butadiene)45-b-(ethylene oxide)55] and assembled in aqueous solution at < 5% block copolymer concentrations, was performed using radical coupling of the double bonds throughout the poly(butadiene) phase [27] (Figure 6.3b). This resulted in a 13% reduction in the core diameter, from 14.2 to 12.4 nm, as measured by small-angle neutron scatter-... 

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-... 

The relaxation times vary with time itself only when the backbone becomes full-stretched (A=q), and then in such a way as to maintain this maximum stretch until the flow no longer tends to stretch the molecules further. The history of relaxation time Zj, needs to be taken into account in the integral part of the dynamic equations, just as for wormlike micelles [72]. The stress itself is a function of both molecular variables ... 

Here, V is the volume of the hydrocarbon chain(s) of the surfactant, the mean cross-sectional (effective) headgroup surface area, and 4 is the length of the hydrocarbon tail in the all-trans configuration. Surfactants with Pcone-shaped and form spherical micelles. For l/3truncated-cone-shaped, resulting in wormlike micelles (the term wormlike is preferred over rodlike to highlight the highly dynamic nature of these micelles). 

This calculation is for spherical micelles, but a similar calculation could be used to obtain estimates of salt concentrations for ionic wormlike micelles. Such salt concentrations for wormlike micelles are expected to be increased in comparison to spherical micelles. In fact, the addition of counterions or a sufficient increase in surfactant concentration often leads to a transition from spherical micelles to wormlike micelles. As the free counterion concentration in solution increases, so does the counterion binding. As a result, electrostatic repulsion between the charged head-groups is increasingly shielded and the mean cross-sectional (effective) headgroup... 

Turner MS, Cates ME. Linear viscoelasticity of wormlike micelles—a comparison of micellar reaction-kinetics. J Phys II 1992 2 503-519. 

Turner MS, Marques C, Cates ME. Dynamics of wormlike micelles—the bond-interchange reaction scheme. Langmuir 1993 9 695-701. 

Padding, J.T., and Boek, E.S. "Evidence for diffusion-controlled recombination kinetics in model wormlike micelles". Eurcrphys. Lett. 66, 756762 (2004). 

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. 

Fig. 2 WAXS pattern of wormlike micelles of PI320A-PFS53. The related period are given above each apparent peak...

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