Non-spherical micelle

Non-spherical micelles of poly(ethylene)(PE)-poly(ethylene-propylene)(PEP) in decane are self-assembhng in the form of extended platelets that have a crystalline PE-core and a planar PEP brush on both sides. Due to the large size of the platelets the centre of mass diffusion is extremely slow and allows a clear separation of the density fluctuation in the brush. NSE experiments [301] have been analysed in terms of the model of de Gennes [300]. The friction coefficient and modulus of the brush were found to be similar to those of a typical gel. 

Possible candidates for aggregates can now be examined. For surfactant-water systems these have been restricted in the past to spherical micelles, non-spherical micelles (globular, cylindrical), vesicles, liposomes, bilayers, and for oil-water-surfactant systems spherical drops, normal or inverted (water in oil) or (oil in water). 

Assuming that the surface area per surfactant molecule is everywhere equal or close to the optimum area ao non-spherical micelles can occur alternatively when v/aok > 1/3. Similar critical conditions for the formation of cylindrical micelles and planar bilayers, respectively, are... 

The appearance of the local minimum in the concentration dependency of the relaxation time of the slow process for concentrated solutions can be connected also with formation of non-spherical micelles [140]. Actually, it is well-known that micelles change their shape with increasing concentration. The increase of the concentration of some counterions can lead to the formation of giant wormlike micelles (living polymers) [141]. In this case the equilibrium size distribution of micelles changes entirely and is described by an exponential law [141]... 

Spherical micelles Non-spherical micelles Vesicles or bilayers Bicontinous plane Inverted stnjcture... 

Sdderman, O., Jonstromer, M. and van Stam, J., Non-spherical micelles in the sodium dodecylsulphate-brine system, J. Chem. Soc. Faraday Trans., 89, 1759-1764 (1993). 

Figure 3.2 Aggregation numbers, n, of surfactants versus the number, m, of carbon atoms in the normal alkyl moiety. Key , ionic surfactants and , non-ionic surfactants. Points above the curve refer to non-spherical micelles. From Schott [66] with permission.

In most cases block copolymers form spherical micelles in dilute solution. In only a few studies was the formation of non-spherical aggregates reported. For example, cylindrical or worm-like micelles were observed for polystyrene-polybutadiene-polystyrene (PSt-PB-PSt) triblock copolymers in ethylacetate [148], PSt-PI (polyisoprene) in N,N-dimethylformamide (DMF), or PEO-PPO-PEO triblock copolymers in aqueous solutions [149]. Conditions for the formation of non-spherical micelles currently seem to be clear only for ionic block copolymers. Due to enormous interfacial tension these systems are in a thermodynamic state close to the super-strong segregation limit (SSSL) [150]. Under these conditions, a sequence of shape transitions from spherical - cylindrical - lamellar is possible. Such transitions can be induced by increasing the ionic strength of the solution or by increasing the relative length of the core block. 

It thus seems that the basic physics of the process of micellization is well understood, but one can hardly expect the theories to be terribly quantitative. Some properties, such as the dimensions of the micelle, are not overly sensitive to the details of the approximation scheme, but other properties, such as cmc, the aggregation number and the thermodynamics of micelle formation are much more volatile in their behaviour. The theories presented all assumed a monodisperse micelle distribution, but in fact one can use the methods to calculate the full distribution from equations (42) and (43), and indeed the distribution does turn out to be narrowly peaked. One can also use the theories to estimate the relative stabilities of spherical micelles vis-a-vis non-spherical micelles, infinite cylinders and bilayers, and preliminary studies indeed indicate the possibility of infinite cylinders at copolymer concentrations less than the cmc. The possible formation of these and other structures should be more thoroughly investigated. 

Time-resolved in situ Small Angle Neutron Scattering (SANS) investigations have provided direct experimental evidence for the initial steps in the formation of the SBA-15 mesoporous material, prepared using the non-ionic tri-block copolymer Pluronic 123 and TEOS as silica precursor. Upon time, three steps take place during the cooperative self-assembly of the Pluronic micelles and the silica species. First, the hydrolysis of TEOS is completed, without modifications of the Pluronic spherical micelles. Then, when silica species begin to interact with the micelles, a transformation from spherical to cylindrical micelles takes place before the precipitation of the ordered SBA-15 material. Lastly, the precipitation occurs and hybrid cylindrical micelles assemble into the two-dimensional hexagonal structure of SBA-15. 

Figure 22.1 The amphiphilic nature of phospholipids in solution drives the formation of complex structures. Spherical micelles may form in aqueous solution, wherein the hydrophilic head groups all point out toward the surrounding water environment and the hydrophobic tails point inward to the exclusion of water. Larger lipid bilayers may form by similar forces, creating sheets, spheres, and other highly complex morphologies. In non-aqueous solution, inverted micelles may form, wherein the tails all point toward the outer hydrophobic region and the heads point inward forming hexagonal shapes.

The non-aqueous system of spherical micelles of poly(styrene)(PS)-poly-(isoprene)(PI) in decane has been investigated by Farago et al. and Kanaya et al. [298,299]. The data were interpreted in terms of corona brush fluctuations that are described by a differential equation formulated by de Gennes for the breathing mode of tethered polymer chains on a surface [300]. A fair description of S(Q,t) with a minimum number of parameters could be achieved. Kanaya et al. [299] extended the investigation to a concentrated (30%, PI volume fraction) PS-PI micelle system and found a significant slowing down of the relaxation. The latter is explained by a reduction of osmotic compressibihty in the corona due to chain overlap. 

Micelles can be spherical or laminar or cylindrical. Micelles tend to be approximately spherical over a fairly wide range of concentrations above CMC (critical micelle concentration) but often they are marked transitions to larger, non spherical liquid crystal structures at high concentrations. For straight chain ionic surfactants, the number of monomer units per micelle ranges between 30 and 80. 

I would also like to mention one type of non-spherical compartment that is much less popular than micelles or vesicles, hut in my view very interesting. These are the cubic phases, so called because of their cubic symmetry. Many different types of cubic structures have been described (Mariani et al., 1988 Lindblom and Rilfors, 1989 Fontell, 1990 Seddon, 1990 Seddon etal., 1990 Luzzati et al., 1993). 

The influence of non-interacting micelles (i.e. spherical micelles or small rod-like micelles not far beyond the cmc) on the viscosity r] of a solution can be described by the Einstein equation ... 

On the assumption that the surface area per amphiphile is everywhere equal to or close to the optimum area we must therefore look for alternative non-spherical shapes once v/aol > h (The way v and 4 are actually determined from the nature of the hydrocarbon chains is model-dependent and not of immediate concern here.) Similarly, the critical condition for cylindrical micelles and planar bilayers is readily found to be respectively... 

As discussed in section 5, once aggregation numbers exceed a certain limit, it is no longer possible to pack amphiphiles into spheres. If the aggregation number is not too large, we can expect micelles to take a globular, near spherical, shape and now consider corrections to the theory which arise from this non-sphericity. 

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