Disc, micelle shapes

The solution behavior of low molecular weight amphiphilic molecules has been intensively investigated in the past (12-16) with respect to the formation of liquid crystalline phases. In very dilute aqueous solutions, the amphiphiles are molecularly dispersed dissolved. Above the critical micelle concentration (CMC), the amphiphiles associate and form micelles (Figure 4) of spherical, cylindrical or disc-like shape. The shape and dimension of the micelles, as a function of concentration and temperature, are determined by the "hydrophilic-hydrophobic" balance of the amphiphilic molecules. The formation of spherical aggregates is preferred with increasing volume fraction of the hydrophilic head group of the amphiphile, because the... 

In the simplest liquid-crystalline phase, namely the uniaxial nematic, there is at rest a special direction designated by a unit vector n called the director (see Fig. 10-2). In the plane transverse to the director, the fluid is isotropic. The most common nematics are composed of oblong molecules that tend to point in a common direction, which defines the director orientation. Oblate, or disc-like, molecules can also form uniaxial nematics for these discotic nematics, the director is defined by the average orientation of the short axis of the molecule. Lath-like molecules or micelles (shaped like rectangular slabs), in which all three dimensions of the molecule are significantly different from each other, can form biaxial nematics (Praefcke et al. 1991 Chandrasekhar 1992 Fialtkowski 1997). A biaxial... 

Lyotropic nematic phases are generally found for short chain surfactants, for both hydrocarbon or fluorocarbon derivatives [55, 56]. Two different micelle shapes can occur (Fig. 10) [57]. One type (N. ) is thought to be composed of small cylindrical micelles and is related to the hexagonal phase, while the other type of nematic (Nj) is composed of planar disc micelles and is related to the lamellar phase. Note that the disc micelles are likely to be matchbox or ruler shaped , rather than the circular discs. Hence the disc nematic phase can have the director along the long axis of ruler micelles or along the shortest micelle dimension, as with match box micelles, while with phases the director always lies... 

Given that micelles are present in solution above the CMC, the most important consideration for the liquid crystal phases is the micelle shape. There are three major types, namely spheres, rods and discs . They can be described by using the packing constraint concepts (5, 41, 42). These give a simple description of the relationship between micelle shape and molecular shape. The micelles are assumed to be smooth, with only the hydrophobic volume in the micelle interior. The main molecular parameters are the hydrophobic group volume, usually taken as being equal to the alkyl chain volume (u), the area that the molecule occupies at the... 

The micelle shape is determined by the molecular structure as described above (see equations (21.5-21.8) and Table 21.1). There is a critical volume fraction (concentration) above which random (disordered) solutions cannot occur for each of the shapes, i.e. spheres, rods and discs (bilayers). An ordered state (liquid crystal) must form at some higher concentrations if the surfactant is sufficiently soluble. Thus the general scheme is as follows ... 

The amphipathic compounds shown in Scheme 2 can form a disc-like micelle(7). The shape of a molecular aggregate depends on the shape of the constituent molecules(8). For instance, conical molecules with large polar head groups prefer to form spherical micelles while cylindrical molecules tend to give flat aggregates. Trans-azobenzene is a rod-like molecule whereas the cis-form is bent. 

The aggregates created by amphiphiles are usually spherical (as in the case of micelles), but may also be disc-like (bicelles), rodlike, or biaxial (all three micelle axes are distinct) (Zana, 2008). These anisotropic self-assembled nanostructures can then order themselves in much the same way as liquid crystals do, forming large-scale versions of all the thermotropic phases (such as a nematic phase of rod-shaped micelles). 

For ionic amphiphiles the first formed aggregates are closely spherical. At higher amphiphile concentrations there is a tendency for the formation of rod-shaped micelles168. Also the addition of salt favours the rod-shape aggregates33. It has been suggested that disc-shaped micelles also occur160 but experimental evidence in favor of this view has only been obtained for mixed micelles of lecithin and sodium cho-late179. ... 

It is of interest to note here that the behaviour of lipid aggregates for which the optimal shape is a spherical vesicle or an infinite bilayer will be quite different from that of rod-shaped micelles. One might anticipate by analogy with rods that finite disc-like bilayers could form with cylindrical rims. For such a system the free energy would take the form = n +akT/N. From section 2, for large a, the system will assemble spontaneously into infinite bilayers. Repetition of an analysis similar to that for rods leads to values of a sufficiently large so that this process always occurs. 

Fig. 1 Association colloids (A) spherical micelle (B) cylindrical micelle (C) flattened disc-shaped micelle (D) microtubular micelle (E) inverted micelle and (F) micelle swollen by the presence of solubilized lipid soluble drug.

The Dill-Flory model may be considered as a more rigorous version of the Hartley model (30). Both models are readily applied to other shapes of micelles, such as rods, discs, bilayers, and vesicles. Also, it follows that diameters of spherical, rodlike, and disclike micelles cannot exceed the total length of two hydrocarbon chains in all-trans conformation. The number of entities in one micelle, i.e. the aggregation number s, is therefore readily estimated for any given chain length r. Assuming equal densities p (= 0.777 g/cm ) for micelles and solid n-alkanes, r may be obtained from the volume v and the constant cross section A (= 2.385 x 10 cm ) of alkane chains ... 

It is observed between the L, and in a narrow band of 34-38% surfactant between 7.5 and 23.4 °C and is made up of disc shaped micelles (Fig. 25). The phase exists up to -12% surfactant (and to = 80% in a biphasic region with water). Clouding is seen over a wide concentration range (up to >90% surfactant) with a lower critical temperature of 33.2°C. 

Fig. 3.1 Building blocks of thermotropic and lyotropic liquid crystalline phases. The upper part of the figure shows two examples of typical thermotropic mesogens. Calamitic mesogens, such as terephthal-bis-(p-butylaniline) (TBBA) [2], can be represented by prolate ellipsoids or rigid rods, while discotic mesogens, such as benzene-hexa-n-octanoate (BH8) [4], are usually described by oblate ellipsoids or discs. The lower part of the figure shows the typical surfactant molecule sodium dodecyl sulfate (SDS), which forms lyotropic phases with water [5], Such a surfactant molecule is basically composed of a polar head group and a flexible hydrophobic tail. These amphiphilic molecules aggregate into different types of micelles, which are the actual mesogens of lyotropic liquid crystals. The shape of the micelles depends mainly on the solvent concentration...

Liquid crystals constitute a distinct thermodynamic state of condensed matter, which combines the fluidity of ordinary liquids with the macroscopic anisotropy of solid crystals. They are quintessential soft matter materials, which are today best known to the broad public for their ubiquitous application as electro-optical material in flat panel liquid aystal displays (LCDs). Systems exhibiting liquid crystalline order range from small rod- or disc-shaped organic molecules (e.g., the classic liquid crystals used in LCD devices), over polymers, biological membranes, dispersions of micelles and nanoparticles to certain quantum electronic materials. 

Fig. 49. Diagrammatic representation of the lecithin-sodium cholate micelle. On the left are represented small micelles containing a larger proportion of bile salt to lecithin. Above are longitudinal sections and below are cross sections of these micelles. On the right are shown larger micelles which have less bile salt and more phospholipid. The micelles are disc-shaped bimolecular leaflets of lecithin surrounded on their hydrophobic parts by a perimeter of bile salt molecules. Wavy lines or hollow circles, alkyl chains of lecithin S, phosphoryl choline of lecithin (67).

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