Packing parameter, micellar

Figure 16.1 Relationship between molecular shape, aggregate structure in dilute dispersions, phase behavior and packing parameter. Micellar phase (L,), cubic micellar phase (I), hexagonal phase (H), bicontinuous cubic phase (Q), La lamellar phase. Subscripts I and II indicate normal and inverted phases, respectively. From M. Scarzello, Aggregation Properties of Amphiphilic DNA-Carriers for Cene Delivery, Ph. D. Thesis University of Groningen, p 6, 2006...

What is meant by the optimal head group area of a surfactant What is the packing parameter (P Explain how packing considerations can be used to determine the possible shapes of the micellar aggregates. 

Bilayers are preferentially formed for Ns = 0.5...1. Lipids that form bilayers cannot pack into micellar or cylindrical structures because of their small head group area and because their alkyl chains are too bulky to fit into a micelle. For bilayer-forming lipids this requires that for the same head group area a a, and chain length Lc, the alkyl chains must have twice the volume. For this reason lipids with two alkyl chains are likely to form bilayers. Examples are double-chained phospholipids such as phophatidyl choline or phophatidyl ethanolamine. Lipids with surfactant parameters slightly below 1 tend to form flexible bilayers or vesicles. Lipids with Ns = 1 form real planar bilayers. At high lipid concentration this leads to a so-called lamellar phase. A lamellar phase consist of stacks of roughly parallel planar bilayers. In some cases more complex, bicontinuous structures are also formed. As indicated by the name, bicontinuous structures consist of two continuous phases. 

Packing parameter Micellar shape Surfactant Mesophase example... 

A useful concept for characterizing micelle geometry is the critical packing parameter (CPP) [2]. The aggregation number N is the ratio between the micellar core volume, V and the volume of one chain, v. 

A theory of micellar structure, based upon the geometry of various micellar shapes and the space occupied by the hydrophilic and hydrophobic groups of the surfactant molecules, has been developed by Israelachvili, Mitchell, and Ninham (1976, 1977) and Mitchell and Ninham (1981). The volume Vh occupied by the hydrophobic groups in the micellar core, the length of the hydrophobic group in the core /,., and the cross-sectional area ao occupied by the hydrophilic group at the micelle-solution interface are used to calculate a packing parameter, Vn/hao, which determines the shape of the micelle. 

Recently, Miller and Cacciuto explored the self-assembly of spherical amphiphilic particles using molecular dynamics simulations [46]. They found that, as well as spherical micellar-type structures and wormlike strings, also bilayers and faceted polyhedra were possible as supracolloidal structures. Whitelam and Bon [47] used computer simulations to investigate the self-assembly of Janus-like peanut-shaped nanoparticles and found phases of clusters, bilayers, and non-spherical and spherical micelles, in accordance with a packing parameter that is used conventionally and in analogy to predict the assembled structures for molecular surfactants. They also found faceted polyhedra, a structure not predicted by the packing parameter (see Fig. 8). In both studies, faceted polyhedra and bilayers coexist, a phenomenon that is still unexplained. 

As an example of the effects of an amphiphilic drug on the structure of surfactant self-assemblies. Figure 1.4 shows part of the phase diagram of monoolein, water, lidocaine base and licocaine-HCl (21). As can be seen, the cubic phase (c) formed by the monoolein-water system transforms into a lamellar liquid crystalline phase on addition of lidocaine-HCl, whereas it transforms into a reversed hexagonal or reversed micellar phase on addition of the lidocaine base. Based on X-ray data, it was inferred that the cubic phase of the monoolein-water system had a slightly reversed curvature (critical packing parameter about 1.2). Thus, on addition of the... 

For lyotropic liquid crystals, the temperature plays a secondary role in the formation of the individual mesophases. The primary influence on the phase sequence is exerted by the solvent concentration. The solvent concentration is directly connected to the packing parameter and thus to the micellar shape (cf. Sect. 3.1), which largely determines the mesophase type. At low solvent concentrations lamellar phases are usually formed. By increasing the solvent concentration, columnar and nematic phases appear. At very high solvent concentrations an isotropic micellar solution dominates. An illustration of this phase behavior is shown in the theoretical phase diagram depicted in Fig. 3.9 (c [14]). The individual phases in Fig. 3.9 are separated by biphase regions. 

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