Micelle shape surfactant packing parameter

Effective Shape of the Surfactant Packing Parameter Aggregate Morphology Cone <1 /3 P = fj Spherical micelles... 

At moderate surfactant concentration, the micelle shape is determined by the value of the surfactant packing parameter P=v/aol, where v and I are the volume and length of the hydrophobic moiety (alkyl chain), and Uq is the optimal surface area occupied by one surfactant at the micelle-water interface. - It is important to realize that the value of is determined by the cross-sectional area of the surfactant head group and also by the various interactions at play in micelle formation.Surfactants characterized by values of P<113 give rise to sphericall... 

As the concentration is increased, the micelles may remain spheroidal or grow and become oblate (disklike) or prolate (or elongated, cylindrical, or rodlike), with the prolate shape much more often encountered than the oblate shape. The micelle shape is determined by the value of the surfactant packing parameter P given by ... 

The packing parameter provides a simple semi quantitative model to interpret the inLuence of the dynamic surfactant structure on the size and shape of the resulting micelles (Israelachvili,... 

The shape of the micelle formed by a particular surfactant is influenced to a large extent by the geometry of the surfactant molecule, as can be seen if we consider the packing of space-filling models of the surfactants. The dimensionless parameter of use in these considerations is called the critical packing parameter (CPP) and is defined as... 

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. 

Molecular dynamics simulations are consistent with calculations based on the critical packing parameter p, which indicate that the structure of the surfactant controls the shape of the micelle at the cmc. Esselink et al. [16] show that the surfactants / 2/5, hihts, and h thts form bilayers, cylindrical micelles, and spherical micelles, respectively, as expected. However, /14/4, expected to form micelles of low curvature based on p, instead forms sphere-like structures due to the coiling of the headgroup. If this increased effective headgroup area is accounted for in the calculation of the packing parameter, then a spherical shape is predicted, in agreement with the result of the simulations. 

Increases in the surfactant concentration lead to changes in the geometric conformation and packing of the micelles in solution. A direct relation between micellar shape and mesophase (surfactant phase in terms of structural properties) has been correlated, and it is known as the packing parameter, g, which describes the geometric parameters of the hydrophobic and hydrophilic sections of the amphiphilic surfactant molecule, and is described as follows ... 

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