Critical concentration, cylindrical

In the case of ordered mesoporous oxides, the templating relies on supramolecular arrays micellar systems formed by surfactants or block copolymers. Surfactants consist of a hydrophihc part, for example, ionic, nonionic, zwitterionic or polymeric groups, often called the head, and a hydrophobic part, the tail, for example, alkyl or polymeric chains. This amphiphiUc character enables surfactant molecules to associate in supramolecular micellar arrays. Single amphiphile molecules tend to associate into aggregates in aqueous solution due to hydrophobic effects. Above a given critical concentration of amphiphiles, called the critical micelle concentration (CMC), formation of an assembly, such as a spherical micelle, is favored. These micellar nanometric aggregates may be structured with different shapes (spherical or cylindrical micelles, layered structures, etc. Fig. 9.8 Reference 70). The formation of micelles. 

Some models of micelle growth take into account the fact that the surfactants located in the part connecting the cylindrical body of rodlike micelles to the endcaps are at a still higher chemical potential than those in the endcaps. This leads one to predict the existence of a second critical concentration, sometimes referred to as second cmc, above which micelles start growing. It also leads one to predict the coexistence of spherical and rodhke micelles, i.e., a bimodal distribution of micelle sizes. This is in contrast to the two-chemical potential approach that predicts a continuous growth of all micelles and a unimodal size distribution curve. 

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. 

In contrast to the above-described kinetic stability, colloids may also be thermodynamically stable. A stable macromolecular solution is an example we have already discussed. Formation of micelles beyond the critical micelle concentration is another example of the formation of a thermodynamically stable colloidal phase. However, when the concentration of the (say, initially spherical) micelles increases with addition of surfactants to the system, the spherical micelles may become thermodynamically unstable and may form other forms of (thermodynamically stable) surfactant assemblies of more complex shapes (such as cylindrical micelles, liquid-crystalline phases, bilayers, etc.). 

Molecules which have hydrophilic head groups attached to hydrocarbon chains are surface active but form micelles in water above a certain concentration (the critical micelle concentration, CMC). These micelles are generally spherical or cylindrical and have a positive, neutral or negative surface with a hydrocarbon like interior. 

The structures formed by polystyrene-poly(propylene imine) dendrimers have also been analyzed. Block copolymers with 8, 16, and 32 end-standing amines are soluble in water. They have a critical micelle concentration of the order of 10"7 mol/1. At 3x10 4 mol/l they form different types of micelles. The den-drimer with eight amine groups (80% PS) form bilayers. The dendrimer with 16 amine groups (65% PS) forms cylinders and the dendrimer with 32 amine groups (50% PS) forms spherical micelles [38,130,131]. These are the classical lamellar, cylindrical, and spherical phases of block copolymers. However, the boundary between the phases occurs at very different volume fractions, due to the very different packing requirements of the linear polymer and spherical dendrimer at the interphase. 

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