Vesicles aggregation number

Experiments have been set up in this direction (Cheng and Luisi, 2003) utilizing extruded oleate vesicles having radii of 31.6 and 64.1 nm. For the same surfactant concentration, the total surface areas are the same for the two families of vesicles (neglecting the differences arising in aggregation number due to the differences... 

As a general result, we conclude that micelle and vesicle formation cannot be explained by cone or cylinder shapes of the monomeric amphiphiles. The key criterion for the curvature of molecular assemblies lies in the saturation solubility or cmc of the amphiphile. A cmc above 10 M usually means appreciable dissociation leading to small aggregation numbers of micelles. A cmc below 10 M means large planar bilayers or, upon their disruption, vesicles. 

Vesicles (Latin vesicula, bladder) are sealed, extremely thin (< 10 nm), often spherical membraneswhich enclose aqueous or other solvent volumes of approximately 10 -10 nm. Aggregation numbers are in the order of 10 -10. The monomers are held together by the same solvophobic effects which produce micelles, and solvation forces together with membrane undulations prevent crystallization. The state of the vesicle membrane is therefore also essentially of a fluid character. Supramolecular ordering within vesicle membranes is negligible. 

Vesicles enclose water volumes between 10 and 10 nm and they can be made so large (diameters from approximately 30 to 3000 nm) or concentrated (up to 10 M lipids) that up to a few percent of the bulk water volume becomes entrapped within the vesicle membrane. Biochemists also use the name hposome (fat particle) instead of vesicle, which is not very descriptive. Aggregation numbers are usually in the order of Ifr -lO molecules per vesicle. They are long-lived, have low critical... 

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 ... 

To prove the formation of vesicles a number of indirect techniques can be used such as dynamic light scattering, the use of fluorescent probes and pulsed field gradient NMR self-diffusion measurements. Some more direct techniques such as freeze-fracture and negative staining electron microscopy are less biased by the interpretation of the scientist, but also these methods have their limitations. Cryo-electron microscopy, as introduced by Dubochet in the 80s, is the method of choice when it comes to visualization of small colloidal structures. Recent developments in the vitrification of specimens make it now possible to observe vesicles and other aggregated structures artifact free. 

Here, v is the surfactant molecular volume, hn is the number of vesicles per unit volume of aggregation number N (N c ), kt = %n( k - -k)/T is the energy per vesicle in units of /cflT, and /r is a Lagrange multiplier which accounts for the conservation of surfactant and is determined from... 

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