Aggregate structures shapes

The aggregation numbers Nagg is determined as 27 for C1-(EO)53-C4-VB and 38 for Cr(EO)53-C7-VB micelles by analysis of fluorescence curves. A micelle formation mechanism is proposed for nonionic polymeric surfactants with weakly hydrophobic groups. At low concentrations of PEO macromonomers, large loosely aggregated structures involving the PEO chains are formed. At higher concentrations normal micelles form. These are star-shaped, with a hydrophobic core surrounded by a corona of PEO chains. 

Regardless of shape, any aggregated structure must satisfy the following two criteria (1) no point within the structure can be farther from the hydrocarbon-water surface than 4 i (2) the total hydrocarbon core volume of the structure V and the total surface area A must satisfy V/v = A (oq = N. This criterion is only approximate since it assumes that the mean surface area per amphiphile is equal to o-... 

More complicated aggregate structures are found in the vanadium-copper and vanadium-silver species [ViMiS SPh CR ]" (M = Cu or Ag) (133), in which the metal sulfido core is in the shape of a cube [Fig. 14(d)] bulk magnetic susceptibility measurements have shown that there is probably a direct V —V bond within these species. These and related complexes are of interest since a vanadium-containing nitrogenase has been discovered (136). 

Despite that the silicate-surfactant mesophase formation resembles the phase separation normally observed in surfactant-polyelecholyte systems, it is interesting to note that it is stiU possible to make qualitative predictions about the influence of inorganic-surfactant phase behavior based on models developed for dilute surfactant systems. The packing parameter concept - is based on a geomettic model that relates the geomehy of the individual surfactant molecule to the shape of the supramolecular aggregate structures most likely to form. N, is defined as... 

The quantity of insoluble substance which can be solubilised in micelles depends to a considerable extent on the chemical structure of the surfactant and is influenced by the presence of other components, which may influence either the micelle formation concentration (CMC) or the micelle geometry (aggregation number, shape). The transition from solubilisation to another important phenomenon, the formation of a micro-emulsions, is continuous. Microemulsions form spontaneously, whereas typical solubilisation systems attain their equilibrium state often only after extreme long periods of intensive mixing of both phases. 

Velocity profiles across the capillary have a Poisseuille shaped flow and the expression predicts that the electroosmotic coefficient of permeability should vary with the square of the radius. In practice, it is found generally that this law is not as satisfactory as the Helmholtz-Smoluchowski approach for predicting electroosmotic behavior in soils. The failure of small pore theory may be because most clays have an aggregate structure with the flow determined by the larger pores [6], Another theoretical approach is referred to as the Spiegler Friction theory [25,6]. Its assumption, that the medium for electroosmosis is a perfect permselective membrane, is obviously not valid for soils, where the pore fluid comprises dilute electrol d e. An expression is derived for the net electroosmotic flow, Q, in moles/Faraday,... 

The minimum in the interfacial free energy predetermines three kinds of geometry in nature spheres, cylinders and planes. Correspondingly, the most stable amphiphile aggregation structures are i) spherical (Hartley) micelles, ii) rod-shaped micelles and anisotropic middle phases, iii) disk-shaped micelles and lamellar mesophases. They exist as aggregates in a water continuum with a hydrocarbon core surrounded by hydrated polar groups (the normal type) and as aggregates in a hydrocarbon continuum (the reverse or inverted type) where water and... 

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...

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