Geometric packing

Optimal Salinities The phase inversion process may be considered to reflect the balanced nature of the adsorbed surfactant species at the oil/water interface. Simple geometric packing... 

The structure and dynamic properties of this interacting array of polymer molecules depend on polymer conformation and flexibility. This also applies to the magnitude of C, which can be calculated on the basis of various geometric packing arrangements of the characteristic domain of the molecules. 

Once the estimates for ah, v and (c t are available, one can determine the preferred shapes of the surfactant aggregates using geometric packing considerations, as discussed in the following subsection and illustrated in Example 8.3. 

Fig. 5.—Geometric packing of a hydrocarbon region of volume v and surface area o at a surface with two radii of curvature Rx and R2. Eqn (5.4) gives the relation between v, a, Rx, R2 and the length of the hydrocarbon /. For both Rx,Rz > 1,sl void region is formed behind the hydrocarbon region.

In section 5, a geometric packing equation was derived that relates the amphiphile surface area a, hydrocarbon volume y, and hydrocarbon thickness / to the curvature at the amphiphile surface. For a spherical vesicle of outer radius Ri the packing equation, eqn (5.4), for the outer layer amphiphiles is... 

The structural units of surfactant-containing liquids are self-assembled aggregates, such as spherical or cylindrical micelles, or bilayers. These supramolecular structural units can then further self assemble into ordered phases, with cubic, hexagonal, smectic, or other symmetry. Consequently, the structural and flow properties of such liquids are amazingly rich. Laws of mass action, combined with geometric packing arguments, allow rationalization, if not prediction, of the phase behavior of many surfactant solutions. 

Two representative clusters that are different in shape are exemplified. One is a compact cluster—that is, a geometrically packed structure—which is located... 

These authors note the importance of geometric packing for the thermodynamic properties of solutions. Indeed, since rigidity affects packing and thus distances between interacting units... 

Almost all mesostructures reported far have been governed by the geometrical packing of surfactants. The mesopores are near-cylindrical channels or near-spherical cages. Here is an exception. KSW-2[156] has a mesostructure of rectangular arrangements of square or lozenge-shaped 1-D channels. KSW-2 was synthesized by mild acid treatment (pH value... 

A spherical micelle should be rather considered as idealized picture, and non-spherical aggregates are often formed due to geometric packing requirements. Very high surfactant concentrations induce transition of spherical micelles into other shapes (rods, disks, vesicles, lamellar structures). 

The importance of geometric packing was considered in detail by MitcheU and Ninham [10], who introduced the concept of the packing ratio P,... 

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