Close-packed spherical phase

Fig. 2.44 Phase diagram for a conformationally-symmetric diblock copolymer, calculated using self-consistent mean field theory. Regions of stability of disordered, lamellar, gyroid, hexagonal, BCC and close-packed spherical (CPS), phases are indicated (Matsen and Schick 1994 ). All phase transitions are first order, except for the critical point which is marked by a dot.

Figure 15. Phase diagram of Ci EOg/water (reproduced from [37]) (Ii, close-packed spherical micelle cubic phase others as for Fig. 14).

Cubic liquid crystalline phases were considered to be built up of close-packed spherical micelles. 

Figure 21.14. Phase diagram of the Ci2E08/water system Ii, close-packed spherical micelle cubic phase other phases, etc. as for Figure 21.13 (reproduced from ref. (46) by permission of The Royal Society of Chemistry)...

Any study of colloidal crystals requires the preparation of monodisperse colloidal particles that are uniform in size, shape, composition, and surface properties. Monodisperse spherical colloids of various sizes, composition, and surface properties have been prepared via numerous synthetic strategies [67]. However, the direct preparation of crystal phases from spherical particles usually leads to a rather limited set of close-packed structures (hexagonal close packed, face-centered cubic, or body-centered cubic structures). Relatively few studies exist on the preparation of monodisperse nonspherical colloids. In general, direct synthetic methods are restricted to particles with simple shapes such as rods, spheroids, or plates [68]. An alternative route for the preparation of uniform particles with a more complex structure might consist of the formation of discrete uniform aggregates of self-organized spherical particles. The use of colloidal clusters with a given number of particles, with controlled shape and dimension, could lead to colloidal crystals with unusual symmetries [69]. 

Transmission electron microscopy (TEM) has been an underutilized yet valuable too in particle size characterization of MC particles in LB films. Monolayer films of trioctylphosphine oxide-capped CdSe (18), spread as a monolayer on an aqueous subphase, were transferred to a TEM grid. A close-packed hexagonal arrangement of 5.3-nm (cr —4%) crystallites was found. TEM images were also obtained for HMP-stabilized CdS incorporated in BeH/octadecylamine films (79) and for CdS formed under an amine-based surfactant monolayer and transferred to a TEM grid (14). In one study, direct viewing of CdS and CdSe particles made from Cd2+-FA films on TEM grids was not possible due to poor phase contrast between the particles and the film (30). Diffraction patterns were observed, however, that were consistent with crystalline (3-CdS or CdSe. Approximately spherical particles of CdSe could... 

An important quantity, which characterizes a macroemulsion, is the volume fraction of the disperse phase 4>a (inner phase volume fraction). Intuitively one would assume that the volume fraction should be significantly below 50%. In reality much higher volume fractions are reached. If the inner phase consists of spherical drops all of the same size, then the maximal volume fraction is that of closed packed spheres (fa = 0.74). It is possible to prepare macroemulsions with even higher volume fractions volume fractions of more than 99% have been achieved. Such emulsions are also called high internal phase emulsions (HIPE). Two effects can occur. First, the droplet size distribution is usually inhomogeneous, so that small drops fill the free volume between large drops (see Fig. 12.9). Second, the drops can deform, so that in the end only a thin film of the continuous phase remains between neighboring droplets. 

If the emulsion consisted of an assembly of closely packed uniform spherical droplets, the dispersed phase would occupy 0.74 of the total volume. Stable emulsions can, however, be prepared in which the volume fraction of the dispersed phase exceeds 0.74, because (a) the droplets are not of uniform size and can, therefore, be packed more densely, and (b) the droplets may be deformed into polyhedra, the interfacia] film preventing coalescence. 

Diffraction studies see Diffraction Methods in Inorganic Chemistry) show pure, sublimed Ceo to be crystalline with the near spherical molecules arranged in a face-centered cubic (fee) array, with a center-to-center inter-Cao distance of 10.02 A. The presence of traces of solvent impurities appears to stabilize an hexagonal close-packed (hep) arrangement (see Close Packing). In the fee phase at room temperature, each Ceo molecule rotates essentially... 

Concentrated emulsions or high internal phase emulsions (HIPE) are systems in which the volume fraction of the dispersed phase is larger than about 0.74, which is the close-packing volume fraction of monodispersed hard spheres. The dispersed soft entities of a concentrated emulsion are no longer spherical. They deform into polyhedra separated by thin films of continuous phase. The structure is thus analogous to a conventional gas-liquid foam with low liquid content. The structure, properties, stability, and applications of highly concentrated emulsions were recently reviewed by Cameron and... 

The mechanism by which the relatively large particles are formed is still a matter of debate. It has been proposed that they are the result of phase separation, presumably between unfolded and native molecules, which leads to small volume elements of a high concentration of denatured molecules, which subsequently form roughly spherical gel particles. Anyway, it has become clear that the particles themselves are not quite rigid and do not (always) consist of closely packed protein molecules. However, other mechanisms cannot be ruled out and the question is far from settled. Nor is it clear why the strands in clear gels can be relatively long and of almost constant diameter. 

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