Aggregate topology

In the aggregate topology the ESU are two spheres (Figure 7.1b). These two spheres are submerged into the effective medium, and their relative concentrations are/and 1 -/, where/is a volume fraction of the constituent A. Using the dipolar approximation of 5(0) for a sphere [12] leads to the Bruggeman equation ... 

Some of the more remarkable examples of this form of topologically controlled radical polymerization were reported by Percec et cii.231 234 Dendron maeromonomers were observed to self-assemble at a concentration above 0.20 mol/L in benzene to form spherical micellar aggregates where the polymerizable double bonds are concentrated inside. The polymerization of the aggregates initiated by AIBN showed some living characteristics. Diversities were narrow and molecular weights were dictated by the size of the aggregate. The shape of the resultant macroniolecules, as observed by atomic force microscopy (ATM), was found to depend on Xn. With A, <20, the polymer remained spherical. On the other hand, with X>20, the polymer became cylindrical.231,232... 

The examples just presented give initial impressions of how DNA can be utilized as a template in the synthesis of nanometric and mesoscopic aggregates. However, the studies emphasize the importance of fundamental research on the interaction between DNA and the various binders, such as metal and organic cations. Of particular importance are the consequences of binding events on the structure and topology of the nucleic acid components involved. 

Two system-dependent interpretative pictures have been proposed to rationalize this percolative behavior. One attributes percolation to the formation of a bicontinuous structure [270,271], and the other it to the formation of very large, transient aggregates of reversed micelles [249,263,272], In both cases, percolation leads to the formation of a network (static or dynamic) extending over all the system and able to enhance mass, momentum, and charge transport through the system. This network could arise from an increase in the intermicellar interactions or for topological reasons. Then all the variations of external parameters, such as temperature and micellar concentration leading to an extensive intermicellar connectivity, are expected to induce percolation [273]. 

Figure 7.5 Two topologically distinct types of mesoporous gold sponge, each with 50 volume % gold, (a) Swiss-cheese morphology produced by de-alloying, (b) aggregated particle morphology produced by sintering of nanoparticles.

The Li20-filled dodecameric clusters 5a and 6a are isotypic and crystallize in the monoclinic space group P2Jn. Their structures are topologically best described as ionogenic aggregates formed by three... 

Dl) A molecular unit is an aggregate of atoms that is linked by a topologically connected network of covalent bonds equivalently, an electronic distribution that links a collection of nuclei by a contiguous network of covalent bonds. 

It is important for the theoretical understanding of the formation of various topologies that these aggregates have entropic contributions on the scale of the objects, i.e. on a much larger scale than set by the molecules. These cooperative entropic effects should be included in the overall Helmholtz energy, and they are essential to describe the full phase behaviour. It is believed that the mechanical parameters discussed above kc,k and J0, control the phase behaviour, where it is understood that these quantities may, in principle, depend on the overall surfactant (lipid) concentration, i.e. when the membranes are packed to such a density that they strongly interact. 

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