Helicates circular

Liquids in turbulent flow in circular helical coils should be handled the same as for gases or use 1.2 Xhj for straight tubes. 

Note that below G = 1,200P , results may be too conservative. Gases in turbulent flow in circular helical coils ... 

Most helicates have linear axes, though a few helicates with circular axes are known - indeed the chiral (D4) molecular squares formed from Zn2+ and 2,5 -bis(2,2 -bipyridin- 6 -yl)pyrazine, 22, may be regarded as circular helicates (450). The formation of circular or linear forms seems to depend on balances between kinetic and thermodynamic control iron(II)-poly-2,2/-diimine systems with their substitutionally-inert metal centers provide useful systems for disentangling thermodynamic and kinetic contributions. The mechanism of formation of circular helicates of this type is believed to entail a kinetically favored triple helicate intermediate (484). Self-assembly of chiral-twisted iron(III)-porphyrin dimers into extended polynuclear species takes place through the intermediacy... 

In order to model this type of flow field geometrically, Beltrami found that it was necessary to consider a three-dimensional circular axisymmetric flow in which the velocity and vorticity field lines described a helical pattern. This helicoidal flow field was unique in that the pitch of the circular helices decreased as the radius from the central axis increased. This produces a specialized shear effect between the field lines of successively larger cylindrical tubes constituting the respective helices. In the limit of such a field, the central axis of the flow also serves as a field line (see Fig. 3). 

Circular helicates exhibit a particular aesthetic appeal as they comprise closed tori of chiral architectures. Hannon and coworkers [138] have reported the self-assembly of the chiral ball ([Cu3l73])42+ (19) assembled from four ho-mochiral, circular helicates [Qi3l73]3+ (18) that are held together via CH-7T interactions (Fig. 14). Each copper ion is tetrahedrally coordinated by two imine-ligands 17, resulting in the solution-stable trimeric helicate 18. The resulting chiral tetramer 19 is quite remarkable as it is self-assembled from a one-pot reaction of 48 simple and achiral building units. 

Fig. 14 Formation of the chiral ball ([Cu3173])42+ (19) assembled via CH-jr interactions from four circular helicates [Cu3173]3+ (18), where each copper(I) ion is tetrahedrally coordinated by two imine-ligands 17 [138]...

Fig. 2 Time-dependent self-assembly of linear and circular helicates...

Fig. 3 Expression of two different circular helicates via anion recognition in a DCL self-assembled by metal coordination. The smaller CL anion amplifies the formation of a pentanuclear helicate, whereas the larger S042, SiF62, and BF4 amplify the formation of a hexanuclear helicate...

Hasenknopf B, Lehn J-M, Boumediene N et al (1997) Self-assembly of tetra- and hexanuclear circular helicates. J Am Chem Soc 119 10956-10962... 

B. Hasenknopf, J.-M. Lehn, N. Boumediene, A. Dupoint-Gervais, A. van Dorsselaer, B. Kneisel, D. Fenske, Self-Assembly of Tetra- and Hexanuclear Circular Helicates , J. Am. Chem. Soc., 119, 10956 (1997)... 

Finally, it must be pointed out that a great deal of work was published on related metal assembled compounds such as linear or circular helicates [57], cages [58], and rack-type complexes [59]. Flowever, since little or no discussion related to charge-transfer spectroscopy or photoinduced electron transfer was reported, they will not be presented here. 

Entropic influences are less significant. However they can be used to selectively stabilize one product over others that have equal enthalpic stability. For example, at high solution concentrations entropy favors the formation of large structures over small ones. Thus, certain binuclear helicates can be transformed into their corresponding tri- or higher multinuclear circular helicates, simply by concentrating the reaction solution some metallocycles can be transformed into catenanes in the same way (vide infra, Sections 1.43.4.2 and 1.43.4.7). 

Another example involves the reaction of Cu1 with the 2,2 2",6" 6",2" -quaterpyridine ligand (3) (Figure 3).15 A stoichiometric mixture of these molecules at ambient temperature and moderate concentration was found by ES-MS to contain a library of compounds which included the diastereomeric binuclear helicates, (4), and the oligonuclear circular helicates (5), (6), and (7). Concentration of the mixture resulted in an increase in the higher nuclearity species. At concentrations below 10 4 M, however, only the helicates were present. Crystallization transformed the mixture into (6) in the solid state. 

When the ethyl-linked bipy3 oligomer was combined with an equimolar quantity of FeCl2 in ethylene glycol at 170 °C, a pentameric circular helicate was exclusively produced (Figure 154).833 This complex is believed to form from templation by the Cl counterion. Further investigations into this system with a variety of counterions revealed a second... 

Inorganic double or triple helices are formed by two or three ligand strands wrapped around linearly disposed metal ions [13], Among cyclic transition metal complexes, circular helicates [nJ cH [ ] "cH is a general notation characterizing circular helicates (cH) with n = number of metal ions and m = helicity (m = 2 for a double helix) have specific features and may be considered as toroidal helices [34]. There are two different kinds of circular helical systems. Some structures self-assemble from the metal ions and the ligands only in the presence of an anion, which could act as a template [34,35,64-67], whereas, in other cases, the circular helicates self-assemble from the metal ions and the ligands alone [68-70]. 

In the presence of the smaller chloride ion the self-assembly generates the pentanuclear circular helicate [i] cH 33 (Figure 21). With the larger anions S04 , BF4 , and SiF ", the hexanuclear architecture is formed while the Br anion of intermediate size yields a mixture of [5] cH and [d] cH. The charge of the anion has apparently little influence on the structure formed as [<5] cH is obtained with mono- and divalent anions. The structure depends rather on the size of the anion to be included in the circular helicates. These differences in the products formed, might be considered as resulting from a templating effect of the anion... 

A further example of a stereospecific self-assembled circular helical structure was prepared from the chiral ligand 43 and silver ions. According to the X-ray crystal structure determination, the spontaneously formed sixfold circular single-stranded helicate [Ag6(43)6](Pp6)6 44 (Figure 26) is formed as a single diastereoisomer. The... 

In contrast to most other circular helical systems, 44 assembles from the metal ions and the ligands alone without the support of an anionic template. 

The helical axis is in general a line, but a recent development is the synthesis of circular helicates in which the ligands twist about a circle, the metal ions being disposed at regular intervals, and these are discussed in section 4.2. Reviews of helicates have appeared recently, and the reader is referred to these [23-25] for a discussion of properties of these complexes. 

A recent development in this field has been the discovery of circular helicates. The geometrical description of these systems is quite simple the metal ions are no longer aligned along a helical axis, but are spaced at equal intervals around a circle, and the ligand strands twist around this circle. The first example was discovered by Lehn... 

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