Into the Third Dimension

The reactions that we considered in Section 6.8 all gave planar macrocyclic systems. It is also possible to introduce a little more three dimensional structure into the macrocyclic ligands by the use of suitable structured diamines in these reactions. For example, the reaction of 6.59 with formaldehyde and ammonia in the presence of nickel(n) salts gives the complex 6.60. Notice that the overall stoichiometry of the reaction involves one equi- 

As a final example of the introduction of three-dimensional structure into the ligand, we consider the reaction of 1,2-diaminoethane with formaldehyde and ammonia in the presence of nickel(n). The optimistic researcher might expect (hope ) to obtain 6.62 from this reaction. The actual product is 6.63, Only one side of each 1,2-diaminoethane ligand has reacted, and the overall stoichiometry is two 1,2-diaminoethane molecules, five formaldehyde molecules and two ammonia molecules. The reaction of 6.63 with formaldehyde and methylamine gives 6.64  

In this chapter we have covered a great deal of material relating to the preparation of macrocyclic complexes. The basic reactions that we have introduced in earlier chapters have now found a synthetic use. At the very end of the chapter we began to ponder ways of introducing three dimensional structure into macrocyclic systems. This is the topic that we consider in the next chapter. 

Lindoy, The Chemistry of Macrocyclic Ligand Complexes, Cambridge University Press, Cambridge, 1989. 

Co-ordination Chemistry of Macrocyclic Compounds, (ed. G.A. Melson),Plenum, 

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The radioscopy gives only information in twodimensional form which means that it is impossible to get informations about the defect extension into the third dimension. 

Then he came to extending the division of continuous two-dimensional space into the third dimension. He restricted his examinations to polyhedra and found one of the five space-filling parallelohedra, which were discovered by E. S. Fedorov as capable of filling the space in parallel orientation without gaps or overlaps. Fedorov was one of the three scientists who determined the number (230) of three-dimensional space groups. The other two were Arthur Schoenflies and the amateur William Barlow. 

Straight out of his world and upwards into the third dimension likewise, he cannot perceive anything but a sheet of water lacking any thickness. Evidently, it is not the water itself which he sees, for this water constitutes three-dimensional matter rather what he perceives is only the manifestation of the water fall in his two-dimensional world. This sheet only appears to him to widen and to extend itself, and this is because he cannot actually see its real source, the colonne d eau tombant upon the plane. 

Right, and if the Flatlanders tried to surround you to keep you in one place, you could escape by moving perpendicularly into the third dimension. In their eyes, you would be a God. ... 

Figure 2.13 Sally lifts a 2-D human into the third dimension. If he were truly two-...

You roll up the window. Sally, I think I can help you understand how a 3-D retina can visualize a human, inside and out, at the same time. First consider a blood transfusion for 2-D creatures via a tube that goes up into the third dimension and back down again into the plane of the creature. As far as the creature is concerned, you are not breaking the skin, which might be represented as a line in a drawing. Can you visualize how 4-D creatures can transfuse us (Fig. 3.5). 

Figure 3.5 A hyperspace blood transfusion in a 2-D world. The transfusion tube goes up and down into the third dimension. The creature s skin is never broken. 

You nod. Sally, if Satan were a 4-D being, it might be possible to confine him in a tesseract prison. If it were an ordinary cube, Satan could flee into the fourth dimension. However, if the cube in our world was really part of a hypercube, he would be trapped. As he leaped upsilon into the fourth dimension, he d just hit his head on a cubical ceiling. Similarly, a Flatlander having the ability to leap into the third dimension would bang himself on a cubical prison that spanned his world. ... 

Not at all. Imagine a 2-D man living in Flatland. Pretend his right eye is brown and his left eye is blue. He wakes up one day and his wife screams, because his eyes have switched places. What actually happened is that a 3-D being rotated him about the center of his body into the third dimension (Fig. 5.1). 

Sally, as I rotate, all that remains is my cross section. Looks like sliced meat. An Omegamorph could turn us into our own mirror images by rotating us, in the fourth dimension, around planes that cut through our bodies. It s just like the Flatlander rotated about a line into the third dimension and then back down into the second dimension. ... 

Since Pedersen s disclosures, and the subsequent extension into the third dimension through Lehn and his macrobicyclic and macrotricyclic cryptands,29 there have been a plethora of papers concerning many aspects of M"+ complexation, the majority being centred on crown ether and related species. Their literature has been extensively reviewed and attention is drawn to articles by Poonia and Bajaj30 and by Vogtle and Weber31 which are comprehensive and provide excellent bibliographies of the area. 

A pair of screw elements is conveying if the flat profiles are extended into the third dimension by helical rotation. In this case, we speak of screw elements. The pitch T of the element is another important dimension here. In today s modular screws, individual elements each have a constant pitch and a pitch variation is achieved by using different types of element. 

Figure 1-12) [30], This pattern was extended by Alan Mackay into the third dimension and he even produced a simulated diffraction pattern that showed 10-foldedness (Figure 1-13) [31], It was about the same time that Dan Shechtman was experimenting with metallic phases of various alloys cooled with different speeds and observed 10-foldedness in an actual electron diffraction experiment (Figure 1-14) for the first time. The discovery of quasicrystals has added new perspective to crystallography and the utilization of symmetry considerations. 

To demonstrate the versatility of this approach, we created binding patterns of different size and allowed different nanoparticles to form superstructures (Fig. 15.7c). Again a fraction of nanoparticles was inactive, and the thermal drift caused a slight distortion of the red structure. However, even the scale bar could be trustfully assembled. The expansion of this approach towards multicomponent structures is straightforward since there exist couplers with orthogonal affinities that can be linked to the transfer DNA. Whereas the assembly of planar nanoparticle structures of arbitrary design can easily be assembled this way, an expansion into the third dimension appears challenging but achievable. 

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