Dimensional Motifs

No special significance need be ascribed to the use of the word ribbon, as opposed to say, tape. By ribbon is meant a generally flat one-dimensional motif. 

To date, by far the best, comprehensive art-historical study of this strictly modernist theme is Henderson, Fourth Dimension. For the most detailed study of the Fourth Dimension as it strictly pertains to Duchamps practices, without however making any references to his significant influences from occultist literature, see Adcock. The best art-historical studies on the strictly occultist interpretations and sources of the fourth-dimensional motif is Gibbons, Cubism and The Fourth Dimension see also Henderson s provocative 1995 essay, Die moderne Kunst und das Unsichtbare Die verborgenen Wellen und Dimensionen des Okkultismus und der Wissenschaften, in Loers, 13-32. 

Moran et al. have also reported the preparation of hyperbranched ferrocenyl. S7-based polymers (Figure 8.1). The construction of ferrocenyl —silicon polymers 40 and 41 was effected by the reaction of dilithioferrocene-TMEDA with the tetrachlorosilane 35 (see Scheme 8.10) and the Pt-mediated hydrosilylation of l,l -divinylferrocene with tetrasilyl-hydride 38. The 3-dimensional motif exhibited by hyperbranched polymers 40 and 41 is analogous to that depicted by the ferrocenyl — silicon network structures 38,43 42 and 43 (Figure 8.2). 

A general and precise description of stereoisomerism in polymers is suggested on the basis of the repetition theory which describes the distinct patterns along a line that can be obtained from a three-dimensional motif. The probability models for describing the" stero-sequence length in various possible cases of interest in stereoregular polymers are discussed. It is shown that for describing the stereosequence structure, the simplest probability model must involve a Markov chain with four probability parameters. 

Classifying Stereoisomerism in Polymers on the Basis of Repetition of a Three-Dimensional Motif... 

Figure 1. Repetition of a three-dimensional motif by Proper Rotation and translation...

Aminopyrimidines [51], diacids [52] and acyclic secondary diamides [53] have long been known to form H-bonded tapes, and cocrystals of compounds incorporating these functionalities also form 1-dimensional objects [54]. Cyclic [55] and acyclic [56] M,M -disubstituted ureas, the Janus analogs of secondary diamides, and bisamidine-dicarboxylic acid cocrystals [57] also generate 1-dimensional motifs. 

The combination of like or unlike 1-dimensional motifs represent two distinct strategies for the generation of 2-dimensional motifs, or jS-networks . Consequently, the challenge in creating a 2-dimensional network lies in the requirement that the composite 1-dimensional motifs be sufficiently robust for their integrity to be maintained. 

Janus recognition groups expressing 1-dimensional motifs may also be combined to form jS-networks (Fig. 16). Modular covalent combination of... 

Fig. 14. Combining like 1-dimensional motifs to yield a 2-dimensional pattern...

Three-dimensional H-bonded networks, or y-networks , may be derived via combination of 2-dimensional motifs or via appendage of non-covalent... 

Fig. 20. y-Networks via modular combination of 2-dimensional motifs of guanidinium and sulfonate components... 

Robinson, F., and Zaworotko, M. J., Triple interpenetration in [Ag(4,4 -bipyridine)][NOj], a cationic polymer with a three-dimensional motif generated by self-assembly of T-shape building blocks, Chem. Commun., 2413-1414 (1995). 

The first approach, that of varying the organic spacer, was pursued using both monosulfonate and polysulfonate ligands. With monosulfonates, it was clear that only a certain size of R group on the sulfonate could be tolerated while retaining a two-dimensional motif, and so this was varied... 

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