Non-linear structures

Abstract This review highlights recent (2000-2004) advances and developments regarding the synthesis of block copolymers with both linear [AB diblocks, ABA and ABC triblocks, ABCD tetrablocks, (AB)n multiblocks etc.] and non-linear structures (star-block, graft, miktoarm star, H-shaped, dendrimer-like and cyclic copolymers). Attention is given only to those synthetic methodologies which lead to well-defined and well-characterized macromolecules. 

For stilbene bromination, a markedly non-linear structure-reactivity relationship is observed (Fig. 5). Detailed analysis of the kinetic effects of two substituents, X and Y, on each aromatic ring shows that the three pathways leading to the C+ and carbocations and to the bromonium ion can... 

The polarization density is a functional of the solute charge density T s(r)= < Fs f s(r) Fs>. The effective Hamiltonian Eq.(16) acquires a non-linear structure via the polarization density term, i.e. the effective Hamiltonian a functional dependence of the wave function ... 

Arylalkene bromination is a typical electrophilic addition to form an a-carbocation, but markedly non-linear structure-reactivity relationships were observed for brominations of styrene [32], trans-stilbene [37] and a-methylstilbene [38] (Ruasse and Dubois, 1972, 1974 Ruasse et al., 1978 Ruasse and Argile, 1983). Some of these curvatures could not be interpreted directly by the Y-T equation but some were related to a mechanistic changeover based on a multipathway scheme (Ruasse, 1990). Three pathways leading to the and carbocations and to the bromonium ion in the bromination of trans-stilbene (Ruasse and Dubois, 1972, 1974) are shown in Scheme 10. 

In the solid state, SnCl2 exhibits a polymeric structure. The spectrum of the compound in the vapor phase at 650 °C can be attributed to a monomeric non-linear structure (Long, 1977, Perry, 1969). 

Since amylopectin acetate produces only brittle films and plastics, its molecules probably have a non-linear structure which may be branched or coiled. A further striking difference between amylose triacetate and amylopectin triacetate is that the former can be obtained in the form of a highly fibrous mass, whereas the latter occurs only as a fine powder. 

FIGURE 23.5 Schematic diagram showing the difference between linearly separable activity classes (a) and an embedded (non-linear) structure (b). For example, the active compounds (yellow) in (a) tend to have higher values of PCI and lower values of PC2 than the inactives (blue). While in (b), activity only occurs within a limited range of values of both PCI and PC2 and compounds outside this region are inactive. Data in (a) could be classified by LDA, while the data in (b) could be analyzed using SIMCA for example. 

OCNCO], [NCNCN] and [N5] are isoelectronic with C3O2, but they are not isostructural with the quasi-linear C3O2. Unambiguously non-linear structures are observed for [OCNCOJ+ (ZC-N-C= 131° in [OCNCO]+[Sb3F,6] ), the dicyanamide ion [NCNCN] (ZC—N—C=124° in Cs[NCNCN]), and [Ns]+ (see Section 14.5). 

However, the observed bond angles at the central atom show that the ions are non-linear in the solid state salts studied. For each ion, if a negative charge is localized on the central N atom, then a Lewis structure consistent with a non-linear structure can be drawn ... 

Ionic borohydrides (e.g., NaBH4) contain discrete BHj ions, which are tetrahedral, and structures of some MBH4 compounds are the same as that of NH4C1 since NH4 and BH4 are isoelectronic and isosteric. One of the most puzzling borohydrides from a structural point of view has been Be(BH4)2, The seemingly obvious linear structure (8-XV) appears to be inconsistent with much physical evidence, but there is, as yet, no unanimity as to which of several non-linear structures is preferable.28 1... 

In addition, other work showed that 3-hydroxy-4,5-dimethyl-2(5H)-furanone can be formed thanks to a Maillard reaction of hexoses and pentoses in the presence of cysteine 20). Due to the non-linear structure of Sotolon, its formation cannot simply be explained directly from sugar cyclization during tire Maillard reaction, like other furanones such as Furaneol. Hence, it is likely tliat Sotolon results from rearrangement of Amadori products of low molecular weight like butan-2,3-dione (diacetyl) and hydroxyacetaldehyde, via an aldol condensation (Figure 6). 

The first compound containing an Si=Si bond was isolated and structurally characterized in 2004. The product of reaction 14.6 (the reducing agent is the intercalation compound KCg, see structure 14.2) is kinetically and thermodynamically stabilized by very bulky silyl substituents. In line with theoretical predictions, the disilyne has a non-linear structure. The Si=Si bond (206 pm) is about 4% shorter than a typical Si=Si bond (214—216 pm), and about 13% shorter than a typical Si-Si bond (2 x = 236 pm). This degree of shortening is significantly less than that observed on going from C-C to C=C to C=C, consistent with less efficient TT-overlap for Si compared with C. 

Given the non-linear structure of the CBER mechanisms [5W]cber and [5lf]cBER+UNi and given the pronounced rate enhancements that can take place, their stability should be questioned. Said another way, is it possible that such mechanisms contribute to product formation from repeated fast and slow rate intervals, or is it possible that such mechanisms contribute to product formation for a brief time but then decay ... 

Concurrently, appropriate modifications should be made to the floor response spectra if significant incursion into the range of non-linear structural response occurs. The value of ductility associated with any item should be consistent with its structural detailing. 

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