Decomposition of polycycles

We have seen in Section 4.5 a full classification of (3, 3)gen, (3,4)gen-, and (4, 3)gen-polycycles. We have also seen that, for all other (r, q), there is a continuum of (r, )-poly cycles. The purpose of this chapter is to introduce a decomposition of polycycles into elementary components in an analogous way to decompose the molecules into atoms. This method will prove to be very effective but only in the elliptic case, since, for all other cases, we will show that there is a continuum of such elementary components (see Theorem 7.2.1). The first occurrence of the method is in [DeSt02b], followed by [DDS05b] and [DDS05c]. 

Given an integer q 3 and a set R c N — 1 (so, 2-gons will be permitted in this chapter), a (R, q)gen-polycycle is a non-empty 2-connected map on a surface S with faces partitioned in two non-empty sets F and F2, so it holds that  

A bridge of an (R, q)gen-polycycle is an edge, which is not on a boundary and goes from a hole to a hole (possibly, the same). An (R, )ge -polycycle is called elementary if it has no bridges. See below illustrations of these notions  

An open edge of an (R, q)gen-polycycle is an edge on a boundary, such that each of its end-vertices have degree less than q. See below the open edges of some (R, q)-polycycles  

The opai edges of a (5,3)-polycycle The open edge of a ( 2,3, 5)-polycycle 

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Fig. 50 Thermal decomposition of polycyclic pigments in the solid phase. Results of differential thermoanalysis performed on pigment powders in a nitrogen atmosphere.

Korfmacher, W.A., Wehry, E.L., Mamantov, G., and Natusch, D.F.S. Resistance to photochemical decomposition of polycyclic aromatic hydrocarbons vapor-adsorbed on coal fly ash. Environ. Sci. Technol, 14(9) 1094-1099, 1980. 

Korfmacher, W. A., E. L. Wehry, G. Mamantov, and D. F. S. Natusch, Resistance to Photochemical Decomposition of Polycyclic Aromatic Hydrocarbons Vapor-Adsorbed on Coal Fly Ash, Environ. Sci. Technol., 14, 1094-1099 (1980). 

Table 18. Cyclic and Oligocyclic Products from the Thermal and Photochemical Decompositions of Polycyclic Diazenes Containing Three-Membered Rings...

The performance of microwave-assisted decomposition of most difficult samples of organic and inorganic natures in combination with the microwave-assisted solution preconcentration is illustrated by sample preparation of carbon-containing matrices followed by atomic spectroscopy determination of noble metals. Microwave-assisted extraction of most dangerous contaminants, in particular, pesticides and polycyclic aromatic hydrocarbons, from soils have been developed and successfully used in combination with polarization fluoroimmunoassay (FPIA) and fluorescence detection. 

Polynitro derivatives of monocychc aromatic systems (trinitrobenzene, trinitrotoluene, tetranitro-iV-methylaniline, trinitrophenol, etc.) have long been used as explosives [1]. It has been found that a series of polynitroderivatives of biphenyl, diphenylmethane and 1,2-diphenylethylene (stilbene) are explosives liable to detonate on grinding or impact [2]. The same may be true of other polynitro derivatives of polycyclic systems not normally used as explosives (e.g. polynitro-fluorenones, -carbazoles, etc. Penta- and hexa-nitrobenzophenones are also high-energy explosives [3]. The thermal stability of 33 polynitroaromatics was studied by DTA [4]. Two empirical equations relating the heat of decomposition to the heat of detonation have been developed and used to calculate the heats of detonation for 47 polynitroaryl compoimds [5]. 

Highly selective formation of phenyl acetate was observed in the oxidation of benzene with palladium promoted by heteropoly acids.694 Lead tatraacetate, in contrast, usually produces acetoxylated aromatics in low yields due to side reac-tions. Electrochemical acetoxylation of benzene and its derivatives and alkoxylation of polycyclic aromatics789 790 are also possible. Thermal or photochemical decomposition of diacyl peroxides, when carried out in the presence of polycyclic aromatic compounds, results in ring acyloxylation.688 The less reactive... 

Consider now an elementary infinite ( 2,3, 5)-polycycle P. Eliminate all 2-gonal faces of P and obtain another (3,5)-polycycle P, which is not necessarily elementary. We do a decomposition of P along its elementary components, which are enumerated in Section 7.3. If snub APrismoo is one of the components, then we are finished and P = P is snub APrismoo If a is one of the components, then we have two edges along which we can extend the polycycle they are depicted below ... 

Proof. If the (9, 3)-polycycle with boundary sequence fc(0,1,0,1) appears in the decomposition of the set of 9-gpnal faces, then we are done. This is so, since an edge of value 0 can belong only to a (9,3)-polycycle with boundary sequence b(0,1,0,1). Hence, a path of such faces appear. By considering the adjacent 9-gons, we see that the structure should close and obtain the announced graph. 

All 1-elementary (5,3)-polycycles appear in decompositions of ( 5, b), 3)-maps that are bR. See below an example of such a decomposition ... 

Proof. Every fc-gonal face of such a sphere G would be adjacent to exactly two 4-gons. This means that the (4,3)-polycycle 4,3 — e cannot appear in the decomposition of the set of 4-gonal faces. Hence, all faces of the sphere MG) are 3- or 4-gonal. So, we can conclude using Theorem 1.2.3(ii). ... 

Intramolecular cyclopropanation of diazoketones to furnish [3.1.0] and [4.1.0] bicyclic systems are the most common and effective reactions in this category. Two recent examples are shown in equations 48 and 49. The bicyclic ketone 34 has been used in the synthesis of polycyclic cyclobutane derivatives77, whereas ketone 35 is the key intermediate in the total synthesis of ( )-cyclolaurene78. When the olefinic double bond is attached to, or is part of, a ring system, the cyclopropanation process also works well. Copper oxide catalysed decomposition of diazoketone 36 produces the strained tricyclic ketone 37 in 86% yield (equation 50)79. In another case, in which the cyclopropanation of diazoketone 38 gave stereospecifically the cyclopropyl ketone 39, copper sulphate catalysis was used. The cyclopropyl ketone 39 is the key intermediate in the total synthesis of ( )-albene 40 (equation 51). ... 

Benzyne is an important reactive intermediate especially useful for the construction of polycyclic compounds via cycloaddition reactions with various dienes. Several benzyne precursors, including diphenyliodonium-2-carboxylate [ 1 ], have been previously used for the generation of benzyne by thermal decomposition. More recently, several new precursors that generate benzyne quantitatively under very mild conditions have been developed [105 -108]. An efficient benzyne precursor, iodonium triflate 109, can be readily prepared by the reaction of l,2-bis(trimethylsilyl)benzene 108 with [(diacetoxy)iodo]benzene in the presence of trifluoromethanesulfonic acid (Scheme 47) [105]. 

Polycyclic aromatics with more than two aromatic rings, or more than one heteroatom are relatively easy to reduce and several reviews have summarized works on their electrochemical behavior. Bicyclic heteroaromatics with one heteroatom are reduced close to or beyond the decomposition of the electrolyte unless acidic solutions are used. Very few compounds of this kind have been preparatively reduced in neutral media. Their cathodic reduction could be carried out at mercury cathodes with TA A+ electrolytes. Depending on the heteroatom and the amount of charge transferred, hydrogenated and/or reductive cleavage products were obtained. 

Because C-H bonds are usually less reactive towards dioxirane oxidation than heteroatoms and C-C multiple bonds, it is instructive to give a few general guidelines on the compatibility of functional groups within the substrate to be submitted to oxidative C-H insertion Substances with low-valent heteroatoms (N, P, S, Se, I, etc.), C-C multiple bonds, and C=X groups (where X is a N or S heteroatom) are normally not suitable for C-H insertions, because these functionalities react preferably. Even heteroarenes are more susceptible to dioxirane oxidation than C-H bonds, whereas electron-rich and polycyclic arenes are only moderately tolerant, but electron-poor arenes usually resist oxidation by dioxiranes. N-oxides and N-oxyl radicals are not compatible because they catalyze the decomposition of the dioxirane. Oxygen insertion into Si-H bonds by dioxirane is more facile than into C-H bonds and, therefore, silanes are not compatible. Substance classes normally resistant towards dioxirane oxidation include the carboxylic acids and their derivatives (anhydrides, esters, amides, and nitriles), sulfonic acids and their de-... 

Humic substances (HS) are polymeric oxidation products that result from the decomposition of plant and animal residues. As a consequence of their colloidal state in natural waters, they play an important role in the transport of organic pollutants. Thus hydrophobic organic pollutants such as polycyclic aromatic hydrocarbons, DDT, and PCBs are known to bind well to humic substances, thereby enhancing the former s water solubility. One important characteristic of... 

While most of the initial studies have involved the transition metal-catalyzed decomposition of a-carbonyl diazo compounds and have been reviewed [3-51], it appears appropriate to highlight again some milestones of these transformations, since polycyclic structures could be nicely assembled from acyclic precursors in a single step. Two main reactivities of metalo carbenoids derived from a-carbonyl diazo precursors, namely addition to a C - C insaturation (olefin or alkyne) and formation of a ylid (carbonyl or onium), have been the source of fruitful cascades. Both of these are illustrated in Scheme 27 [52]. The two diazo ketone functions present in the same substrate 57 and under the action of the same catalyst react in two distinct ways. The initially formed carbenoid adds to a pending olefin to form a bi-cyclop. 1.0] intermediate 58 that subsequently cyclizes to produce a carbonyl ylide 59, that is further trapped intramolecularly in a [3 + 2] cycloaddition. The overall process gives birth to a highly complex pentacyclic structure 60. 

Thermal decomposition of branched chain methylsiloxane polymers has been studied before [5, 76-79], Methylsiloxane rings and polycycles were detected as volatile products of the methylsiloxane resin pyrolysis [5,76-79], The results indicate that pyrolysis decomposition of methylsiloxane resins is similar to that observed for methylsiloxane chain polymers [4],... 

Copper compounds are catalysts for the Michael addition reaction (249), olefin dimerizations (245, 248), the polymerization of propylene sulfide (142), and the preparation of straight-chain poly phenol ethers by oxidation of 2,6-dimethylphenol in the presence of ethyl- or phenyl-copper (209a). Pentafluorophenylcopper tetramer is an intriguing catalyst for the rearrangement of highly strained polycyclic molecules (116). The copper compound promotes the cleavage of different bonds in 1,2,2-tri-methylbicyclo[1.1.0]butane compared to ruthenium or rhodium complexes. Methylcopper also catalyzes the decomposition of tetramethyllead in alcohol solution (78, 81). 

Butler, A. R. Gilbert, B. C. Hulme, P Irvine, L. R. Renton, L. Whitwood, A. C. EPR evidence for the involvement of free radicals in the iron-catalysed decomposition of qinghaosu(artemisinin) and some derivatives Antimalarial action of some polycyclic endoperoxides. Free Rad. Res., 1998, 28 471 76. 

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