Theoretical interest

Of practical as well as theoretical interest, this book shows how general concepts can help solve specific organizational problems. 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

The interpretation of emission spectra is somewhat different but similar to that of absorption spectra. The intensity observed m a typical emission spectrum is a complicated fiinction of the excitation conditions which detennine the number of excited states produced, quenching processes which compete with emission, and the efficiency of the detection system. The quantities of theoretical interest which replace the integrated intensity of absorption spectroscopy are the rate constant for spontaneous emission and the related excited-state lifetime. 

Direct time-dependent detection is limited by the response time of detectors, which depends on the frequency range, and the electronics used for data acquisition. In the most favourable cases, modem detector/oscilloscope combinations achieve a time resolution of up to 100 ps, but 1 ns is more typical. Again, this reaction has been of fiindamental theoretical interest for a long time [59, 60]. 

Pure Elements. AH of the hehum-group elements are colorless, odorless, and tasteless gases at ambient temperature and atmospheric pressure. Chemically, they are nearly inert. A few stable chemical compounds are formed by radon, xenon, and krypton, but none has been reported for neon and belium (see Helium GROUP, compounds). The hehum-group elements are monoatomic and are considered to have perfect spherical symmetry. Because of the theoretical interest generated by this atomic simplicity, the physical properties of ah. the hehum-group elements except radon have been weU studied. 

Melamine. Melamine (cyanurotriamide, 2,4,6-ttiainino-j -triazine) C H N, is a white crystalline soHd, melting at approximately 350°C with vaporization, only slightly soluble in water. The commercial product, recrystallized grade, is at least 99% pure. Melamine was synthesized eady in the development of organic chemistry, but it remained of theoretical interest until it was found to be a usehil constituent of amino resins. Melamine was first made commercially from dicyandiamide [461-58-5] (see Cyanamides), but is now made from urea, a much cheaper starting material (9—12) (see also... 

Exotic Decays. In addition to the common modes of nuclear decay, two exotic modes have been observed. These decay modes are of theoretical interest because theh long half-Hves place strict constraints on the details of any theory used to calculate them. 

Because of the unique nature of electron-transfer reactions, these have been of great theoretical interest. More recently, research has centered on a microscopic picture of the electron-transfer reactions and predicting reaction rate constants (5,6). 

The theoretical interest that these reactions aroused was enormous. Presently 1,3-dipolar cycloadditions are one of the cornerstones of theoretical chemistry and many references are to be found in the publications quoted in Table 36. For some recent publications related to this chapter see (78JA5701, 79TL2621, JST(89)147). 

The present method is adapted from that of Loven. The resolution has been carried out with d-a-bromocamphor-TT-sulfonic acid (f-form) 2.3 with /-and d/-malic acids (d- and /-forms) with /-quinic acid and d-tartaric acid (d- and /-forms) and with d- and /-6,6 -dinitrodiphenic acids (d- and /-forms). Methods employing d-benzyimethylacetyl chloride, d-oxymeth-ylenecamphor, /-quinic acid, and d-camphoric anhydride are of theoretical interest only. The d/-amine is not resolved by the active camphor-lo-sulfonic acids or mandelic acids. ... 

The study of the behavior of reactions involving a single species has attracted theoretical interest. In fact, the models are quite simple and often exhibit IPT. In contrast to standard reversible transitions, IPTs are also observed in one-dimensional systems. The study of models in ID is very attractive because, in some cases, one can obtain exact analytical results [100-104]. There are many single-component nonequilibrium stochastic lattice reaction processes of interacting particle systems [100,101]. The common feature of these stochastic models is that particles are created autocatalytically and annihilated spontaneously (eventually particle diffusion is also considered). Furthermore, since there is no spontaneous creation of particles, the zero-particle... 

A completely different approach has been taken by Hine, who has considered that the substituent and reaction center are not really distinct, both being substituents in a benzene nucleus, and has then related substituent and reaction constants. Although of considerable theoretical interest, Hine s work has little bearing on practical applications of the Hammett equation since he starts from the premise of unique, single-valued substituent constants. This premise is invalid whether we are utilizing the naive approach with three separate, well-defined sets or the more refined methods with a continuous range of para values. 

Whereas the fulvalenes 1-6 are relatively unstable hydrocarbons and therefore largely of theoretical interest, their heteroatom analogs demand considerable attention in synthetic chemistry and material sciences. Tlie general principle of heterocyclic chemistry to relate heterocyclic compounds to carbocyclic ones was the driving force for the synthesis and their application to heteroful-valenes. Numerous heterocyclic derivatives iso-rr-electronic with, for example, heptafulvalene 3 were accessible in which pairs of carbon atoms linked by double bonds were replaced by heteroatoms capable of contributing two tt-electrons. By this principle, the well-known tetrathiafulvalene and its derivatives have been synthesized successfully (Scheme 2). 

The use of cyclopentadiene as a diene provides a route to the [2.2.1]bicycloheptane skeleton, which is of considerable theoretical interest. Cyclopentadiene, however, exists as its Diels-Alder dimer at room temperature and must be cracked thermally to... 

The lack of rotation around carbon-carbon double bonds is of more than just theoretical interest it also has chemical consequences. Imagine the situation for a disubstifitted alkene such as 2-butene. Disubstitilted means that two substituents other than hydrogen are bonded to the double-bond carbons.) The two methyl groups in 2-bulene can be either on the same side of the double bond or on opposite sides, a situation similar to that in disubstitutecl cycloalkanes (Section 4.2). 

The three different benzoxepins are simply assigned by the position of the oxygen 1 -benzoxepin, 2-benzoxepin, 3-benzoxepin. Among the four possible dibenzoxepins only dibenz[6,d]oxepin and dibenz[6,/]oxepin are of importance whereas the two other isomers are only of theoretical interest because they contain unfavorable o-quinoid structures. Benzannulation across all of the C-C double bonds leads to tribenz[6,rf,/]oxepin. 

Considering their potential antiaromatic character, thiepins are also of theoretical interest. HMO calculations of -resonance energies, using reference data from 27 acyclic polyenes containing sulfur, predict antiaromatic character for thiepin and 2-benzothiepin, whereas 1- and... 

As the presumption of the identity of the function for all the reactions of the system may not be always fulfilled, this method has not met with wide application by catalytic chemists. Rather, it attracts theoretical interest (29, 30, 33-36), even though, for example, the authors of the last mentioned paper (36) used their own experimental data on the isomeriza-... 

The Shot Noise Process.—In this and the next section we shall discuss two specific random processes—the shot noise process53 and the gaussian process. These processes play a central role in many physical applications of the theory of random processes as well as being of considerable theoretical interest in themselves. 

The kinetics of carbonate decompositions have been studied for both their technical importance and their theoretical interest. While both isothermal and non-isothermal techniques have been used, data obtained by rising temperature methods may be unreliable where the influence on the reverse reaction of C02 gas present has not been positively characterized. 

The polarography of sulphones has been fairly extensively studied, sometimes with an analytical bias and sometimes with more theoretical interest. It is generally accepted that a two-electron reduction takes place, to sulphinate ... 

The structural features and the spectroscopic characteristics of the thiirene dioxide system (22) are of special theoretical interest since, on the basis of analogy with cyclopropenone (23), it is a possible nonbenzenoid aromatic system with all the physical and chemical implications involved. Aromatic and/or conjugative effects, if any, require transmission through the d-orbitals of the sulfur atom. 

Dittmer and Christy64 studied the reactions of thiete sulphone. Included in these was an attempt to synthesize thiete itself, a highly strained olefin of theoretical interest, by the LAH reduction of thiete sulphone. The reduction was expected to be feasible since Bordwell and McKellin63 had found that thietane sulphone was readily reduced, but the only product that Dittmer and Christy isolated was 1-propanethiol (equation 23). Reduction of the thiete sulphone with sodium borohydride in basic aqueous methanol gave a 61% yield of the saturated ring, thietane sulphone. 

The reaction given here has been described before as a general reaction,2 and there can be a wide variety of alkyl, aryl, and halo substituents on the diene and phosphorus. Dibromophosphines are appreciably more reactive than dichlorophosphincs. If a free-radical catalyst is used instead of an inhibitor, the copolymers can be made in good yield.3 The 1,4-addition of dichloro-phosphines to 1,3-dienes is of theoretical interest because of its analogy to the well-known 1,4-addition of sulfur dioxide to 1,3-dienes. 

Benzocyclopropene is an intriguing example in which the electronic structure of benzene is greatly perturbed by the fusion of the smallest alicyclic ring, cyclopropene, to the aromatic system. Benzocyclopropene thus arouses theoretical interest and the high strain energy (approximately 68 kcal./mole)3 associated with the compound suggests unusual chemical reactivity. A review article has recently appeared.4... 

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