Single radicals

In the derivation of the kinetic relations it was assumed that free radicals enter the particles one by one the initiation process just described satisfies this condition. This is not the case when radicals are formed by thermal decomposition of an oil-soluble initiator. Such decomposition produces pairs of radicals in the hydrocarbon phase. One would expect a pair of radicals, confined to the extremely small volume of a latex particle, to recombine rapidly. The kinetics of this type of polymerization have been described above. It is recalled here that the subdivision factor, z, and hence rate and degree of polymerization are smaller than 1 and decrease with a. These predictions from kinetic theory are in contradiction to experimental observations. Although some oil-soluble initiators, which are good catalysts in solution systems, are poor initiators in emulsion polymerizations—e.g., benzoyl peroxide—other thermally decomposing peroxides and azo compounds produce polymer in emulsion at rates comparable to those observed in polymerization initiated by water-soluble catalysts, where the radicals enter the particles one by one. Such is the case for cumene hydroperoxide, which at low concentrations yields a rate of polymerization per particle equal to that of a persulfate-initiated reaction. It must therefore be concluded that, although oil-soluble initiators may decompose into radical pairs within the particles, polymer radicals are formed one by one. The following mechanisms are consistent with formation of polymer radicals singly. 

Figure 5.12 Quartet states of radicals. Single electron excitations leading to a configuration with a single unpaired electron are marked with a full arrow, those leading to a configuration with three unpaired electrons with a dashed arrow...

The free radical, single-electron forms of FAD are very reactive, and FADH can lose its electron through exposure to water or the initiation of chain reactions. As a consequence, FAD must remain very tightly, sometimes covalently, attached to its enzyme while it accepts and transfers electrons to another group bound on the enzyme (Fig 20.6). Because FAD interacts with many functional groups on amino acid side chains in the active site, the E° for enzyme-bound FAD varies greatly and can be greater or much less than that of NAD. In contrast, NAD and NADH are more like substrate and product than coenzymes. 

The systems discussed up to now produce free radicals singly, so the free radical yield is equal to unity. However, certain redox systems produce free radicals in pairs, so that cage effects and reduced free radical yield are produced. The potassium persulfate and mercaptan systems, for example, belong to this category... 

FIGURE 9.13 Limit forms of an ionized vinyl ether stabilized by resonance. Top limit forms involving delocalization of the radical (single arrow mechanism). Bottom limit forms involving delocalization of the charge (double arrow mechanism). 

After the primary step in a photochemical reaction, the secondary processes may be quite complicated, e.g. when atoms and free radicals are fcrnied. Consequently the quantum yield, i.e. the number of molecules which are caused to react for a single quantum of light absorbed, is only exceptionally equal to exactly unity. E.g. the quantum yield of the decomposition of methyl iodide by u.v. light is only about 10" because some of the free radicals formed re-combine. The quantum yield of the reaction of H2 -f- CI2 is 10 to 10 (and the mixture may explode) because this is a chain reaction. 

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

Figure 4. Wavepackec dynamics of photoexcitadon, shown as snapshots of the density (wavepacket amplitude squared) at various times. The model is a 2D model based on a single, uncoupled, state of the butatriene redical cation. The initial structure represents the neutral ground-state vibronic wave function vertically excited onto the A state of the radical cation.

A distinction must be made between single-point GAUSSIAN calculations or optimizations and the energy output G2 (0 K). Individual GAUSSIAN calculations produce the energy coming out of the system when all the nuclei and electrons come together to form a molecule, radical, or ion, in this case. 

Semiempirical programs often use the half-electron approximation for radical calculations. The half-electron method is a mathematical technique for treating a singly occupied orbital in an RHF calculation. This results in consistent total energy at the expense of having an approximate wave function and orbital energies. Since a single-determinant calculation is used, there is no spin contamination. 

The mechanism includes two single electron transfers (steps 1 and 3) and two proton transfers (steps 2 and 4) Experimental evidence indicates that step 2 is rate determining and it is believed that the observed trans stereochemistry reflects the dis tribution of the two stereoisomeric alkenyl radical intermediates formed in this step... 

We say the molecule AB has been ionized by electron impact The species that results called the molecular ion, is positively charged and has an odd number of electrons—it IS a cation radical The molecular ion has the same mass (less the negligible mass of a single electron) as the molecule from which it is formed... 

Radicals derived from monocyclic substituted aromatic hydrocarbons and having the free valence at a ring atom (numbered 1) are named phenyl (for benzene as parent, since benzyl is used for the radical C5H5CH2—), cumenyl, mesityl, tolyl, and xylyl. All other radicals are named as substituted phenyl radicals. For radicals having a single free valence in the side chain, these trivial names are retained ... 

The multiplying affixes di-, tri-, tetra-, penta-, hexa-, hepta-, octa-, nona-, deca-, undeca-, and so on are used to indicate a set of identical unsubstituted radicals or parent compounds. The forms bis-, tris-, tetrakis-, pentakis-, and so on are used to indicate a set of identical radicals or parent compounds each substituted in the same way. The affixes hi-, ter-, quater-, quinque-, sexi-, septi-, octi-, novi-, deci-, and so on are used to indicate the number of identical rings joined together by a single or double bond. 

Any one of these expressions gives the rate of initiation Rj for the particular catalytic system employed. We shall focus attention on the homolytic decomposition of a single initiator as the mode of initiation throughout most of this chapter, since this reaction typifies the most widely used free-radical initiators. Appropriate expressions for initiation which follows Eq. (6.6) are readily derived. 

The single subscript used to label r is the index of the radical. 

Although ri is descriptive of radical Mi-, it also depends on the identity of the other the pair of parameters ri and r2 are both required to characterize a particular system and the product ri r2 is used to quantify this by a single parameter. 

The sample labeled atactic in Fig. 7.10 was prepared by a free-radical mechanism and, hence, is expected to follow zero-order Markov statistics. As a test of this, we examine Fig. 7.9 to see whether the values of p, P, and Pj, which are given by the fractions in Table 7.9, agree with a single set of p values. When this is done, it is apparent that these proportions are consistent with this type... 

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