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The reaction involves the transfer of an electron from the alkali metal to naphthalene. The radical nature of the anion radical has been established from electron spin resonance spectroscopy and the carbanion nature by their reaction with carbon dioxide to form the carboxylic acid derivative. The equilibrium in Eq. 5-65 depends on the electron af nity of the hydrocarbon and the donor properties of the solvent. Biphenyl is less useful than naphthalene since its equilibrium is far less toward the anion radical than for naphthalene. Anthracene is also less useful even though it easily forms the anion radical. The anthracene anion radical is too stable to initiate polymerization. Polar solvents are needed to stabilize the anion radical, primarily via solvation of the cation. Sodium naphthalene is formed quantitatively in tetrahydrofuran (THF), but dilution with hydrocarbons results in precipitation of sodium and regeneration of naphthalene. For the less electropositive alkaline-earth metals, an even more polar solent than THF [e.g., hexamethylphosphoramide (HMPA)] is needed. The naphthalene anion radical (which is colored greenish-blue) transfers an electron to a monomer such as styrene to form the styryl radical anion (XIX)



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Hint: Use a Taylor series expansion of exp (

5-66

4.5 Draw Caves's diagrams for the fields in each of the ports of the beam splitter used in homodyne detection. Use these diagrams to write down an expression for the difference in the fluctuations of the average photon number of c and d.

The styryl radical anion is shown as a resonance hybrid of the forms wherein the anion and radical centers are alternately on the a- and b-carbon atoms. The styryl radical anion dimerizes to form the dicarbanion (XX)

16Sonoluminescence is the emission of intense bursts oflight by ultrasonically driven gas bubbles in liquids, when they collapse suddenly. The cause of this phenomenon is still an open question. For a brief history of sonoluminescence, see [221.

5-67





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Instead of the menus and toolbars found in earlier versions of Office, Office 2010 features the Ribbon, which offers an intuitive way to locate and execute commands. The Ribbon is grouped into tabs, each containing groups of related commands. For example, the Home tab in Microsoft Word contains commands for changing the font, setting text alignment, indenting text and so on. Some tabs appear only when needed, such as when you are working with a table or picture in a document. The Ribbon is maximised by default, but you can minimise it to view more of your program window.

Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box Sergio M. Dutra Copyright 2005 John Wiley & Sons, Inc.

That this reaction occurs is shown by electron spin resonance measurements, which indicate the complete disappearance of radicals in the system immediately after the addition of monomer. The dimerization occurs to form the styryl dicarbanion instead of :CH2 CHfCHfCH2 : , since the former is much more stable. The styryl dianions so-formed are colored red (the same as styryl monocarbanions formed via initiators such as n-butyllithium). Anionic propagation occurs at both carbanion ends of the styryl dianion

5-68

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Let matter be!

Although the suggestion that the styryl anion radical adds a few monomer molecules prior to dimerization has not been discounted, the reaction kinetics clearly show that better than 99% of the propagation occurs through the dianion. Dimerization of radical centers is highly favored by their high concentrations, typical 10 3 10 2 M (much higher than in a radical polymerization) and the larger rate constants (106 108 L mol 1 s 1 ) for radical coupling [Wang et al., 1978, 1979]. Electron-transfer initiation from other radical-anions, such as those formed by reaction of sodium with nonenolizable ketones, azomthines, nitriles, azo and azoxy compounds, has also been studied. In addition to radical anions, initiation by electron transfer has been observed when one uses certain alkali metals in liquid ammonia. Polymerizations initiated by alkali metals in liquid ammonia proceed by two different mechanisms. In some systems, such as the polymerizations of styrene and methacrylonitrile by potassium, the initiation is due to amide ion formed in the system [Overberger et al., 1960]. Such polymerizations are analogous to those initiated by alkali amides. Polymerization in other systems cannot be due to amide ion. Thus, polymerization of methacrylonitrile by lithium in liquid ammonia proceeds at a much faster rate than that initiated by lithium amide in liquid ammonia [Overberger et al., 1959]. The mechanism of polymerization is considered to involve the formation of a solvated electron:

Matter has always been and will always be one of the main objects of physics. -Wolfgang Pauli [479]

Li + NH3 Li+(NH3) + e (NH3)

When there are source charges, the quantization of the radiation field is a bit more subtle than what we saw in 2 . . For the free field, the classical dynamics is described completely by the sourceless Maxwell equations in the vacuum

5-69

V E=O, V B=O,

Such ammonia solutions are noted by their characteristic deep blue color. The solvated electron is then transferred to the monomer to form a radical anion,

(5 . 1) (5.2)

(NH3)

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