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5-3 ANIONIC POLYMERIZATION OF THE CARBON CARBON DOUBLE BOND Anionic chain polymerizations show many of the same characteristics as cationic polymerizations, although there are some distinct differences. The propagating species are anionic ion pairs and free ions with relative concentrations that depend on the reaction media as in cationic polymerization. Unlike cationic polymerization, there is a large difference between the reactivities of ion pairs and free ions in anionic polymerization. Although anionic polymerizations generally proceed rapidly at low temperatures, they are seldom as temperature-sensitive as cationic polymerizations. Further, most anionic polymerizations possess positive ER values and proceed well at and somewhat above ambient temperatures. Many anionic polymerizations are easier to understand, since the identities of the initiating species and counterions are much better established. The range of solvents useful for anionic polymerization is limited to aliphatic and aromatic hydrocarbons and ethers. Halogenated solvents, suitable for cationic polymerization, cannot be used for anionic polymerization because of their facile nuceophilic substitution reactions with carbanions. Other polar solvents such as esters and ketones are also excluded as a result of reaction with carbanions. Termination occurs by transfer of a positive fragment, usually a proton, from the solvent or some transfer agent (often deliberately added), although other modes of termination are also known. Many anionic polymerizations are living polymerizations when the reaction components are appropriately chosen. 5-3a 5-3a-1 Initiation Nucleophilic Initiators



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A variety of basic (nucleophilic) initiators have been used to initiate anionic polymerization [Bywater, 1975, 1976, 1985; Fontanille, 1989; Hsieh and Quirk, 1996; Morton, 1983; Morton and Fetters, 1977; Quirk, 1995, 1998, 2002; Richards, 1979; Szwarc, 1983; Young et al., 1984]. These include covalent or ionic metal amides such as NaNH2 and LiN(C2 H5 )2 , alkoxides, hydroxides, cyanides, phosphines, amines, and organometallic compounds such as n-C4 H9 Li and fMgBr. Initiation involves the addition to monomer of a nucleophile (base), either a neutral (B:) or negative (B: ) species. Alkyllithium compounds are probably the most useful of these initiators, employed commerically in the polymerizations of 1,3-butadiene and isoprene. Initiation proceeds by addition of the metal alkyl to monomer





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we find that the difference in photon number is given by (4.133) As the coherent state la(t)} is very intense (a laser beam), we can neglect the second term square brackets on the right-hand side of (4.133). Now ~el(e - wt) is the variance of the quadrature el in a reference frame rotated by e - wt in relation to the old reference frame. The rotation by -wt allows it to follow the movement of ein phase space due to its free time evolution, so that ~el(e - wt) does not change in time. The dependence on e allows us to choose the direction in which we want to measure the field fluctuations (i.e., it allows us to choose which quadrature we want to look at).

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In Section 4.1 we saw how an open system becomes entangled to the immense number of degrees of freedom of the environment. This entanglement leads to a mixed reduced-density matrix for the open system. Controlled entanglement, rather than this ordinary entanglement with the inaccessible degrees of freedom of the environment, has many interesting applications, including teleportation, quantum cryptography, and quantum computing. For more on these applications that are now part of the new field of quantum information, see

followed by propagation:

[71].

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The Glauber-Sudarshan quasiprobability distribution seen in Section 4.1 is not the only one used in quantum optics. Another example of quasiprobability distribution is the Wigner function [644], which is associated with symmetrical ordering rather than normal ordering. It introduces the idea of phase-space in quantum mechanics (for a phase space approach to quantum optics, see Schleich's book [537]). Some of the advantages of the Wigner function are that unlike P, it is not singular for coherent states and for physical quantum states, and that it makes important features such as quantum interference easy to identify visually.

The extensive use of alkyllithium initiators is due to their solubility in hydrocarbon solvents. Alkyls or aryls of the heavier alkali metals are poorly soluble in hydrocarbons, a consequence of their more ionic nature. The heavier alkali metal compounds, as well as alkyllithiums, are soluble in more polar solvents such as ethers. The use of most of the alkali metal compounds, especially, the more ionic ones, in ether solvents is somewhat limited by their reactivity toward ethers. The problem is overcome by working below ambient temperatures and/or using less reactive (i.e., resonance-stabilized) anions as in benzylpotassium, cumylcesium and diphenylmethyllithium. Alkyl derivatives of the alkaline-earth metals have also been used to initiate anionic polymerization. Organomagnesium compounds are considerably less active than organolithiums, as a result of the much less polarized metal carbon bond. They can only initiate polymerization of monomers more reactive than styrene and 1,3-dienes, such as 2- and 4-vinylpyridines, and acrylic and methacrylic esters. Organostrontium and organobarium compounds, possessing more polar metal carbon bonds, are able to polymerize styrene and 1,3-dienes as well as the more reactive monomers. In the relatively few anionic polymerizations initiated by neutral nucleophiles such as tertiary amines or phosphines the proposed propagating species is a zwitterion [Cronin

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