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The method used in drawing the ionic species in these two equations and throughout this chapter is meant to show that the ionic species usually do not exist as free ions but as ion pairs. The parentheses around the anionic fragment is used to indicate that the negative counterion remains close to the positive fragment. (Even when the counterion is not shown, one should understand it is present.) However, keep in mind that free ions coexist with the ion pairs, and it is the relative concentrations that determine the overall polymerization rate.

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The nomenclature for positively charged organic ions has undergone some change. The older term, no longer used, for the trivalent, trigonal sp2 -hybridized species such as those in Eqs. 5-1 and 5-2 is carbonium ion. Olah [1972, 1988] proposed that carbenium ion be used instead with the term carbonium ion being reserved for pentavalent charged carbon ions (e.g., nonclassical ions) and the term carbocation encompassing both carbenium and carbonium ions. The term carbenium ion for the trivalent carnbon ion has not taken rm hold. Most text and journal references use the term carbocation, and so will this text. The term carbocation polymerization is used synonymously with cationic polymerization in the literature. The requirement for the anion not to be excessively nucleophilic generally limits the utility of most strong acids as cationic initiators. Hydrogen halides are ineffective as initiators of cationic polymerization because of the highly nucleophilic character of halide ions. One forms only the 1:1 addition product of alkene and hydrogen halide under most conditions. Hydrogen iodide shows some tendency to initiate polymerization of the most reactive monomers, such as vinyl ethers and N-vinylcarbazole (Sec. 5-2g-3). Other strong acids with less nucleophilic anions, such as perchloric, sulfuric, phosphoric, uoro- and chlorosulfonic, methanesulfonic, and tri uoromethanesulfonic (tri ic) acids, initiate polymerization, but the polymer molecular weights rarely exceed a few thousand. 5-2a-2 Lewis Acids





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Various Lewis acids are used to initiate cationic polymerization, generally at low temperatures, with the formation of high-molecular-weight polymers in high yield. These include metal halides (e.g., AlCl3 , BF3, SnCl4 , SbCl5 , ZnCl2 , TiCl4 ) and their organometallic derivatives (e.g., RAlCl2 , R2 AlCl, R3 Cl). Lewis acids are the most important means of initiating cationic polymerization. Aluminium, boron, tin, and titanium halides are the most frequently used Lewis acids. Initiation by Lewis acids almost always requires and/or proceeds much faster in the presence of either a proton donor (protogen) such as water, hydrogen halide, alcohol, and carboxylic acid, or a carbocation donor (cationogen) such as an alkyl halide (e.g., t-butyl chloride and triphenylmethyl chloride), ester, ether, or anhydride. Thus, dry isobutylene is unaffected by dry boron tri uoride but polymerization occurs immediately when trace amounts of water are added [Evans and Meadows, 1950]. The terminology of Kennedy and Marechal [1982] is used in this book; the protogen or cationogen is referred to as the initiator, while the Lewis acid is the coinitiator. The reader is cautioned that much of the published literature until 1990 or so used the reverse terminology. The protogen or cationogen is referred to as the initiator since it supplies the proton or cation that ultimately adds to monomer to initiate polymerization. The initiator and coinitiator, representing an initiating system, react to form an initiator coinitiator complex (or syncatalyst system), which then proceeds to donate a proton or carbocation to monomer and, thus, to initiate propagation [Dunn, 1979; Kennedy, 1976]. The initiation process for boron tri uoride and water is

and (4.37) are the classical probabilities (Le., PI + P2 = 1) of finding S in states I } or I l..}, respectively. When 0 < I(RIR'}1 2 < I, I'I/I} will still be an entangled state, but ps will be a mixture with some degree of quantum coherence left in it. This quantum coherence is revealed by the presence of off-diagonal components in (4.33) in this case. The amount of quantum coherence present will depend on how close to 1 I(RIR') 12 is, covering a continuous range from a pure state to a mixture devoid of coherence. In general, however, it might not be obvious whether a given reduced density matrix is pure or a mixture just by inspecting its expression. There might not even be an expression for Ps. In this case, the trace of p~ can be very helpful. Even though Tr(ps) is always unity, as ('I/II'I/I) = I, the trace of p~ lets us distinguish reduced density matrices that represent pure states from those that represent mixtures. From (4.33) we find that Tr (p~) = ( 1 2)2 l+p

BF3 + H2O BF3 OH2 (CH3)3C +(BF3OH)

(1 + p4 + 2p2 1(RIR'}1 2 )

The initiator coinitiator complex BF3 OH2 is often shown as H (BF3 OH) . Initiation by aluminum chloride and t-butyl chloride is described by

(4.38)

AlCl3 + (CH3)3CCl (CH3)3C +(AlCl4) (CH3)3CCH2CH (AlCl4)

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