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Monomer chain-transfer constants are shown in Tables 5-4 and 5-5 for various polymerizations of styrene and isobutylene. It is apparent that the CM values for styrene are, is general, larger than those for isobutylene by one to two orders of magnitude. This corresponds to the greater reactivity of isobutylene toward propagation. Although extensive data are not available, one generally observes that the monomers with the larger kp values usually possess lower CM values. The values of CS for some compounds in the polymerization of styrene are shown in Table 5-6. The larger transfer constants are associated with transfer agents that possess a



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providing the required definition of the "real" quadrature of an'. Together, (9.24) and (9.25) define the non-Hermitian operators an' uniquely. We can now obtain an expression for iLn' in terms of the global operators a( k) in the following way. First, multiply (9.24) by sin([x + L]kn ) and integrate over x from -L to 0 using (9.2). We find the "imaginary" quadrature of an' this way,

TABLE 5-5 Monomer Transfer Constants in Cationic Polymerization of Isobutylene in CH2 Cl2 Coinitiator Initiator TiCl4 -H2 Oa Temperature ( C) 20 50 78 20 50 78 20 50 78 25 50 CM 104 21.2 6.60 1.52 26.9 5.68 2.44 60.0 36.0 5.7 15 3.9

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Data from Imanishi et al. [1961]. Data from Kennedy and Feinberg [1978], Kennedy et al. [1977].

roc> dk {k { Vk;.

TABLE 5-6 Chain-Transfer Constants in Styrene Polymerization Initiator or Coinitiator SnCl4 H2 SO4 SnCl4 SnCl4 SnCl4 SnCl4 SnCl4 SnCl4 SnCl4 BF3 SnCl4 SnCl4 H2 SO4 CCl3 COOH

x {eikL.c(k)a(k) - e-ikL.c*(k)at(k)}. (9.26)

Solvent fH (CH2 Cl)2 C6 H12 CCl4 -fNO2 (3 : 7) CCl4 fH (CH2 Cl)2 fH (CH2 Cl)2 fH fH fH (CH2 Cl)2 None

To find the "real" quadrature, we multiply (9.25) by cos([x over x from -L to 0 using (9.3). We obtain

Temperature ( C) 30 25 0 0 30 30 30 30 30 30 30 30 25 25

+ an'

Transfer Agent fH (CH3 )2 CHf (CH3 )2 CHf CH3 Of CCl4 CH3 OH CH3 OH CH3 COOH CH3 COOH CH3 COOH (CH3 CO)2 O CH3 COOC2 H5 (C2 H5 )2 O Benzoquinone

{eikL.c(k)a(k)

Data from Biddulph and Plesch [1960]. Data from Jenkinson and Pepper [1961]. c Data from Overberger et al. [1956]. d Data from Endres and Overberger [1955]. e Data from Okamura and Higashimura [1956a,b]. f Data from Brown and Mathieson [1957, 1958].

+ e-ikL *(k)at(k)}.

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weakly bonded negative fragment (e.g., CH3 O in CH3 OH) or are readily alkylated (CH3 Of). However, the value of CS for a transfer agent is seen to vary considerably when the initiator, coinitiator, or solvent is changed. 5-2f Effect of Reaction Medium The nature of the reaction medium can play a signi cant role in cationic polymerization. Changes in rate and/or degree of polymerization often occur when the solvent or counterion are changed. The effect of reaction medium can affect the reaction in several ways. The equilibrium between free ions and ion pairs will be shifted toward free ions by high-polarity solvents. This usually results in an increased polymerization rate since free ions propagate faster than ion pairs, but the effect is not huge since kp typically does not exceed kp by more than an order of magnitude. However, large solvent effects can be observed for systems in which the counterion has a signi cant tendency to form a covalent bond to the carbocation. Lowpolarity solvents drive the reaction system toward the covalent species I, (see Sec. 5-1), which does not propagate, or at most, propagates much more slowly than does the free ion or ion pair. In addition, solvent can affect the rate and degree of polymerization by changing propagation rate constants. 5-2f-1 Propagation by Covalent Species; Pseudocationic Polymerization

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(9.27)

The major species in most cationic polymerization systems are covalent, including halides and esters. There has been considerable controversy as to whether covalent species undergo propagation by direct monomer insertion into a covalent bond or only through ionization to

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