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under these conditions. Thus, Rp is rst-order in [M], 1-order in both light intensity and 2 photoinitiator concentration when there is negligible attenuation of light intensity in traversing the reaction system. When the photoexcitation process involves monomer (A M), the dependence of Rp on [M] increases to 3-order. The dependence of Rp on [M] decreases to 12 2 order in some systems with high monomer concentrations, such as in the photopolymerization of methyl methacrylate with ketone photoinitiators [Lissi et al., 1979]. With increasing [M], monomer quenches the excited state for photoinitiation. Quenching is a generally observed phenomenon, leading to a lower than expected dependence of Rp on some component in the system that acts as the quencher. A quencher (which can be any compound present in the reaction system) undergoes energy transfer with the photoexcited species to dissipate the excitation energy. For most practical photopolymerizations there is appreciable attenuation of light intensity with penetration and the dependence of polymerization rate on monomer, photoinitiator, and light intensity is more complex (see Eqs. 3-54 and 3-55 for exact de nitions). Equation 3-54 is especially useful for analyzing the practical aspects of a photopolymerization. When polymerizing any speci c thickness of reaction system it is important to know Rp at various depths (e.g., front, middle, and rear surfaces) than to know only the total Rp for that system thickness. If the thickness is too large, the polymerization rate in the rear (deeper) layers will be too low, and those layers will be only partially polymerized the result would be detrimental because the product s properties (especially the physical properties) would be



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(5.88)

Another approach to block copolymer is the mutual termination of a living cationic polymer with a living anionic polymer, but the ef ciency of coupling is generally low because of proton transfer from the carbocation to the carbanion, resulting in two homopolymers instead of the block copolymer [Richards et al., 1978]. 5-4d Transformation Reactions

(5.89)

Another approach to block copolymers involves changing the type of propagating center part way through the synthesis via a transformation reaction [Burgess et al., 1977; Richards, 1980; Souel et al., 1977; Tung et al., 1985]. For example, after completion of the living anionic polymerization of monomer A, the carbanion centers are transformed into carbocations

A description of the electromagnetic field in terms of potentials introduces extra degrees of freedom that cannot possibly be independent. This is reflected in the fact that the fields remain unchanged under the following gauge transformations of the potentials:





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Note: You can press multiple times to cycle through mixed, relative and absolute references. Note: You can also delete the dollar sign characters in the Formula bar to make a reference relative.

5-123

A(r, t)

by reaction with excess phosgene followed by silver hexa uoroantimonate. The carbocations are then used to polymerize monomer B. Anionic propagating centers are transformed into radical centers in the presence of a second monomer that undergoes radical propagation, by reaction with trimethyl lead chloride followed by heating:

A(r, t)

AAA Pb(CH3)3

+ VF(r, t),

5-124

The potential of transformation reactions for synthesizing a wider range of block copolymers has not been realized because either the reactions are not quantitiative or deterimental side reactions occur. Thus coupling of two propagating carbanions by one phosgene competes with the 1 : 1 transformation in Eq. 5-123. The anionic-to-radical transformation in Eq. 5-124 involves the formation of trimethyllead radical, which initiates homopolymerization of monomer B.

(5.90) (5.91)

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5-5 DISTINGUISHING BETWEEN RADICAL, CATIONIC, AND ANIONIC POLYMERIZATIONS There is sometimes a question as to whether a particular initiator or initiator system initiates polymerization by radical, cationic, or anionic means. Such a question can easily arise, for example, in polymerizations initiated by ionizing radiation. The mode of initiation of a particular initiator can be distinguished by a consideration of its characteristics compared to those of known radical, cationic, and anionic initiators: 1. Ionic polymerizations usually proceed at lower temperatures than radical polymerizations. Although ionic reaction temperatures are usually below 0 C, there are numerous ionic polymerizations that proceed at temperatures somewhat above 0 C. Radical polymerizations, on the other hand, almost always proceed at temperatures appreciably above approximately 50 C. Furthermore, ionic polymerizations invariably have lower

U(r, t)

activation energies than their radical counterparts and, in some cases, they may actually possess negative activation energies. Ionic polymerizations are distinguished by their marked sensitivity to changes in the polarity and solvating ability of the reaction media and counterion effects. Radical polymerizations do not show such effects. The addition of known radical scavengers such as the DPPH radical to a polymerizing system will halt polymerization if it is a radical reaction. Ionic polymerizations will be unaffected by such additions. One must be careful, however, not to use a radical scavengers that also affects ionic polymerization. Thus, benzoquinone would be a poor choice as a radical scavenger, since it can also act as an inhibitor in ionic polymerization. The chain transfer constant for an additive or solvent in the polymerization can be determined. This value can then be compared with the transfer constants for the same substance in the polymerization of the same monomer by known radical, cationic, and anionic initiators. Copolymerization behavior can also be used to distinguish between radical and ionic polymerizations (see Chap. 6).

U(r, t) - -!'IF(r, t),

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