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Unlike Huttner and Barnett [306, 307], we have a strictly microscopic model for the medium, where each constituent atom sits in the vacuum a given distance away from the others. The medium is discrete rather than continuous. From a practical point of view, however, there is no need to account for all this microscopic detail. So we take the macroscopic average of the physical variables in our theory. As we have done in Section 7.4, we expand the Dirac delta functions in (7.2) into Fourier sine series inside the cavity. Robinson's in'elevant spatial Fourier components are here all those with a spatial frequency higher than w e / c.



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and octamethylcyclotetrasiloxane:

Dielectric permittivity is a classical concept. Thus, the permittivity in our quantum theory should be the same that we obtain in classical electrodynamics. In this section we temporarily disregard the quantum nature of the radiation field to calculate the dielectric permittivity in our model. Later in this chapter this will be compared with the dielectric permittivity that appears in the Huttner-Barnett theory. We will denote the classical counterparts of a, E, and Y(T/) by a/../fi, f3/../fi, and Y(T/)/../fi, respectively. Making these replacements in (7.96) and using Poisson

7-4

brackets rather than commutators (see 2), we obtain the following equations of motion:





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7-1 GENERAL CHARACTERISTICS 7-1a Scope; Polymerizability A wide variety of cyclic monomers have been successfully polymerized by the ring-opening process [Frisch and Reegan, 1969; Ivin and Saegusa, 1984; Saegusa and Goethals, 1977]. This includes cyclic amines, sul des, ole ns, cyclotriphosphazenes, and N-carboxy-a-amino acid anhydrides, in addition to those classes of monomers mentioned above. The ease of polymerization of a cyclic monomer depends on both thermodynamic and kinetic factors as previously discussed in Sec. 2-5. The single most important factor that determines whether a cyclic monomer can be converted to linear polymer is the thermodynamic factor, that is, the relative stabilities of the cyclic monomer and linear polymer structure [Allcock, 1970; Sawada, 1976]. Table 7-1 shows the semiempirical enthalpy, entropy, and free-energy changes for the conversion of cycloalkanes to the corresponding linear polymer (polymethylene in all cases) [Dainton and Ivin, 1958; Finke et al. 1956]. The lc (denoting liquid-crystalline) subscripts of H, S, and G indicate that the values are those for the polymerization of liquid monomer to crystalline polymer. Polymerization is favored thermodynamically for all except the 6-membered ring. Ringopening polymerization of 6-membered rings is generally not observed. The order of thermodynamic feasibility is 3,4 > 8 > 5,7 which follows from the previous discussion (Sec. 2-5c) on bond angle strain in 3- and 4-membered rings, eclipsed conformational strain in the 5-membered ring, and transannular strain in 7- and 8-membered rings. One notes that

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:t a = -iwea - iG (3 + (3*),

3 4 5 6 7 8

(7.100)

Hlc (kJ mol 1 ) 113.0 105.1 21.2 2.9 21.8 34.8

dry V(ry)Y(ry),

Glc (kJ mol 1 ) 92.5 90.0 9.2 5.9 16.3 34.3

Click the Page Layout tab on the Ribbon. Click the Columns button. Click More Columns. The Columns dialog box appears.

Data from Cubbon [1964]; all other data are from Dainton and Ivin [1958] and Finke et al. [1956].

(7.101) (7.102)

Hlc is the major factor in determining Glc for the 3- and 4-membered rings, while Slc is very important for the 5- and 6-membered rings. The enthalpy and entropy factors Hlc and Slc contribute about equally for larger-sized rings. Since both Hlc and Slc are negative, Glc becomes less negative with increasing temperature. Above some temperature (the ceiling temperature) Glc becomes positive, and polymerization is no longer favorable. For all-sized rings the presence of substituents decreases thermodynamic feasibility for polymerization. Interactions between substituents are more severe in the linear polymer than in the cyclic monomer [Cubbon, 1964; Sawada, 1976]; Hlc is less negative, while Slc is more negative. Exceptions to this generalization occur when the substituents are linked to each other to form a second ring in such a manner that there is increased strain in the ring containing the polymerizable functional group. Structures I and II, cis- and trans-8-oxabicyclo[4.3.0]-nonane, illustrate this point. The 5-membered ring in the cis isomer (I), is almost completely free of strain and does not polymerize. However, the trans isomer undergoes polymerization since the tetrahydrofuran ring is twisted and highly strained [Kops and Spangaard, 1975].

!Y(rt) = -iry Y(ry) - iV*(ry) (3.

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