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star polystyrene can also be synthesized by reaction XL with polystyryl carbanion to form XLII, which is then terminated with water or methanol. XLII can be used to produce a miktostar polymer containing three branches each of two different polymers: for instance, reaction with 1,3-butadiene forms a 6-arm star polymer containing three polystyrene branches and three polybutadiene branches. Coupling of GTP living polymers with halide-terminating agents to form star polymers has been achieved [Hertler, 1996; Webster and Sogah, 1989]. Star polymers are also synthesized by using polyfunctional initiators or by copolymerization with dimethacrylate monomers. Star and miktostar polymers have been synthesized by living cationic polymerization using dienes and trienes as coupling agents and/or multifunctional initiators [Faust and Shaffer, 1997; Hadjichristidis, et al., 1999; Hadjikyriacou and Faust, 2000; Kennedy and Jacob, 1998; Puskas et al., 2001; Sawamoto, 1991]. Multifunctional halides such as hexaiodomethylmelamines have also been used to obtain star and comb polymers [Ryu and Hirao, 2001; Zhang and Goethals, 2001]. Hyperbranched and dendritic polymers have also been studied.



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Use C# or Visual Basic .NET source code below for PDF conversion. renderer.RenderPageRangeToMultipageTIFFFile (0, renderer.GetPageCount()-1, TIFFCompression.LZW, "multipage.tiff" ); // Open the first output file in default image viewer.

~ L mo<r~ + VCoul + Htrans,

to replace f by f f0, where f0 is the number of radicals produced per light photon absorbed and f is the previously de ned initiator ef ciency. Also, quantum yields can be de ned in terms of the quantum yield for reaction of the initiator species or quantum yield for monomer polymerized. These quantum yields are not synonymous with the quantum yield for initiation.) An expression for the polymerization rate is obtained by combining Eqs. 3-50 and 3-25 to yield

(5.82)

Rp kp M 1=2 fIa kt 3-51

is the Coulomb energy of the charged particles, (5.84)

The absorbed light intensity Ia is obtained from a consideration of the Beer Lambert law in the form





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The first term in (5.84) is the sum of the Coulomb self-energies of each particle and the second term is the Coulomb interaction between pairs of charges. The former diverges. This is in part due to the fact that it is inconsistent to try to account, in a nonrelativistic theory, for the interaction of the particles with the high-frequency modes of the field. An immediate solution is to introduce a cutoff kor in all integrals over k in reciprocal space. For each particle 0: the cutoff must be on the order of

3-52

LET MATTER BE!

or click Enter (

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0 where I0 is the incident light intensity at the outer surface of the reaction system and Ia is the 0 intensity of absorbed light on a layer at a distance D (cm) into the reaction system. Ia is not the same as the quantity Ia in Eqs. 3-50 and 3-51. Ia is the volumetric light intensity (with 0 units of mol cm 3 s 1 or, more often, mol L 1 s 1 ). Ia and I0 are surface area intensities (with units of mol cm 2 s 1 ). [A] is the molar concentration of light-absorbing photoinitiator. a is the absorption coef cient of A and varies with wavelength and temperature. a has units of L mol 1 cm 1 . (The molar absorptivity E, formerly called the extinction coef cient, is often used instead of a. a and E are related by a E ln 10 2:3E and result from the use of the base e instead of 10, respectively, in the Beer Lambert law.) Ia and, therefore, Rp vary with depth of penetration D into the reaction system [Calvert and Pitts, 1967; Terrones and Pearlstein, 2001]. The variation of Ia with D is obtained as the 0 differential of Ia with respect to D

merc/Ii so as to leave out interactions with modes whose energy is comparable to merc'2. Such a cutoff gives a finite value for the Coulomb self-energy on the order of

3-53

The term 103 is a conversion factor (103 mL L 1 ) that converts Ia from units of mol cm 3 s 1 to mol L 1 s 1 . Combination of Eqs. 3-51 and 3-53 yields the polymerization rate as a function of D

(2'71-)3 ker'

Rp kp M 1=2 fa A I0 103 e a A D kt 3-54

(5.85)

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