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In our single-mode model, the high spatial frequencies describing the unwanted microscopic detail are, of course, all those above w / c. Discarding them from (7.60) and using the resulting expression in (7.2), we find that the macroscopic polarization is given by

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The polymerization of unconjugated dienes [eg, diallyl phthalate, diethylene glycol bis(allyl carbonate), diallyl maleate] and trienes (eg, triallyl cyanurate) to form highly crosslinked thermoset products is a commercially important process An example is the use of various dimethacrylate dental lling materials [Nicholson and Anstice, 1999] This is also true of the use of such monomers to bring about crosslinking in copolymerization systems (Sec 6-6a) The crosslinking reaction is almost always found to be somewhat inef cient in that the experimental gel points occur at higher extents of reaction than those predicted by theory There is a wastage of the diene or triene monomer which has been ascribed to intramolecular cyclization of the diene or triene This phenomenon is encountered not only in homo- and copolymerizations involving dienes and trienes but also in step polymerizations with trifunctional reactants (Sec 2-10c).

(x) =





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The extent of cyclization varies considerably depending on the particular reaction system There are some reactants for which cyclization is very extensive The competition between the intermolecular and intramolecular reactions in the polymerization of a diene is depicted in Eqs 6-98 through 6-100, where Z is a structural unit such as the benzene ring in divinylbenzene or the trimethylene group in 1,6-heptadiene Intermolecular propagation proceeds according to the horizontal set of reactions (Eq 6-98) to produce a linear polymer with pendant double bonds The pendant double bonds of a propagating or terminated polymer chain give rise to a crosslinked nal product by copolymerizing with either unreacted monomer or the pendant double bonds of other chains Cyclization occurs when propagating species IV reacts intramolecularly with its own pendant double bond in preference to intermolecular propagation.

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Attachment of the radical center at the methylene and methine carbons of the pendant double bond yields different-sized ring structures as shown in VIII and IX, respectively Similar reaction sequences would apply for the competition between inter- and intramolecular propagations in polymerizations involving trienes or copolymerizations in which one of the monomers is a diene or triene Copolymerizations are more complicated since cyclization can occur before as well as after the addition of the second monomer to a propagating species such as IV..

(~x) ~(bj + b)., sin (~Xj) .

6-98

6-99

(7.61)

6-100

Using the definitions of gj, fJ, G and G', we can express (7.61) in terms of the collective atomic operators fJ and fJt:

The importance of intramolecular cyclization was emphasized when Butler and coworkers found that the radical polymerization of N, N, N, N-diallyldimethylammonium chloride (DADMAC) gave soluble, uncrosslinked polymers with little or no unsaturation (Eq. 6-101) [Butler and Angelo, 1957; Butler and Ingley, 1951; Wandrey et al., 1999]. There is a very low tendency for radical IV to propagate intermolecularly and undergo crosslinking. The predominant reaction is intramolecular cyclization, and the product is a linear product with cyclic structures in the backbone. The reaction is referred to as alternating intra/intermolecular polymerization or cyclopolymerization.

P(x)

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6-101

(7.62)

The size of the ring structure that can be formed determines whether intermolecular polymerization or intramolecular cyclization is the predominant reaction for a particular monomer [Butler, 1986, 1989, 1992, 1996, 2000; Kodaira, 2000; Marvel and Vest, 1957, 1959] The extent of cyclization generally increases in the following order: 5- and 6-membered rings appreciably greater than 7-membered rings and the latter greater than larger sized rings 1,6-Dienes (Z in Eqs 6-98 through 6-100 contains three ring atoms) such as acrylic and methacrylic anhydrides, diallyl quaternary ammonium salts, methyl allyl maleate and fumarate, and allyl methacrylate cyclopolymerize to 5- or 6-membered rings or mixtures of the two Formation of the 5-membered ring involves kinetic control of the cyclization process proceeding through the less stable radical VII to form polymer IX instead of thermodynamic control, proceeding through radical VI to form the more stable 6-membered ring structure VIII.

We can now see that fJ and fJt are the annihilation and creation operators of macroscopic polarization quanta. Substituting (7.62) in (7.59), we find the following expression for the macroscopic electric field

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I want to convert pdf to Word using C# | The ASP.NET Forums
I want to convert pdf to Word using C# but i am not able to do it .Please share me code so that i can convert pdf to word using C#.

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13 Jul 2015 ... Convert PDF to Word Using C# The first step will be to get the PdfBox package using the Nuget Package Manager. Now, import the following DLLs into your .cs file: The third step will be to install the DocX NuGet Package from the NuGet Package Manager: Let's read a PDF file and try to get the text from it.












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