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whatever the values of the gj's. This suggests that if we can find a complete set of collective annihilation and creation operators for the atoms of the medium with BN being one of its elements, we mi~ht be able to rewrite (7.8) in an exact yet much simpler form: a form where only BN and B1 couple to the cavity mode, with all the other N - 1 collective atomic operators decoupled. This would effectively reduce the problem of describing the atomic medium to the single pair of creation and annihilation operators BNand rather than N pairs, as the dynamics of the uncoupled N - 1 pairs would be irrelevant then. To make this decoupling come true, our set of collective atomic operators should not only be complete but also be such that the Hamiltonian of the medium L j b1bj remain diagonal when expressed in terms of the collective operators in the set. Such



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3-85)

a set of N pairs of. collective atomic-medium creation and annihilation operators containing Bl and Bi can be constructed in the following way. Let

The photolysis of benzildimethylketal yields benzoyl and benzylketal radicals in the primary cleavage. The latter radical undergoes decay within the cage to yield methyl benzoate and

Gn~ ~ i:a"

methyl radical. Coupling of the methyl and benzoyl radicals decrease f :

(7.12)

3-86)





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The initiator ef ciency and quantum yield for initiation are generally independent of monomer concentration and of the radical coupling reactions occurring outside the solvent cage (Eqs. 3-74, 3-75). The prime reason for f < 1 is the reactions occurring within the solvent cage. Once a radical has diffused out of the solvent cage, the reaction with monomer (Eq. 3-71) occurs predominantly in preference to other reactions [Fink, 1983]. Even if Reaction 3-72 occurs this will be followed by Reaction 3-73 in preference to the two radical combination reactions (Eqs. 3-74, 3-75). The preference for initiation of polymerization arises from the much greater monomer concentrations (10 1 10 M) compared to the radical concentrations (10 7 10 9 M) that are normally present in polymerization systems. However, one can observe a variation of f with the monomer concentration at low monomer concentrations. Figure 3-3 shows this effect in the AIBN initiation of styrene polymerization. The initiator ef ciency increases very rapidly with [M] and a limiting value is quickly reached. Theoretical predictions [Koenig and Fischer, 1973] indicate that an effect of [M] on f would be expected at monomer concentrations below 10 1 10 2 M, and this is the general observation. f is affected at lower concentrations as one increases the initiation rate, since the radical radical reactions become more probable. An example is the photopolymerization of methyl methacrylate using benzoin methyl ether [Carlblom and Pappas, 1977],

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Jul 13, 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.

5 6 7

(7.13)

Fig. 3-3 Effect of styrene concentration on the initiator ef ciency of azobisisobutyronitrile. *, * and refer to experiments with initiator concentrations of 0.20, 0.50, and 1.00 g L 1 , respectively. After Bevington [1955] (by permission of Faraday Society, and Royal Society of Chemistry, London).

L (gJbk+1 - 9k+1gjbj ),

The initial product is essentially poly(methyl methacrylate) homopolymer Little styrene is incorporated into copolymer chains unitl most or all of the methyl methacrylate is exhausted Reports of signi cant amounts of styrene in products from anionic copolymerization of styrene methyl methacrylate are usually artifacts of the particular reaction system, a consequence of heterogeneity of the propagating centers and/or counterion The anionic copolymerization of methyl methacrylate and styrene with lithium emulsion and n-butyllithium initiators is interesting [Overberger and Yamamoto, 1966; Richards, 1978; Tobolsky et al, 1958] Bulk copolymerization of an equimolar mixture of the two monomers with a lithium emulsion yields a copolymer with a high percentage of styrene, whereas n-butyllithium yields a copolymer with essentially no styrene Further, the product from the lithium emulsion reaction is essentially a block copolymer The results with lithium emulsion have been attributed to insolubility of lithium counterion.

(7.14)

The lithium ion is part of an insoluble lithium particle and propagation takes place on that particle surface Styrene is more strongly adsorbed than methyl methacrylate on these surfaces because of its dense p-electron system Reaction occurs with a very high styrene concentration at the reaction site and initial reaction involves a polystyryl homopropagation At some point the propagating chains detach from the metal surface and become solubilized in the bulk solution, where there is a much higher concentration of methyl methacrylate Polystyryl anions add methyl methacrylate with very little tendency for reverse crossover back to styrene, and the result is a block copolymer On the other hand, polymerization initiated by n-butyllithium proceeds in solution from the very beginning The greater reactivity of methyl methacrylate coupled with the very small tendency for crossover from poly(methyl methacrylate) propagating centers to polystyryl results in the product being essentially poly(methyl methacrylate) homopolymer.

where k = 1,2,3, ... ,N - 1. You can easily check that they all commute with each other and with ih and that together with their Hermitian conjugates, they satisfy the commutation relations of annihilation and creation operators,

Copolymer with signi cant amounts of styrene is obtained only at higher conversion where the feed composition is low in methyl methacrylate 6-4b-3 Effect of Temperature.

(7.15)

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