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compositions f1 and f2 , respectively. The average or cumulative composition of the copolymer as a function of conversion is also shown. The copolymer produced is slightly richer in methyl methacrylate than the feed because methyl methacrylate has a slighly larger monomer reactivity ratio than styrene. The feed becomes richer in styrene with conversion leading to an increase in the styrene content of the copolymer with conversion. Figure 6-3 also shows the average composition of all the copolymer formed up to some degree of conversion as a function of conversion. The average copolymer composition becomes richer in styrene than methyl methacrylate but less so than the instantaneous copolymer composition. One can show the drift of copolymer composition with conversion for various comonomer feed compositions by a three-dimensional plot such as that in Fig. 6-4 for the radical copolymerization of styrene (M1)-2-vinylthiophene (M2). This is an ideal copolymerization with r1 0:35 and r2 3:10. The greater reactivity of the 2-vinylthiophene results in its being incorporated preferentially into the rst-formed copolymer. As the reaction proceeds, the feed and therefore the copolymer become progressivley enriched in styrene. This is shown by Fig. 6-5, which describes the distribution of copolymer compositions at 100% conversion for several different initial feeds. Corresponding data for the alternating radical copolymerization of styrene (M1)-diethyl fumarate (M2)(r1 0:30 and r2 0:07) are shown in Figs. 6-6 and 6-7. This system undergoes azeotropic copolymerization at 57 mol% styrene. Feed compositions near the azeotrope yield narrow distributions of copolymer composition except at high conversion where there is a drift to pure styrene or pure fumarate depending on whether the initial feed contains more or less than 57 mol% styrene. The distribution of copolymer compositions becomes progressively wider as the initial feed composition differs more from the azeotropic composition.

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Fig. 6-5 Distribution of copolymer composition at 100% conversion for styrene 2-vinylthiophene at the indicated values of mole fraction styrene in the initial comonomer feed. After Billmeyer [1984] (by permission of Wiley-Interscience, New York) from plot in Mayo and Walling [1950] (by permission of American Chemical Society, Washington, DC).

Fig. 6-6 Dependence of the instantaneous copolymer composition F1 on the initial comonomer feed composition f1 and the percent conversion of styrene (M1) diethyl fumarate (M2) with r1 0:30 and r2 0:07. After Walling [1957] (by permission of Wiley, New York) from plot in Mayo and Walling [1950] (by permission of American Chemical Society, Washington, DC).

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The first and second sibling data tables have foreign keys into the grandparent data, and the grandchild data has foreign keys into the first sibling data When a row is selected in the GrandParentSet table, the sibling tables update to only show those rows related to the currently selected grandparent row Likewise, when a row is selected in the first sibling table, the grandchild table updates to only show the related grandchild rows This is all accomplished by chaining the binding sources Listing 42 shows the code used to set up the data binding

Fig. 6-7 Distribution of copolymer composition at 100% conversion for styrene diethyl fumarate at the indicated values of mole fraction styrene in the initial comonomer feed. After Billmeyer [1984] (by permission of Wiley-Interscience, New York) from plot in Mayo and Walling [1950] (by permission of American Chemical Society, Washington, DC).

The LT of (3.53) and (3.55) are then identical by introducing z and ck0 . The underlying physical problem is the following: The monochromatic source of frequency o 2pf ck0 is radiating into a semi-in nite one-dimensional medium whose refractive index is n x 1 em x . Only propagation toward

In the commercial use of copolymerization it is usually desirable to obtain a copolymer with as narrow a distribution of compositions as possible, since polymer properties (and therefore utilization) are often highly dependent on copolymer composition [Athey, 1978]. Two approaches are simultaneously used to minimize heterogeneity in the copolymer composition. One is the choice of comonomers. Choosing a pair of monomers whose copolymerization behavior is such that F1 is not too different from f1 is highly desirable as long as that copolymer has the desired properties. The other approach is to maintain the feed composition approximately constant by the batchwise or continuous addition of the more reactive monomer. The control necessary in maintaining f1 constant depends on the extent to which the copolymer composition differs from the feed. Although the monomer reactivity ratios in living radical polymerizations are generally the same as in nonliving polymerizations, there is a difference in the distribution of copolymer compositions for different polymer molecules [Hawker et al., 2001; Matyjaszewski and Xia, 2001]. All polymer chains do not have the same composition in nonliving systems because chains are initiated at different times in a polymerization and propagate under different feed compositions as conversion progresses. Almost all polymer chains have the same composition in living systems because all chains are initiated at time close to zero and propagate

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