Variation of Composition with Conversion

In general, Fi =/i, that is, the composition of the copolymer formed at any instant will differ i om that of the monomer mixture from which it is being formed. Thus, as the reaction proceeds, the unreacted monomer mixture will be depleted in the more reactive monomer, and as the composition of the unreacted monomer changes, so will that of the polymer being formed, in accordance with (12.11). 

Example 1. Draw curves of instantaneous copolymer composition, Fi, vs. monomer composition,/i, for the following systems, and indicate the direction of composition drift as the reaction proceeds in a batch reactor. 

Solution. Application of (12.11) gives the plots in Fig. 12.1. Note that systdm (a) approximates ideal copolymerization, case 4 above. In system b), styrene is the preferred monomer, regardless of the terminal radical hence, the copolymer is largely styrene until styrene monomer is nearly used up. System (c) approximates case 1 above. 

The direction of composition drift with conversion is indicated by arrows. Note that system (c) forms an azeotrope at Fi=fi= 0.493. To the left of the azeotrope. Mi is the more reactive monomer (Fi /i), but to the right, M2 is more reactive (Fi /i). Therefore, with an initial monomer composition fio 0.493, Fi and/i decrease with conversion, but iffio 0.493, they will 

Consider a batch consisting of a total of M moles of monomer (M = Ml + M2). At time t, the monomer has a composition fi. In the time interval dM moles of monomer polymerize to form copolymer with a composition Fi- Therefore, at time t -l- dt, there are left (M — dM) moles monomer whose composition has been changed to ( — dfi). Writing a material balance on monomer 1 gives Mi in monomer at r = Mi in monomer at (t + dr) -f- Mi in 

Expanding and neglecting second-order differentials gives 

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Variation of Composition with Conversion The amount of styrene incorporated into an experimental h -trans SBR at any given conversion is compared (Fig. 16) with that for a polymer prepared by free-radical emulsion polymerization and one... 

The predicted variation in composition with conversion for a terpolymer prepared by batch and by semicontinuous polymerization is shewn in Figure 5, The average ccitposition on a mole basis, for the terpolymer is approximately 74% monomer A, 21% moncmer B> and 5% monomer C, The nearly uniform conpositicn of the semi-ocsitinuous polymer is evident. Monomer C is soluble in water as well as in the monomer mixture, whereas the other two monomers are sparingly soluble in water. Because the relative amount of monomer mixture to water is low during the initial portion of the somi-continuous reaction, practically edl of C resides in the aqueous phase and little is incorporated in polymer formed in the first part of the reacticxi. 

Figure 6. Variation of the instantaneous copolymer composition with conversion for a starting monomer composition of 20 mol% of...

Equation 6-34 or its equivalent has been used to correlate the drift in the feed and copolymer compositions with conversion for a number of different copolymerization systems [Capek et al., 1983 O Driscoll et al., 1984 Stejskal et al., 1986 Teramachi et al., 1985], The larger the difference in the t and r2 values of a comonomer pair, the greater is the variation in copolymer composition with conversion [Dadmun, 2001]. 

Fig. 6-3 Variations in feed and copolymer compositions with conversion for styrene (MJ-methyl methacrylate (M2) with (/i)0 = 0.80, (/2)0 = 0.20 and r = 0.53, r2 = 0.56. After Dionisio and O Driscoll [1979] (by permission of Wiley, New York).

Since most polymers prepared fw practical purposes are copolymers, it is important to consider the effects of having more than one monomer present in a batch emulsion polymerization. Obviously, the introduction of a second monomer brings with it the need to take into account the effects of differences in monomer reactivity on the composition of the copolymer formed and the variation of copolymer composition with conversion. For a bulk or solution polymerization, the copolymer composition equation can be applied directly (Equations (1.33) and (1.34) in Section 1.6.1). However, for emulsion polymerizations, the situation is... 

Fig. 3. Time variation of the catalyst bed temperature and the relative S03 signal in the stream leaving the cycled bed for composition forcing of the final stage of a S02 converter with an air stream and effluent from the previous stage (a) half cycle with air feed, (b) half cycle with S03/S02 feed. Feed to the system contains 12.4 vol% S02, conversion in the first stage = 90% and t = 26 min, s = 0.5. (Figure adapted from Briggs etal., 1977, with permission, 1977 Elsevier Science Publishers.)...

Variation of Styrene Content with Extent of Conversion. Figure 8 gives the relationship between copolymer composition and the extent of conversion for copolymers of butadiene and styrene (25 wt.7. styrene) prepared in toluene, at 30°C, with n-BuLi and barium salts of t-butanol and water. For comparison purposes, the copolymer composition curve is shown for the reaction initiated using n-BuLi alone. Copolymerization using n-BuLi results in very little incorporation of styrene into the copolymer chain until about 757. conversion, after which the styrene content increases very rapidly. In contrast, copolymerization using the barium salts and n-BuLi results in an increased incorporation of styrene at the same extents of conversion. 

The alternating tendency of the copolymers is advantageous in that the polymerizations can be carried out to high conversions with little or no compositional drift. For random copolymerizations in which there is preferential incorporation of one monomer due to a mismatch in reactivity ratios, the compositional variations with conversion can be substantial. Such compositional heterogeneities in resist materials can lead to severe problems during image development. 

CAI s that were once molten (type B and compact type A) apparently crystallized under conditions where both partial pressures and total pressures were low because they exhibit marked fractionation of Mg isotopes relative to chondritic isotope ratios. But much remains to be learned from the distribution of this fractionation. Models and laboratory experiments indicate that Mg, O, and Si should fractionate to different degrees in a CAI (Davis et al. 1990 Richter et al. 2002) commensurate with the different equilibrium vapor pressures of Mg, SiO and other O-bearing species. Only now, with the advent of more precise mass spectrometry and sampling techniques, is it possible to search for these differences. Also, models prediet that there should be variations in isotope ratios with growth direction and Mg/Al content in minerals like melilite. Identification of such trends would verify the validity of the theory. Conversely, if no correlations between position, mineral composition, and Mg, Si, and O isotopic composition are found in once molten CAIs, it implies that the objects acquired their isotopic signals prior to final crystallization. Evidence of this nature could be used to determine which objects were melted more than once. 

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