Nonstoichiometry of Functional Groups in .NET

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Nonstoichiometry of Functional Groups
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Using the Macosko Miller approach for the A B B0 0 system, we introduce r1 A B B and r2
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r1 r2 B 0 A 0 B0 0 A 0 2-116a 2-116b 2-116c
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pA r1 pB r2 pB0
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PROCESS CONDITIONS
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to describe the relative amounts and extents of reaction of the three reactant groups and reformulate Eqs. 2-103 and 2-110 as
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wo pB r1 wiB pB0 r2 wiB0 A U 2wiA 2Mo pB r1 Mo pB0 r2 Mo 1 p2 r1 p2 0 r2 =2 B B 2-117 2-118
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The expressions for M w, M n , and PDI are complicated but can be solved numerically [Ozizmir and Odian, 1990]. When B and B0 groups together are in excess over A groups r1 r2 > 1 and the reactivities of B and B0 are the same s 1 , PDI is very slightly decreased at all conversions in comparison to the stoichiometric case r1 r2 1 . The nal PDI is 1.98. For s > 1 (B0 more reactive than B), PDI is initially decreased but increases with conversion and the nal PDI is above 2. The trends are more exaggerated when B0 is in excess over B and less exaggerated when B is in excess over B0 . For example, for the case r1 r2 1:25, s 20, the nal PDI is 2.63, 6.50, and 2.16, respectively, when r1 =r2 is 1, 3, and 1. When A groups are in excess over B and B0 , PDI is very slighly decreased at all 3 conversions in comparison to the stoichiometric case. The nal PDI is 1.98 independent of s; r1 =r2 , and r1 r2 . Nonstoichiometric amounts of reactants decrease PDI at all conversions for A B 0 A B polymerizations [Gandi and Babu, 1979, 1980]. The decrease in PDI is greater the larger the difference in the reactivities of B and B0 groups when B 0 is in excess over A The B A. decrease in PDI is independent of the difference in reactivities of B and B0 when A is A in excess. The trend is the same with A in excess when B and B0 have the same initial A reactivity but the reactivity of each group changes on reaction of the other. However, a different trend is seen when B 0 is in excess. PDI increases with a limiting value at complete B conversion of 2 or greater than 2 depending on whether the difference in reactivity of B and B0 is less than or greater than 2.
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2-8 PROCESS CONDITIONS 2-8a Physical Nature of Polymerization Systems
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Several considerations are common to all processes for step polymerizations in order to achieve high molecular weights. One needs to employ a reaction with an absence or at least a minimum of side reactions, which would limit high conversions. Polymerizations are carried out at high concentrations to minimize cyclization and maximize the reaction rate. Highpurity reactants in stoichiometric or near-stoichiometric amounts are required. The molecular weight is controlled by the presence of controlled amounts of monofunctional reagents or an excess of one of the bifunctional reagents. Equilibrium considerations are also of prime importance. Since many step polymerizations are equilibrium reactions, appropriate means must be employed to displace the equilibrium in the direction of the polymer product. Distillation of water or other small molecule products from the reaction mixture by suitable reaction temperatures and reduced pressures are often employed for this purpose. Table 2-8 shows values of some kinetic and thermodynamic characteristics of typical step polymerizatiosn [Bekhli et al., 1967; Chelnokova et al., 1949; Fukumoto, 1956; Hamann et al., 1968; Malhotra and Avinash, 1975, 1976; Ravens and Ward, 1961; Saunders and Dobinson, 1976; Stevenson, 1969; Ueberreiter and Engel, 1977]. These data have implications on the temperature at which polymerization is carried out. Most step polymerizations
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88 T ( C) Ea (kJ mol 1) 59.4 10.9 41 188 58.6 100.4 24 0.40e 0.23f 1.1g 0.048g 31.4 35.0 77.4 76.6 161 161 150 58.8 275 275 185 1.0 107 108 235 60 60 75 75 7.5 10 2 1.6 2.9 0.5 10 k 103 (L mol 1 s 1) H (kJ mol 1)
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