Ideal copolymerization, equation

Equation (7.113b) gives the instantaneous copolymer composition in terms of the feed composition and the reactivity ratio. Figure 7.18 shows the copolymer composition for an ideal copolymerization (r,r2 = 1). In this case, the copolymer composition equation becomes ... 

A similar situation is encountered in so-called ideal copolymerizations, characterized by the relation r,xrm = 1, but in this case the above equations are valid over the entire composition range... 

Table 1.13. Copolymer composition for the ideal copolymerization, for which r- = 1//2 f- and 2 are the molar feed ratios of monomers, Mi and M2, and Fi and F2 are the mole fractions of the repeat units in the copolymer (Equation (1.82))...

Equation (7.18) may be used to calculate the instantaneous composition of copolymer as a function of feed composition for various monomer reactivity ratios. A series of such curves are shown in Fig. 7.1 for ideal copolymerization, i.e., r r2 = 1. The term ideal copolymerization is used to show the analogy between the curves in Fig. 7.1 and Aose for vapor-liquid equilibria in ideal liquid mixtures. The vapor-liquid composition curves of ideal binary mixtures have no inflection points and neither do the polymer-composition curves for random copolymerization in which riV2 = 1. Such monomer systems are therefore called ideal. It does not in any sense imply an ideal type of copolymerization. 

By using the mathematical condition that defines the ideal copolymerization, the two forms of the copolymer equation. Equations 6.7 and 6.11, adopt simplified forms given by Equations 6.13 and 6.14, respectively ... 

Equations 8.5 and 8.9 give the instantaneous polymer composition as a function of feed composition for various reactivity ratios. Figure 8.1 shows a series of curves calculated from these equations for ideal copolymerization. The range of feed composition that gives copolymers containing appreciable amounts of both monomers is small except the monomers have very similar reactivities. 

Ideal copolymerization is a special case of ta > U fB < 1 copolymerization for which rA h = 1- From the definitions of and given as Equation (1.32), these conditions correspond to... 

The relative placement of monomers A and B is independent of the active center in what in known as ideal copolymerization. In this case, A aa/ ab ba/ bb or a == 1 / B- Equation (22-15) then reduces to... 

Ideal copolymerization. In ideal azeotropic copolymerization (rj = V2 = 1), equation (22-14) reduces to rf[Mi]/d[M2] = [Mi]/[M2]. The copolymer composition is therefore equal to the monomer composition at all conversions (Figure 22-3). 

The relative reactivity of monomers in copolymerization was calculated from the following equation based on ideal copolymerization. 

Another general treatment of the copoljnnetization equilibrium was provided by Szymanski, ° who used, while deriving his relationships, similarly as O Driscoll and co-workers, the reverse conditional probabilities (of a copolymer unit to be preceded by the same or a different unit). This treatment looks simpler than the one proposed earlier by Szwarc and Perrin, and similarly their equations can be applied to the systems of any number of comonomers and any average degree of polymerization. The proposed solution also applies to the systems of ideal copolymerization Besides, the... 

Case 4 r r2=1. This is the so-called ideal copolymerization, where each chain displays the same preference for one of the monomers over the other kjjlkj2 = 2// 22> so it does not matter what is at the end of the chain. In this case. Equation 11.11 reduces to... 

Solution. Application of Equation 11.11 gives the plots in Figure 11.1. Note the system (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. 

A b) increases. Equation (2.95) also predicts that ideal copolymerization will occur when since this gives r/sjr = 1. 

In such ideal copolymerization, the Fj-/, curve never crosses the F,-/, diagonal, whereas when r,r2 1, there can be a point where they cross to give an azeotrope at which F, = /, (Figure 4.19). Equation 4.38 can be rewritten as... 

Preference for reaction with the unlike monomer occurs when ri is less than 1. When r and T2 are approximately equal to 1, the conditions are said to be ideal, with a random (not alternating) copolymer produced, in accordance with the Wall equation. Thus, a random copolymer (ideal copolymer) would be produced when chlorotrifluoroethylene is copolymerized with tetrafluoroethylene (Table 7.1). 

Equation (26) is the ideal copolymer composition equation suggested [203] early in the development of copolymerization theory but which had to be abandoned in favour of eqn. (23) as a general description of radical copolymerization. Only in this particular case are the rates of incorporation of each monomer proportional to their homopolymerization rates. It was shown that the reactivity of a series of monomers in stannic chloride initiated copolymerization followed the same order as their homopolymerization rates [202] and so eqn. (26) could be at least qualitatively correct for carbonium-ion polymerizations and possibly for reactions carried by carbanions. This, in fact, does not seem to be correct for anionic polymerizations since the reactivities of the ion-paired species at least, differ greatly. The methylmethacrylate ion-pair will, for instance, not add to styrene monomer, whereas the polystyryl ion-pair adds rapidly to methylmethacrylate [204]. This is a general phenomenon no reaction will occur if the ion-pair is on a monomer unit which has an appreciably higher electron affinity than that of the reacting monomer. The additions are thus extremely selective, more so than in radical copolymerization. There is no evidence that eqn. (26) holds and the approximate agreement with eqn. (25) results from other causes indicated below. 

Equation (7.13) means that k /ki2 and k2i/k22 wiU be simultaneously either greater or less than unity or in other words, that both radicals prefer to react with the same monomer. Ail copolymers whose Vir2 product equals 1 are therefore called ideal copolymers or random copolymers. Most ionic copolymerizations are characterized by the ideal type of behavior. 

The simple linear relation between and x shown in Figure 15.3 is found only for a few copolymers composed of compatible monomer pairs, such as styrene copolymerized with either methyl acrylate or butadiene. A simple ideal mixing rule can be applied to these systems, but when the comonomer properties differ markedly, the linear dependence is lost and a nonlinear equation has to be developed. 

The curve does not intercept the ideal azeotrope line, either, in nonideal nonazeotropic copolymerization. But, in contrast to ideal nonazeotropic copolymerization, the curve is no longer symmetrical. In azeotropic nonideal copolymerizations, behavior depends on whether both copolymerization parameters are or are not of the same magnitude. If they are also equal, then, according to Equation (22-15), the azeotropic point must occur at a 1 1 composition ratio, that is, at a mole fraction of 0.5. If the molar fraction is less than 0.5 for monomer B, then the azeotropic ordinate point must be above the 45° ideal azeotropic line because of the tendency to alternate, but the point... 

With ideal nonazeotropic copolymerization (r = l/r2), equation (22-14) therefore reduces to... 

This case may always be anticipated whenever the monomers show approximately equal e values (e.g., styrene with c = -0.8 and butadiene with e = —1.05). For systems of this kind, = l/r2, and consequently the equation for the ideal nonazeotropic copolymerization is... 

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