Nonideal copolymerization

If, instead, the dyad probability depends on the nature (m or r) of the preceding dyad, the distribution follows a first-order Markov process, with two independent statistical parameters and Pr , (the probability that after a m dyad a r dyad follows and vice versa, respectively). The corresponding equations are listed in Table 4, column 3. They correspond to those of a nonideal copolymerization and are reduced to the previous case when p + p = 1 ... 

Comparing the reactivity ratios of the DADMAC/AAM copolymerization with results of the copolymerization of other cationic monomers with AAM, significant differences can be identified. The differences between rx and r2 are much lower, and the cationic monomer even reacts preferentially during the copolymerization. As an example, for cationic methacrylic esters and methacrylamid derivatives, 1 acrylic acid and acrylamide, 0.34azeotropic copolymerization, preferring the cationic monomer only at low content in the comonomer mixture. 

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... 

Both parameters are greater than unity in block polymerizations. The growing active centers preferentially add on like monomer units and the result is more or less long blocks. The shape of the curve is exactly the reverse of that of nonideal copolymerization. In the limiting case of infinitely large copolymerization parameters, homopolymer blends are formed, even at lowest conversions. 

The more polar the solvent or the system, the greater will be the ionic dissociation, and the lower will be the tendency to complex formation. In copolymerizations of this kind, differences in polarity have maximum effect, so that usually only block copolymers or polymer blends are obtained. The influence of the gegenion increases as dissociation decreases, leading in some cases into the realm of nonideal copolymerizations. The stronger the complex-forming tendency between different monomers, the more the system tends toward alternating copolymerization. 

The free radical polymerization of DADMAC (M,) with vinyl acetate (M2) in methanol proceeds as a nonideal and nonazeotropic copolymerization with monomer reactivity ratios rx=1.95 and r2=0.35 were obtained [75]. The resulting low molar mass copolymers were reported to be water soluble over their whole range of composition. Modification of the vinyl acetate unit by hydrolysis, ace-talization, and acylation resulted in DADMAC products with changed hydrophilic or polyelectrolyte properties [75]. For the copolymerization of DADMAC and AT-methyl-AT-vinylacetamide (NMVA) a nearly ideal copolymerization behavior could be identified [45]. The application properties of the various copolymer products will be discussed in Sect. 8. 

The second type of nonideal models takes into account the possible formation of donor-acceptor complexes between monomers. Essentially, along with individual entry of these latter into a polymer chain, the possibility arises for their addition to this chain as a binary complex. A theoretical analysis of copolymerization in the framework of this model revealed (Korolev and Kuchanov, 1982) that the statistics of the succession of units in macromolecules is not Markovian even at fixed monomer mixture composition in a reactor. Nevertheless, an approach based on the "labeling-erasing" procedure has been developed (Kuchanov et al., 1984), enabling the calculation of any statistical characteristics of such non-Markovian copolymers. 

Figure 7.2 shows curves for several nonideal cases, that is, where r T2 1. It is seen that when both r and T2 are less than 1 there exists some point on the i i-versus-/i curve where the copolymer composition equals the feed composition and at this point the curve crosses the line F = f (that is, the diagonal line). At this point of intersection, polymerization proceeds without change in either feed or copolymer composition. Distillation terminology is again borrowed for this instance. Azeotropic copolymerization is said to occur at such points and the resulting copolymers are called azeotropic copolymers. 

Figure 22-3. Dependence of the mole fraction (jfa)o of monomeric unit a in the copolymer initially formed at the mole fraction (jca)o of monomer in the initial mixture. (I) Ideal, azeotropic copolymerization r = re = I). (II) Nonideal, nonazeotropic copolymerization (rA = 0.1 and re = 2.0). (Ill) Ideal, nonazeotropic copolymerization (rA = 0.5, r = 2). (IV) Nonideal, azeotropic copolymerization (rA = re = 0.2). (V) Strictly alternating copolymerization (rA = re = 0).

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