Ideal copolymerization

Since the copolymerization of chemically similar monomers does not necessarily lead to the most interesting products, an attempt has been made to find a general condition according to which two monomers will copolymerize ideally 32), i.e. under which conditions is Eq. (V) valid ... 

The variability and potential of the graft polymerization technique is best discussed in terms of the various parameters involved. The graft reaction is, to a large extent, controlled by the structure of the backbone prepolymer. The temperature at which grafting can take place and the number of grafted chains can be controlled via the type and concentration of the azo functions. Additionally, the molar mass of the backbone prepolymer has an influence on the number of azo groups per polymer chain and thus on the number of side chains. The comonomer for the backbone can be freely chosen unless quantitative conversions are required. In this case a comonomer should be used which copolymerizes ideally with the azo monomer. 

These copolymerize ideally and changes in monomer composition are without effect either on rate of polymerization or polymer molecular weight [78b]. 

These monomers copolymerize ideally. Halogen substituents reduce the rate of polymerization while methyl or ethyl groups in the para position have a slight activating effect. This is in conformity with the view that monomer entry into the polymer chain is determined only by individual reaction rates (Table 24) [200]. 

Thus, the copolymerization ideality in ethylene copolymerizations—i.e., the proximity of rjr2 to unity—is strictly dependent on the e value of the comonomer. Hence, we see that since ethylene, because of its lack of substituent groups, resides at the center of the e scale, relatively large positive or negative e values may be tolerated without seriously affecting the ideality of the copolymerization. 

Problem 7.3 It is desired to form a copolymer from CH2=CHX (Mj) and CH2=CHY (M2), containing twice as many X groups as Y groups. The monomers copolymerize ideally, with MJ adding Mi twice as fast as M2. Describe the procedure as well as the feed composition you might use to make this polymer. 

Problem 7.2 It is desired to form a copolymer of Mi and M2 containing twice as many Mi as M2. The monomers copolymerize ideally with monomer reactivity ratios ry = 2.0 and ri = 0.5. Describe the feed composition one should use to make this copolymer. 

When Fj = 1/f2, the copolymer composition curve will be either convex or concave when viewed from the Fj axis, depending on whether Fj is greater or less than unity. The further removed from unity rj is, the farther the composition curve will be displaced from the 45° line. This situation is called ideal copolymerization. The example below explores the origin of this terminology. 

At the other end of the commonly encountered range we find the product rjr2 1. As noted above, this limit corresponds to ideal copolymerization and means the two monomers have the same relative tendency to add to both radicals. Thus if rj = 10, monomer 1 is 10 times as likely to add to Mj- than monomer 2. At the same time r2 = 0.1, which also means that monomer 1 is 10 times as likely to add to M2 than monomer 2. In this case the radicals exert the same influence, so the monomers add at random in a proportion governed by the specific values of the r s. 

VEs can also copolymerize by free-radical initiation with a variety of comonomers. According to the and rvalues of 0.023 and —1.77 (isobutyl vinyl ether), VEs are expected to form ideal copolymers with monomers of similar and e values or alternating copolymers with monomers such as maleic anhydride (MAN) that have high values of opposite sign (Q = 0.23 e = 2.25). 

Both and T2 are approximately unity ia an ideal copolymerization. In this case, k 2 22 21 growing chains show Htde preference for... 

Thiols react more rapidly with nucleophilic radicals than with electrophilic radicals. They have very large Ctr with S and VAc, but near ideal transfer constants (C - 1.0) with acrylic monomers (Table 6.2). Aromatic thiols have higher C,r than aliphatic thiols but also give more retardation. This is a consequence of the poor reinitiation efficiency shown by the phenylthiyl radical. The substitution pattern of the alkanethiol appears to have only a small (<2-fokl) effect on the transfer constant. Studies on the reactions of small alkyl radicals with thiols indicate that the rate of the transfer reaction is accelerated in polar solvents and, in particular, water.5 Similar trends arc observed for transfer to 1 in S polymerization with Clr = 1.4 in benzene 3.6 in CUT and 6.1 in 5% aqueous CifiCN.1 In copolymerizations, the thiyl radicals react preferentially with electron-rich monomers (Section 3.4.3.2). 

Copolymerizations. The uniform chemical environment of a CSTR makes it ideally suited for the production of copolymers. If the assumption of perfect mixing is justified, there will be no macroscopic composition distribution due to monomer drift, but the mixing time must remain short upon scaleup. See Sections 1.5 and 4.4. A real stirred tank or loop reactor will more closely... 

Indeed, cumyl carbocations are known to be effective initiators of IB polymerization, while the p-substituted benzyl cation is expected to react effectively with IB (p-methylstyrene and IB form a nearly ideal copolymerization system ). Severe disparity between the reactivities of the vinyl and cumyl ether groups of the inimer would result in either linear polymers or branched polymers with much lower MW than predicted for an in/mcr-mediated living polymerization. Styrene was subsequently blocked from the tert-chloride chain ends of high-MW DIB, activated by excess TiCU (Scheme 7.2). 

Fig. 24.—Incremental polymer composition (mole fraction Fi) plotted against the monomer composition (mole fraction/i) for ideal copolymerizations (ri — X/r F). Values of r are indicated.

The instantaneous composition of a copolymer X formed at a monomer mixture composition x coincides, provided the ideal model is applicable, with stationary vector ji of matrix Q with the elements (8). The mathematical apparatus of the theory of Markov chains permits immediately one to wright out of the expression for the probability of any sequence P Uk in macromolecules formed at given x. This provides an exhaustive solution to the problem of sequence distribution for copolymers synthesized at initial conversions p l when the monomer mixture composition x has had no time to deviate noticeably from its initial value x°. As for the high-conversion copolymerization products they evidently represent a mixture of Markovian copolymers prepared at different times, i.e. under different concentrations of monomers in the reaction system. Consequently, in order to calculate the probability of a certain sequence Uk, it is necessary to average its instantaneous value P Uk over all conversions p preceding the conversion p up to which the synthesis was conducted. 

Currently this model is one of the most commonly used in the theory of free-radical copolymerization. The formation of a donor-acceptor complex Ma... iVlbetween monomers Ma and in some systems is responsible for a number of peculiarities absent in the case of the ideal model. Such peculiarities are due to the fact that besides the single monomer addition to a propagating radical, a possibility also exists of monomer addition in pairs as a complex. Here the role of kinetically independent elements is played by ultimate units Ma of growing chains as well as by free (M ) and complex-bound (M ) monomers, whose constants of the rate of addition to the macroradical with a-th ultimate unit will be... 

It is easy to notice a certain formal resemblance between this expression and the expression (11) for the composition inhomogeneity of the products of high-conversion copolymerization describable by the ideal model. In both expressions angular brackets denote the operation of averaging the bracketed quantity... 

This assumption is implicitly present not only in the traditional theory of the free-radical copolymerization [41,43,44], but in its subsequent extensions based on more complicated models than the ideal one. The best known are two types of such models. To the first of them the models belong wherein the reactivity of the active center of a macroradical is controlled not only by the type of its ultimate unit but also by the types of penultimate [45] and even penpenultimate [46] monomeric units. The kinetic models of the second type describe systems in which the formation of complexes occurs between the components of a reaction system that results in the alteration of their reactivity [47-50]. Essentially, all the refinements of the theory of radical copolymerization connected with the models mentioned above are used to reduce exclusively to a more sophisticated account of the kinetics and mechanism of a macroradical propagation, leaving out of consideration accompanying physical factors. The most important among them is the phenomenon of preferential sorption of monomers to the active center of a growing polymer chain. A quantitative theory taking into consideration this physical factor was advanced in paper [51]. 

Heterogeneous combustion, 7 449-454 Heterogeneous copolymerization of acrylonitrile, 11 203—204 with VDC, 25 698-699 Heterogeneous enzyme systems, 10 255-256 Heterogeneous gas-solid catalytic reactions, 21 340-341 Heterogeneous Ideal Adsorbed Solution Theory (HIAST), gas separation under, 1 628, 629... 

Figure 2.9 Idealized representation of a linear pol3fmer resulting from radical poUmerization of a mono-O-methacroyl-sucrose (left) and a 1 1 copolymerization product with styrene. Di-O-substituted vinyl-sucroses are deemed to lead to cross-linked pol3miers (right).

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