Copolymerization Mayo Lewis equation

Styrene-SQ., Copolymers. I would now like to discuss two systems which illustrate the power of C-13 nmr in structural studies. The first is the styrene-SO system. As already indicated, this is of the type in which the chain composition varies with monomer feed ratio and also with temperature at a constant feed ratio (and probably with pressure as well.) The deviation of the system from simple, first-order Markov statistics, —i.e. the Lewis-Mayo copolymerization equation—, was first noted by Barb in 1952 ( ) who proposed that the mechanism involved conplex formation between the monomers. This proposal was reiterated about a decade later by Matsuda and his coworkers. Such charge transfer com-... 

From these four basic kinetic equations, the Mayo-Lewis instantaneous copolymerization equation can be derived. Equation 7.31 (see also Chapter 6) ... 

On the other hand copolymer with a trioxane unit at the cationic chain end (Pi+) may be converted intp P2+ by cleavage of several formaldehyde units. These side reactions change the nature of the active chain ends without participation of the actual monomers trioxane and dioxo-lane. Such reactions are not provided for in the kinetic scheme of Mayo and Lewis. In their conventional scheme, conversion of Pi+ to P2+ is assumed to take place exclusively by addition of monomer M2. Polymerization of trioxane with dioxolane actually is a ternary copolymerization after the induction period one of the three monomers—formaldehyde— is present in its equilibrium concentration. Being the most reactive monomer it still exerts a strong influence on the course of copolymerization (9). This makes it impossible to apply the conventional copolymerization equation and complicates the process considerably. 

Schuller [150] and Guillot [98] both observed that the copolymer compositions obtained from emulsion polymerization reactions did not agree with the Mayo Lewis equation, where the reactivity ratios were obtained from homogeneous polymerization experiments. They concluded that this is due to the fact that the copolymerization equation can be used only for the exact monomer concentrations at the site of polymerization. Therefore, Schuller defined new reactivity ratios, TI and T2, to account for the fact that the monomer concentrations in a latex particle are dependent on the monomer partition coefficients (fCj and K2) and the monomer-to-water ratio (xp) ... 

Eq. (11.14) is known as the copolymerization equation and was first derived by Mayo and Lewis on a kinetic basis. A derivation on a probabUity basis was later published. Feinman and Ross derived the linear equations. ... 

Although 1,1-diphenylethylene does not hompolymerize, it will copolymerize with styrene and diene monomers. The anionic copolymerization behavior of 1,1-diphenylethylene with these monomers can be described in terms of the Mayo-Lewis copolymerization equation (Eq.22) [123, 124] ... 

Simultaneous polymerization of a mixture of cyclosiloxanes gives polymers whose microstructure is not easily predictable. Typically, the kinetics of ring-opening copolymerization is analyzed in terms of the Mayo-Lewis copolymerization equations (Scheme 5). The aim of such analysis is to determine the Mayo-Lewis reactivity ratios rD = feDD/feox and rx = fexx/fexD, which define the composition of a copolymer." The task is relatively easy when the propagation reactions are irreversible. 

The first method was proposed by Lewis and Mayo. It consists of linearizing the relationship between the reactivity ratios starting from the copolymerization equation previously established, we obtain... 

Several important assumptions are involved in the derivation of the Mayo-Lewis equation and care must be taken when it is applied to ionic copolymerization systems. In ring-opening polymerizations, depolymerization and equilibration of the heterochain copolymers may become important in some cases. In such cases, the copolymer composition is no longer determined by die four propagation reactions. 

Polymerization equilibria frequently observed in the polymerization of cyclic monomers may become important in copolymerization systems. The four propagation reactions assumed to be irreversible in the derivation of the Mayo-Lewis equation must be modified to include reversible processes. Lowry114,11S first derived a copolymer composition equation for the case in which some of the propagation reactions are reversible and it was applied to ring-opening copalymerization systems1 16, m. In the case of equilibrium copolymerization with complete reversibility, the following reactions must be considered. 

Penultimate Group Effects Copolymerization Model. This model represents an extension of the Mayo-Lewis model in which the next to last or penultimate group is assumed to affect the reaction rate. Under this assumption the eight reactions represented by the following equations are of importance ( ) ... 

A number of copolymerizations involving macromonomer(s) have been studied and almost invariably treated according to the terminal model, Mayo-Lewis equation, or its simplified model [39]. The Mayo-Lewis equation relates the instantaneous compositions of the monomer mixture to the copolymer composition ... 

Copolymerization refers to the process by which two monomers (Mj and M2) are simultaneously polymerized. Mayo and Lewis [149] developed the following equation to describe copolymerization kinetics... 

Equation 17 is known as the copolymerization or Mayo Lewis equation. 

An investigation of the copolymer composition demonstrated the important effect of monomer transport on the copolymerization. The droplets in the macroemulsion act as monomer reservoirs. In this system, the effect of monomer transport will be predominant when an extremely water-insoluble comonomer, such as DOM, is used. In contrast with the macroemulsion system, the miniemulsion system tends to follow the integrated Mayo Lewis equation more closely, indicating less influence from mass transfer. 

In studies of the kinetics of copolymerization of cyclic compounds the Mayo—Lewis equations [150] for kinetics of copolymerization have been applied, often with deserved caution. Many monomer reactivity ratios have been derived in this way. A large number of them have been summarized previously [7, 151] and we will not repeat them here nor attempt to update the lists. Instead we shall concentrate on some of the factors that seem to be important in regulating the copolymerizations and on some of the newer approaches that have been suggested for dealing with the complicated kinetics and give only a few examples of individual rate studies. 

If the complexed radical is inactive (k n = kx 2 = k22 = k21 = 0), Eq. (7.8) reduces to the ordinary Mayo-Lewis equation and no solvent effect on the reactivity ratio will be observed. Busfield et al.108) studied the solvent effect on the free radical copolymerization of vinyl acetate and methyl methacrylate. The methyl methacrylate content is unaffected by benzene and ethyl acetate. This result seems to be consistent with our assumption that the complexed radical is inactive in propagation. However, the solvent effect might not be observed in the case in which the reactivity of the complexed radical is proportional to that of the uncomplexed radical, because also in this case Eq. (7.8) reduces to the Mayo-Lewis form. It is difficult, therefore, to expect from the copolymerization experiment some evidence to support the concept of the complex formation. 

Equation 6.7 is known as the copolymerization or the Mayo-Lewis equation. The physical meaning of Equation 6.7 is better appreciated by writing it in terms of mole fractions. If /j is the mole fraction of unreacted monomer i and F is the mole fraction of monomer i in the copolymer formed instantaneously, then... 

Tip 13 (related to Tip 12) Copolymerization, copolymer composition, composition drift, azeotropy, semibatch reactor, and copolymer composition control. Most batch copolymerizations exhibit considerable drift in monomer composition because of different reactivities (reactivity ratios) of the two monomers (same ideas apply to ter-polymerizations and multicomponent cases). This leads to copolymers with broad chemical composition distribution. The magnirnde of the composition drift can be appreciated by the vertical distance between two items on the plot of the instantaneous copolymer composition (ICC) or Mayo-Lewis (model) equation item 1, the ICC curve (ICC or mole fraction of Mj incorporated in the copolymer chains, F, vs mole fraction of unreacted Mi,/j) and item 2, the 45° line in the plot of versus/j. 

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. This leads to a collection of N x N component reactions and x 1) binary reactivity ratios, where N is the number of components used. The equation for copolymer composition for a specific monomer composition was derived by Mayo and Lewis [74], using the set of binary reactions, rate constants, and reactivity ratios described in Equation 12.13 through Equation 12.18. The drift in monomer composition, for bicomponent systems was described by Skeist [75] and Meyer and coworkers [76,77]. The theory of multicomponent polymerization kinetics has been treated by Ham [78] and Valvassori and Sartori [79]. Comprehensive reviews of copolymerization kinetics have been published by Alfrey et al. [80] and Ham [81,82], while the more specific subject of acrylonitrile copolymerization has been reviewed by Peebles [83]. The general subject of the reactivity of polymer radicals has been treated in depth by Jenkins and Ledwith [84]. 

The use of acrylic acid not only led to a functionalization of nanoparticles, but also was important as a structure-directing monomer for the formation of nanocapsules. In this case, the hydrophilic groups of the acrylic acid [30] or methacrylic acid [31] resulted in the formation of a nanocapsule structure, instead of Janus-like or even separate nanoparticles. The copolymerization of the functional n-methylol acrylamide with vinyl acetate was found to follow (in batch miniemulsion) the Mayo-Lewis equation, despite huge differences in the solubility of the monomers in the aqueous continuous phase [32]. A functionality of fluori-nated particles could be easily introduced by copolymerizing fluoroalkylacrylates with protonated monomers, such as acrylic acid and methacryloxyethyltrimethyl ammonium chloride [33]. 

A significant study [13] of the copolymerization in acetonitrile with t-butyl ammonium perchlorate as the electrolyte confirmed that the composition of the copolymer depends on applied potential as well as feed ratio. The authors demonstrated that the copolymer composition obeys the Mayo-Lewis copolymer equation [14] and reported reactivity ratios for the pyrrole/ bithiophene pair for the first time. At a polymerization potential of 1.3 V, r, =4.9 and r2 = 0.04 for pyrrole and bithiophene, respectively, and at 1.5 V, r — 4.3 and a-2 = 0.24. 

For the foUwing estimation of the copolymerization parameters it is useful to discern between the ovmaU or mixed parameters and the true oopolymerization parameters. First we assume that there are only uniform active centres located on the catalyst sur ce, (i.e., one centre model), and use ethene and comonomer peaks in the NMR spectrum of the polymer mixture for the estimation of the oopolymerization parameters according to the Mayo Lewis equqtion This evaluation, via the r versus diagram, leads to the overall or mixed copolymerization parameters. However, for the estimation of the true copolymerization parameters we now use the following considerations. The Mayo-Lewis equation describes the composition of the copolymer as a function of the initial monomers mixture and the oopolymerization parameters. If we know these and the monomers mixture we can calculate not only the copolymer composition but also, by means of statistical considerations, the sequence length distribution of Mj and M2 sequences in the copolymer... 

Using Eq. (32) and feed and terpolymer composition data, a copolymerization composition diagram can be drawn, compared with the theoretical curves, and the coefficients of the Mayo-Lewis equation, riK and / 2jK estimated (Table 10.23). Fineman-Ross plots may also be used to estimate the Mayo-Lewis coefficients. These dimensioned apparent or modified reactivity ratios deviate from the true reactivity ratio values the more greatly the equilibrium constants differ from unity. 

Assuming copolymerization between [M1M2] and [M1M3] charge-transfer complexes, the Mayo-Lewis equation for copolymer composition may be modified to obtain Eq. (48). 

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