Lewis-Mayo copolymerization

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) ... 

Mayo FR, Lewis FM. Copolymerization. I. A basis for comparing the behavior of monomers in copolymerization the copolymerization of styrene and methyl methacrylate. J Am Chem Soc 1944 66 1594-1601. 

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. 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Mayo-Lewis Binary Copolymeriration Model. In this exeimple we consider the Mayo-Lewis model for describing binary copolymerization. The procedure for estimating the kinetic parameters expressed as reactivity ratios from composition data is discussed in detail in our earlier paper (1 ). Here diad fractions, which are the relative numbers of MjMj, MiMj, M Mj and MjMj sequences as measured by NMR are used. NMR, while extremely useful, cannot distinguish between MiM and M Mi sequences and... 

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 ( ) ... 

As a check on our experimental and calculation procedures, we examined the copolymerization of 1-hexene and 1-decene (Table V) which had been investigated by Lipman (30). The copolymer composition was determined by using 300 MHz H-NMR and the reactivity ratios were calculated by the Tidwell-Mortimer method (22). The values of r (1-hexene) = 1.1 + 0.2 and r2 (1-decene) = 0,9 + 0,2 are in excellent agreement with Lipman s values of 1,3 and 0.9, respectively. It should be noted that in the latter investigation the copolymers were analyzed by IR spectroscopy and the reactivity ratios were calculated according to the method of Mayo and Lewis (32). 

Table 9 Reactivity ratios determined for 2-oxazoline copolymerizations utilizing both the Mayo-Lewis terminal model (MLTD) and the extended Kelen-Tiidds (KT) method. Initial defines - 20% conversion and final defines >50% conversion...

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 ... 

The effect of polarity on vinyl monomer copolymerization has long been recognized and is a major factor in the Q, e scheme and copolymerization theory. Mayo, Lewis, and Walling tabulated a number of vinyl monomers into an average activity series and an electron donor-acceptor series (62). The activity series showed the effect of substituents on the ease with which an ethylene derivative reacted with an average radical and on stabilizing the radical which was formed thereby. The electron donor-acceptor series indicated the ability of the substituents to serve as donors or acceptors in radical-monomer interactions. It is significant that in both series the dominant factor is the radical-monomer interaction. 

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. 

The values of these coefficients for the system described within the framework of Mayo-Lewis scheme are to be equal to unity according to relations (6.13) at any monomer feed composition. This condition holds strictly under the copolymerization of styrene with methyl methacrylate (see Table 6.5) while it holds considerably worse under the copolymerization of styrene with acrylonitrile (see Table 6.7). The... 

Thus, through the body of the mentioned experimental evidence obtained via different methods that characterize the composition and structure of macromolecules one arrives at a simple conclusion concerning the kinetic model of the binary copolymerization of styrene with methyl methacrylate (I) and with acrylonitrile (II). The former of these systems is obviously described by the terminal model, and the latter one by the penultimate model. However, the latter system characteristics in those cases when high accuracy of the results is not required, may be calculated within the framework of the Mayo-Lewis model. Such a simplified approach was found to be quite acceptable to solve many practical problems. One should note that the trivial terminal model is able to describe a vast majority (at least, 90% according to Harwood [303]) of copolymerization systems which have been already studied. 

Fig. 18. Determination of copolymerization parameters by the Mayo-Lewis method. See p. 255 of ref. 170.

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. 

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) ... 

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. 

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