Lewis-Mayo equation

This allows elimination of the radical concentrations from the above equation and the copolymer composition equation (eq. 5),14-16 also known as the Mayo-Lewis equation, can now be derived. 

It is also possible to derive reactivity ratios by analyzing the monomer (or polymer) feed composition v.v conversion and solving the integrated form of the Mayo Lewis equation.10 123 The following expression (eq. 44) was derived by Meyer and Lowry 12j... 

The Mayo-Lewis equation expressing the copolymer composition can be derived from these four elementary reactions. It reads... 

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. 

The copolymer composition produced by these two catalysts can be estimated using the Mayo-Lewis equation [38] and these values of i and r2. Figure 10 depicts the hypothetical comonomer content in the polymer (F2) as a function of the mole fraction of comonomer in the reactor (f2). The good incorporator produces a material with higher F2 as f2 increases. In contrast, the composition from the poor incorporator is relatively flat across a broad range and increases only at very high values of/2. The F2 required to render the copolymer amorphous is comonomer-dependent for 1-octene, this value is near 0.19. In this hypothetical system, the good incorporator produces that composition at f2 = 0.57, at which the poor incorporator incorporates very little comonomer (F2 = 0.01). 

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 ... 

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) ... 

The Mayo Lewis equation, using reactivity ratios computed from Eq. 18, will give very different results from the homogenous Mayo Lewis equation for mini-or macroemulsion polymerization when one of the comonomers is substantially water-soluble. Guillot [151] observed this behavior experimentally for the common comonomer pairs of styrene/acrylonitrile and butyl acrylate/vinyl acetate. Both acrylonitrile and vinyl acetate are relatively water-soluble (8.5 and 2.5%wt, respectively) whereas styrene and butyl acrylate are relatively water-insoluble (0.1 and 0.14%wt, respectively). However, in spite of the fact that styrene and butyl acrylate are relatively water-insoluble, monomer transport across the aqueous phase is normally fast enough to maintain equilibrium swelling in the growing polymer particle, and so we can use the monomer partition coefficient. 

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. 

The transfer reactions to the solvent and the initiator have been described for butadiene, isoprene, or vinyl acetate polymerizations using thermally decomposed hydrogen peroxide in methanol or rm-pentanol (Table 3.5)l55). The Mayo-Lewis equation has been applied... 

Using an improved Mayo-Lewis equation, the ratio of termination constant (kt) and propagation constant (kp) can be determined 154). This ratio is 8.3 for polymerization of MMA at 60 °C. 

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... 

A flrst important question concerns whether the goal is to discriminate between competing models (i.e., terminal vs penultimate model kinetics) or to seek the best parameter estimates. We flrst assume that terminal model kinetics are being considered and later discuss implications regarding the assumption of penultimate model kinetics. As seen in the previous section, for terminal model kinetics, reactivity ratios are typically estimated using the instantaneous copolymer composition equation or the Mayo-Lewis equation, expressed in two common forms. Equations 6.7 and 6.11. 

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]. 

The copolymerisation of A-cyclohexylmaleimide (CHMI) and methyl methacrylate (MMA) using azobisisobutyronitrile as the initiator using rapid scan IR. Using the Mayo-Lewis equation, the reactivity ratios of CHMI and MMA were calculated (64). 

The copolymerisation of N-cyclohexylmaleimide (CHMI) and methyl methacrylate (MMA) with azobisisobutyronitrile as the initiator is investigated. IR spectroscopy is applied to determine the copolymer compositions of the copolymers synthesised at 60, 70, 80 and 90 deg.C while the conversions of the copolymerisations are controlled to be below 10%. According to the Mayo-Lewis equation, the reactivity ratios of N-cyclohexylmaleimide and methyl methacrylate are calculated. It is proved that N-cyclohexylmaleimide is less reactive, and the optimum temperature of the copolymerisation is 80 deg C. 8 refs. CHINA... 

In Equation 2.108, the copolymer composition distribution is quantified by the variable y, defined in Equation 2.109. The variable y measures the difference between the molar fraction of monomer A in a given polymer chain to the average molar fraction of monomer A in all the chains, already defined in Equation 2.104. The classical Mayo-Lewis equation can... 

The Mayo-Lewis equation [8] describing terminal model binary copolymerisation was given in section 2.2.3 and is also given below ... 

The instantaneous composition for the copol3onerization of a macromonomer Mj with another monomer M can be described in terms of the Mayo-Lewis equation, Eq. 39, where r and r are the respective monomer reactivity ratios. 

The average fraction of comonomer in the copol5uner can be estimated as usual using the Mayo-Lewis equation ... 

The condition to produce a latex with a given copolymer composition is that the ratio of the monomer concentrations in the polymer particles must be kept at the value that ensures the production of the desired composition. This comonomer ratio can be calculated from the Mayo-Lewis equation, Eq. (75), where ri and t2 are the reactivity ratios and yu is the instantaneous composition referred to monomer 1. 

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