Mayo-Lewis terminal model

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 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. 

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 ... 

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. 

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. 

As early as the 1940s, radical copolymerization models were already developed to describe specific features of the process. Initially, these models were relatively simple models where the reactivity of chain-ends was assumed to depend only on the nature of the terminal monomer unit in the growing chain (Mayo-Lewis model or terminal model (TM)). This model by definition leads to first-order Markov chains. 

These propagation steps are entirely analogous to those given for the first-order Markov model, except that addition probabilities have been replaced by rate constants. Mayo and Lewis derived the following differential equation to describe terminal model copolymerisation [8] ... 

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

Kinetic studies of the solution (benzene) and bulk polymerization of methyl methacrylate with MA have been run at 60°C and 70°C, using AIBN initiator. The microstructure of the purified copolymers was determined by H-NMR and IR spectroscopy. Analysis of the comonomer pair sequence distribution for the solution-prepared copolymers supported a copolymerization mechanism involving participation of an association species between the two monomers. A terminal model or the classical Mayo-Lewis concept more adequately explained the results of bulk copolymerization, where the comonomer sequence distribution was more random. Theoretically, the concentration of associating species should be greatest in bulk, which was... 

According to the terminal model for copolymerisation of two monomers (Alfrey Goldfinger, 1944 Mayo Lewis, 1944) the instantaneous copolymer composition y can be related to the monomer fractions in the locus of polymerisation ... 

This result is known as the Mayo-Lewis equation expressing the polymer composition in terms of the fundamental polymerization parameters. For the terminal model, there is a nonlinear relationship between the polymer composition ratio and x, the monomer feed ratio. 

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