Penultimate model copolymerization

The various copolymerization models that appear in the literature (terminal, penultimate, complex dissociation, complex participation, etc.) should not be considered as alternative descriptions. They are approximations made through necessity to reduce complexity. They should, at best, be considered as a subset of some overall scheme for copolymerization. Any unified theory, if such is possible, would have to take into account all of the factors mentioned above. The models used to describe copolymerization reaction mechanisms arc normally chosen to be the simplest possible model capable of explaining a given set of experimental data. They do not necessarily provide, nor are they meant to be, a complete description of the mechanism. Much of the impetus for model development and drive for understanding of the mechanism of copolymerization conies from the need to predict composition and rates. Developments in models have followed the development and application of analytical techniques that demonstrate the inadequacy of an earlier model. 

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. 

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 ( ) ... 

The ability to determine which copolymerization model best describes the behavior of a particular comonomer pair depends on the quality of the experimental data. There are many reports in the literature where different workers conclude that a different model describes the same comonomer pair. This occurs when the accuracy and precision of the composition data are insufficient to easily discriminate between the different models or composition data are not obtained over a wide range of experimental conditions (feed composition, monomer concentration, temperature). There are comonomer pairs where the behavior is not sufficiently extreme in terms of depropagation or complex participation or penultimate effect such that even with the best composition data it may not be possible to conclude that only one model fits the composition data [Hill et al., 1985 Moad et al., 1989]. 

The sequence distributions expected for the different models have been described [Hill et al., 1982, 1983 Howell et al., 1970 Tirrell, 1986] (Sec. 6-5a). Sequence distributions obtained by 13C NMR are sometimes more useful than composition data for discriminating between different copolymerization models. For example, while composition data for the radical copolymerization of styrene-acrylonitrile are consistent with either the penultimate or complex participation model, sequence distributions show the penultimate model to give the best fit. 

The kinetic copolymerization models, which are more complex than the terminal one, involve as a rule no less than four kinetic parameters. So one has no hope to estimate their values reliably enough from a single experimental plot of the copolymer composition vs monomer feed composition. However, when in certain systems some of the elementary propagation reactions are forbidden due to the specificity of the corresponding monomers and radicals, the less number of the kinetic parameters is required. For example, when the copolymerization of two monomers, one of which cannot homopolymerize, is known to follow the penultimate model, the copolymer composition is found to be dependent only on two such parameters. It was proposed [26, 271] to use this feature to estimate the reactivity ratios in analogous systems by means of the procedures similar to ones outlined in this section. 

There are two cases to consider when predicting flie effect of solvent polarity on copolymerization propagation kinetics (1) the solvent polarity is dominated by an added solvent and polarity is thus independent of the comonomer feed ratio, or (2) the solvent polarity does depend on the comonomer feed ratio, as it would in a bulk copolymerization. In the first case, the effect on copolymerization kinetics is simple. The monomer reactivity ratios (and additional reactivity ratios, depending on which copolymerization model is appropriate for that system) would vary fi om solvent to solvent, but, for a given copolymerization system they would be constant as a function of the monomer feed ratios. Assuming of course that there were no additional types of solvent effect present, fliese copolymerization systems could be described by their appropriate base model (such as the terminal model or the explicit or implicit penultimate models), depending on the chemical structure of the monomers. 

Copolymerization models based upon a Bootstrap effect were first proposed by Harwood and Semchikov" (see references cited therein). Harwood suggested that the terminal model could be extended by the incorporation of an additional equilibrium constant relating the effective and bulk monomer feed ratios. Different versions of this so-called Bootstrap model may be derived depending upon the baseline model assumed (such as the terminal model or the implicit or explicit penultimate models) and the form of equilibrium expression used to represent the Bootstrap effect. In the simplest case, it is assumed that the magni-... 

Many analytical techniques have been utilized to analyze the SAN microstructure including LALLS [38], CNMR [19,31,39-44], infrared spectroscopy [45-49], ultraviolet spectroscopy [50-52], pyrolysis GC [8,27,53], pyrolysis mass spectroscopy [54,55], fluorescence [20,56], GPC-IR [57,58], and GPC-UV [52]. Since the terminal model allows the calculation of sequence distribution, the calculated and measured sequence distributions can be compared. This comparison generally shows deviation of the measured sequence distribution vs that predicted using the terminal model. Ham [59] was the first to notice the deviation and explained the deviation based upon penultimate effects. Since that time several other researchers have also notic deviation of their data from the terminal model and have applied more elaborate copolymerization models (Scheme 4) to explain the mechanism of SAN copolymerization. The penultimate [60,61] and complex participation models [33,62,63] have both been evaluated and give a better fit to the SAN system than the terminal model. 

The use of sequence distribution measurements to compare cakulated with actual sequence data is a common technique to evaluate the accuracy of copolymerization models. Recently, Hill et ai [40,56,65, compared all three models and found that the penultimate model gave the best fit to their NMR sequence distribution data obtained fixan SAN copolymers made using bulk polymerization at 60 °C. 

Versions of the Bootstrap model have also been fitted to systems in which monomer-monomer complexes are known to be present, demonstrating that the Bootstrap model may provide an alternative to the MCP and MCD models in these systems. For instance, Klumperman and co-woikers have snccessfiilly fitted versions of the penultimate Bootstrap model to the systems styiene with maleic anhydride in butanone and toluene, " and styrene with acrylonitrile in varions solvents. This latter woik confirmed the earUer observations of Hill et alP for the behavior of styrene with aciylonitiile in bulk, acetonitrile and toluene. They had concluded that, based on sequence distribution data, penultimate unit effects were operating but, in addition, a Bootstrap effect was evident in the coexistent curves obtained when triad distribution was plotted against copolymer composition for each system. In the copolymerization of styrene with aciylonitiile Klumperman et alP a variable Bootstrap effect was required to model the data. Given the strong polarity effects expected in this system (see Section 12.2.2), part of this variation may in fact be caused by the variation of the solvent polarity and its affect on the reactivity ratios. In aity case, as this work indicates, it may be necessary to simultaneously consider a number of different influences (such as, for instance, penultimate unit effects. Bootstrap effects, and polarity effects) in order to model some copolymerization systems. 

These observations suggest how the terminal mechanism can be proved to apply to a copolymerization reaction if experiments exist which permit the number of sequences of a particular length to be determined. If this is possible, we should count the number of Mi s (this is given by the copolymer composition) and the number of Mi Mi and Mi Mi Mi sequences. Specified sequences, of any definite composition, of two units are called dyads those of three units, triads those of four units, tetrads those of five units, pentads and so on. Next we examine the ratio NmjMi/Nmi nd NmjMiMi/NmiMi If these are the same, then the mechanism is shown to have terminal control if not, it may be penultimate control. To prove the penultimate model it would also be necessary to count the number of Mi tetrads. If the tetrad/triad ratio were the same as the triad/dyad ratio, the penultimate model is proved. 

The early kinetic models for copolymerization, Mayo s terminal mechanism (41) and Alfrey s penultimate model (42), did not adequately predict the behavior of SAN systems. Copolymerizations in DMF and toluene indicated that both penultimate and antepenultimate effects had to be considered (43,44). The resulting reactivity model is somewhat compHcated, since there are eight reactivity ratios to consider. 

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