Model copolymerization reactions

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 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. 

Using copolymerization theory and well known phase equilibrium laws a mathematical model is reported for predicting conversions in an emulsion polymerization reactor. The model is demonstrated to accurately predict conversions from the head space vapor compositions during copolymerization reactions for two commercial products. However, it appears that for products with compositions lower than the azeotropic compositions the model becomes semi-empirical. 

Development of a reduced-order model for metallocene-catalyzed ethylene-norbornene copolymerization reaction... 

For the copolymerization of epoxides with cyclic anhydrides and curing of epoxy resins, Lewis bases such as tertiary amines are most frequently used as initiators. In this case, terminal epoxides react with cyclic anhydrides at equimolar ratios. The time dependence of the consumption of epoxide and anhydride is almost the same for curing 35-36> and for model copolymerizations 39,40,45). The reaction is specific 39,40) to at least 99 %. In contrast, the copolymerization with non-terminal epoxides does not exhibit this high specificity, probably because of steric hindrances. The copolymerization of vinylcyclohexene oxide or cyclohexene oxide is specific only to 75-80 % and internal epoxides such as alkylepoxy stearates react with anhydrides only to 60-65 %. On the other hand, in the reaction of epoxy resins with maleic anhydride the consumption of anhydride is faster 65the products are discoloured and the gel is formed at a low anhydride conversion 39). Fischer 39) assumes that the other resonance form of maleic anhydride is involved in the reaction according to Eq. (33). 

In conclusion, even though there is the definite correlation between carboxylic group index and minimum in respect to graftability in our system, a detailed work with model compounds would be required to futher elucidate the mechanism of lignin participation in the copolymerization reaction. 

These examples do not mean that copolymerization reactions defy understanding. The simple copolymer model described here accounts for the behavior of... 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

A model system for the synthesis of lignin-like polymers showed that jols would react with the quinone-methlde intermediates in this system by a 1-6 addition (J ). Utilizing this model system, chloroanilines were copolymerized with coniferyl alcohol in the presence of horseradish peroxidase Type II enzyme, hydrogen peroxide, vanillyl alcohol initiator and pH 7.2 buffer (J57). The mechanism of this copolymerization reaction is shown in Equation 36. The... 

These equations are similar to those assumed for the reactivity ratio determination. In contrast to what has been observed for conventional styrene-MMA copolymers, however, these equations indicate that a substantial proportion of the (SMM+MMS)-type resonance appears to occur in the C-area. The proportion of methoxy resonance observed in the C-area, in fact, exceeds P(SMS) by a substantial amount for many of the copolymers. This can be due to the assumption of an inadequate model for the copolymerization reaction, to the use of incorrect reactivity ratios and cyclization constants for the calculations or to an inadequate understanding of the methoxy proton resonance patterns of S/MMA copolymers. It is possible that intramolecular reactions between propagating radicals and uncyclized methacrylic anhydride units present on propagating chains result in the formation of macrocycles. Failure to account for the formation of macrocycles would result in overestimation of rc and rc and in underestimation of the proportions of MMA units in SMS triads in the derived S./MMA copolymers. This might account for the results obtained. An alternate possibility is that a high proportion (>50%) of the M-M placements in the copolymers studied in this work can be expected to have meso placements (], J2), whereas only a small proportion of such placements ( 20%) are meso in conventional S/MMA copolymers. Studies with molecular models (20) have indicated that the methoxy protons on MMA units centered in structures such as the following can experience appreciable shielding by next nearest styrene units. 

Hamielec AE, MacGregor JE. In Reichert KH, Geiseler W, editors. Polymer Reaction Engineering, Modelling Copolymerizations. Munich Hanser Publishers 1983. p 21ff. 

In the first part of this chapter, the two most common copolymerization models will be discussed. Most importantly, this is done in order to show the models with consistent nomenclature. Furthermore, the two models are believed to provide physically the most realistic descriptions of copolymerization reactions. 

The ATRP is based on a sequence of ATRA reactions and ATRA can be used to prepare various dimeric species that model the expected chain ends in a copolymerization reaction. An ESR study of radicals generated from these mixed dimers can be used to clarify the penultimate unit effects relevant to copolymerization. The ESR spectra of monomeric radicals of (meth)acrylates were previously investigated by Fischer et Gilbert et al., and Matsumoto et al. However, no ESR... 

Nuclear magnetic resonance monitoring of the synthesis of amphiphilic copolymers has also been reported by Larazz et al. [174] for the copolymerization of a methacrylic macromonomer with amphiphilic character derived from Triton X-100 (MT) with acrylic acid (AA). In situ H NMR analysis was used to monitor comonomer consumption throughout the copolymerization reactions, initiated by AIBN in deuterated dioxane, at 60 °C. The results from two different approaches used by the authors to estimate the reactivity ratio of the macromonomer indicate that AA is less reactive than the macromonomer MT and a model monomer with lower molecular weight but same structure, suggesting that methacrylic double bond reactivity was not affected by poly(oxyethylene oxide) chain length. 

Recently, ACOMP capabilities were expanded to follow the evolution of different copolymer features during copolymerization reactions. A first study reported the online monitoring of the copolymerization of MMA and styrene [17]. Simultaneous, model-independent evolution of the average composition and mass distributions during free radical copolymerization reactions were determined. Also, model-dependent calculations of reactivity ratios and sequence length distributions were made. 

A main advantage of the SEC detection is that it follows the evolution of the MWD, particularly important in living -type reactions and in copolymerization reactions where complex mixtures of reagents make unfractionated spectroscopic resolution of comonomers difficult. On the other hand, continuous detection provides a much more detailed characterization of the reaction and, interestingly, in the case where a bimodal MWD was produced, the continuous method automatically detected the onset of the second mode in a model independent fashion, whereas SEC conld only discern the bimodaUty by applying preconceived models. 

There has been a significant amount of work reported on controlling composition during copolymerization reactions. The Kalman filter method is based on a linear approximation of the nonlinear process [55] but has problems with stability and convergence [56-58]. For that reason, numerous nonlinear methods have been developed. Kravaris et al. [59] used temperature tracking as another nonlinear method to control copolymer composition. Model predictive control (MPC) [60-63], as well as nonlinear MPC (NLMPC) [64-67] algorithms have been suggested for control of nonlinear systems. 

The semibatch approach, where policies are developed for selective reagent feeds to the reactor, has been extensively elaborated, especially for emulsion polymerization, and in the context of controlling composition during copolymerization reactions [68-72,109]. Discussions are provided in Chapters 4, 7, 12, 17-19, and 21. Sun et al. developed model-based semibatch monomer feeding policies for controlled radical polymerization (CRP) [73, 74]. Vicente et al. [75,76] controlled composition and molecular weight distribution in emulsion copolymerization in an open-loop method by maintaining the ratio of comonomers. Yanjarappa et al. [77] synthesized, via a sanibatch method, copolymers with constant composition for biofunctionalization. General semibatch policies are reviewed by Asua [78]. 

The real advantage of GRP lies in the ability to synthesize block copolymers from free radical monomers without the very stringent polymerization conditions necessary for ionic polymerization. Since the chains remain living, one monomer can be completely polymerized and then another monomer added to form a second block on the same (living) chains. This process can be repeated to form multiblock polymers. This aspect of GRP will be addressed in the following as part of the modeling of copolymerization reactions. 

Araujo PHH, de la Cal JC, Asua JM, Pinto JC. Modeling particle size distribution (PSD) in emulsion copolymerization reactions in a continuous loop reactor. In Piemcci S, editor. ESCAPE-10. Amsterdam Elsevier Science B.V. 2000. p 565-570. 

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