Copolymerization equation monomer partitioning

By combining thermodynamically-based monomer partitioning relationships for saturation [170] and partial swelling [172] with mass balance equations, Noel et al. [174] proposed a model for saturation and a model for partial swelling that could predict the mole fraction of a specific monomer i in the polymer particles. They showed that the batch emulsion copolymerization behavior predicted by the models presented in this article agreed adequately with experimental results for MA-VAc and MA-Inden (Ind) systems. Karlsson et al. [176] studied the monomer swelling kinetics at 80 °C in Interval III of the seeded emulsion polymerization of isoprene with carboxylated PSt latex particles as the seeds. The authors measured the variation of the isoprene sorption rate into the seed polymer particles with the volume fraction of polymer in the latex particles, and discussed the sorption process of isoprene into the seed polymer particles in Interval III in detail from a thermodynamic point of view. 

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 apparent reactivity ratios that govern the copolymerization in the solvents were determined and are significantly different. Nevertheless, the triad distribution as a funrtion of copolymer composition shows that within experimental error, one set of curves describes all three situations. This again is clear evidence that solvents do not affect the tme monomer reactivity ratios, but only the monomer partitioning. In the derivations by Klumperman and O Driscoll it is clearly shown that these partitioning effects cancel from the sequence distribution versus copolymer composition equations. 

The situation is more complex when a copolymerization is considered because as two or more monomers are involved and the partitioning of the monomer between the phases might be different, this may lead to variations in the copolymer composition. In emulsion copolymerization, the evolution of the copolymer composition depends, in addition to the reactivity ratios, on the partition of the monomer between the aqueous and polymer particle phases (see Section 3.14.2.1.2(iv)). Furthermore, if the monomer is hydrophobic enough, transport limitations through the aqueous phase might control the concentration of the monomer in the polymer particles. On the other hand, in miniemulsion polymerization, the transport of monomer is reduced to such levels that the incorporation of hydrophobic monomers is favored as compared with conventional emulsion polymerization, and the copolymer compositions achieved in batch miniemulsion copolymetiza-tion are closer to those expected from the Mayo-Lewis equation (eqn [3]) under bulk conditions. This trend was experimentally observed by several authors who investigated the copolymer composition produced in batch emulsion and miniemulsion copolymerization using monomers with different water solubilities and reactivity ratios. 

Barrett and Thomas (10)proposed that these effects of differential monomer adsorption could be modeled by correcting homogeneous solution copolymerization reactivity ratios with the monomer s partition coefficient between the particles and the diluent. The partition coefficient is measured by static equilibrium experiments. Barrett s suggested equations are ... 

Here Jta(x) denotes the a-th component of the stationary vector x of the Markov chain with transition matrix Q whose elements depend on the monomer mixture composition in microreactor x according to formula (8). To have the set of Eq. (24) closed it is necessary to determine the dependence of x on X in the thermodynamic equilibrium, i.e. to solve the problem of equilibrium partitioning of monomers between microreactors and their environment. This thermodynamic problem has been solved within the framework of the mean-field Flory approximation [48] for copolymerization of any number of monomers and solvents. The dependencies xa=Fa(X)(a=l,...,m) found there in combination with Eqs. (24) constitute a closed set of dynamic equations whose solution permits the determination of the evolution of the composition of macroradical X(Z) with the growth of its length Z, as well as the corresponding change in the monomer mixture composition in the microreactor. 

For emulsion copolymerization, monomers may show different partitioning behavior among the emulsified monomer droplets, the latex particles, and the continuous aqueous phase. This can have a significant influence on the polymerization kinetics and the copolymer composition. The following empirical equation can be used to estimate the individual saturated concentration of comonomer i in latex particles ([M ]p) [30, 82-84] ... 

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