Chain copolymerization monomer partitioning

It was reported by Barb in 1953 that solvents can affect the rates of copolymerization and the composition of the copolymer in copolymerizations of styrene with maleic anhydride [145]. Later, Klumperman also observed similar solvent effects [145]. This was reviewed by Coote and coworkers [145]. A number of complexation models were proposed to describe copolymerizations of styrene and maleic anhydride and styrene with acrylonitrile. There were explanations offered for deviation from the terminal model that assumes that radical reactivity only depends on the terminal unit of the growing chain. Thus, Harwood proposed the bootstrap model based upon the study of styrene copolymerized with MAA, acrylic acid, and acrylamide [146]. It was hypothesized that solvent does not modify the inherent reactivity of the growing radical, but affects the monomer partitioning such that the concentrations of the two monomers at the reactive site (and thus their ratio) differ from that in bulk. 

Carboxylated rubber latices are commonly produced hy hatch emulsion polymerization. The reaction system comprises the monomers, water, surfactant, initiator, modifier and (usually) inorganic electrolytes. It is essential that polymerization takes place under acid conditions (typically pH ca.4) in order to ensure that the carboxylic acid monomer does become copolymerized in the main polymer molecule which is being produced. If the reaction is carried out under alkaline conditions, then the carboxylating monomer partitions strongly in the aqueous phase as the salt form if it polymerizes at all under these conditions, it is in the aqueous phase that it polymerizes, and the polymer chains in which it becomes incorporated will be far more hydrophilic than the majority of polymer molecules which are produced in the reaction system. In contrast to the production of, say, solid styrene-butadiene rubber by emulsion polymerization, where it is common practice to shortstop the reaction at ca. 65 conversion in order to prevent "undue branching and crosslinking within the polymer, reaction systems for the production of carboxylated latices by emulsion polymerization are usually taken to as near complete conversion as possible. 

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. 

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