Binary systems, polymerization

On the other hand, very few ncdels for nulticonponent systans have been reported in the literature. Apart from models for binary systems, usually restricted to "zero-one" systans (5) (6), the most detailed model of this type has been proposed by Hamielec et al. (7), with reference to batch, semibatch and continuous emilsion polymerization reactors. Notably, besides the usual kinetic informations (nonomer, conversion, PSD), the model allows for the evaluation of IWD, long and short chain brandling frequencies and gel content. Comparisons between model predictions and experimental data are limited to tulK and solution binary pwlymerization systems. 

An equimolar binary system consisting of aluminum trichloride and (—)-menthoxytriethyltin, -germanium, or-silicon is effective for asymmetric cationic polymerization of prochiral benzofuran (Scheme 69) (158). 

Examples of preparation of copolymers are scarce. Mun et al. [81, 82] showed that the binary system of cobaltocene/ bis(ethylacetoacetato) copper (II) effectively initiates the living radical polymerizaton of MMA at 25 °C in acetonitrile. The polymerization activity of this initiator system was markedly affected by the solvent used. The synthesis of PMMA-b-PS copolymers with molecular weights reaching 700000 was successfully attempted by adding styrene to the living PMMA. The yield of the copolymers reached 80% when the MMA polymerization was carried out for three days. The same team [91] also synthesized PS-b-PMMA copolymers from the polymerization of MMA with polystyrene obtained in the presence of reduced nickel/halide systems. The yields range from 84 to 91% depending on the halide complex used. 

In addition to protonic acids, Lewis acids are the most common initiators of carbocationic polymerizations. Two mechanisms are possible. Direct initiation is rare and usually slow. The more prevalent mechanism is by cocatalysis in binary systems, with the Lewis acid acting as a coinitiator or catalyst rather than as initiator. Cationating or protonating species are the true initiators, which are therefore the species incorporated at the polymer s end group. The most common initiator is adventitious water in insufficiently dried systems. Thus, mechanistic studies should be performed under stringently dry conditions or in the presence of proton traps such as hindered pyridines. In addition to water, the protonating reagent may be an alcohol, carboxylic acid, amine, or amide [Eq. (28)]. 

Due to the nature of free radical polymerization, i.e., the reacting system is essentially a binary mixture composed of monomer and high polymer, another approach was used to calculate p d, and therefore tyu This alternate method is based on the free volume theory, which predicts a relationship between Tg and the volume fractions of polymer and monomer in a binary system ... 

Another type of activation of aluminum alkyl was found in the asymmetric-selective polymerization of epichlorohydrin (ECH) with an optically active cobalt-salen type complex [Co (II)]. The structure of the salen-type cobalt complex was shown previously (13, 14). In a benzene solution of the binary system consisting of [Co (II)] and AlEt, no evolution of ethane or ethylene was observed at room temperature. The NMR signals of the methyl protons for AlEt shifted down field on mixing with [Co (II)]. These observations together with a circular dichroism study indicated that AlEt and [Co (II)] formed a molecular complex in benzene, none of Al-Et bonds being cleaved by this complexation. 

Mathematical models of the frontal copolymerization process were developed, studied and compared with experimental data in [67, 90]. An interesting observation was that the propagation speed of the copolymerization wave was not necessarily related to the propagation speeds in the two homopolymerization processes, in which the same two monomers were polymerized separately. For example, the propagation speeds in the homopolymerization processes could be 1 cm/min in each, but in the copolymerization process, the speed could be 0.5 cm/min. Mathematical models of free-radical binary frontal polymerization were presented and studied in [66, 91]. Another model in which two different monomers were present in the system (thiol-ene polymerization) was discussed in [21]. A mathematical model that describes both free-radical binary frontal polymerization and frontal copolymerization was presented in [65]. The paper was devoted to the linear stability analysis of polymerization waves in two monomer systems. It turned out that the dispersion relation for two monomer systems was the same as the dispersion relation for homopolymerization. In fact, this dispersion relation held true for W-monomer systems provided that there is only one reaction front, and the final concentrations of the monomers could be written as a function of the reaction front temperature. 

Elemental analysis (EA) is a convenient method for determination of copolymer and blend composition if one homopolymer contains an element not present in the second one. For example, EA can be properly used to quantify nitrogen in copolymers containing acrylonitrile units and oxygen in polymeric surfactants such as poly(oxy-alkylene). Therefore, for a binary system, every element can be balanced according to the following equation ... 

The S-S equation of state, extended to binary systems, Eqs. (6.39) and (6.53), has been used for the interpretation of properties of particulate-filled polymeric composites [Simha et al., 1984]. The reduced bulk modulus, K, was derived by differentiation of Eq. (6.39), and that of the thermal expansion coefficient at ambient pressure by... 

The critical temperature is identical with the maximum of the cloud-point curve for binary systems (see Section 6.6.3). The dependence of the critical temperature on the degree of polymerization is given by combining Equations (6-49) and (6-96) (with o = 0) ... 

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