Differential complex, consecutive

One of the possibilities is to study experimentally the coupled system as a whole, at a time when all the reactions concerned are taking place. On the basis of the data obtained it is possible to solve the system of differential equations (1) simultaneously and to determine numerical values of all the parameters unknown (constants). This approach can be refined in that the equations for the stoichiometrically simple reactions can be specified in view of the presumed mechanism and the elementary steps so that one obtains a very complex set of different reaction paths with many unidentifiable intermediates. A number of procedures have been suggested to solve such complicated systems. Some of them start from the assumption of steady-state rates of the individual steps and they were worked out also for stoichiometrically not simple reactions [see, e.g. (8, 9, 5a)]. A concise treatment of the properties of the systems of consecutive processes has been written by Noyes (10). The simplification of the treatment of some complex systems can be achieved by using isotopically labeled compounds (8, 11, 12, 12a, 12b). Even very complicated systems which involve non-... 

Crosslinking of many polymers occurs through a complex combination of consecutive and parallel reactions. For those cases in which the chemistry is well understood it is possible to define the general reaction scheme and thus derive the appropriate differential equations describing the cure kinetics. Analytical solutions have been found for some of these systems of differential equations permitting accurate experimental determination of the individual rate constants. 

One can differentiate two main methods for obtaining polymer-polymer complexes 1) formation of complexes from pre-existing chemically and structurally complementary macromolecules 2) polymerization of monomers in the presence of matrix macromolecules introduced in the reaction media. Such matrix polymerization is accompanied by the formation of polymer complexes. In the first case, the chemical reaction proceeds via complex formation by random contacts between reacting chains. Then, these sequences of pairs of connected chains grow. In matrix polymerization, the complex is formed by the mechanism of consecutive addition of monomer along the chain leading to the formation of the so-called zip-up (double-stranded) structure, due to matrix control of polymerization. One can expect that the various mechanisms lead to the formation of complexes with a different structure and properties. Indeed, a difference in the composition and properties of complexes obtained by various methods has been found So, the comparison of complexes poly(methacry-lic acid)-poly(2-N,N-dimethylaminoethyl methacrylate), obtained by mixing of equimolar quantities of components in solution and also by the matrix polymerization of dimethylaminoethyl methacrylate in water in the presence of PMAA, shows a difference in composition. In the first case, the content of acid in the complex is always... 

The above analysis reveals that apparently true isosbestic points may also be observed in consecutive reactions, which means that the occurrence of an isosbestic point cannot be treated as support for the simple one-step mechanism. On the other hand, the absence of a true isosbestic point can provide an efficient way to differentiate between the complex and the one-step mechanisms as long as the absorbance of the intermediate is significant. In order to obtain spectral evidence for an intermediate at the isosbestic point... 

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