Polymers, kinetic modeling polymer-analogous reactions

This closure property is also inherent to a set of differential equations for arbitrary sequences Uk in macromolecules of linear copolymers as well as for analogous fragments in branched polymers. Hence, in principle, the kinetic method enables the determination of statistical characteristics of the chemical structure of noncyclic polymers, provided the Flory principle holds for all the chemical reactions involved in their synthesis. It is essential here that the Flory principle is meant not in its original version but in the extended one [2]. Hence under mathematical modeling the employment of the kinetic models of macro-molecular reactions where the violation of ideality is connected only with the short-range effects will not create new fundamental problems as compared with ideal models. 

When the statistical moments of the distribution of macromolecules in size and composition (SC distribution) are supposed to be found rather than the distribution itself, the problem is substantially simplified. The fact is that for the processes of synthesis of polymers describable by the ideal kinetic model, the set of the statistical moments is always closed. The same closure property is peculiar to a set of differential equations for the probability of arbitrary sequences t//j in linear copolymers and analogous fragments in branched polymers. Therefore, the kinetic method permits finding any statistical characteristics of loopless polymers, provided the Flory principle works for all chemical reactions of their synthesis. This assertion rests on the fact that linear and branched polymers being formed under the applicability of the ideal kinetic model are Markovian and Gordonian polymers, respectively. 

Two useful review articles on the theory of the kinetics and statistics of reactions of functional groups on polymers have appeared. Both polymer-analogous and intramolecular transformation reactions are influenced by a number of specifically macromolecular effects. These include neighbouring-group effects, configurational and conformational effects, electrostatic and supermolecular effects. The incorporation of all these factors into a general theory of macromolecular reactions is extremely difficult. These reviews provide introductions to the mathematical models as well as state-of-the-art overviews. 

Figure 4.6 shows the electrochemical activity of deposited poly(MG) onto RVC, and in each case, a nonlinear dependence that resembles Michaelis-Menten-type kinetics is observed. This observation agrees with the model proposed in 1985 by Gorton et al. [51] for mediator-modified electrodes for NADH oxidation, and it agrees with similar studies in 1990 and 2001 [53,105]. This model postulates the formation of a charge transfer (CT) complex in the reaction sequence between NADH and the mediator, because the observed reaction rate starts to decrease with the increase in NADH concentration, analogous to the Michaelis-Menten kinetics of enzymatic reactions. Catalytic activity of poly(MG) is inversely proportional to the thickness of the polymer, and the number of deposition cycles is consistent with observations in the literature for other NADH mediators [26,44,47,49]. This is attributed to the low partition coefficient of NADH and the diffusion coefficient of NADH within the... 

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