Kinetic models of macromolecular reactions

When deriving a material balance equation, the rate of transformation of each component in a reactor is normally governed by the mass action law. However, unlike for the reactions in which only low molecular weight substances are involved, the number of such components in a polymer system and, consequently, the number of the corresponding kinetic equations describing their evolution are enormous. The same can be said about the number of the rate constants of the reactions between individual components. The calculation of such a system becomes feasible because certain general principle can be invoked under the description of the kinetics of the majority of macromolecular reactions. Let us discuss this principle in detail. 

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Soucek, M.D. Abu-Shanab, O.L. Anderson, C.D. Wu, S. (1998). Kinetic Modeling of the Crosslinking Reaction of Cycloaliphatic Epoxides with Carboxyl Functionalized Acrylic Resins Hammett Treatment of Cycloaliphatic Epoxides. Macromolecular Chemistry and Physics, Vol.199, No.6, (December 1998), pp. 1035-1042, ISSN 1022-1352. 

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. 

The effects of macromolecules other than surfactants on the rates of organic reactions have been investigated extensively (Morawetz, 1965). In many cases, substrate specificity, bifunctional catalysis, competitive inhibition, and saturation (Michaelis-Menten) kinetics have been observed, and therefore these systems also serve as models for enzyme-catalyzed reactions and, in these and other respects, resemble micellar systems. Indeed, in some macromolecular systems micelle formation is very probable or is known to occur, and in others mixed micellar systems are likely. Recent books and reviews should be consulted for a more detailed description of macromolecular systems and for their applicability as models for enzymatic catalysis and other complex interactions (Morawetz, 1965 Bruice and Benkovic, 1966 Davydova et al., 1968 Winsor, 1968 Jencks, 1969 Overberger and Salamone, 1969). 

A recent paper describes a mathematical model for the chlorination of polyethylene in a bubble column reactor, the model was used to optimize product quality in the continuous chlorination of polyethylene. Another theoretical treatment deals with the change in polymer reactivity during the course of a macromolecular reactions in solution or in the melt. The reactivity of a transforming unit in the polymer depends on its microenvironment, including nearest neighbours on the same chain and on other chains, as well as small molecules in the reacting system. The equations derived describe the kinetic curve, the distribution of units, and the compositional heterogeneity of the products. 

We can now give precise definitions of some words and phrases that are often used loosely. A reaction rate is a rate of change of the concentration of some chemical species at a particular moment it is derived from a set of observations, in which the course of a reaction is monitored over a period of time. Such observations are the basic experimental data. By analysing the relation between these rates and the corresponding concentrations, one obtains a rate law that fits both the data and (often) some standard form (e.g., first-order, in which the rate is proportional to the concentration of one of the reactants). These rate laws, along with known structural data, may be given some interpretation in terms of reaction kinetics, one would describe a scheme of molecular motions that would explain the rate law. Often there are several alternative schemes that would be consistent with a particular set of data further experimentation would then be needed in order to choose between them. Such schemes in terms of chemical kinetics describe events on the microscopic scale, involving atoms and molecules, as distinct from rate laws which are expressed in terms of macromolecular quantities (time and concentration). The schemes may in turn be interpreted in terms of a reaction mechanism, which relates them to chemical dynamics, i.e., to theories of how molecules behave, in terms either of some particular model with limited scope (such as collison theory, or transition-state theory) or of the more fundamental body of theory based upon quantum mechanics. 

In particular, above said may be applied also to photoinitiated radical (co)polymerization of mono- and polyfimctional monomers. Two diamet-rically-opposite concepts are used to deseribe the kinetics of photoinitiated (co)polymeiization. The first one is the concept of diffusion-controlled reactions, based on the assumption about the diffusion control of elementary acts of macromolecular chain propagation and decay [14]. The second concept is the radieal polymerization model, based on the notion of mi-... 

Hence, the results stated above showed that the extreme change in melt viscosity of HDPE/EP nanocomposites can be accurately described within the frameworks of the fractal model. The main structural parameter controlling this effect is the change of the fractal dimension of macromolecular coil in melt. The main physical cause defining the mentioned effect is a partial interaction of the HOPE matrix and epoxy polymer particles. In this case the extreme change in the melt flow index is accurately described within the frameworks of chemical reactions fractal kinetics. 

The calculation of the amount of (V)-EPTM which should be transformed by reacting with NQ on t) basis of the kinetic rate constant reported in the previous section, can an idea of how much the presence of a macromolecular chain influences the reaction extent of a substituted cydopentadienyl group involved in a Diels-Alder reaction. According to the data of Tdrle 24 about 80% of (V), present in cwr EPTM containing 0.125 M of triene and dissolwd (2%) in toluene, reacts with a twofold excess of NQ in 24 hours, wher according to tl kinetic rate constant of tlK model compound 95.0% of (V) diould be transformed in 12.1 hours. 

Most importantly, reaction rates in nanofluidic systems can be controlled both by shape and volume changes. The important interplay between chemical reactions and geometry has been conceptualized within a theoretical framework for ultra-small volumes and tested on a number of experimental systems, opening pathways to more complex, dynamically compartmentalized ultra-small volume reactors, or artificial model cells, that offer more detailed understanding of cellular kinetics and biophysical phenomena, such as macromolecular crowding. 

New elastomeric networks based on saturated ethylene-propylene rubbers grafted with succinic anhydride groups (EPR-g-SA) crosslinked with a hydroxyl-terminated polybutadiene (HTPB) are hereafter described. Infrared techniques are employed to follow the kinetics of the monoesterification reaction and to assess its potential thermoreversibility, either on the macromolecular system (EPR-g-SA-I-HTPB), or on a model system, formed by EPR-g-SA and a low molecular weight diol, namely 1,9-nonandiol. 

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