Steady-state approximation copolymerization

Since the composition of a copolymer chain is critical for determining its properties, understanding how the kinetics of the copolymerization impact the composition is an important consideration. To cut to the chase, the composition of a copolymer formed under a particular set of conditions depends on the relative rates of the four principal reactions. This in turn depends on the rate constants (e.g., those shown in Figure 12) and concentrations of reactive species and monomers. Using either a steady-state approximation or a polymerization statistics derivation, one can determine the following expression for the relative amount of monomer A in copolymer given the amount in the feed through equation [12] where Fa is the mole fraction of A in the copolymer and/a is the mole fraction of A in the feed ... 

The ratio S[A ]/2[B ] can be evaluated by making a steady-state approximation. In the case of copolymerization the assumption is that the concentration of each of the two types of active centre remains constant... 

Since it is experimentally observed that the number of growing chains remains approximately constant throughout the duration of most copolymerizations (i.e., a steady state in the number of growing chains), the concentrations of Mj and are constant, and the rate of conversion of Mj to Mj is equal to the conversion of Mj to Mj i.e., i2[Mj][M2] = k2 [Mj][Mi]. Solving for Mj gives... 

Fig. 27. Boundaries separating the regions of steady-state and auto-oscillation regimes of binary copolymerization in CSTR. Curve 2 is calculated for kinetic parameters resulting in the best approximation of experimental data reported in Ref. [345] curves 1 and 3 are calculated at the limits of confidence interval of the values of these parameters [17, 6]...

Both physical and technological properties of copolymers are influenced by the sequence distribution in the macromolecular chains. The mathematical relationships governing the distribution, first developed by Alfrey and Goldfinger (7), are based upon kinetic and statistical considerations implying three fundamental assumptions a) steady state copolymerization, b) terminal effect only (i.e. influence of the last, but not of the penultimate unit of a growing chain on the addition of the next monomeric unit), and c) constant monomer feed. Under these assumptions, which may be defined as a first order approximation, the copolymers are described by two quantities, the ratio / of the molar fractions of the two monomers and the product of reactivity ratios... 

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