Copolymer approximate kinetic

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... 

All IR investigations of sequence distribution so far published rely on the terminal copolymerization model, which assumes that the kinetics of copolymerization are governed only by the probability that monomer units from the feed will be added to the last unit of the growing chain, and that there is only one active site present in the catalyst system, whether homogeneous or heterogeneous. As will be shown later (Section 3.4), this is only an approximation multiple active species are formed by many soluble Ziegler-Natta catalysts, so that the product of reactivity ratios determined from the normal copolymerization equation does not always exactly predict the actual sequence distribution in the copolymer. 

The hydrolytic degradation of the biopolymer and the derivatives (the copolymer PHBV, and the blend PHB/PLA 1 1) has been monitored for 3 months tmder con-ditiorr, which is realistically approximated to physiological conditions, namely, in vitro phosphate buffer, pH = 7.4, and temperature 37°C. The analysis of kinetic curves for all samples shows that the highest rate of weight loss is observed for PLA with the smallest MW 70 kDa and for PHB with relatively low MW 150... 

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 ... 

One of the main applications of Crystaf analysis is the estimation of the CCD of semicrystalline copolymers, specifically LLDPE. The CCD of copolymers can be obtained from the Crystaf profile with the help of a cahbration curve relating the CC and the crystallization temperature. For routine analysis, a calibration curve can also give a quick estimation of the CC from the Crystaf peak temperature. Evidently, because of the crystallization kinetics and cocrystalhzation effects described before, in general only an approximation of the actual CCD is possible with Crystaf and Tref. 

Using MAS C NMR, the resonances at 127 and 136 ppm were attributed to the cis and trans double bonds and that at 178 ppm was for the carbonyl groups. The composition of the copolymers was determined by elemental analysis, radioassay of C content in the labeled copolymers and NMR. The copolymers were found to have a composition of 95, 90, and 87 mol% acetylene. The molecular weight of the insoluble copolymers was determined by radioassay of the T content after adjustment for the kinetic isotope effect (KEF). At a reaction temperature of —78 C, copolymers in the form of thin film were obtained with A/n = approximately 4000, whereas at a reaction temperature of 25 C, only powder-like products with A/n = approximately 1000 were obtained. The homopolyacetylene was found to have A/ = 11 000 using... 

Under a number of aspects the process resembles homogeneous nucleation and consequently the rate of block copolymer self-assembly is often approximated by the expression for homogeneous nucleation kinetics [50]. 

Copolymer compositions also affect polymer degradation. Table 7.3 shows the approximate degradation times for neat polymers and their derived copolymers. One of the main reasons for the change in degradation kinetics of a copolymer is that the additional monomer affects the crystallinity and reduces the steric effects (Hiemenz, 1984). The rate of chain cleavage has been found to be accelerated with increasing glycolide portion. Conversely, however, copolymerization of... 

The fact that copolymer and homopolymer runaway envelops agreed both qualitatively and quantitatively suggests that perhaps complex copolymerization kinetics might be successfully approximated by simpler kinetics, similar to the homopolymer form. It Is proposed that be replacing parameters in the homopolymer balances by their copolymer analogs, i.e., Xm, Xq and e = Xa Ac by A, ... 

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