Statistical copolymer Copolymerization equation

Styrene-SQ., Copolymers. I would now like to discuss two systems which illustrate the power of C-13 nmr in structural studies. The first is the styrene-SO system. As already indicated, this is of the type in which the chain composition varies with monomer feed ratio and also with temperature at a constant feed ratio (and probably with pressure as well.) The deviation of the system from simple, first-order Markov statistics, —i.e. the Lewis-Mayo copolymerization equation—, was first noted by Barb in 1952 ( ) who proposed that the mechanism involved conplex formation between the monomers. This proposal was reiterated about a decade later by Matsuda and his coworkers. Such charge transfer com-... 

The composition of instantaneously generated chains is not sufficiently described by the copolymerization equation which only informs us about the mean populations of monomers in a statistical copolymer. This problem was studied by Goldfinger and Kane [190] based on the following considerations. 

The phenomenon may be simulated (78) by a blend of two or more copolymers obeying the copolymerization equation, e.g. two or more of the above-mentioned fractions, and the statistical quantities of the blend may be expressed as a function of the same quantities in the starting copolymers. For C2-C3 copolymers, we evaluated (69) this relationship for the fraction of bonds and checked it by means of the IR measurement of the distribution index theoretical predictions, they also supported the assumptions we had previously made to justify the dependence of the ratio of IR absorptions at 10.30 and 10.67 p upon the ratio between the fractions of C2-C3 and C3-C3 bonds. 

The melting point of a polymer will also be affected by copolymerization. In the case of random or statistical copolymers (Section 1.2.3) the structure is very irregular and so crystallization is normally suppressed and the copolymers are usually amorphous. In contrast, in block and graft copolymers crystallization of one or more of the blocks may take place. It is possible to analyse the melting behaviour for a copolymer system in which there are a small number of non-crystallizable comonomer units incorporated in the chain, using Equation (4.39). These units will act as impurities (cf. chain ends) and so the melting point of the copolymer will be given by... 

Statistical copolymers are obtained when two different AB monomers are copolymerized (equation 88) (231). 

When such a stirring is absolutely absent in a continuous flow system, as it takes place in the piston reactor (PR), regularities of the batch processes with the same residence time 0 are realized. This implies that in order to describe copolymerization in continuous PR one can apply all theoretical equations known for a common batch process having replaced the current time t for 0. As for the equations presented in Sect. 5.1, which do not involve t al all, they remain unchanged, and one can employ them directly to calculate statistical characteristics of the products of continuous copolymerization in PR. It is worth mentioning that instead of the initial monomer feed composition x° for the batch reactor one should now use the vector of monomer feed composition xin at the input of PR. In those cases where copolymer is being synthesized in CSTR a number of specific peculiarities inherent to the theoretical description of copolymerization processes arises. 

Obviously, what we would really like to do is not just have a feel for tendencies, useful as this is, but also calculate copolymer composition and sequence distributions, things that can also be measured by spectroscopic methods. We will start by using kinetics to obtain an equation for the instantaneous copolymer composition (it changes as the copolymerization proceeds). Later we will use statistical methods to describe and calculate sequence distributions. In deriving the copolymer equation, we only have to consider the propagation step and apply our old friend, the steady-state assumption, to the radical species present in the polymerization, and... 

Another important recent contribution is the provision of a good measurement of the precision of estimated reactivity ratios. The calculation of independent standard deviations for each reactivity ratio obtained by linear least squares fitting to linear forms of the differential copolymer equations is invalid, because the two reactivity ratios are not statistically independent. Information about the precision of reactivity ratios that are determined jointly is properly conveyed by specification of joint confidence limits within which the true values can be assumed to coexist. This is represented as a closed curve in a plot of r and r2- Standard statistical techniques for such computations are impossible or too cumbersome for application to binary copolymerization data in the usual absence of estimates of reliability of the values of monomer feed and copolymer composition data. Both the nonlinear least squares and the EVM calculations provide computer-assisted estimates of such joint confidence loops [15]. 

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 ... 

For the foUwing estimation of the copolymerization parameters it is useful to discern between the ovmaU or mixed parameters and the true oopolymerization parameters. First we assume that there are only uniform active centres located on the catalyst sur ce, (i.e., one centre model), and use ethene and comonomer peaks in the NMR spectrum of the polymer mixture for the estimation of the oopolymerization parameters according to the Mayo Lewis equqtion This evaluation, via the r versus diagram, leads to the overall or mixed copolymerization parameters. However, for the estimation of the true copolymerization parameters we now use the following considerations. The Mayo-Lewis equation describes the composition of the copolymer as a function of the initial monomers mixture and the oopolymerization parameters. If we know these and the monomers mixture we can calculate not only the copolymer composition but also, by means of statistical considerations, the sequence length distribution of Mj and M2 sequences in the copolymer... 

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