Monomer mixture, composition

WalF first called attention to the close analogy between the copolymer-monomer mixture composition relationships and vapor-liquid... 

The instantaneous composition of a copolymer X formed at a monomer mixture composition x coincides, provided the ideal model is applicable, with stationary vector ji of matrix Q with the elements (8). The mathematical apparatus of the theory of Markov chains permits immediately one to wright out of the expression for the probability of any sequence P Uk in macromolecules formed at given x. This provides an exhaustive solution to the problem of sequence distribution for copolymers synthesized at initial conversions p l when the monomer mixture composition x has had no time to deviate noticeably from its initial value x°. As for the high-conversion copolymerization products they evidently represent a mixture of Markovian copolymers prepared at different times, i.e. under different concentrations of monomers in the reaction system. Consequently, in order to calculate the probability of a certain sequence Uk, it is necessary to average its instantaneous value P Uk over all conversions p preceding the conversion p up to which the synthesis was conducted. 

Because the dependence of probability P Uk on x should be established by means of the theory of Markov chains, in order to make such an averaging it is necessary to know how the monomer mixture composition drifts with conversion. This kind of information is available [2,27] from the solution of the following set of differential equations ... 

Here Jta(x) denotes the a-th component of the stationary vector x of the Markov chain with transition matrix Q whose elements depend on the monomer mixture composition in microreactor x according to formula (8). To have the set of Eq. (24) closed it is necessary to determine the dependence of x on X in the thermodynamic equilibrium, i.e. to solve the problem of equilibrium partitioning of monomers between microreactors and their environment. This thermodynamic problem has been solved within the framework of the mean-field Flory approximation [48] for copolymerization of any number of monomers and solvents. The dependencies xa=Fa(X)(a=l,...,m) found there in combination with Eqs. (24) constitute a closed set of dynamic equations whose solution permits the determination of the evolution of the composition of macroradical X(Z) with the growth of its length Z, as well as the corresponding change in the monomer mixture composition in the microreactor. 

Alongside the radical distinction of the mechanism of this process from that of chain polymerization, linear polycondensation features a number of specific peculiarities. So, for instance, the theory of copolycondensation does not deal with the problem of the calculation of a copolymer composition which normally coincides with the initial monomer mixture composition. Conversely, unlike chain polymerization, of particular importance for the products of polycondensation processes with the participation of asymmetric monomers is structural isomerism, so that the fractions of the head-to-head and head-to-tail patterns of ar-... 

Figure 31 Copolymer composition as a function of monomer mixture composition in the case of styrene methyl methacrylate mixtures. Reproduced from Mercier and Marechal [15], Reproduit avec I autorisation de I editeur. Tous droits reserves.

As pointed out in the foregoing, there are two specific peculiarities qualitatively distinguishing these systems from the classical ones. These peculiarities are intramolecular chemical inhomogeneity of polymer chains and the dependence of the composition of macromolecules X on their length l. Experimental data for several nonclassical systems indicate that at a fixed monomer mixture composition x° and temperature such dependence of X on l is of universal character for any concentration of initiator and chain transfer agent [63,72,76]. This function X(l), within the context of the theory proposed here, is obtainable from the solution of kinetic equations (Eq. 62), supplemented by thermodynamic equations (Eq. 63). For heavily swollen globules, when vector-function F(X) can be presented in explicit analytical form... 

Under the quasi-homogeneous approach the monomer mixture composition is characterized by vector x with components xi = Mj/M and x2 = M2/M, whose drift with conversion is described by equations [84]... 

Fig. 8 Dependencies on conversion p of monomer mixture composition x (a), instantaneous X (b) and average X) (c) copolymer composition as well as dispersion a2 (d) of the composition distribution calculated at different values of the initial compositions of monomers x°. The calculations have been carried out at values of parameters a and a2 = 1 - fli (Eq. 100) equal to 0.3 and 0.7, respectively... 

Fig. 9 Evolution with conversion p of composition distribution of the products of interphase copolymerization calculated at the initial monomer mixture composition x° = 0.6 and parameter a (Eq. 100) equal to 0.3...

As mentioned in Chapter 2, if two comonomers are not connected with the template by covalent bonds, reactivity ratios can be calculated on the basis similar to the conventional copolymerization. The only difference is that reactivity ratios ri and T2 for both monomers depend on the concentration of the template. In order to compare experimental data with these considerations, copolymerization of methacrylic acid with styrene was carried out in the presence of PEG (mol. wt. 20,000) as the template. The reactivity ratios rf and r2 can be calculated according to the Kellen-Tiidos method. The results are shown in the Figure 5.4. According to this method, a proper functions of monomer mixture composition, R, and copolymer composition, E, were plotted ... 

Unfortunately, there are practically no systematic investigations that allow to survey the changes in physical parameters of copolymers for a broad interval of copolymer compositions. Moreover, in a majority of works published the copolymer composition was not specially determined but was accepted to be equal to the initial monomer mixture composition. This complicates the establishment of correlations between copolymer composition and properties. Nevertheless some conclusions for the first group of copolymers, as well as for the second can be made. 

The second type of nonideal models takes into account the possible formation of donor-acceptor complexes between monomers. Essentially, along with individual entry of these latter into a polymer chain, the possibility arises for their addition to this chain as a binary complex. A theoretical analysis of copolymerization in the framework of this model revealed (Korolev and Kuchanov, 1982) that the statistics of the succession of units in macromolecules is not Markovian even at fixed monomer mixture composition in a reactor. Nevertheless, an approach based on the "labeling-erasing" procedure has been developed (Kuchanov et al., 1984), enabling the calculation of any statistical characteristics of such non-Markovian copolymers. 

Fig. 23. Space diagram of the copolymerization surface. Copolymer composition as a function of the monomer mixture composition and conversion (S-AN).

By means of the spatially intermittent reactor, Ito and O Driscoll determined, for example, the absolute rate constant of termination, fct, for methyl methacrylate copolymerization with butyl or dodecyl methacrylate. The value of /ct is a function of the monomer mixture composition [89]. 

In the industrial production of structured AN-Bu-St (ABS) latex particles, the grafting copolymerization of AN and St on crossUnked polybutadiene (PB) seed latex is carried out in emulsion polymerization. Therefore, information on the effect of PB crosslinking density on the swelling of PB latex particles by a St-AN monomer mixture is very important for the production of ABS copolymers with desired properties. Mathew et al. [177] studied the effect of several thermodynamic parameters, such as the crosslinking density, particle size and monomer mixture composition on the swelling behavior of PB latex particles by pure St and AN, and St-AN mixtures of various compositions. They reported... 

Ijy the method of continuous recycle copolymerization, a monomeric mixture can be polymerized to yield a copolymer of the same composition as the monomer feed mixture—regardless of disproportionate monomer reactivities—because the system automatically adjusts the monomer mixture composition in the reaction zone in order to reach a steady state. The copolymer thus obtained showed a very good composition homogeneity, and the conditions and reasons leading to it were discussed (3) along with two aspects of continuous recycle polymerization attainment of the steady state conditions and maintenance of a close material balance. 

---