Binary copolymer composition

The monomer reactivity ratios r and r2 can be determined from the experimental conversion-composition data of binary copolymerization using both the instantaneous and integrated binary copolymer composition equations, described previously. However, in the former case, it is essential to restrict the conversion to low values (ca. < 5%) in order to ensure that the feed composition remains essentially unchanged. Various methods have been used to obtain monomer reactivity ratios from the instantaneous copolymer composition data. Several procedures for extracting reactivity ratios from the differential copolymer equation [Eq. (7.11) or (7.17)] are mentioned in the following paragraphs. Two of the simpler methods involve plotting of r versus r2 or F versus f. ... 

Tire simplest model for describing binary copolyinerization of two monomers, Ma and Mr, is the terminal model. The model has been applied to a vast number of systems and, in most cases, appears to give an adequate description of the overall copolymer composition at least for low conversions. The limitations of the terminal model generally only become obvious when attempting to describe the monomer sequence distribution or the polymerization kinetics. Even though the terminal model does not always provide an accurate description of the copolymerization process, it remains useful for making qualitative predictions, as a starting point for parameter estimation and it is simple to apply. 

The overall composition at low conversion of binary copolymers formed in the presence of a chain transfer agent can be predicted analytically using an expression analogous to that used to describe terpolymerization where one monomer does not undergo propagation (Section 7.3.2.4),2j6 Making the appropriate substitutions, eq. 37 becomes eq. 70 ... 

Extensive work on radical copolymerization has shown that the composition in a binary copolymer, consisting of monomers Mi and M2, is determined by four rate constants ky for a propagating chain ending with adding to monomer Mj. 

Table XIX.—Results of Copolymer Composition Studies on Typical Binary Monomer Mixtures...

Bajoras and Makuska investigated the effect of hydrogen bonding complexes on the reactivities of (meth)acrylic and isotonic acids in a binary mixture of dimethyl sulfoxide and water using IR spectroscopy (Bajoras and Makuska, 1986). They demonstrated that by altering the solvent composition it was possible to carry out copolymerization in the azeotropic which resulted in the production of homogeneous copolymers of definite compositions at high conversions. Furthermore, it was shown that water solvent fraction determines the rate of copolymerization and the reactivity ratios of the comonomers. This in turn determines the copolymer composition. 

When one wants to determine the compositional heterogeneity of a given binary copolymer, a series of reference samples with different composition are required to... 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

It should be emphasized that copolymerizations that conform to the premises of binary-copolymerization theory produce copolymers of well defined structure. The kinetics of the competitive propagation-reactions determine not only the copolymer composition but also the sequence distribution. The mathematical procedures needed for calculating number-average sequence-lengths of mers, and sequence length-distributions of mers, are well known and have been... 

T. C. Tranter (36) has studied the binary copolymers based on hexamethylene diamine and -phenylene dipropionic, 3-(/>-carboxy-methyl)phenyl-butyric, 2-(/>-carbomethoxy)phenylpropionic, hydro-quinone diacetic, terephthalic, adipic, or sebacic acids. In spite of the fact that only the copolymers of hexamethylene diamine with/>-phenylene dipropionic and with 2-(/>-carbomethoxy)phenylpropionic acids show a linear softening point composition curve, Tranter claims for isomorphism in the copolymers of all the systems. In fact, their X-ray examination shows that they behave in the same basic manner, the second component dissolving in the lattice of the first until a certain critical concentration is reached, where the lattice structure changes quite abruptly to that of the second component. 

Isomorphous replacement in isotactic polyaldehydes was shown by A. Tanake, Y. Hozumi, K. Hatada, S. Endo, and R. Fujishige (42). These authors studied the binary polymer systems formed by acetaldehyde, propionaldehyde, n-butyraldehyde, iso-butyraldehyde and w-heptanal. All the copolymers are crystalline over the whole range of compositions. In the case of binary copolymers of acetaldehyde, propionaldehyde and K-butyraldehyde the unit cells have the same tetragonal space group UJa, with the same chain axis (4.8 A), while the dimensions of the a axis change continuously as a function of the copolymer composition. In the case of copolymers of isobutyraldehyde with other aldehydes, the continuous variation of the lattice constants a and c were observed. 

In the binary copolymer the two molecular weights of the monomeric units are MoA and MoB, the corresponding refractive index increments vA and vB, and the overall composition (mole fractions) nA and nB. This overall composition will in general differ from the composition of individual molecules. Thus, the molecular weight MXI of the i-th isomer with polymerization degree x is given by... 

Figure 3. Copolymer composition diagram of CPT-SOj-AN expressed as a binary copolymer...

Binary copolymerization of the CPT-AN system was carried out at 40°C using AIBN as initiator. From the Finemann-Ross plot of the copolymer composition and monomer feed ratios, the monomer reactivity ratios were determined. (CPT) = 0, r2 (AN) = 1.97. The increase of the relative reactivity of CPT by forming a complex with SC is calculated as follows. 

Even in the first publications concerning the copolymerization theory [11, 12] their authors noticed a certain similarity between the processes of copolymerization and distillation of binary liquid mixtures since both of them are described by the same Lord Rayleigh s equations. The origin of the term azeotropic copolymerization comes just from this similarity, when the copolymer composition coincides with monomer feed composition and does not drift with conversion. Many years later the formal similarity in the mathematical description of copolymerization and distillation processes was used again in [13], the authors of which, for the first time, classified the processes of terpolymerization from the viewpoint of their dynamics. The principles on which such a classification for any monomer number m is based are presented in Sect. 5, where there is also demonstrated how these principles can be used for the copolymerization when m = 3 and m = 4. 

The parameters a = l/rij5 the number of which equals m(m — IX are reciprocal reactivity ratios (2.8) of binary copolymers. Markov chain theory allows one, without any trouble, to calculate at any m, all the necessary statistical characteristics of the copolymers, which are formed at given composition x of the monomer feed mixture. For instance, the instantaneous composition of the multicomponent copolymer is still determined by means of formulae (3.7) and (3.8), the sums which now contain m items. In the general case the problems of the calculation of the instantaneous values of sequence distribution and composition distribution of the Markov multicomponent copolymers were also solved [53, 6]. The availability of the simple algebraic expressions puts in question the expediency of the application of the Monte-Carlo method, which was used in the case of terpolymerization [85,99-103], for the calculations of the above statistical characteristics. Actually, the probability of any sequence MjMjWk. .. Mrl 4s of consecutive monomer units, selected randomly from a polymer chain is calculated by means of the elementary formula ... 

In Refs. [173-176] it was suggested to use the weight composition distributions instead of the molar ones and the results of their numerical calculation for some systems were reported The authors of Ref. [177] carried out a thorough theoretical study of the composition distribution and derived an equation for it without the Skeist formula. They, as the authors of Ref. [178], proposed to use dispersion of the distribution (5.3) as a quantitative measure of the degree of the composition inhomogeneity of the binary copolymers and calculated its value for some systems. Elsewhere [179-185] for this purpose there were used other parameters of the composition distribution. In particular the discussion of the different theoretical aspects of the binary copolymerization is reported in a number of reviews by Soviet authors [186-189], By means of numerical calculations there were analyzed [190-192] the limits of the validity of the traditional assumption which allows to ignore the instantaneous component of composition distribution of the copolymers produced at high conversions. 

Fig. 4. Unimodal (1) and bimo-dal (2) composition distribution of binary copolymers prepared at complete conversion p = 1...

Calculations of copolymer composition are based on kinetic considerations and procedures. In spite of this, less attention has been paid to the copropagation rate than to other copolymerization problems. Today a single concise theory is available, solving the rate of the simplest radical binary copolymerization. Other cases described have not been generalized so far they treat the kinetic behaviour of specific monomer pairs or triplets in specific polymerization circumstances. 

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]. 

The simple copolymer model, with two reactivity ratios for a binary comonomer reaction, explains copolymer composition data for many systems. It appears to be inadequate, however, for prediction of copolymerization rates. (The details of various models that have been advanced for this purpose are omitted here, in view of their limited success.) Copolymerization rates have been rationalized as a function of feed composition by invoking more complicated models in which the reactivity of a macroradical is assumed to depend not Just on the terminal monmomer unit but on the two last monomers in the radical-ended chain. This is the penultimate model, which is mentioned in the next Section. 

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