Copolymerization copolymer composition

Tip 13 (related to Tip 12) Copolymerization, copolymer composition, composition drift, azeotropy, semibatch reactor, and copolymer composition control. Most batch copolymerizations exhibit considerable drift in monomer composition because of different reactivities (reactivity ratios) of the two monomers (same ideas apply to ter-polymerizations and multicomponent cases). This leads to copolymers with broad chemical composition distribution. The magnirnde of the composition drift can be appreciated by the vertical distance between two items on the plot of the instantaneous copolymer composition (ICC) or Mayo-Lewis (model) equation item 1, the ICC curve (ICC or mole fraction of Mj incorporated in the copolymer chains, F, vs mole fraction of unreacted Mi,/j) and item 2, the 45° line in the plot of versus/j. 

Entropy, enthalpy, and free energy of reversible polymerization Arrhenius relationship for rate constants Subcritical damped oscillations during thermal polymerization Polyrate of terpolymerization of AMS-AN-Sty Enthalpy of random copolymers Effect of chain sequence distribution Entropy and free energy of copolymerization Copolymer composition with and without ceiling temperature effect... 

When Fj = 1/f2, the copolymer composition curve will be either convex or concave when viewed from the Fj axis, depending on whether Fj is greater or less than unity. The further removed from unity rj is, the farther the composition curve will be displaced from the 45° line. This situation is called ideal copolymerization. The example below explores the origin of this terminology. 

The parameters rj and T2 are the vehicles by which the nature of the reactants enter the copolymer composition equation. We shall call these radical reactivity ratios, although similarly defined ratios also describe copolymerizations that involve ionic intermediates. There are several important things to note about radical reactivity ratios ... 

The reactivity ratios of a copolymerization system are the fundamental parameters in terms of which the system is described. Since the copolymer composition equation relates the compositions of the product and the feedstock, it is clear that values of r can be evaluated from experimental data in which the corresponding compositions are measured. We shall consider this evaluation procedure in Sec. 7.7, where it will be found that this approach is not as free of ambiguity as might be desired. For now we shall simply assume that we know the desired r values for a system in fact, extensive tabulations of such values exist. An especially convenient source of this information is the Polymer Handbook (Ref. 4). Table 7.1 lists some typical r values at 60°C. 

These observations suggest how the terminal mechanism can be proved to apply to a copolymerization reaction if experiments exist which permit the number of sequences of a particular length to be determined. If this is possible, we should count the number of Mi s (this is given by the copolymer composition) and the number of Mi Mi and Mi Mi Mi sequences. Specified sequences, of any definite composition, of two units are called dyads those of three units, triads those of four units, tetrads those of five units, pentads and so on. Next we examine the ratio NmjMi/Nmi nd NmjMiMi/NmiMi If these are the same, then the mechanism is shown to have terminal control if not, it may be penultimate control. To prove the penultimate model it would also be necessary to count the number of Mi tetrads. If the tetrad/triad ratio were the same as the triad/dyad ratio, the penultimate model is proved. 

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. The theory of multicomponent polymerization kinetics has been treated (35,36). 

Fig. 24. Relationship between feed composition and copolymer composition of styrene—acrylonitrile copolymerization. See text.

In the Type II case, the copolymerization tends toward an alternating arrangement of monomer units. Curve II of Figure 1 shows an example of an alternating copolymer that has an azeotropic copolymer composition, ie, a copolymer composition equal to the monomer feed at a single monomer feed composition. This case is analogous to a constant Foiling mixture ia vapor—Hquid equihbria.T) III... 

Heterogeneous copolymerization of acrylamide causes redistribution comonomers between phases I and II. This leads to a change of copolymer composition in phases I and II. As a result, the values of ri and change. This accounts for anomalous widening of the experimental composition distribution curves as compared with theoretical curves. 

Methyl-2-furaldehyde gave a similar overall behaviour, but a penultimate effect was observed in its copolymerization with isopropenylbenzene whereby two molecules of the aldehyde could add together if the penultimate unit in the growing chain was from the olefin. This was borne out by the copolymers composition and spectra. The values of the reactivity ratios showed this interesting behaviour rx = 1.0 0.1, r2 = 0.0 0.1. An apparent paradox occurred the aldehyde, which could not homo-polymerize, had equal probability of homo- and copolymerization and the olefin, which homopolymerized readily, could only alternate. The structure arising from this situation was close to a regular sequence of the type ... 

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. 

For many systems, the copolymer composition appears to be adequately described by the terminal model yet the polymerization kinetics demand application of the penultimate model. These systems where rAAB=rliAR and aha bba hut sAfsB are said to show an implicit penultimate effect. The most famous system of this class is MMA-S copolymerization (Section 7.3.1.2.3). 

Rased on the above data, it would seem unusual if reactivity of the propagating species in copolymerization were insensitive to the nature of the last added monomer units. However, while there are ample experimental data to suggest that copolymerizations should be subject to penultimate unit effects that affect the rate and/or copolymer composition, the origin and magnitude of the effect is not always easily predictable. 

It has been argued that for a majority of copolymerizations, composition data can be adequately predicted by the terminal model copolymer composition equation (eqs. 5-9). However, in that composition data are not particularly good for model discrimination, any conclusion regarding the widespread applicability of the implicit penultimate model on this basis is premature. 

Methods for evaluation of reactivity ratios comprise a significant proportion of the literature on copolymerization. There are two basic types of information that can be analyzed to yield reactivity ratios. These are (a) copolymer composition/convcrsion data (Section 7.3.3.1) and (b) the monomer sequence distribution (Section 7.3.3.2). The methods used to analyze these data are summarized in the following sections. 

One final point should be made. The observation of significant solvent effects on kp in homopolymerization and on reactivity ratios in copolymerization (Section 8.3.1) calls into question the methods for reactivity ratio measurement which rely on evaluation of the polymer composition for various monomer feed ratios (Section 7.3.2). If solvent effects arc significant, it would seem to follow that reactivity ratios in bulk copolymerization should be a function of the feed composition.138 Moreover, since the reaction medium alters with conversion, the reactivity ratios may also vary with conversion. Thus the two most common sources of data used in reactivity ratio determination (i.e. low conversion composition measurements and composition conversion measurements) are potentially flawed. A corollary of this statement also provides one explanation for any failure of reactivity ratios to predict copolymer composition at high conversion. The effect of solvents on radical copolymerization remains an area in need of further research. 

The solvent in a bulk copolymerization comprises the monomers. The nature of the solvent will necessarily change with conversion from monomers to a mixture of monomers and polymers, and, in most cases, the ratio of monomers in the feed will also vary with conversion. For S-AN copolymerization, since the reactivity ratios are different in toluene and in acetonitrile, we should anticipate that the reactivity ratios are different in bulk copolymerizations when the monomer mix is either mostly AN or mostly S. This calls into question the usual method of measuring reactivity ratios by examining the copolymer composition for various monomer feed compositions at very low monomer conversion. We can note that reactivity ratios can be estimated for a single monomer feed composition by analyzing the monomer sequence distribution. Analysis of the dependence of reactivity ratios determined in this manner of monomer feed ratio should therefore provide evidence for solvent effects. These considerations should not be ignored in solution polymerization either. 

Several important assumptions are involved in the derivation of the Mayo-Lewis equation and care must be taken when it is applied to ionic copolymerization systems. In ring-opening polymerizations, depolymerization and equilibration of the heterochain copolymers may become important in some cases. In such cases, the copolymer composition is no longer determined by die four propagation reactions. 

Polymerization equilibria frequently observed in the polymerization of cyclic monomers may become important in copolymerization systems. The four propagation reactions assumed to be irreversible in the derivation of the Mayo-Lewis equation must be modified to include reversible processes. Lowry114,11S first derived a copolymer composition equation for the case in which some of the propagation reactions are reversible and it was applied to ring-opening copalymerization systems1 16, m. In the case of equilibrium copolymerization with complete reversibility, the following reactions must be considered. 

In the anionic copolymerization of lactams, this exchange reaction is faster than the propagation reaction and the copolymer composition is determined by this reaction and not by the propagation reaction127. A general solution of the copolymerization problem considering this equilibrium has not as yet been obtained. 

Fig. 4. Dependence of copolymer composition on monomer feed in copolymerization of BCMO with THF at 30 and 120 °C...

Anionic copolymerization of lactams presents an interesting example of copolymerization. Studies of the copolymerization of a-pyrrolidone and e-caprolactam showed that a-pyrrolidone was several times more reactive than e-caprolactam at 70 °C, but became less reactive at higher temperatures due to depropagation210 2U. By analyzing the elementary reactions Vofsi et al.I27 concluded that transacylation at the chain end occurred faster than propagation and that the copolymer composition was essentially determined by the transacylation equilibrium and the acid-base equilibrium of the monomer anion together with the usual four elementary reactions of the copolymerization. 

Copolymerization. The solid phase of the precipitation polymerization also influences copolymer composition, since differential monomer adsorption on the polymer particles considerably modifies the effective reactivity ratios of the comonomers. This problem has been discussed by several authors (22,23,24,25,26). 

The heterogeneous copolymerization of styrene and acrylonitrile in various diluents as reported by Riess and Desvalois (22). Although the copolymer composition in these studies was not strongly influenced by the diluent choice, the preferential adsorption of acrylonitrile monomer onto the polymer particles shifted the azeotropic copolymerization point from the 38 mole % acrylonitrile observed in solution to 55 mole % acrylonitrile. 

Data of Nomura and Funita (12). The predictive capabilities of EPM for copolymerizations are shown in Figures 8-9. Nomura has published a very extensive set of seeded experimental data for the system styrene-MMA. Figures 8 and 9 summarize the EPM calculations for two of these runs which were carried out in a batch reactor at 50 °C at an initiator concentration of 1.25 g dm 3 water. The concentration of the seeded particles was 6x10 dm 3 and the total mass of monomer was 200 g dm 3. The ratio of the mass of MMA to the total monomer was 0.5 and 0.1 in Figures 8 and 9 respectively. The agreement between the measured and predicted values of the total monomer conversion, the copolymer composition, and the concentration of the two monomers in the latex particles is excellent. The transition from Interval II to Interval III is predicted satisfactorily. In accordance with the experimental observations, EPM predicted no new particle formation under the conditions of this run. 

If the chains are long, the composition of the copolymer and the arrangement oi units along the chain are determined almost entirely by the relative rates of the various chain propagation reactions. On the other hand, the rate of polymerization depends not only on the rates of these propagation steps but also on the rates of the termination reactions. Copolymer composition has received far more attention than has the rate of copolymerization. The present section will be confined to consideration of the composition of copolymers formed by a free radical mechanism. 

It has been shown by Barb and by Dainton and Ivin that a 1 1 complex formed from the unsaturated monomer (n-butene or styrene) and sulfur dioxide, and not the latter alone, figures as the comonomer reactant in vinyl monomer-sulfur dioxide polymerizations. Thus the copolymer composition may be interpreted by assuming that this complex copolymerizes with the olefin, or unsaturated monomer. The copolymerization of ethylene and carbon monoxide may similarly involve a 1 1 complex (Barb, 1953). 

In thermal polymerization where the rate of initiation may also vary with composition, an abnormal cross initiation rate may introduce a further contribution to nonadditive behavior. The only system investigated quantitatively is styrene-methyl methacrylate, rates of thermal copolymerization of which were measured by Walling. The rate ratios appearing in Eq. (26) are known for this system from studies on the individual monomers, from copolymer composition studies, and from the copolymerization rate at fixed initiation rate. Hence a single measurement of the thermal copolymerization rate yields a value for Ri. Knowing hm and ki22 from the thermal initiation rates for either monomer alone (Chap. IV), the bimolecular cross initiation rate constant kii2 may be calculated. At 60°C it was found to be 2.8 times that... 

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

V. Copolvmerization Kinetics. Qassical copolymerization kinetics commonly provides equations for instantaneous property distributions (e.g. sequence length) and sometimes for accumulated instantaneous (i.e. for high conversion samples) as well (e.g. copolymer composition). These can serve as the basis upon whkh to derive nations which would reflect detector response for a GPC separation based upon properties other than molecular weight. The distributions can then serve as c bration standards analagous to the use of molecular weight standards. 

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