Copolymer composition conversion

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/conversion 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. 

Elimination of unreacted monomers can be accompHshed by two methods dual initiators to enhance conversion of monomers to product (73—75) and steam stripping (70,76). Several process improvements have been claimed for dewatering beads (77), to reduce ha2e (78—81), improve color (82—86), remove monomer (87,88), and maintain homogeneous copolymer compositions (71,72,89). 

Fig. 25. Drift ia monomer composition (—) and copolymer composition (-) with conversion for three initial monomer mixtures. Ratios are based on...

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 existence of an azeotropic composition has some practical significance. By conducting a polymerization with the monomer feed ratio equal to the azeotropic composition, a high conversion batch copolymer can be prepared that has no compositional heterogeneity caused by drift in copolymer composition with conversion. Thus, the complex incremental addition protocols that arc otherwise required to achieve this end, are unnecessary. Composition equations and conditions for azeotropic compositions in ternary and quaternary eopolymerizations have also been defined.211,21... 

The traditional method for determining reactivity ratios involves determinations of the overall copolymer composition for a range of monomer feeds at zero conversion. Various methods have been applied to analyze this data. The Fineman-Ross equation (eq. 42) is based on a rearrangement of the copolymer composition equation (eq. 9). A plot of the quantity on the left hand side of eq. 9 v.v the coefficient of rAa will yield rAB as the slope and rUA as the intercept. 

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. 

In comparing observed reactivity ratios between various polymerization systems, it is important to take into account the possible effect of molecular weight on copolymer composition.3475 19 In conventional radical eopolymeri/.ation, the specificity shown in the initiation and termination steps can have a significant effect on the composition of low molecular weight copolymers (usually <10 units). These effects are discussed in Section 7.4.5. In a living polymerization molecular weights are low at low conversion and increase with conversion. In these... 

Example 13.7 A 50/50 (molar) mixture of st5Tene and acrylonitrile is batch polymerized by free-radical kinetics until 80% molar conversion of the monomers is achieved. Determine the copolymer composition distribution. 

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

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. 

Calculated monomer proportions In solubilized copolymer at each conversion level are compared to unreacted monomer proportions in Table I. At low conversion levels, T3-T5, the copolymer appeared to be rich In methylacrylate. This anomaly was not detected In unreacted monomer measurements, possibly because the amount of copolymer was small relative to the large excess of unreacted monomers. As conversion Increased (T5-Tj 4> calculated copolymer composition approached the 75/25 AN/MA target and averaged exactly 75/25. 

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,. ... 

Very similar variations in average copolymer composition with conversion have recently been observed in the styrene methyl methacrylate system by both Johnson et al ( and by Dionisio and O Driscoll (. The reason for the variation may be due to a viscosity effect on propagation rate constants QO). 

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. 

A user-friendly computer program has been developed (A.S.Yakovlev, S.LKuch-anov Copolymerization for Windows ) which makes it possible at any values of conversion to calculate for m=2-6 along with the composition of monomer mixture x, such statistical characteristics as instantaneous X and average (x j copolymer composition as well as the fractions (P Uk of sequences Uk with k=2-4 and... 

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-... 

Variation of Styrene Content with Extent of Conversion. Figure 8 gives the relationship between copolymer composition and the extent of conversion for copolymers of butadiene and styrene (25 wt.7. styrene) prepared in toluene, at 30°C, with n-BuLi and barium salts of t-butanol and water. For comparison purposes, the copolymer composition curve is shown for the reaction initiated using n-BuLi alone. Copolymerization using n-BuLi results in very little incorporation of styrene into the copolymer chain until about 757. conversion, after which the styrene content increases very rapidly. In contrast, copolymerization using the barium salts and n-BuLi results in an increased incorporation of styrene at the same extents of conversion. 

Figure 8. Copolymer composition variation with percent conversion. Conditions butadiene-styrene (75/25) in toluene at 30°C.

Butadiene-Styrene Copolymers from Ba-Mg-Al Catalyst Systems. Figure 13 shows the relationship between copolymer composition and extent of conversion for copolymers of butadiene and styrene (25 wt.7. styrene) prepared in cyclohexane with Ba-Mg-Al and with n-BuLi alone. Copolymerization of butadiene and styrene with barium salts and Mg alkyl-Al alkyl exhibited a larger initial incorporation of styrene than the n-BuLi catalyzed copolymerization. A major portion of styrene placements in these experimental SBR s are more random however, a certain fraction of the styrene sequences are present in small block runs. 

The gas chromatographic analysis of the unreacted monomers in the experiments from Table II discloses a constant C5/C8 ratio comparing the starting comonomer composition to the final composition. This means that monomer conversion is the same for 1,5-cyclooctadiene and cyclopentene in the copolymerization so that copolymer compositions are equal to the charge ratios. This result is consistent with the product analysis by 13C NMR spectroscopy where the copolymer composition is nearly identical to the starting comonomer composition. 13C NMR is used to determine the composition of the cyclopentene/1,5-cyclooctadiene copolymers as part of a detailed study of their microstructure (52). The areas of peaks at 29-30 ppm (the pp carbon from cyclopentene units) and at 27.5 ppm (the four ap carbons from the 1,5-cyclooctadiene) are used to obtain the mole fractions of the two comonomers (53, 54, 55). 13C NMR studies and copolymer composition determinations are described by Ivin (51, 56, 57) for various systems. 

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. 

By virtue of the conditions xi+X2 = 1>Xi+X2 = 1, only one of two equations (Eq. 98) (e.g. the first one) is independent. Analytical integration of this equation results in explicit expression connecting monomer composition jc with conversion p. This expression in conjunction with formula (Eq. 99) describes the dependence of the instantaneous copolymer composition X on conversion. The analysis of the results achieved revealed [74] that the mode of the drift with conversion of compositions x and X differs from that occurring in the processes of homophase copolymerization. It was found that at any values of parameters p, p2 and initial monomer composition x° both vectors, x and X, will tend with the growth of p to common limit x = X. In traditional copolymerization, systems also exist in which the instantaneous composition of a copolymer coincides with that of the monomer mixture. Such a composition, x =X, is known as the azeotrop . Its values, controlled by parameters of the model, are defined for homophase (a) [1,86] and interphase (b) copolymerization as follows... 

When deriving this expression for the average composition distribution, authors of paper [74] entirely neglected its instantaneous constituent, having taken (as is customary in the quantitative theory of radical copolymerization [3,84]) the Dirac delta-function < ( -X) as the instantaneous composition distribution. Its averaging over conversions, denoted hereinafter by angular brackets, leads to formula (Eq. 101). Note, this formula describes the composition distribution only provided copolymer composition falls in the interval between X(0) and X(p). Otherwise, this distribution function vanishes at all values of composition lying outside the above-mentioned interval. 

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... 

Block copolymer synthesis from living polymerization is typically carried out in batch or semi-batch processes. In the simplest case, one monomer is added, and polymerization is carried out to complete conversion, then the process is repeated with a second monomer. In batch copolymerizations, simultaneous polymerization of two or more monomers is often complicated by the different reactivities of the two monomers. This preferential monomer consumption can create a composition drift during chain growth and therefore a tapered copolymer composition. 

Figure 6. Variation of the instantaneous copolymer composition with conversion for a starting monomer composition of 20 mol% of...

Akbulut and Toppare also found very similiar effects upon copolymer composition, total conversion and R.M.M. control in the styrene-isoprene copolymer system [83] with the analogous traces to Figs. 6.19 and 6.20 shifted to slightly more anodic values and with a better total conversion at high potential in the presence of 25 kHz ultrasound. 

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