Copolymers composition determination

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. 

In mean field theory, two parameters control the phase behavior of diblock copolymers the volume fraction of the A block /A, and the combined interaction parameter xTak- V. where Xab is the Flory-Huggins parameter that quantifies the interaction between the A and B monomers and N is the polymerization index [30], The block copolymer composition determines the microphase morphology to a great extent. For example, comparable volume fractions of block copolymer components result in lamella structure. Increasing the degree of compositional asymmetry leads to the gyroid, cylindrical, and finally, spherical phases [31]. 

Polymerization Results. A batch polymerization of MMA-MAA comonomer was analyzed for the determination of the reactivity ratios of the two monomers. The change in the ratio of the copolymer composition determined by GC was plotted against conversion as shown in Figure 1. Similarly, the calculated curves for some assumed reactivity ratios are also shown in the same Figure. The optimum values of the reactivity ratio for the emulsion poly-... 

Poly(M,M-diethylacrylamide-co-M,W-dimethylacrylamide) P(DEA-co-DMA) copolymers with different amounts of DMA can be synthesized by free radical polymerization in THF with AIBN as the initiator (1 mol%). In a typical reaction, the solution mixture is bubbled with dry nitrogen for 30 min prior to polymerization. The temperature is then gradually raised to 68 °C in a period of 2 h and maintained for 18 h. Each reaction mixture was precipitated in ether or hexane after the polymerization. The copolymer composition determined by JH NMR spectra is normally close to the feed ratio of monomers prior to polymerization. The nomenclature used hereafter for these copolymers is P(DEA-co-DMA/x), where x denotes the mol % content of DMA. The chemical structure of P(DEA-co-DMA) is as shown in Scheme 6. 

The problem of the computation accuracy of these kinetic parameters is dependent first of all on the validity of the copolymer composition determination. As a criterion here one may use the closeness to each other of the values of this composition obtained via the different experimental methods. It is possible to judge about the degree of such a closeness using Tables 6.1 and 6.2 where the data on both chemical analysis and spectroscopy are presented. One can see that, as for the considered cases, the different experimental methods provide quite close values of the copolymer compositions within the accuracy in the range of 5%. Authentic evidence concerning the feasibility to reach such a degree of accuracy is furnished by the data on copolymer composition obtained via independent methods in the different systems, for instance, under the copolymerization of p-chlorstyrene with methyl acrylate [32], of 4-methylstyrene with methyl methacrylate or acrylonitrile [213], and also of styrene with acrylic or methacrylic acids [214],... 

The data analyzed from the UV-LALLS-RI chromatograms by applying equation 7 resulted in a calculated average p for the copolymer of 0.1732 mL/g. This compares well with a theoretical value of 0.1799 mL/g assuming the values of p s and p eo to be 0.185 and 0.050 mL/g, respectively, (5) and a composition of 96.2% PS. The marginal diflFerence could be attributed to error in the value assumed for p eo or error in the copolymer composition determined by NMR. For example, a composition of 91.5% PS would give a theoretical of 0.1735 mL/g. However, in the absence of more experimental results, the original NMR composition has to be accepted. 

Spectrometric Analysis. Spectroscopy has been extensively used for polymer and copolymer analysis. (59-69). The kind of information available from different spectroscopic techniques as well as the instrumentation required depends on the region of the electromagnetic spectrum in which absorption is taking place. Recent investigations (63) on the use of spectrophotometers for copolymer analysis have shown that the response from spectrophotometers is sometimes sensitive to the microstructure of the polymer molecules and that calibration of spectrophotometers with absolute measurements on the microstructure (i.e. NMR) may be necessary in order to obtain reliable quantitative information on concentration and copolymer composition determinations. 

Weidner S, Falkenhagen J, Bressler I. Copolymer composition determined by LC-MALDI-TOF MS coupling and MassChrom2D data analysis. Macromol Chem Phys, http //dx.doi.org/10.1002/macp.201200169 2012. 

Equations (7.40) and (7.41) suggest a second method, in addition to the copolymer composition equation, for the experimental determination of reactivity ratios. If the average sequence length can be determined for a feedstock of known composition, then rj and r2 can be evaluated. We shall return to this possibility in the next section. In anticipation of applying this idea, let us review the assumptions and limitation to which Eqs. (7.40) and (7.41) are subject ... 

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. 

The copolymer composition equation relates the r s to either the ratio [Eq. (7.15)] or the mole fraction [Eq. (7.18)] of the monomers in the feedstock and repeat units in the copolymer. To use this equation to evaluate rj and V2, the composition of a copolymer resulting from a feedstock of known composition must be measured. The composition of the feedstock itself must be known also, but we assume this poses no problems. The copolymer specimen must be obtained by proper sampling procedures, and purified of extraneous materials. Remember that monomers, initiators, and possibly solvents are involved in these reactions also, even though we have been focusing attention on the copolymer alone. The proportions of the two kinds of repeat unit in the copolymer is then determined by either chemical or physical methods. Elemental analysis has been the chemical method most widely used, although analysis for functional groups is also employed. 

This equation relates the (instantaneous) copolymer composition with the monomer feed of M and M2. Values for and are usually determined by graphical methods (9,10). Today, with the prevalence of powerful desktop computers, numerical minimisa tion methods are often used (11—14). 

From this scheme it can be seen that the copolymer composition is determined by the values of four monomer reactivity ratios. 

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. 

It is also possible to process copolymer composition data to obtain reactivity ratios for higher order models (e.g. penultimate model or complex participation, etc.). However, composition data have low power in model discrimination (Sections 7.3.1.2 and 7.3.1.3). There has been much published on the subject of the design of experiments for reactivity ratio determination and model discrimination.49 "8 136 137 Attention must be paid to the information that is required the optimal design for obtaining terminal model reactivity ratios may not be ideal for model discrimination.49... 

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 copolymer composition equation only provides the average composition. Not all chains have the same composition. There is a statistical distribution of monomers determined by the reactivity ratios. When chains are short, compositional heterogeneity can mean that not all chains will contain all monomers. 

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. 

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. 

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. 

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. 

Determine the copolymer composition for a styrene-acrylonitrile copolymer made at the azeotrope (62 mol% styrene). Assume = 1000. One approach is to use the Gaussian approximation to the binomial distribution. Another is to synthesize 100,000 or so molecules using a random number generator and to sort them by composition. 

The Markov 3 order or hi er model can be used to account Bar tire effect of a tertiary norbomene in the polymer drain on the reaction rate and copolymer composition. Higher order models, however, require an inerted number of traction parameters to be determined. For example, in penpmultimate mo l (Markov 3 order model), 16 propa tion rate ranstants should be determined, whraeas 8 rate constants are needed in the penuLtiinate model. In this work, we propose a reduced-order Markov model (ROMM) to effectively reduce the number of reaction parameters. 

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. 

---