Copolymer, composition fractionation

The study of ethylene and propylene copolymerisation, on vanadium and titanium catalysts of various compositions [70], led to the conclusion that studied catalytic systems contain two or three types of AC. This conclusion has been made as a result of the analysis of the MWD curves, carbon nuclear magnetic resonance spectroscopy analysis, and copolymers composition fractionation data. The analysis of a large number of copolymer fractions, produced by their dissolution in several solvents at various temperatures, has indicated the existence of several types of AC different both in stereospecificity and in reactivity. According to the authors of [70], a combination of copolymer fractionation results with gel chromatography data indicates the presence of two or three types of AC. 

An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. 

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. 

Figure 7.8 Mole fractions styrene (Mj) and methyl methacrylate (M2) in feedstock (f) and copolymers (F) as a function of the extent of polymerization. Average copolymer compositions are also shown. [From V. E. Meyer and R. K. S. Chan, Polym. Prepr. 8 209(1967), used with permission.]...

Mole fraction of styrene in unreacted monomer Cumulative copolymer composition (Equation 5)... 

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-... 

More recently, the same author [41] has described polymer analysis (polymer microstructure, copolymer composition, molecular weight distribution, functional groups, fractionation) together with polymer/additive analysis (separation of polymer and additives, identification of additives, volatiles and catalyst residues) the monograph provides a single source of information on polymer/additive analysis techniques up to 1980. Crompton described practical analytical methods for the determination of classes of additives (by functionality antioxidants, stabilisers, antiozonants, plasticisers, pigments, flame retardants, accelerators, etc.). Mitchell... 

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. 

Fig. 4 Curves Xsp versus copolymer composition X = X for macromolecules of length / = 103 at values of parameters (Eq. 20) equal to b- 0.01 and h-2 (2) 5 (3) 15 (4). Asymptotic dependences at h 0 and h oo are depicted by thin lines (Eq. 1) and (Eq. 5), respectively. Volume fraction of monomeric units in a globule = 0.9...

The copolymer composition produced by these two catalysts can be estimated using the Mayo-Lewis equation [38] and these values of i and r2. Figure 10 depicts the hypothetical comonomer content in the polymer (F2) as a function of the mole fraction of comonomer in the reactor (f2). The good incorporator produces a material with higher F2 as f2 increases. In contrast, the composition from the poor incorporator is relatively flat across a broad range and increases only at very high values of/2. The F2 required to render the copolymer amorphous is comonomer-dependent for 1-octene, this value is near 0.19. In this hypothetical system, the good incorporator produces that composition at f2 = 0.57, at which the poor incorporator incorporates very little comonomer (F2 = 0.01). 

Equation 6-15 gives the copolymer composition as the mole fraction of monomer Mi in the copolymer and is often more convenient to use than the previous form (Eq. 6-12) of the copolymerization equation. 

Fig. 6-5 Distribution of copolymer composition at 100% conversion for styrene-2-vinylthiophene at the indicated values of mole fraction styrene in the initial comonomer feed. After Billmeyer [1984] (by permission of Wiley-Interscience, New York) from plot in Mayo and Walling [1950] (by permission of American Chemical Society, Washington, DC).

There have been many studies directed at using adsorption and re versed-phase HPLC to separate copolymers by composition (1.-3) interacting problems associated with these approaches ares o The presence of one property distribution interferes with separation on the basis of the other. For example, in adsorption chromatography, the degree of adsorption can be affected by both the molecular weight and by the composition of the molecule. For a linear copolymer, adequate fractionation requires that the ccmposltlon differences completely dominate. 

Figure 6 Schematic diagreun of Orthogonal Chromatography showing size fractionation of a linear copolymer by SBC 1, the variety of molecules of the same molecular size within a chromatogram "slice" (in this case A refers to styrene units and B to n-butyl methacrylate units) and composition fractionation by SBC 2. (Reproduced from Ref. 6. Copyright 1983, American Chemical Society.)...

The diode array UV/vis spectrophotometer was used to both Identify the polymer exiting and to obtain a quantitative analysis of the copolymer composition distribution. Figure 9 (6) shows the result of summing many individual fraction analyses to see the total copolymer composition distribution. The result had the correct average composition but not the skewed shape expected from theory. Part of the difficulty was the relatively small number of cross fractionations done. 

Figure 9 Copolymer composition distribution for Whole polymer as sum of distributions obtained from individual cross fractionations. (Reproduced from Ref. 6. Copyright 1983,...

Figure 4. Relationship between copolymer composition (mole fraction Mi in copolymer) and monomer feed composition (mole fraction Mi in feed) for various reactivity ratio combinations. A, n = r2 = 1 B, ri > 1, r2 < 1 C, n r2 0 D, n < 1, r2 < 1. (Adopted from ref. 21.)...

Figure 5. Relationship between copolymer composition and monomer feed composition (molar fraction of Mi in both) for the combinations HPGA-co-MMA (— —) GA-co-MMA (—A—) GA-co-S (— —) and HPGA-co-S (-O-).

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