COPOLYMER COMPOSITION Subject

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 ... 

Evaluation of reactivity ratios from the copolymer composition equation requires only composition data—that is, analytical chemistry-and has been the method most widely used to evaluate rj and t2. As noted in the last section, this method assumes terminal control and seeks the best fit of the data to that model. It offers no means for testing the model and, as we shall see, is subject to enough uncertainty to make even self-consistency difficult to achieve. 

The toughness of interfaces between immiscible amorphous polymers without any coupling agent has been the subject of a number of recent studies [15-18]. The width of a polymer/polymer interface is known to be controlled by the Flory-Huggins interaction parameter x between the two polymers. The value of x between a random copolymer and a homopolymer can be adjusted by changing the copolymer composition, so the main experimental protocol has been to measure the interface toughness between a copolymer and a homopolymer as a function of copolymer composition. In addition, the interface width has been measured by neutron reflection. Four different experimental systems have been used, all containing styrene. Schnell et al. studied PS joined to random copolymers of styrene with bromostyrene and styrene with paramethyl styrene [17,18]. Benkoski et al. joined polystyrene to a random copolymer of styrene with vinyl pyridine (PS/PS-r-PVP) [16], whilst Brown joined PMMA to a random copolymer of styrene with methacrylate (PMMA/PS-r-PMMA) [15]. The results of the latter study are shown in Fig. 9. 

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 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... 

During the semi-continuous polymerization, 4-5 small samples were withdrawn from the polymerization for the determination of the comonomer and copolymer composition. A few drops of the sample latex were mixed with hydroquinone, cooled in ice, and subjected to GC analysis to determine the amounts of unreacted monomer. The rest of the sample (5-8 ml) was poured into mixed solvent of ispropanol/hexane (45/55) containing hydroquinone, and the precipitated polymer, after it was washed with hexane, was dried in a vacuum oven at 45°C for more than 5 hours. A certain amount of the dried polymer was dissolved in dimethyl formamide (DMF), and titrated for the carboxyl content with NaOH solution using phenolphthalein as the indicator. 

Besides the above methods, Tosi suggested a new method called method of grouping, which was claimed to have minimal computation difficulty, but only provides approximate values. Tidwell and Mortimer proposed a nonlinear least square method by minimizing the difference between the observed and calculated copolymer compositions. This method was claimed to circumvent the subjective judging of experimental data and lead to better results compared to other methods, although its computation process is quite complicated. 

The detomination of trajectories for the addition of monomers and/or initiators, and/or control of temperature in batch or semi-batch polymerizations are almost alwa rs dme off-line. These trajectories may be the result of operating experience, or they may be developed by calculating optimal trajectories to achieve certain goals (reduced kettle time, desired MMD or copolymer composition distribution (CCD)) subject to constraints on heat transfer capacity, etc. [33]. The rigorous calculation of optimal trajectories requires a reasonably accurate model of the polymerization process. 

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. This leads to a collection of N x N component reactions and x 1) binary reactivity ratios, where N is the number of components used. The equation for copolymer composition for a specific monomer composition was derived by Mayo and Lewis [74], using the set of binary reactions, rate constants, and reactivity ratios described in Equation 12.13 through Equation 12.18. The drift in monomer composition, for bicomponent systems was described by Skeist [75] and Meyer and coworkers [76,77]. The theory of multicomponent polymerization kinetics has been treated by Ham [78] and Valvassori and Sartori [79]. Comprehensive reviews of copolymerization kinetics have been published by Alfrey et al. [80] and Ham [81,82], while the more specific subject of acrylonitrile copolymerization has been reviewed by Peebles [83]. The general subject of the reactivity of polymer radicals has been treated in depth by Jenkins and Ledwith [84]. 

Applications of SEC/MALDI also proved important in the field of copolymer characterization. The calibration of SEC traces of copolymers is a difficult problem, and it requires some additional effort compared to the case of homopolymers. In fact, copolymer chains having the same MM may possess a different comonomer composition. A change in the comonomer composition may cause a variation in the overall dimensions of the copolymer chains. As a consequence, alffiough having the same mass, their hydrodynamic volumes may be different and the elution volume of isobaric molecules will be subject to change as ffie copolymer composition varies. This poses a serious problem for the calibration of SEC traces. 

Electron-withdrawing substituents in anionic polymerizations enhance electron density at the double bonds or stabilize the carbanions by resonance. Anionic copolymerizations in many respects behave similarly to the cationic ones. For some comonomer pairs steric effects give rise to a tendency to altemate. The reactivities of the monomers in copolymerizations and the compositions of the resultant copolymers are subject to solvent polarity and to the effects of the counterions. The two, just as in cationic polymerizations, cannot be considered independently from each other. This, again, is due to the tightness of the ion pairs and to the amount of solvation. Furthermore, only monomers that possess similar polarity can be copolymerized by an anionic mechanism. Thus, for instance, styrene derivatives copolymerize with each other. Styrene, however, is unable to add to a methyl methacrylate anion, though it copolymerizes with butadiene and isoprene. In copolymerizations initiated by w-butyllithium in toluene and in tetrahydrofuran at-78 °C, the following order of reactivity with methyl methacrylate anions was observed. In toluene the order is diphenylmethyl methacrylate > benzyl methacrylate > methyl methacrylate > ethyl methacrylate > a-methylbenzyl methacrylate > isopropyl methacrylate > t-butyl methacrylate > trityl methacrylate > a,a -dimethyl-benzyl methacrylate. In tetrahydrofuran the order changes to trityl methacrylate > benzyl methacrylate > methyl methacrylate > diphenylmethyl methacrylate > ethyl methacrylate > a-methylbenzyl methacrylate > isopropyl methacrylate > a,a -dimethylbenzyl methacrylate > t-butyl methacrylate. 

IR spectroscopy was used for quantitative analysis of the composition of three ethylene-acrylate copolymers, i.e. ethylene-methyl acrylate, ethylene-butyl acrylate and ethylene-2-ethylhexyl acrylate copolymers. Based on a simple model which explicitly considered vibrational band intensities characteristic for CH and for C 0, copolymer composition could be derived from the ratio of C 0 and CH integrated absorbances with a precision of + or -3 mol %. It was not necessary to know the optical path length of the copolymer samples which were subjected to IR analysis as pressed films. 15 refs. 

Rizzarelli et al. [23] synthesized a series of copolymers with units of butylene succinate (BSu) and butylene adipate (BA) with different composition. The copolymers were subjected to enzymatic hydrolysis by lipase (actually two different lipase enzymes, obtained from Mucor miehei or from Rhizopus arrhizus). The degradation products were water soluble. Thus, they were injected in an LC apparatus (the column was a Cl 8) coupled with an ESI-MS. The LC trace displayed more than 20 peaks that were easily identified using MS. These are due to the monomers (BSu and BA), the dimers, the trimers, and the tetramers. LC peaks due to the oligomers rich in BA (e.g., BA3) are weak. On the other hand, LC peaks due to the oligomers rich in BSu (e.g.,BSus) are strong. The results indicate a preferential hydrolytic cleavage. In particular, succinic ester bonds are hydrolyzed faster than adipic ester bonds in BSu-BA copolyesters. 

A welcome textbook on the determination of polymer sequence structure using n.m.r. has been published. The book describes in detail the statistical treatment of both tacticity and copolymer composition, and also provides a sensible discussion of the experimental conditions necessary for accurate quantitative analysis. The numerous examples given involve almost exclusively vinyl polymerizations. Two reviews, by Bovey, and Katritzky and Weiss, of the subject have appeared, that by the latter being a useful elementary review suitable for undergraduate use. More general reviews of the application of n.m.r. to structural determination have appeared in Japanese, English, and Russian with an English... 

The combination of monomers to form copolymers can be compared with the mixing of metals to form solid solutions, which is the basis of alloy formation. The chemical engineer by small variations in copolymer composition can synthesize polymers with subtly different properties. The properties which are controlled by changes in copolymer composition include elastic modulus, toughness, melt viscosity, and thermal stability (l.N.ll). We return to this subject again in Chapters 4 and 5. Copolymers are also polymerized with block or graft structures (see Fig. l.S) for specific purposes (1.N.12). 

A biodegradable polyanhydride has been prepared by polycondensation of a lithocholic acid dimer (Scheme 11b). The homopolymer has a Tg of 85°C and a melting point of >250°C, both of which can be lowered by the incorporation of a comonomer (sebacic acid). The polymers have been subjected to degradation and release studies, using p-nitroanUine as the model drug. The degradation and release rates are found to be dependent on the copolymer composition, and no apparent toxicity is observed in vivo [110]. 

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