Polymer kinds

The composition of the pyrolysis products is primarily determined by the means of disintegration of the macromolecule to the molecules of gas, oil, and solid residue. Thus to anticipate the pyrolysis oil composition of a plastic material, the chemical composition and structure of the polymer and its thermal decomposition reactions should be consistently considered. Typical thermal decomposition pathways of the various polymer kinds are abundantly treated in the relevant scientific literature [18-20]. Thermal decomposition of the polymer component of a plastic material is expected to begin at the weakest chemical bonds of the macromolecule. However, there are decomposition pathways which require lower energy than the direct breakage of the bonds, when rearrangement over four or six neighbouring atoms leads to the elimination of a volatile compound or to the scission of the macromolecular chain. 

Figure Bl.25.4. C Is XPS spectrum of a polymer, illustrating that the C Is binding energy is influenced by the chemical enviromnent of the carbon. The spectrum clearly shows four different kinds of carbon, which corresponds well with the structure of the polymer (courtesy of M W G M Verhoeven, Eindhoven).

The expense is justified, however, when tackling polymer chains, where reconstruction of an entire chain is expressed as a succession of atomic moves of this kind [121]. The first atom is placed at random the second selected nearby (one bond length away), the third placed near the second, and so on. Each placement of an atom is given a greater chance of success by selecting from multiple locations, as just described. Biasing factors are calculated for the whole multi-atom move, forward and reverse, and used as before in the Metropolis prescription. For fiirther details see [122, 123. 124. 125]. A nice example of this teclmique is the study [126. 127] of the distribution of linear and branched chain alkanes in zeolites. 

In this section we look briefly at the problem of including quantum mechanical effects in computer simulations. We shall only examine tire simplest technique, which exploits an isomorphism between a quantum system of atoms and a classical system of ring polymers, each of which represents a path integral of the kind discussed in [193]. For more details on work in this area, see [22, 194] and particularly [195, 196, 197]. 

Copolymerization. Copolymerization occurs when a mixture of two or more monomer types polymerizes so that each kind of monomer enters the polymer chain. The fundamental structure resulting from copolymerization depends on the nature of the monomers and the relative rates of monomer reactions with the growing polymer chain. A tendency toward alternation of monomer units is common. 

Just as it is not necessary for polymer chains to be linear, it is also not necessary for all repeat units to be the same. We have already mentioned molecules like proteins where a wide variety of different repeat units are present. Among synthetic polymers, those in which a single kind of repeat unit are involved are called homopolymers, and those containing more than one kind of repeat unit are copolymers. Note that these definitions are based on the repeat unit, not the monomer. An ordinary polyester is not a copolymer, even though two different monomers, acids and alcohols, are its monomers. By contrast, copolymers result when different monomers bond together in the same way to produce a chain in which each kind of monomer retains its respective substituents in the polymer molecule. The unmodified term copolymer is generally used to designate the case where two different repeat units are involved. Where three kinds of repeat units are present, the system is called a terpolymer where there are more than three, the system is called a multicomponent copolymer. The copolymers we discuss in this book will be primarily two-component molecules. We shall discuss copolymers in Chap. 7, so the present remarks are simply for purposes of orientation. 

With copolymers, it is not sufficient merely to describe the empirical formula to characterize the molecule. Another question that can be asked concerns the distribution of the different kinds of repeat units in the molecule. Starting from monomers A and B, the following distribution patterns are obtained in linear polymers ... 

In a cross-linked polymer, the junction units are different kinds of monomers than the chain repeat units, so these molecules might be considered to be still another comonomer. While the chemical reactions which yield such cross-linked substances are copolymerizations, the products are described as cross-linked rather than as copolymers. In this instance, the behavior due to cross-linking takes precedence over the presence of an additional type of monomer in the structure. 

It is apparent from items (l)-(3) above that linear copolymers-even those with the same proportions of different kinds of repeat units-can be very different in structure and properties. In classifying a copolymer as random, alternating, or block, it should be realized that we are describing the average character of the molecule accidental variations from the basic patterns may be present. In Chap. 7 we shall see how an experimental investigation of the sequence of repeat units in a copolymer is a valuable tool for understanding copolymerization reactions. This type of information along with other details of structure are collectively known as the microstructure of a polymer. 

No polymer is ever 100% crystalline at best, patches of crystallinity are present in an otherwise amorphous matrix. In some ways, the presence of these domains of crystallinity is equivalent to cross-links, since different chains loop in and out of the same crystal. Although there are similarities in the mechanical behavior of chemically cross-linked and partially crystalline polymers, a significant difference is that the former are irreversibly bonded while the latter are reversible through changes of temperature. Materials in which chemical cross-linking is responsible for the mechanical properties are called thermosetting those in which this kind of physical cross-linking operates, thermoplastic. 

The molecular weights obtained by this method are averages. This is particularly evident from the situations where additives are present. In these cases, two different kinds of chains result, with those terminated by the same end group being stunted in growth compared to the normal polycaprolactam. Yet it is the total weight of polymer and the total number of ends that are... 

This kind of perfect flexibility means that C3 may lie anywhere on the surface of the sphere. According to the model, it is not even excluded from Cj. This model of a perfectly flexible chain is not a realistic representation of an actual polymer molecule. The latter is subject to fixed bond angles and experiences some degree of hindrance to rotation around bonds. We shall consider the effect of these constraints, as well as the effect of solvent-polymer interactions, after we explore the properties of the perfectly flexible chain. Even in this revised model, we shall not correct for the volume excluded by the polymer chain itself. 

Single crystals such as those shown in Fig. 4.11 are not observed in crystallization from the bulk. Crystallization from dilute solutions is required to produce single crystals with this kind of macroscopic perfection. Polymers are not intrinsically different from low molecular weight compounds in this regard. 

To see why the assumption of equal reactivity is so important to step-growth polymers, recall from Table 1.2 the kind of chemical reactions which produce typical condensation polymers ... 

An equivalent way of looking at the conclusion of item (2) is to recall that Eq. (5.40) gives the (number average) number of monomers of both kinds in the polymer and multiply this quantity by the average molecular weight of the two kinds of units in the structure (88 + 112)/2 = 100. 

Equation (5.47) is of considerable practical utility in view of the commercial importance of three-dimensional polymer networks. Some reactions of the sort we have considered are carried out on a very large scale Imagine the consequences of having a polymer preparation solidify in a large and expensive reaction vessel because the polymerization reaction went a little too far Considering this kind of application, we might actually be relieved to know that Eq. (5.47) errs in the direction of underestimating the extent of reaction at... 

The kind of reaction which produces a dead polymer from a growing chain depends on the nature of the reactive intermediate. These intermediates may be free radicals, anions, or cations. We shall devote most of this chapter to a discussion of the free-radical mechanism, since it readily lends itself to a very general treatment. The discussion of ionic intermediates is not as easily generalized. 

The active centers that characterize addition polymerization are of two types free radicals and ions. Throughout most of this chapter we shall focus attention on the free-radical species, since these lend themselves most readily to generalization. Ionic polymerizations not only proceed through different kinds of intermediates but, as a consequence, yield quite different polymers. Depending on the charge of the intermediate, ionic polymerizations are classified as anionic or cationic. These two types of polymerization are discussed in Secs. 6.10 and 6.11, respectively. 

As with the rate of polymerization, we see from Eq. (6.37) that the kinetic chain length depends on the monomer and initiator concentrations and on the constants for the three different kinds of kinetic processes that constitute the mechanism. When the initial monomer and initiator concentrations are used, Eq. (6.37) describes the initial polymer formed. The initial degree of polymerization is a measurable quantity, so Eq. (6.37) provides a second functional relationship, different from Eq. (6.26), between experimentally available quantities-n, [M], and [1]-and theoretically important parameters—kp, k, and k. Note that the mode of termination which establishes the connection between u and hj, and the value of f are both accessible through end group characterization. Thus we have a second equation with three unknowns one more and the evaluation of the individual kinetic constants from experimental results will be feasible. 

In the discussion of these combined topics, we use statistics extensively because the description of microstructure requires this kind of approach. This is the basis for merging a discussion of copolymers and stereoregular polymers into a single chapter. In other respects these two classes of materials and the processes which produce them are very different and their description leads us into some rather diverse areas. 

Recognition of these differences in behavior points out an important limitation on the copolymer composition equation. The equation describes the overall composition of the copolymer, but gives no information whatsoever about the distribution of the different kinds of repeat units within the polymer. While the overall composition is an important property of the copolymer, the details of the microstructural arrangement is also a significant feature of the molecule. It is possible that copolymers with the same overall composition have very different properties because of differences in microstructure. Reviewing the three categories presented in Chap. 1, we see the following ... 

In Sec. 7.3 we noted that variations in the 1 12 product led to differences in the microstructure of the polymer, even when the overall composition of two compared systems is the same. Structures [I]-[III] are examples of this situation. In this section we shall take a closer look at this variation, using the approach which is best suited for this kind of detail statistics. 

The successive repeat units in strucutres [VI]-[VIII] are of two different kinds. If they were labeled Mj and M2, we would find that, as far as microstructure is concerned, isotactic polymers are formally the same as homopolymers, syndiotactic polymers are formally the same as alternating copolymers, and atactic polymers are formally the same as random copolymers. The analog of block copolymers, stereoblock polymers, also exist. Instead of using Mj and M2 to differentiate between the two kinds of repeat units, we shall use the letters D and L as we did in Chap. I. 

With this kind of information it is not difficult to evaluate the average lengths of isotactic and syndiotactic sequences in a polymer. As a step toward this objective, we define the following ... 

In the next section we shall examine the catalysts which are able to introduce this kind of regularity into polymers. 

We shall see in Sec. 9.10 that sedimentation and diffusion data yield experimental friction factors which may also be described-by the ratio of the experimental f to fQ, the friction factor of a sphere of the same mass-as contours in solvation-ellipticity plots. The two different kinds of contours differ in detailed shape, as illustrated in Fig. 9.4b, so the location at which they cross provides the desired characterization. For the hypothetical system shown in Fig. 9.4b, the axial ratio is about 2.5 and the protein is hydrated to the extent of about 1.0 g water (g polymer)". ... 

Polydisperse polymers do not yield sharp peaks in the detector output as indicated in Fig. 9.14. Instead, broad bands are produced which reflect the polydispersity of synthetic polymers. Assuming that suitable calibration data are available, we can construct molecular weight distributions from this kind of experimental data. An indication of how this is done is provided in the following example. 

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