Repeating unit, definition

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. 

We assume that the mixture contains Ni solvent molecules, each of which occupies a single site in the lattice we propose to fill. The system also contains N2 polymer molecules, each of which occupies n lattice sites. The polymer molecule is thus defined to occupy a volume n times larger than the solvent molecules. Strictly speaking, this is the definition of n in the derivation which follows. We shall adopt the attitude that the repeat units in the polymer are equal to solvent molecules in volume, however, so a polymer of degree of... 

Because proteins are not composed of identical repeating units, but of different amino acids, they do not fall within the formal definition of polymers given at the start of this chapter. They are nevertheless macromolecular and techniques developed for the study of tme polymers have been applied to them with success. However, for the most part they are outside the scope of this book and accordingly will receive very little attention in the chapters that follow. 

A repeat unit is the sequence of atoms that is repeated to build a polymer chain. This definition, although very simple, distinguishes between X-Y and X-XY-Y units. For instance, the repeat units of polyamide 6 and polyamide 6610 are ... 

The contrast between formulas 20 and 21, both pertaining to isotactic polyethylidene, should be noted This contrast occurs because the polymer repeating unit has only one carbon atom in the chain and thus there is no correspondence between such periodicity and that of the zigzag representation. The classical definition of an isotactic polymer (as one in which all substituents are on the same side of the chain) holds true, in general terms, only if the polymer is represented in the Fischer projection. Analogous considerations pertain to syndiotactic polyethylidene 22 and 23. 

It is immaterial whether (1) or (2) is taken as the configurational repeating unit and ster corep eating unit of isotactic polypropene (see Definition 1.7) this is so because the two infinite chains, one built up of identical configurational units (1) and the other built up of... 

Note As the definition above indicates, a regular polymer, the configurational base units of which contain one site of stereoisomerism only, is atactic if it has equal numbers of the possible types of configurational base units arranged in a random distribution. If the constitutional repeating unit contains more than one site of stereoisomerism, the polymer may be atactic with respect to only one type of site if there are equal numbers of the possible configurations of that site arranged in a random distribution. 

The configurational sequence and stereosequence coincide in this particular case because there is only one site of stereoisomerism in each constitutional repeating unit (compare Definitions 2.1.3 and 2.1.4). 

Rule 2.1 The formula of a regular polymer ([1], Definition 2.15) with the constitutional repeating unit ([1], Definition 1.15) —R— is given as ... 

These definitions are clarified by considering a portion of a polymer chain such as XVII. Chain segment XVII has a total of 9 repeating units but only 8 dyads and 7 triads. There are 6 meso dyads and 2 racemic dyads (m) —, (r) —, There are 4 isotactic, 2 heterotactic, and 1 syndiotactic triads mm) = (mr) — j, (rr) — A. 

The physical significance of 2 in Equation (73) is somewhat harder to define. At first glance it appears to be the length of the repeating unit, about 0.25 nm for a vinyl polymer. We must remember, however, that the derivation of Equation (73) assumed that the coil was connected by completely flexible joints. Molecular segments are attached at definite bond angles, however, so an actual molecule has less flexibility than the model assumes. Any restriction on the flexibility of a joint will lead to an increase in the dimensions of the coil. The effect of fixed bond angles on the dimensions of the chain may be incorporated into the model as follows. 

In addition to the types of structure and chemical compositions, the properties of a polyrotaxane are determined by the amount of cyclic incorporated. To define such quantities, the min value was introduced [7, 12], Min, file threading efficiency, was defined for systems of Types 4-6, 9, and 10 as the average number of cyclic molecules per repeat unit [7, 12]. However, this definition seems a little awkward for polyrotaxanes of Types 7, 8, 11, and 12, because in these polyrotaxanes the linear component penetrates through the polymeric cyclic instead of the cyclic being threaded on to the linear species. To fit all the types in Table 1, we redefine min as the proportion of rotaxane repeat units in the polymer. 

It can be shown that the ratio v3lvg is equal to the ratio of polymer packing densities coefficients in the amorphous and crystalline states, KJKC at Tg, because, by definition, Ka = NA V /va and Kc - NA Vi/yC)where vj is the Van der Waals volume of the chain repeat unit. The calculated values of (ATc)g correlate with the characteristic chain parameter a/o, the relationship between them being expressed by a linear equation... 

Electron diffraction studies by Roche et al.96) of annealed fibres have revealed a fibre repeat of 1,24 nm which remains constant even when the processing conditions are varied. This value is in good agreement with the length of 1.247 nm of t-bisthiazole as measured by the C(8) to C(5 )separation by Wellmann et al. 97). This implies that the PBT chain has the fully extended conformation, since the fibre repeat consists of only one repeat unit. The electron diffraction patterns have also been interpreted in terms of monoclinic and triclinic unit cells but a more definite assignment may be possible with more highly ordered fibres. 

Because of the one-step polymerization procedure, hyperbranched polymers often contain not only D and T but also L repeating units. This can be expressed by DB, which is an important structural parameter of hyperbranched polymers. DB is estimated as the sum of the D and T units divided by the sum of all the three structural units, that is, D, T and L [41]. By definition, a linear polymer has no dendritic units and its DB is zero, while a perfect dendrimer has no linear units and its DB is thus unity. Frey has pointed out that DB statistically approaches 0.5 in the case of polymerization of AB2 monomers, provided that all the functional groups possess the same reactivity [42]. The structures of the hb-PYs could be analyzed by spectroscopic methods such as NMR and FTIR. The DB value of the phosphorous-containing polymer hb-F21, for example, was estimated to be 53% from its 31P NMR chemical shifts (Chart 1). 

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