Polymer molecule, number structural units

Polyester (Section 20 17) A polymer in which individual structural units are joined by ester bonds Polyether (Section 16 4) A molecule that contains many ether linkages Polyethers occur naturally in a number of antibi otic substances... 

The reaction is complete within a few minutes at room temperature, and the unmistakable decrease in viscosity may be observed even without resort to quantitative measurement. It is apparent therefore that the polymer contains a minor proportion of head-to-head linkages. The number of such interunit linkages should equal the increase in the number of molecules brought about by the reagent. The increase in the number of molecules per gram mole (44 g.) of structural units is given by... 

The symbol x is used here and in following pages in a somewhat different sense than in earlier portions of the book, where it represents the number of structural units. The segment employed in mixing problems often is conveniently defined as that portion of a polymer molecule requiring the same space as a molecule of solvent it is unrelated to the size of the structural unit, which is of no interest here. The present x, like the previous one, defines the size of a polymer species, however. 

For some purposes, as for example in the treatment of crystallization, it is more convenient to deal with the chemical potential per mole of structural units instead of per mole of polymer, as expressed in the formulas given above. Dividing Eq. (32) by the number of units per polymer molecule, which is xYi/Yu where Vi and v are the molar volumes of the solvent and of the. structural unit, respectively, we obtain for the chemical potential difference per unit... 

Number of structural units in the given polymer molecule (Chaps. I through XII), or its number of segments (Chap. XII et seq,). 

A nonlinear molecule of N atoms with 3N degrees of freedom possesses 3N — 6 normal vibrational modes, which not all are active. The prediction of the number of (absorption or emission) bands to be observed in the IR spectrum of a molecule on the basis of its molecular structure, and hence symmetry, is the domain of group theory [82]. Polymer molecules contain a very high number of atoms, yet their IR spectra are relatively simple. This can be explained by the fact that the polymer consists of identical monomeric units (except for the end-groups). 

The main statistical characteristic of the chemical structure of a heteropolymer among those pertaining to the first type is the distribution of molecules f( h, 12) for numbers l and h of their constituent monomeric units Mi and M2. In dealing with a high-molecular weight polymer, these numbers may be taken as continuous variables, uniquely specifying chemical size l=l + h and composition f = li/l of a macromolecule. Under such a consideration, it is more convenient instead of function /(Zi, l2) to use the equivalent function of Size-Composition Distribution (SCD) f(l, < ) This is possible to represent... 

Since N x is synonymous with the mole or number fraction of molecules in the polymer mixture that are x-mers (i.e., that contain x structural units), then... 

The quantity l/ — p) is called the number-average degree of polymerization, x , which represents the initial number of structural units present in the monomer relative to the total number of molecules, both monomer and polymer chains, present at any time t ... 

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. 

Let us first address linear polymers, whose topological structure is the simplest. Depending on the number m of types of monomeric units, homopolymers (m = 1) and copolymers (m > 1) are distinguished. In the most trivial case, homopolymers molecules are identified only by number l of constituent monomeric units, whereas the composition of a copolymer macromolecule is characterized by vector 1, whose components are... 

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