Polymerization repeating unit

Alternatively, the COD series can be described as a single series consisting of multiples of half a monomer unit, (C4H6)m = 54m for m 3. This indicates that the significant polymeric repeat unit contains only one double bond and is not necessarily an original monomer unit. 

The composition of a given macrocyclic mixture is controlled primarily by its polymeric repeat unit. 

Here ),p, the specific viscosity, is equal to the relative viscosity minus one. Staudinger designates C as the concentration of the solution in basal moles or the number of moles of the polymeric repeating unit per liter thus, for a starch acetate, it is the number of grams per liter divided by 288. K , is a constant particular to a definite series of homologues measured in a definite solvent, and M is the molecular weight. Ordinarily, this equation is employed for viscosity values extrapolated to zero concentration. Although the relationship is by no means exact " ... 

N (a) Number of non-hydrogen atoms in a molecule or a polymeric repeat unit. 

Nbb Total number of atoms in the backbone of a polymeric repeat unit. 

BBrot Number of rotational degrees of freedom in the backbone of a polymeric repeat unit. Njj Number of hydrogen atoms bonded to a given non-hydrogen atom. 

Connectivity indices, and therefore also correlations utilizing them, are not derived from first principles. They are obtained empirically, by considering the correlation of the topological features of molecules (polymeric repeat units in this work) with the properties of interest. Such empirical correlations serve two purposes. Firstly, they enable the prediction of many physical properties and are therefore practically useful. Secondly, they reveal trends and patterns in the physical properties, and the discovery of these trends and patterns can suggest directions for future efforts to provide a more rigorous understanding of the physical phenomena involved. 

Linear regression equations are usually used, in terms of a few indices most likely to be important for a given property. The general forms of the two types of correlation equations used for most of the structure-property relationships for polymers in this manuscript will be presented in Section 2.C. The total number and the types of the required connectivity indices are determined by the extent to which a property depends on certain types of interactions. It should be emphasized that the values of the connectivity indices are exactly determined by the structure of a molecule or a polymeric repeat unit. The only adjustable parameters are the coefficients multiplying the connectivity indices in the regression equations. 

As mentioned in a footnote to Table 2.1, the use of 8v=l/3 or 8v=4/9 for silicon atoms, as obtained from the definition of 8V (Equation 2.1), causes the overestimation of the effect of the extra inner shell of electrons in silicon atoms on certain physical properties. Whenever this happens, the replacement Si—>C (i.e., 8V=3 or 4) will be made in calculating the valence connectivity indices to correlate that property. For such properties, the differences between Si and C atoms will be taken into account by introducing an atomic correction term for the number of silicon atoms in the repeat unit. The alternative sets of °%v and values obtained for silicon-containing polymers by making the replacement Si—>C in the hydrogen-suppressed graph of the polymeric repeat unit, are listed in Table 2.3. 

As can be seen from equations 2.4-2.7, from Table 2.2, and most dramatically from figures 2.5-2.8, the % values are also extensive properties. They are sums over all vertices or edges of the hydrogen-suppressed graph. The number of terms in each summation increases in direct proportion to the size of the molecule or the polymeric repeat unit. This is the reason why the % values are proportional to N to a good approximation. They are, therefore, logical choices of topological descriptors to correlate with extensive properties. 

E. Shortest Path Across the Backbone of a Polymeric Repeat Unit... 

This situation also holds in assigning quantitative descriptors to polymeric repeat units for the purpose of predicting certain locally anisotropic physical properties. Some locally anisotropic properties of polymers are more sensitive to the total number NBB of atoms on the... 

The molecular weight per polymeric repeat unit is determined exactly from the structure of the polymeric repeat unit. The specific volume and the density are therefore both known if the molar volume is known. 

Ncyc and Nfused are examples of structural parameters describing the presence of certain general types of structural features in the polymeric repeat unit, independently of the specific types of atoms or groups of atoms which constitute these structural features. 

Nq is the total number of chlorine atoms in the polymeric repeat unit. 

N(backbone ester) s L 1C number of ester (-COO-) groups in the backbone of the polymeric repeat unit, which is defined as described in Section 2.D. For example, N one ester) 0 for poly(vinyl acetate) and for poly(methyl methacrylate), 1 for poly(e-caprolactone) and for poly(glycolic acid) (see Figure 2.4), and 2 for polyethylene terephthalate). 

Nether is the total number of ether (-0-) linkages in the polymeric repeat unit. For example,... 

This result is an example of a general difference between all corresponding pairs of extensive and intensive properties. The extensive property spans a much wider range, most of which incorporates the effects of the large differences between the sizes of polymeric repeat units. The intensive property, which reflects the true differences between the properties of the polymers independently of the sizes of their repeat units, spans a much narrower range and is hence predicted with somewhat lower accuracy and certainty than the extensive property. 

Thirteen structural parameters (xj to x ) will be defined and used in the correlation for Tg. These parameters were developed by a detailed analysis of the structure-property relationships determining the 320 experimental Tg values in the dataset. Their definitions make extensive use of concepts such as the backbone and the side groups of the polymeric repeat unit (Section 2.D) and the shortest path across the chain backbone (Section 2.E). 

Figure 6.10. Examples of application of rules for calculating the stmctural parameter x3. In (a)-(g), the quantity of interest is the contribution of the rigid backbone ring unit enclosed in the box to x3, as a result of its bonding environment. In (h) and (i), x3 is calculated for complete polymeric repeat units. The rules listed in the text for calculating x3 are completely general, and can be applied to any other structural unit of interest.

The predicted surface tensions of the remaining six polymers listed in Table 7.5 cannot be compared with experimental data due to the lack of such data. They do, however, follow trends which may be expected from basic physical considerations. They are predicted to increase with increasing fractions of (a) units of high cohesive energy density and (b) aromatic moieties in the hydrocarbon portions of the polymeric repeat units, and to decrease with increasing fraction of saturated aliphatic moieties. 

Table 8.2. Experimental refractive index n at room temperature, number of rotational degrees of freedom Nrot and correction index Nref used in the correlation for n, and the fitted value of n, for 183 polymers. The number N of vertices in the hydrogen-suppressed graph of the polymeric repeat unit, and the connectivity indices °%, °%v and 1%v, all of which are also used in the correlation equation for n, are listed in Table 2.2. 

Figure 11.2. Calculation of a rough estimate for the length of a polymeric repeat unit in its fully extended conformation, with poly(methyl methacrylate) as the example, (a) The repeat unit structure. The distance defined as lm is shown, (b) Use of simple trigonometry (i.e., the...

The correlations summarized above provide a general method to estimate the moduli, compliances and Poisson s ratio for glassy amorphous polymers, as functions of the structure of the polymeric repeat unit and the temperature of measurement. Independent correlations for B(T) and G(T) will now be discussed, and compared with the correlations presented above. 

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