Chapter II: Packing of Macromolecules and Polymer Density

II.1. Increments Method and Basic Physical Assumptions

After discussing briefly the chemical structure of polymers, let us pass to the volumetric representation of macromolecules, which is necessary for understanding the features of structure formation in polymers. These considerations will be based on the assumptions developed by A.I. Kitaigorodsky in organic crystal chemistry [75]. According to these assumptions, every atom is presented as a sphere with intermolecular radius R. Values of these radii are determined from the data of X-ray structural analysis of ideal crystals of organic substances. In this case, it is assumed that valency-unbonded atoms, entering into an intermolecular (but not chemical) interaction, contact each other along the borders of the spheres. This is schematically represented in Figure 3. Then, if two identical atoms are in contact, the intermolecular radius will be determined from the relation:

(II.1)

where l is the distance between mass centers of two identical valency-unbonded atoms, which, however, are capable of intermolecular physical interaction.

Figure 3: Schematic representation of intermolecular (Van-der-Waals) interaction of two atoms

According to the same assumptions, chemical interaction between two atoms always causes their compression, because the length of the chemical bond d _i is always shorter than the sum of two intermolecular radii:

(II.2)

This is clear from Figure 4, which schematically depicts two chemically bonded atoms. If the intermolecular radii R _i for all atoms participating in the repeat unit, and all lengths of chemical bonds between these atoms are known, their own (Van-der-Waals) volume...