Modelling the shape of a polymer molecule

If 0 = 0, atoms that are covalently bonded to Ci and to C4 come into close contact consequently the potential energy of that shape or conformation is high. However, if 0 = 180°, atom C4 is at a maximum distance from Ci, and none of the atoms bonded to C4 comes close to an atom bonded to Ci. Hence, the potential energy has a minimum value. This is referred to as the trans t) conformation of the bond C2—C3. Further sub-minima at ( = -f 60° are referred to as gauche (g ) and gauche (g ) conformations. In the rotational isomeric approximation each C—C bond is assumed to be in a gauche or a trans conformation, and the shape of the polymer chain is defined by these conformations. 

A chain of four carbon atoms has three rotational isomers, those of the bond C2—C3. A chain of five carbon atoms has 3 rotational isomers—the three possibilities of bond C2—C3 being combined with the three possibilities of bond C3—C4, Consequently, a polymer chain of n carbon atoms has rotational isomers. Only very few of these contain regularly repeating sets of bond rotations, such as the sW-trans conformation that occurs in the polyethylene crystal, and the repeating sequence tg tg tg. .. that occurs in the monoclinic crystalline form of isotactic polypropylene (Fig. 3.19). The overwhelming majority of conformations are irregular, and we now consider how to generate typical members of this set. 

In the liquid state the C—C bonds transform from one rotational isomeric state to another, and the lifetime of a rotational isomer is about 10 s. For the polyethylene chain the potential energy A of the gauche isomers is about 2kJmol higher than that of the trans isomers. The relative numbers n(g ) and n t) of bonds in the isomeric states can be calculated using 

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