Assume the deformation energy of a diatomic molecule can be expressed by the harmonic potential (shifted in coordinate and energy axes, in general).

The energy of the bond was measured for different interatomic distances:

U(r = 1 Anstrom)= 0.1 Ha; U(r 1.5 Anstrom)0.01; U(r 2.0 Anstrom) 5;

Determine the equilibrium distance and the force constant.

On solidification from a melt, the polymer polyethylene forms a semi-crystalline spherulite structure. (i) sketch an individual spherulite and label the amorphous and crystalline regions. (ii) draw a schematic to show the changes in specific volume with temperature during cooling from the melt, comparing it to the theoretical extremes of fully crystalline and fully amorphous (indicate tm and tg)