Take the density of perfectly crystalline polyethylene as 1.000 g/cm³ and that of fully amorphous polyethylene as 0.850 g/cm³. Which value is closest to the crystallinity (mass fraction) of a sample with a density of 0.925 g/cm³?

Answer: C. About 54%

Assuming the volumes of the crystalline and amorphous regions are additive, the crystallinity by mass is Xc = ρc(ρs − ρa)/[ρs(ρc − ρa)] = 1.000 × (0.925 − 0.850)/[0.925 × (1.000 − 0.850)] = 0.075/0.13875 ≈ 0.54, about 54%. About 50% is the volume fraction obtained from (ρs − ρa)/(ρc − ρa), which differs from the mass fraction by the ratio of densities. About 46% is the mass fraction of the amorphous regions (1 − 0.54). The density method is a simple way to measure crystallinity; it can also be obtained from the heat of fusion by DSC or the ratio of crystalline peak areas in X-ray diffraction. The density of the perfect crystal can be calculated from the lattice parameters of the crystal structure.