Question

The density of an amorphous polymer is \(0.77 \, {g/cm}^3\) and that of its crystalline counterpart is \(0.99 \, {g/cm}^3\). The density of a semi-crystalline sample of this polymer is found to be \(0.88 \, {g/cm}^3\).
The degree of crystallinity (on weight basis) of this semi-crystalline sample is ............ {(Round off to two decimal places)}

Hint:

Always use the extended crystallinity formula for weight basis, which includes the ratio \(\frac{\rho_c}{\rho}\) — this corrects for the actual mass fractions.

Answer 1

We use the formula based on the rule of mixtures for semi-crystalline polymers: \[ X = \frac{\rho - \rho_a}{\rho_c - \rho_a} \cdot \frac{\rho_c}{\rho} \] where
\(\rho = 0.88\) g/cm³ (sample density),
\(\rho_a = 0.77\) g/cm³ (amorphous),
\(\rho_c = 0.99\) g/cm³ (crystalline).
Substituting, \[ X = \frac{0.88 - 0.77}{0.99 - 0.77} \cdot \frac{0.99}{0.88} = \frac{0.11}{0.22} \cdot \frac{0.99}{0.88} = 0.5 \cdot 1.125 = 0.5625 \approx 0.56 \]