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 0.88 g/cm\(^3\). Find the degree of crystallinity (on weight basis) of this semi-crystalline sample. (Round off to two decimal places)

Hint:

The degree of crystallinity can be quickly estimated using density values since crystalline polymers are denser than amorphous ones.

Answer 1

Correct Answer: 0.52

Step 1: Formula for degree of crystallinity.
\[ X_c = \frac{\rho_s - \rho_a}{\rho_c - \rho_a} \times 100 \] where, \(\rho_s = \text{density of sample}, \; \rho_a = \text{density of amorphous polymer}, \; \rho_c = \text{density of crystalline polymer}\).

Step 2: Substitute values.
\[ X_c = \frac{0.88 - 0.77}{0.99 - 0.77} \times 100 \] \[ X_c = \frac{0.11}{0.22} \times 100 = 50.00% \] Final Answer: \[ \boxed{50.00%} \]