Discussion
Two miscible polymers A and B are blended in weight ratio of 30:70. If the glass transition temperature, Tg of polymer A is -50°C and that of polymer B is 100°C, then the Tg of the blend is
Answer: C
The Tg of the blend is about 37.5°C.
For a miscible blend the Fox equation weights the reciprocal glass transition temperatures (in kelvin) by mass fraction:
\[ \begin{aligned} \frac{1}{T_{g}} &= \frac{0.3}{223.15} + \frac{0.7}{373.15} \\ &= 0.0013444 + 0.0018759 = 0.0032203 \\ T_{g} &= 310.5\ \text{K} \approx 37.4^{\circ}\text{C} \end{aligned} \]
A simple linear rule of mixtures would give 0.3(-50) + 0.7(100) = 55°C, which is not offered. The other options do not follow from the Fox equation with these weight fractions.
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