Question

Under which combination of conditions does the glass transition of a polymer increase?

• A. Increase in molecular weight and increase in plasticizer content
• B. Increase in plasticizer content and decrease in cross-linking
• C. Increase in branching and decrease in inter-chain interactions
• D. Increase in chain length and decrease in plasticizer content

Hint:

Glass transition temperature increases with chain rigidity, molecular weight, and cross-linking, but decreases with plasticizers and flexible side groups.

Answer 1

The Correct Option is D

Step 1: Recall what glass transition temperature (T\(_g\)) is.
The glass transition temperature is the temperature at which a polymer transitions from a hard, glassy state to a soft, rubbery state. It depends on chain mobility and intermolecular interactions.

Step 2: Effect of chain length / molecular weight.
- As molecular weight (or chain length) increases, the freedom of chain end groups reduces, chain entanglements increase, and segmental mobility decreases. - This results in \(\uparrow T_g\).

Step 3: Effect of plasticizers.
- Plasticizers insert themselves between polymer chains, increasing free volume and enhancing chain mobility. - This lowers the T\(_g\). - Therefore, decreasing plasticizer content removes this mobility-enhancing effect, which leads to \(\uparrow T_g\).

Step 4: Evaluate options.
- (A) Increase in molecular weight and increase in plasticizer content → conflicting effects (plasticizer reduces T\(_g\)), so wrong.
- (B) Increase in plasticizer content and decrease in cross-linking → plasticizer reduces T\(_g\), so wrong.
- (C) Increase in branching and decrease in inter-chain interactions → branching often decreases packing efficiency and reduces T\(_g\), so wrong.
- (D) Increase in chain length and decrease in plasticizer content → both lead to increase in T\(_g\). Correct. Final Answer: \[ \boxed{\text{(D) Increase in chain length and decrease in plasticizer content}} \]