Question

Which option(s) correctly match(es) the Polymer property with its appropriate Units? \[ \begin{array}{|c|c|} \hline \text{Polymer property} & \text{Units} \\ \hline P: \text{Hildebrand solubility parameter} & 1: \text{Pa} \\ Q: \text{Loss modulus} & 2: \text{J m}^{-3} \\ R: \text{Toughness} & 3: (\text{MPa})^{1/2} \\ S: \text{Flexural strength} & 4: \text{Kg m}^{-1}\text{s}^{-2} \\ \hline \end{array} \]

• A. P-2; Q-1; R-3; S-4
• B. P-2; Q-4; R-3; S-1
• C. P-3; Q-1; R-2; S-4
• D. P-3; Q-4; R-2; S-1

Hint:

Remember: - Solubility parameter → \((\text{MPa})^{1/2}\), - Moduli → Stress units (Pa), - Toughness → Energy/Volume (\(\text{J m}^{-3}\)), - Flexural strength → Stress (Pa).

Answer 1

The Correct Option is C, D

Step 1: Hildebrand solubility parameter.
- Defined as square root of cohesive energy density. - Units: \((\text{J m}^{-3})^{1/2} = (\text{MPa})^{1/2}\). \(\Rightarrow P-3\).

Step 2: Loss modulus.
- Storage and loss moduli are stress/strain quantities → units of stress. - Stress has SI unit \(\text{Pa} = \text{N m}^{-2} = \text{Kg m}^{-1} \text{s}^{-2}\). \(\Rightarrow Q-1\).

Step 3: Toughness.
- Defined as energy absorbed per unit volume (area under stress-strain curve). - Units: Energy/Volume = \(\text{J m}^{-3}\). \(\Rightarrow R-2\).

Step 4: Flexural strength.
- A stress quantity. - Units: \(\text{Pa} = \text{Kg m}^{-1} \text{s}^{-2}\). \(\Rightarrow S-4\). Final Mapping: \[ P-3, \; Q-1, \; R-2, \; S-4 \] Final Answer: \[ \boxed{\text{(C) P-3; Q-1; R-2; S-4}} \]