Question

Mechanical stress is applied on a polymer. Identify the correct match(es) between the statements (1, 2, 3, 4, 5) that describe the deformations and the regimes (P, Q, R). Regime and Statement 

Regime	Statement
P	Rubbery regime
Q	Region around glass transition temperature (\(T_g\))
R	Sample under deformed state

Additional Statements:

• 1. Stress-relaxation takes place and the excess free energy is dissipated
• 2. The motions of the molecules are long-range
• 3. Segmental motion of the molecules is important
• 4. The maximum relaxation time is strongly dependent on the molecular weight
• 5. The deformations are independent of the molecular weight and primarily depend on the local structure

• A. P-2; Q-5; R-1
• B. P-1; Q-5; R-1
• C. P-2; Q-3; R-4
• D. P-4; Q-3; R-1

Hint:

Remember the hierarchy: \textbf{around $T_g$} = segmental/local control (structure-driven, MW-independent); \textbf{rubbery} = chain-scale/long-range motions; \textbf{deformed sample} = time-dependent stress relaxation.

Answer 1

The Correct Option is A, D

Step 1: Understand each regime physically.
Rubbery regime (P): Above $T_g$, chains have high mobility; entire chain (long-range) motions such as reptation/conformational changes occur.
Region around $T_g$ (Q): Deformation is governed by segmental (local) motions; responses depend mainly on local chemical structure, and are only weakly dependent on molecular weight.
Deformed sample (R): After deformation, viscoelastic materials undergo stress relaxation, dissipating stored free energy with time.
Step 2: Match statements to regimes.
- P $\Rightarrow$ 2 (long-range molecular motions dominate in rubbery state).
- Q $\Rightarrow$ 5 (near $T_g$ the response is governed by local structure; MW has little effect).
- R $\Rightarrow$ 1 (stress relaxation and energy dissipation under deformation).
Step 3: Select the option.
The mapping $P\!\to\!2,\; Q\!\to\!5,\; R\!\to\!1$ corresponds to option (A). Final Answer: \[ \boxed{\text{(A) } P\!-\!2,\; Q\!-\!5,\; R\!-\!1} \]