IIT-JAM │ GATE │ CSIR-NET │ TIFR │ BARC │ Polymer Chemistry
Statement
A polymer's intrinsic viscosity ([η]) is related to its molecular weight (M) by constants (K and a) specific to the polymer-solvent system and temperature, allowing for polymer characterization by determining molecular weight from viscosity or vice versa, with 'a' indicating polymer shape (e.g., random coil, rigid rod).
[η] = K Mᵃ
where
[η] = Intrinsic viscosity (dL/g or cm³/g)
M = Viscosity-average molecular weight (Mᵥ)
K and a = Mark-Houwink constants (depend on polymer, solvent & temperature)
Logarithmic Form (Most Used in Numericals)
log[η] = log K + a log M
Physical Significance of Exponent ‘a’
| Value of ‘a’ | Chain Conformation | Example System | |
|---|---|---|---|
| 0 | Hard sphere (no solvent effect) | — | |
| 0.5 | Theta solvent (ideal chain, Flory condition) | PS in cyclohexane at 34°C | |
| 0.5 – 0.8 | Good solvent (random coil, expanded chain) | Most polymers in good solvents | |
| 0.8 | Theoretical maximum for random coil | — | |
| 1.0 – 1.8 | Rigid rod | DNA, poly(isocyanates), xanthan | |
| > 1.8 | Not possible for flexible chains | — |
Typical Values of K and a (Important for Exams)
| Polymer | Solvent | Temp (°C) | K × 10⁵ (dL/g) | a |
|---|---|---|---|---|
| Polystyrene | Toluene | 25 | 7.5 – 16 | 0.71 – 0.74 |
| Polystyrene | Cyclohexane (theta) | 34 | 84 | 0.50 |
| Poly(methyl methacrylate) | Acetone | 25 | 7.7 | 0.70 |
| Polyethylene | Decalin | 135 | 67 | 0.67 |
| DNA (double helix) | Aqueous buffer | 25 | — | 1.0 – 1.7 |
Applications (Repeatedly Asked)
- Determination of viscosity-average molecular weight Mᵥ from single [η] measurement
- Quick estimation of molecular weight in industry
- Study of polymer–solvent interaction (value of ‘a’)
- Theta solvent identification (a = 0.5)
- Conformational analysis (coil ↔ rod)
Limitations
- Valid only in a certain molecular weight range (usually 10⁴ – 10⁶)
- K and a are specific to polymer + solvent + temperature
- Not applicable for polyelectrolytes without salt
- Gives Mᵥ, not Mₙ or Mₓ (Mₙ ≤ Mᵥ ≤ Mₓ)
High-Yield Exam Questions
1. The exponent ‘a’ in Mark-Houwink equation is 0.5 for a polymer in
Answer: Theta solvent
2. For a rigid rod-like polymer, the value of ‘a’ lies in the range
Answer: 1.0 – 1.8 (commonly 1.7–1.8)
3. If [η] = 1.2 dL/g for a polymer sample and K = 1.0 × 10⁻⁴ dL/g, a = 0.7, then Mᵥ ≈
(Calculation: log 1.2 = log(10⁻⁴) + 0.7 log M → M ≈ 1.58 × 10⁵ g/mol)
(Calculation: log 1.2 = log(10⁻⁴) + 0.7 log M → M ≈ 1.58 × 10⁵ g/mol)
Answer: ≈ 1.6 × 10⁵ g/mol
4. Assertion: In a good solvent, the intrinsic viscosity of a polymer increases with molecular weight more rapidly than in a theta solvent.
Reason: In good solvent, the exponent ‘a’ > 0.5.
Reason: In good solvent, the exponent ‘a’ > 0.5.
Answer: Both A and R are true and R is correct explanation of A
5. The molecular weight obtained from Mark-Houwink equation is
Answer: Viscosity-average molecular weight (Mᵥ)
MPSET 2024
6. The intrinsic viscosity (η) of a polymer solution is related with molecular weight (M) of the polymer (k and a are constants):
A. η = kMa
B. η = kM1/a
C. η = 1/akM
D. η = kaM
6. The intrinsic viscosity (η) of a polymer solution is related with molecular weight (M) of the polymer (k and a are constants):
A. η = kMa
B. η = kM1/a
C. η = 1/akM
D. η = kaM
Answer: η = kMa