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T3 · Kinetics / RatePolymer ChemistryGATE 2027 Syllabus (XE5)
Mayo-Lewis Copolymerization Equation
Relates the instantaneous copolymer composition ratio (d[M1]/d[M2]) to monomer feed ratio ([M1]/[M2]) and reactivity ratios (r1, r2).
Mathematical Canonical Relation
Plain Formula: d[M1]/d[M2] = ([M1]/[M2]) * (r1*[M1] + [M2]) / (r2*[M2] + [M1])
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feedRatio
Range: 0.1 – 10 ratio
r1
Range: 0.01 – 5 dimensionless
r2
Range: 0.01 – 5 dimensionless
Calculated Engineering Result:
Ratio 1.36 : 1 (57.6% M1)
Engineering Verification:Calculates instantaneous polymer chain composition.
When & Where to Apply
Use when synthesizing commercial copolymers (SAN, SBR, NBR, ABS) to predict copolymer composition drift and azeotropic feed composition.
Common Engineering Pitfalls
- Inverting monomer reactivity ratios r1 and r2
- Assuming feed composition remains constant during batch reactions without continuous feeding
Physical Assumptions & Validity Limits
- Terminal radical reactivity model applies
- Steady-state radical concentrations
- High molecular weight long-chain approximation
Variable Symbols, SI Units & Dimensional Specifications
| Symbol | Variable Meaning | SI Unit | Typical Industrial Range |
|---|---|---|---|
| d[M_1]/d[M_2] | Ratio of monomers in copolymer | molar ratio | — |
| [M_1]/[M_2] | Ratio of monomers in feed | molar ratio | 1.0 |
| r_1 | Reactivity ratio for Monomer 1 | dimensionless | 0.41 |
| r_2 | Reactivity ratio for Monomer 2 | dimensionless | 0.04 |
Worked Industrial Numerical Example: Styrene-Acrylonitrile (SAN) Instantaneous Copolymer Composition
Problem Statement:
Styrene (M1) and Acrylonitrile (M2) are copolymerized with a feed ratio [M1]/[M2] = 1.0 (50 mol% Styrene feed). Given r1 = 0.41 and r2 = 0.04, calculate the instantaneous copolymer composition ratio.
Step-by-Step Numerical Solution:
- Apply Mayo-Lewis: d[M1]/d[M2] = 1.0 * (0.41*1.0 + 1.0) / (0.04*1.0 + 1.0)
- Numerator = 1.41
- Denominator = 1.04
- Calculate ratio: 1.41 / 1.04 = 1.355
Final Answer: d[M1]/d[M2] = 1.355 (57.5 mol% Styrene, 42.5 mol% AN)
💡 Engineering Interpretation: The polymer is enriched in Styrene relative to feed, necessitating continuous monomer feeding in industrial SAN manufacturing to avoid compositional haze.
Authoritative Technical Reference & Source Provenance
Principles of Polymerization by George Odian (Wiley-Interscience, 2004), 4th Edition, Page 135-142.
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