Polymers

🟢 Lite — Quick Review (1h–1d)

Rapid summary of polymer chemistry for quick revision.

Classification of Polymers:

1. Addition polymers — formed by addition of monomer units without elimination of any byproduct. Examples: polyethylene, polypropylene, polystyrene, PVC, PTFE (Teflon), PMMA.

2. Condensation polymers — formed by elimination of small molecules (H₂O, HCl, NH₃, etc.) between monomer units. Examples: nylon-6,6, terylene (PET), Bakelite, melamine-formaldehyde resin.

3. Copolymers — polymers formed from two or more different monomers. Examples: ABS (acrylonitrile + butadiene + styrene), SBR (styrene + butadiene rubber).

Key Monomers and Their Polymers:

Polymer	Monomer	Structure
Polyethylene (PE)	Ethylene	—(CH₂—CH₂)—ₙ
Polyvinyl chloride (PVC)	Vinyl chloride	—(CH₂—CHCl)—ₙ
Polystyrene (PS)	Styrene	—(CH₂—CH(C₆H₅))—ₙ
Teflon (PTFE)	Tetrafluoroethylene	—(CF₂—CF₂)—ₙ
Nylon-6,6	Hexamethylene diamine + adipic acid	—[NH(CH₂)₆NHCO(CH₂)₄CO]—ₙ
Terylene (PET)	Ethylene glycol + terephthalic acid	—[OCH₂CH₂OOC(C₆H₄)CO]—ₙ

⚡ Exam tip: Remember Teflon uses tetrafluoroethylene, not PTFE as a monomer — PTFE is the polymer itself. The monomer of natural rubber is isoprene (2-methyl-1,3-butadiene).

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding of polymer chemistry.

Chain-Growth Polymerisation (Free Radical Mechanism):

Initiation: $R• + M → RM•$ (where M = monomer, R• = initiator radical) Propagation: $RM• + M → RM_2• → RM_3• → …$ Termination: $RM_x• + RM_y• → RM_{x+y}R$ (combination) or $→ RM_x + RM_y$ (disproportionation)

Initiators used:

• Thermal decomposition: benzoyl peroxide (BPO), $C₆H₅COO—OCC₆H₅ → 2C₆H₅COO• →$ radicals
• Redox: H₂O₂ + Fe²⁺ → OH• + OH⁻
• Azo compounds: AIBN (azobisisobutyronitrile), generates CN radicals at 60–70°C

The rate of polymerisation: $R_p = k_p [M] \sqrt{\dfrac{k_d[I]}{2k_t}}$ Number-average degree of polymerisation: $\bar{X}_n = \dfrac{k_p[M]}{2f k_d[I]^{1/2}} \times \dfrac{[M]}{[I]^{1/2}}$

Step-Growth Polymerisation:

Monomers have two or more functional groups (e.g., —OH, —COOH, —NH₂). Every monomer can react with every other. Chain length grows slowly at first, then rapidly near complete conversion. Carothers’ equation: $\bar{X}_n = \dfrac{1}{1 - p}$ where p = extent of reaction (fraction of functional groups that have reacted). For p = 0.99, $\bar{X}_n = 100$.

Mechanism of Nylon-6,6 Synthesis: Hexamethylenediamine (H₂N(CH₂)₆NH₂) + adipic acid (HOOC(CH₂)₄COOH) → nylon-6,6 + H₂O

The reaction is an interfacial polymerisation: hexamethylenediamine in water is layered over adipic acid in an organic solvent. Polymer forms at the interface and can be drawn out as a continuous fibre.

HOOC—(CH₂)₄—COOH + H₂N—(CH₂)₆—NH₂ → HOOC—(CH₂)₄—CONH—(CH₂)₆—NH₂ + H₂O Repeating: —[OC—(CH₂)₄—CO—NH—(CH₂)₆—NH]—ₙ

Mechanism of Terylene (PET) Synthesis: Ethylene glycol + terephthalic acid → PET + H₂O Terephthalic acid: HOOC—C₆H₄—COOH (para isomer, pta) The ester linkage: —O—C(=O)—C₆H₄—C(=O)—O—

Bakelite Formation: Phenol + formaldehyde → Bakelite (phenolic resin) + H₂O Mechanism: phenol is electrophilically substituted at ortho/para positions by HCHO in presence of base (NaOH) or acid (HCl). Methylol intermediates condense to form methylene bridges (—CH₂—) linking phenol rings. The resin is a cross-linked thermosetting polymer — it cannot be remelted on heating.

Vulcanisation of Natural Rubber: Natural rubber is cis-1,4-polyisoprene (from Hevea brasiliensis). It has random coiled chains with weak van der Waals forces between them, making it sticky and brittle at low temperatures, soft and tacky at high temperatures. Vulcanisation involves heating with sulphur (2–5% by mass). Sulphur forms cross-links (—S—S— or —S—) between polymer chains at the allylic positions (C=C double bonds in the isoprene unit). The cross-linked rubber has improved tensile strength, elasticity, and thermal stability. Vulcanised rubber is a thermosetting elastomer.

Natural Polymers — Key Details:

Polymer	Monomer/Unit	Linkage	Function
Cellulose	β-D-glucose	β-1,4-glycosidic	Plant cell walls
Starch (amylose)	α-D-glucose	α-1,4-glycosidic	Energy storage in plants
Starch (amylopectin)	α-D-glucose	α-1,4 + α-1,6	Branched storage
Protein	α-amino acids	Peptide (amide) bonds	Structural, enzymatic
Nucleic acids	Nucleotides	Phosphodiester bonds	Genetic information
Rubber	Isoprene (2-methyl-1,3-butadiene)	Cis-1,4-polymerisation	Elastic material

Cellulose and starch both have formula (C₆H₁₀O₅)ₙ but differ in glycosidic linkage (β vs α), giving them very different properties. Humans lack the enzyme cellulase (which cleaves β-1,4 linkages) and cannot digest cellulose as a food source. Starch (α-linkages) is digestible.

Molecular Mass Determination:

1. Number-average molecular mass ($M_n$): $M_n = \dfrac{\sum N_i M_i}{\sum N_i}$

   • Measured by: osmometry (osmotic pressure)
   • $\pi = CRT/M_n$ where π = osmotic pressure

2. Weight-average molecular mass ($M_w$): $M_w = \dfrac{\sum N_i M_i^2}{\sum N_i M_i}$

   • Measured by: light scattering, sedimentation (ultracentrifuge)

3. Polydispersity Index (PDI): $PDI = \dfrac{M_w}{M_n}$

   • For monodisperse polymer, PDI = 1
   • Step-growth polymers typically have PDI ≈ 1.5–2
   • Chain-growth with termination by combination, PDI ≈ 1.5
   • Chain-growth with termination by disproportionation, PDI ≈ 2

4. Viscosity method: $[\eta] = K M^\alpha$ (Mark-Houwink equation), where K and α are polymer-solvent specific constants determined experimentally.

JEE Advanced Problem-Solving: Q: Calculate the degree of polymerisation of polyethylene with $M_n = 28,000$. A: The repeating unit is —CH₂—CH₂— with molecular weight = 28 g/mol. $\bar{X}_n = 28000/28 = 1000$

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🔴 Extended — Deep Study (3mo+)

Comprehensive theory for complete mastery of polymer chemistry.

Free Radical Polymerisation — Detailed Kinetics:

Initiation step: $I → 2R•$ (rate = k_d[I]) $R• + M → RM•$ (fast, rate = k_i[R•][M]$)

Propagation: $RM• + M → RM_2•$ (rate = k_p[RM•][M]) $RM_2• + M → RM_3•$ (generally written as $P• + M → P•$ with rate = k_p[P•][M])

Termination: $P• + P• → P_2$ (combination, rate = k_t_c[P•]²) $P• + P• → P + P’$ (disproportionation, rate = k_t_d[P•]²)

Overall rate of polymerisation: $R_p = -\dfrac{d[M]}{dt} = k_p[M][P•]$

Using steady-state approximation for free radical concentration: $\dfrac{d[P•]}{dt} = 2f k_d[I] - 2k_t[P•]² = 0$ $[P•] = \sqrt{\dfrac{f k_d[I]}{k_t}}$

Therefore: $R_p = k_p [M] \sqrt{\dfrac{f k_d[I]}{k_t}}$

Since rate of monomer consumption = 2f k_d[I] at steady state, and termination consumes two radicals: $R_t = 2k_t[P•]² = 2k_t \cdot \dfrac{f k_d[I]}{k_t} = 2f k_d[I]$

This gives the kinetic chain length: $\nu = R_p/R_t = \dfrac{k_p[M]}{2k_t^{1/2}} \cdot \dfrac{1}{\sqrt{f k_d[I]}}$

The number-average degree of polymerisation ($\bar{X}_n$) depends on termination mechanism:

• Termination by combination: $\bar{X}_n = \dfrac{\nu}{1}$
• Termination by disproportionation: $\bar{X}_n = \dfrac{\nu}{2}$

Copolymerisation — Reactivity Ratios:

Copolymer composition is determined by reactivity ratios r₁ and r₂: $r_1 = \dfrac{k_{11}}{k_{12}}$, $r_2 = \dfrac{k_{22}}{k_{21}}$

where k₁₁ = rate constant for M₁ adding to a chain ending in M₁ k₁₂ = rate constant for M₂ adding to a chain ending in M₁ (and similarly for r₂)

For ideal copolymerisation (r₁·r₂ = 1): monomers add in proportion to their concentrations but not alternatingly. For alternating copolymerisation (r₁ → 0 and r₂ → 0): M₁ and M₂ alternate strictly. For block copolymerisation (r₁ >> 1 and r₂ >> 1): long blocks of each monomer form.

Example: Styrene (M₁) and butadiene (M₂) in SBR rubber: r₁(styrene) ≈ 0.64, r₂(butadiene) ≈ 1.38 (SBR has roughly alternating tendency)

Step-Growth — Carothers Equation in Detail:

For a condensation polymerisation with A—A + B—B type monomers:

• Initially: N₀ bifunctional molecules
• After extent of reaction p: N = N₀(1 − p) (number of molecules remaining)
• Number of structural units = N₀/2 (since each structural unit combines 2 molecules)
• $\bar{X}_n = \dfrac{N_0}{N} = \dfrac{1}{1-p}$

For unequal functional groups (A—A + B—B where [A] > [B]): $p = \dfrac{[B]_0 - [B]}{[B]_0}$, $\bar{X}_n = \dfrac{1 + r}{1 + r - 2rp}$ where r = [A]₀/[B]₀ ≥ 1

Biodegradable Polymers:

Polymer	Source	Biodegradation mechanism
Polylactic acid (PLA)	Corn starch, sugarcane	Hydrolysis of ester bond; enzymatic cleavage
Polyhydroxyalkanoates (PHA)	Bacterial fermentation	Intracellular depolymerase enzymes
Polycaprolactone (PCL)	Petrochemical	Hydrolytic + enzymatic degradation
Cellulose acetate	Cellulose + acetic anhydride	Enzymatic deacetylation, then cellulose degradation
Starch-based plastics	Thermoplastic starch	Water absorption, then microbial attack

PLA is used in medical sutures and food packaging. Its hydrolysis produces lactic acid, which is metabolised by the body. The degradation rate depends on crystallinity: amorphous regions degrade faster.

Structure-Property Relationships:

Glass transition temperature (Tg) is the temperature at which amorphous polymers change from glassy to rubbery state:

• Above Tg: polymer is rubbery (flexible, ductile)
• Below Tg: polymer is glassy (hard, brittle)

For polyethylenes:

• LDPE (low density): highly branched, irregular packing → Tg ≈ −120°C, soft and flexible
• HDPE (high density): linear chains, close packing → Tg ≈ −120°C but higher melting point
• LLDPE (linear low density): short chain branches → intermediate properties

Polystyrene has Tg ≈ 100°C — it is glassy at room temperature. Adding 5–10% oil reduces Tg, making it impact-resistant (HIPS — high impact polystyrene).

PTFE (Teflon) has an exceptionally low friction coefficient due to CF₂ groups rotating freely. The polymer chains adopt a helical conformation. Used in non-stick cookware and chemical liners.

Melamine-Formaldehyde Resin: Melamine (C₃N₆H₆) has three —NH₂ groups. Reaction with formaldehyde at pH 8.5–10 forms methylolmelamine intermediates, which condense to form a cross-linked thermosetting resin. It is fire-resistant (does not melt, forms carbonaceous char), scratch-resistant, and used in kitchenware (Melamine brand). The resin contains —N(CH₂OH)— bridges between melamine rings.

Previous Year JEE Advanced Patterns:

Year	Topic Tested
2023	Nylon-6,6 synthesis, condensation polymer
2022	Polyethylene degree of polymerisation
2021	Vulcanisation mechanism, natural rubber
2020	Copolymerisation, reactivity ratios
2019	Molecular mass by osmotic pressure
2018	PTFE structure, Teflon polymerisation
2017	Bakelite formation, cross-linking
2016	Cellulose vs starch, glycosidic linkages

Numerical Problem Examples:

Q1. The osmotic pressure of a polymer solution is found to be 2.4 × 10⁻³ atm at 300 K. The concentration is 1 g/L. Calculate M_n. π = CRT/M → M = CRT/π = (0.0821 × 300 × 1)/(2.4 × 10⁻³ × 1) = 10262 g/mol

Q2. A polymer has M_w = 3.0 × 10⁵ and M_n = 1.5 × 10⁵. Calculate PDI and comment on homogeneity. PDI = 3.0 × 10⁵ / 1.5 × 10⁵ = 2.0. The polymer is moderately polydisperse (chain-growth polymerisation with disproportionation termination).

Q3. For a condensation polymerisation with p = 0.998, calculate X_n. X_n = 1/(1 − p) = 1/(1 − 0.998) = 1/0.002 = 500. Even a small increase in p (from 0.99 to 0.998) doubles the degree of polymerisation.

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