Polymers: structure and properties

Polymerisation, molecular weight and degree of polymerisation, chain architecture and tacticity, crystallinity, Tg and Tm, thermoplastics, thermosets and elastomers, and viscoelastic behaviour.

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Why it matters

Polymers now replace metals in car bumpers, fuel tanks, gears, pipes, bearings and electrical housings because they are light, corrosion-proof, insulating and cheap to mould into complex shapes. They also behave very differently from metals — their stiffness falls sharply with temperature and they creep at room temperature — so a production engineer must understand what controls their properties to choose a grade and a process (injection moulding, extrusion, compression moulding) correctly.

Key ideas

Chains and polymerisation. A polymer is a long chain of covalently bonded repeat units (mers) built from small monomers.

  • Addition (chain-growth) polymerisation: monomers with a C=C double bond add one after another with no by-product (polyethylene, PVC, polypropylene, polystyrene, PMMA).
  • Condensation (step-growth) polymerisation: two different monomers react and release a small molecule such as water (nylon 6,6, PET, phenolics, polyesters).
  • Degree of polymerisation (DP): the average number of repeat units per chain. Properties such as strength and melt viscosity rise with chain length.
  • A real polymer contains chains of many lengths, described by the number-average (Mn) and weight-average (Mw) molecular weights; Mw ≥ Mn, and Mw/Mn is the polydispersity index (PDI).

Molecular architecture.

  • Linear: long chains held together by weak secondary (van der Waals, hydrogen) bonds; e.g. HDPE, nylon. Can pack and crystallise.
  • Branched: side branches prevent close packing, lowering density and crystallinity (LDPE vs HDPE).
  • Cross-linked: adjacent chains joined by covalent bonds at a few points (vulcanised rubber, where sulphur cross-links natural rubber).
  • Network: three-dimensional covalent network (epoxy, phenol-formaldehyde, melamine).
  • Configuration (tacticity): isotactic (side groups all on one side), syndiotactic (alternating) or atactic (random). Isotactic and syndiotactic chains can crystallise; atactic ones (e.g. ordinary polystyrene) are amorphous.
  • Copolymers: random, alternating, block or graft combinations of two monomers (ABS, SBR).

Crystallinity. Polymers are never fully crystalline; regions of folded-chain crystallites (spherulites) sit in an amorphous matrix. Higher crystallinity raises density, stiffness, strength, chemical resistance and melting point, and lowers transparency and impact toughness. It increases with linear, regular, tactic chains and slow cooling.

Thermal transitions.

  • Glass transition temperature Tg: below Tg the amorphous regions are rigid and glassy; above Tg chain segments can rotate and the polymer becomes leathery or rubbery. Stiffness can fall by a factor of 1000 across Tg. Glassy plastics (PS, PMMA, PC) are used below Tg; elastomers are used well above Tg.
  • Melting temperature Tm: only crystalline regions melt; Tm > Tg (roughly Tg ≈ 0.5–0.8 Tm in kelvin).

Three classes.

  • Thermoplastics: linear or branched; soften on heating and harden on cooling reversibly, so they can be remoulded and recycled. Processed by injection moulding, extrusion, blow moulding, thermoforming. PE, PP, PVC, PS, PMMA, nylon, PC, PET, PTFE.
  • Thermosets: cure irreversibly into a network on heating or with a hardener; they char rather than melt, are harder, stiffer, more dimensionally stable and heat-resistant, and cannot be recycled by remelting. Compression or transfer moulding. Epoxy, phenolics (Bakelite), polyester resins, melamine, urea-formaldehyde.
  • Elastomers: lightly cross-linked, used above Tg; large recoverable elastic strains (hundreds of percent) as coiled chains uncoil and recoil. Natural rubber, SBR, neoprene, silicone, nitrile.

Mechanical behaviour. Polymers are viscoelastic: response depends on time, temperature and strain rate. They creep and relax stress at room temperature; faster loading or lower temperature makes them stiffer and more brittle. Moduli are low (about 0.2–4 GPa for unfilled plastics against 200 GPa for steel), so designers use ribs, thicker sections or fibre reinforcement. Additives include fillers, plasticisers (lower Tg, make PVC flexible), stabilisers (UV and heat), flame retardants and colorants.

Degradation. Polymers swell or dissolve in some solvents, degrade under UV light and oxidation, and absorb moisture (nylon), which changes dimensions and properties.

Formulas

DP = Mn / m DP = number-average degree of polymerisation; Mn = number-average molecular weight (g/mol); m = molar mass of the repeat unit (g/mol).

Mn = Σ xi·Mi and Mw = Σ wi·Mi xi = number fraction and wi = weight fraction of chains in size class i; Mi = mean molar mass of class i (g/mol); wi = xi·Mi / Mn.

PDI = Mw / Mn Polydispersity index (dimensionless, ≥ 1).

% crystallinity = ρc·(ρs − ρa) / [ρs·(ρc − ρa)] × 100 ρs = density of the sample; ρc = density of fully crystalline polymer; ρa = density of fully amorphous polymer (all in kg/m³ or g/cm³; ρc and ρa from a data book).

Worked examples

Example 1 (standard): degree of polymerisation of PVC. Given: PVC repeat unit C₂H₃Cl; atomic masses C = 12.01, H = 1.008, Cl = 35.45 g/mol; Mn = 31 250 g/mol.

  1. m = 2 × 12.01 + 3 × 1.008 + 35.45 = 62.5 g/mol.
  2. DP = 31 250 / 62.5 = 500 repeat units.

Example 2 (GATE level): average molecular weights and crystallinity. (a) A polymer has three size classes: number fractions 0.2, 0.5, 0.3 with mean molar masses 10 000, 30 000 and 50 000 g/mol.

  1. Mn = 0.2 × 10 000 + 0.5 × 30 000 + 0.3 × 50 000 = 32 000 g/mol.
  2. Weight fractions wi = xi·Mi/Mn: 2000/32 000 = 0.0625; 15 000/32 000 = 0.469; 15 000/32 000 = 0.469.
  3. Mw = 0.0625 × 10 000 + 0.469 × 30 000 + 0.469 × 50 000 = 38 125 g/mol.
  4. PDI = 38 125 / 32 000 = 1.19. (b) A polyethylene sample has density 0.925 g/cm³; take ρc = 0.998 and ρa = 0.870 g/cm³.
  5. % crystallinity = 0.998 × (0.925 − 0.870) / [0.925 × (0.998 − 0.870)] × 100.
  6. = 0.05489 / 0.11840 × 100 = 46.4 % (a typical LDPE).

Common mistakes

  • Assuming polymers have a single sharp melting point; amorphous polymers only soften through Tg, and semicrystalline ones melt over a range.
  • Thinking thermosets can be remelted and recycled like thermoplastics.
  • Confusing Mn and Mw, or using weight fractions in the Mn formula.
  • Treating polymer modulus as constant; it depends on temperature, time and loading rate.
  • Believing more cross-linking always improves a rubber; heavy cross-linking turns it into a hard, brittle thermoset (ebonite).
  • Using the monomer formula instead of the repeat-unit formula for condensation polymers (a water molecule is lost).

For GATE PI

Expect one-mark questions classifying common polymers as thermoplastic, thermoset or elastomer, matching polymers with processes and applications, the meaning of Tg, cross-linking and tacticity, and addition versus condensation polymerisation. Numericals ask for degree of polymerisation, Mn and Mw from a distribution, PDI, or percent crystallinity from densities.

Quick check

  1. Which is always larger, Mn or Mw?
  2. Classify: Bakelite, nylon 6,6, natural rubber.
  3. What happens to a glassy polymer heated above Tg?
  4. Polyethylene has Mn = 140 000 g/mol and a repeat unit of 28.05 g/mol. Find DP.
  5. Why does LDPE have a lower density than HDPE?

Answers: 1. Mw (equal only if all chains are the same length); 2. Thermoset, thermoplastic, elastomer; 3. It becomes rubbery/leathery and its stiffness drops sharply; 4. About 4990; 5. Branching prevents close packing and lowers crystallinity.

Interview questions

All Engineering Materials interview questions

Try answering each one aloud before you open it.

  1. 1.What is a polymer, and how is it different from a monomer?Concept

    A polymer is a large molecule composed of repeating structural units called monomers, which are covalently bonded together. Monomers are small, simple molecules that can join together to form polymers. The key difference is that monomers are the building blocks, while polymers are the complex structures formed from these blocks.

  2. 2.Explain the difference between thermoplastic and thermosetting polymers.Concept

    Thermoplastic polymers can be melted and reshaped multiple times without undergoing any chemical change. They become soft when heated and harden upon cooling. Thermosetting polymers, on the other hand, undergo a chemical change when heated, forming a rigid structure that cannot be remelted or reshaped. Once set, they cannot be reformed.

  3. 3.What is the glass transition temperature (Tg) in polymers, and why is it important?Concept

    Tg is the temperature range over which the amorphous regions of a polymer change from a rigid, glassy state to a soft, rubbery or leathery state as chain segments gain enough energy to rotate. Stiffness can drop by about three orders of magnitude across Tg, so it sets the service limits: glassy plastics such as polystyrene, PMMA and polycarbonate must be used below their Tg, while elastomers are used well above theirs (natural rubber has Tg near −70 °C). Tg is lowered by plasticisers and raised by stiff chains, bulky side groups and cross-linking.

  4. 4.Why are polymers used in the automotive industry?Application

    Polymers are used in the automotive industry because they are lightweight, which helps improve fuel efficiency. They also offer good resistance to corrosion, can be easily molded into complex shapes, and provide excellent insulation properties. Additionally, polymers can be engineered to have specific properties, such as impact resistance and flexibility, which are beneficial in automotive applications.

  5. 5.What happens to a polymer when it is exposed to UV radiation for an extended period?Application

    When a polymer is exposed to UV radiation for an extended period, it can undergo degradation. This process involves the breaking of chemical bonds within the polymer, leading to changes in its physical properties such as discoloration, loss of strength, and brittleness. UV stabilizers are often added to polymers to mitigate these effects.

  6. 6.How does cross-linking affect the properties of a polymer?Application

    Cross-linking in polymers involves the formation of chemical bonds between different polymer chains. This process increases the rigidity and thermal stability of the polymer, making it less soluble and more resistant to deformation. Cross-linked polymers are typically stronger and more durable than their non-cross-linked counterparts.

  7. 7.Why is polyethylene commonly used for packaging materials?Application

    Polyethylene is commonly used for packaging materials because it is lightweight, flexible, and has good moisture resistance. It is also relatively inexpensive and can be easily processed into various forms such as films, bags, and containers. Its chemical inertness makes it suitable for food packaging as it does not react with the contents.

  8. 8.Calculate the number of repeating units in a polymer chain with a molecular weight of 100,000 g/mol, given that the molecular weight of the monomer is 100 g/mol.Numerical

    To calculate the number of repeating units in the polymer chain, divide the molecular weight of the polymer by the molecular weight of the monomer: Number of repeating units = 100,000 g/mol / 100 g/mol = 1,000.

  9. 9.Explain how the tacticity of a polymer affects its properties.Concept

    Tacticity refers to the arrangement of side groups along the polymer chain. It affects the polymer's crystallinity, melting temperature, and mechanical properties. Isotactic polymers, where side groups are on the same side, tend to be more crystalline and have higher melting points. Atactic polymers, with random side group arrangement, are usually amorphous and have lower melting points.

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