Polymers Notes FE Sem 1 Applied Chemistry | Mumbai University

Polymers such as polyethylene, PVC, nylon and polycarbonate are now among the most widely used engineering materials. This module builds the basic ideas of macromolecular science: what polymers are, how their chains are bonded, and how they are classified. It then covers the properties that decide how a polymer is used, starting with molecular weight averages and crystallinity, followed by glass transition temperature and the mechanical, electrical and optical properties. Molecular weight numericals and Tg are favourite MU exam topics.

Summary

Macromolecular science studies very large molecules. A polymer is a high molecular weight compound (macromolecule) formed by the repeated linking of many small units called monomers through covalent bonds; the process is polymerisation. The number of repeating units in a chain is the degree of polymerisation (DP), so molecular weight of polymer = DP x molecular weight of the repeating unit. For a monomer to polymerise it must have a functionality (number of bonding sites) of at least two; bifunctional monomers give linear chains and tri- or polyfunctional monomers give branched or cross-linked networks.

Chemical bonding in polymers is of two kinds. Atoms along the chain (backbone) are held by strong primary covalent bonds, and cross-linked polymers also have covalent bonds between chains. Separate chains are held by weaker secondary forces: van der Waals (dispersion) forces, dipole-dipole forces (as in PVC because of polar C-Cl) and hydrogen bonds (as in nylons and cellulose). The strength of these secondary forces strongly influences melting point, Tg, crystallinity, strength and solubility.

Polymers are classified (i) by origin: natural (cellulose, starch, natural rubber, proteins), semi-synthetic (cellulose acetate, vulcanised rubber) and synthetic (PE, PVC, nylon); (ii) by structure: linear (HDPE), branched (LDPE) and cross-linked or network (bakelite); (iii) by monomer: homopolymers (one monomer, e.g. PVC) and copolymers (two or more, e.g. Buna-S), which may be random, alternating, block or graft; (iv) by mode of polymerisation: addition or chain-growth (PE, PVC, PS) and condensation or step-growth (nylon 6,6, polyester, bakelite), the latter eliminating small molecules such as water; (v) by thermal behaviour: thermoplastics, which soften on heating and can be remoulded (PE, PVC), and thermosets, which set permanently into a cross-linked network (bakelite, epoxy); (vi) by tacticity: isotactic, syndiotactic and atactic; (vii) by intermolecular forces: elastomers, fibres, thermoplastics and thermosetting resins.

Since a polymer sample contains chains of different lengths, its molecular weight is an average. The number average molecular weight Mn is the total weight divided by the total number of molecules, Mn = sum(NiMi)/sum(Ni); it is measured by colligative methods such as osmometry. The weight average molecular weight Mw weights each chain by its mass, Mw = sum(NiMi^2)/sum(NiMi); it is measured by light scattering. Mw is always greater than or equal to Mn, and the ratio Mw/Mn, the polydispersity index (PDI), measures the spread of chain lengths; PDI = 1 for a monodisperse sample.

Crystallinity is the degree of ordered arrangement of chains. In crystalline regions chains are packed in a regular, parallel manner; in amorphous regions they are randomly coiled and entangled. Most polymers are semi-crystalline. Crystallinity is favoured by linear, regular, stereoregular (isotactic or syndiotactic) chains and strong intermolecular forces, so HDPE is more crystalline than branched LDPE, and nylon is highly crystalline. Higher crystallinity raises density, tensile strength, stiffness, hardness, chemical resistance and melting point, but lowers transparency and impact toughness. Crystalline polymers have a sharp melting point Tm; amorphous ones soften over a range.

The glass transition temperature Tg is the temperature below which an amorphous polymer (or the amorphous part of a semi-crystalline one) is hard, rigid and glassy, and above which it becomes soft, flexible and rubbery because segments of the chains gain mobility. Tg rises with stiff chains, bulky or polar side groups, strong intermolecular forces, cross-linking and higher molecular weight, and falls with flexible chains and added plasticisers. Approximate values: natural rubber about -70 C (rubbery at room temperature), PVC about 80 C and polystyrene about 100 C (rigid at room temperature). A plastic is used below its Tg, an elastomer above it.

Mechanical properties: hardness is resistance to indentation or scratching (measured by Shore or Rockwell tests); tensile strength is the maximum stress a specimen can bear in tension before breaking; creep is slow, time-dependent deformation under constant load, important for polymers even at room temperature; fatigue is failure under repeated cyclic loading at stresses below the tensile strength; impact resistance is the ability to absorb energy of a sudden blow without fracture (Izod and Charpy tests). Electrical properties: dielectric strength is the maximum electric field (kV/mm) an insulator can withstand without breakdown; insulation resistance is the resistance offered by the insulating material between two conductors; surface resistivity is the resistance to leakage current along the surface, expressed in ohms per square. Most polymers are excellent insulators.

Optical properties: refractive index is the ratio of the speed of light in vacuum to that in the polymer (about 1.49 for PMMA and 1.59 for polystyrene); transmittance is the fraction of incident light passing through, high for amorphous polymers such as PMMA and polycarbonate used for lenses and glazing; photoelectric property is the change of electrical behaviour on illumination, shown by photoconducting polymers such as poly(N-vinylcarbazole) used in photocopying and by conjugated polymers used in organic solar cells and light-emitting devices; colour depends on chromophores in the chain or on added dyes and pigments, most pure polymers being colourless or white.

Mind map

Method to calculate Mn, Mw and PDI of a polymer sample

Important definitions

Formulas

Key points to remember

• Backbone bonds are covalent; interchain forces are van der Waals, dipole-dipole or hydrogen bonds; cross-links are covalent.
• Addition polymers retain the full monomer formula; condensation polymers lose small molecules like H2O.
• Thermoplastics: linear/branched, recyclable. Thermosets: cross-linked, not remouldable.
• Mw is greater than or equal to Mn; equal only for a monodisperse sample.
• Mn by osmometry (colligative); Mw by light scattering.
• HDPE is more crystalline, denser and stronger than LDPE because it is unbranched.
• Crystalline regions scatter light, so highly crystalline polymers are translucent or opaque.
• Plasticisers lower Tg; cross-linking and bulky side groups raise it.
• Rubbers are used above Tg; rigid plastics below Tg.
• Creep and fatigue are important for polymer components under long-term or cyclic loads.
• PMMA has high transmittance (used as acrylic glass); poly(N-vinylcarbazole) is photoconductive.

Solved examples

Example 1. A polymer sample contains 30 molecules of molecular weight 20,000, 40 molecules of 30,000 and 30 molecules of 60,000. Calculate Mn, Mw and PDI.

Step 1: sum Ni = 100. sum NiMi = 30(20,000) + 40(30,000) + 30(60,000) = 6.0 x 10^5 + 1.2 x 10^6 + 1.8 x 10^6 = 3.6 x 10^6. Step 2: Mn = 3.6 x 10^6/100 = 36,000. Step 3: sum NiMi^2 = 30(4 x 10^8) + 40(9 x 10^8) + 30(3.6 x 10^9) = 1.2 x 10^10 + 3.6 x 10^10 + 1.08 x 10^11 = 1.56 x 10^11. Step 4: Mw = 1.56 x 10^11/3.6 x 10^6 = 43,333. Step 5: PDI = 43,333/36,000 = 1.20.

Example 2. A polymer contains 20% by weight of molecules of molecular weight 10,000, 50% of 50,000 and 30% of 100,000. Calculate Mn and Mw.

Step 1: Mn = 1/sum(wi/Mi) = 1/(0.2/10,000 + 0.5/50,000 + 0.3/100,000) = 1/(2.0 x 10^-5 + 1.0 x 10^-5 + 3.0 x 10^-6) = 1/(3.3 x 10^-5) = 30,303. Step 2: Mw = sum wiMi = 0.2(10,000) + 0.5(50,000) + 0.3(100,000) = 2000 + 25,000 + 30,000 = 57,000. Step 3: PDI = 57,000/30,303 = 1.88.

Example 3. A sample contains 10 molecules of molecular weight 10,000 and 10 molecules of molecular weight 100,000. Find Mn, Mw and PDI.

Step 1: Mn = (10 x 10,000 + 10 x 100,000)/20 = 1.1 x 10^6/20 = 55,000. Step 2: sum NiMi^2 = 10(10^8) + 10(10^10) = 1.01 x 10^11; Mw = 1.01 x 10^11/1.1 x 10^6 = 91,818. Step 3: PDI = 91,818/55,000 = 1.67. Though the numbers of molecules are equal, Mw is closer to the heavier fraction because heavy chains carry most of the mass.

Example 4. Calculate the degree of polymerisation of (a) polyethylene of molecular weight 28,000 and (b) PVC of molecular weight 1,25,000. (C = 12, H = 1, Cl = 35.5)

(a) Repeating unit -CH2-CH2- = 2(12) + 4(1) = 28. DP = 28,000/28 = 1000. (b) Repeating unit -CH2-CHCl- = 2(12) + 3(1) + 35.5 = 62.5. DP = 1,25,000/62.5 = 2000.

Example 5. A polystyrene sample has a degree of polymerisation of 500. Calculate its molecular weight. (C = 12, H = 1)

Step 1: Repeating unit -CH2-CH(C6H5)- = C8H8 = 8(12) + 8(1) = 104. Step 2: Molecular weight = DP x 104 = 500 x 104 = 52,000 g/mol.

Example 6. Show that Mw = Mn for a sample in which all 50 molecules have molecular weight 40,000.

Mn = (50 x 40,000)/50 = 40,000. Mw = (50 x 40,000^2)/(50 x 40,000) = 40,000. PDI = 1, so the sample is monodisperse. Any spread of chain lengths makes Mw greater than Mn.

Important questions and answers

Q1. Define polymer, monomer and degree of polymerisation with an example. (3 marks)

A polymer is a macromolecule formed by covalent linking of a large number of small repeating units. A monomer is the small molecule with at least two bonding sites from which the polymer is built. Degree of polymerisation is the number of repeating units in a chain. Example: n CH2=CH2 gives -(CH2-CH2)n-, polyethylene; ethylene is the monomer and n is the DP.

Q2. Explain chemical bonding in polymers. (4 marks)

Primary bonds: atoms in the backbone are joined by strong covalent bonds (C-C, C-O, C-N), which give the chain its integrity; in thermosets, covalent cross-links join neighbouring chains into a network. Secondary bonds between chains: van der Waals or dispersion forces (weak, in PE), dipole-dipole forces (in PVC due to polar C-Cl), and hydrogen bonds (in nylons, between N-H and C=O). Stronger secondary forces raise Tg, Tm, crystallinity and strength; cross-linking makes the polymer rigid and infusible.

Q3. Classify polymers with examples. (6 marks)

Origin: natural (cellulose, natural rubber), semi-synthetic (cellulose acetate), synthetic (PE, nylon). Structure: linear (HDPE), branched (LDPE), cross-linked (bakelite). Composition: homopolymer (PVC), copolymer (Buna-S): random, alternating, block, graft. Polymerisation: addition (PE, PS, PVC) and condensation (nylon 6,6, terylene, bakelite). Thermal response: thermoplastic (PE, PVC, PS) and thermosetting (bakelite, epoxy, urea-formaldehyde). Tacticity: isotactic (all substituents on one side), syndiotactic (alternate sides), atactic (random). Intermolecular forces: elastomers, fibres, thermoplastics, thermosets.

Q4. Differentiate between thermoplastic and thermosetting polymers. (4 marks)

Thermoplastics: linear or slightly branched chains; held by weak secondary forces; soften on heating and harden on cooling reversibly; can be remoulded and recycled; generally soluble in suitable solvents; usually formed by addition polymerisation; e.g. PE, PVC, PS. Thermosets: three-dimensional cross-linked network; covalent cross-links; set permanently on heating; cannot be remoulded; insoluble and harder, stronger, more brittle; usually formed by condensation; e.g. bakelite, epoxy resins.

Q5. Define number average and weight average molecular weight. Calculate both for a sample with 30 molecules of 20,000, 40 of 30,000 and 30 of 60,000. (5 marks)

Mn = sum NiMi/sum Ni = total mass/total number of molecules. Mw = sum NiMi^2/sum NiMi. Mn = 3.6 x 10^6/100 = 36,000; Mw = 1.56 x 10^11/3.6 x 10^6 = 43,333; PDI = 1.20.

Q6. What is crystallinity of polymers? Compare crystalline and amorphous polymers and state factors affecting crystallinity. (5 marks)

Crystallinity is the extent of regular, ordered packing of polymer chains. Crystalline: ordered, closely packed chains, sharp Tm, higher density, strength, hardness, chemical resistance, usually opaque (HDPE, nylon). Amorphous: random coiled chains, soften over a range at Tg, lower density and strength, often transparent (PS, PMMA). Factors: linear unbranched chains, regular repeat structure, stereoregularity (isotactic, syndiotactic), strong intermolecular forces (hydrogen bonding), and slow cooling or stretching favour crystallinity; branching, bulky groups, atactic structure and copolymerisation reduce it.

Q7. What is glass transition temperature? Explain the factors affecting it. (5 marks)

Tg is the temperature below which an amorphous polymer is hard, brittle and glassy and above which it is soft, flexible and rubbery, because chain segments begin to rotate and move. Factors: (1) chain flexibility: flexible backbones (Si-O, C-O) give low Tg; (2) bulky side groups (phenyl in PS) hinder rotation and raise Tg; (3) polar groups and hydrogen bonding raise Tg; (4) cross-linking raises Tg; (5) molecular weight: Tg increases with molecular weight up to a limit; (6) plasticisers increase free volume and lower Tg; (7) copolymerisation changes Tg between those of the homopolymers. Significance: decides whether a polymer is used as a rigid plastic (below Tg) or a rubber (above Tg).

Q8. Explain the mechanical properties of polymers: hardness, tensile strength, creep, fatigue and impact resistance. (5 marks)

Hardness: resistance to indentation or scratching; measured by Shore durometer or Rockwell test. Tensile strength: maximum tensile stress before fracture; increases with molecular weight, crystallinity and cross-linking. Creep: slow continuous deformation under constant load with time; polymers creep even at room temperature, so long-term loads must be limited. Fatigue: failure under repeated cyclic loads below tensile strength, e.g. in gears and hinges. Impact resistance: ability to absorb energy of a sudden blow without breaking; measured by Izod or Charpy test; polycarbonate and ABS have high impact resistance.

Q9. Write a note on electrical properties of polymers. (4 marks)

Dielectric strength: maximum voltage per unit thickness (kV/mm) an insulator withstands before breakdown; high for PE, PTFE, so used for cable insulation. Insulation resistance: resistance between two conductors separated by the polymer; high values mean low leakage. Surface resistivity: resistance to current along the surface, in ohms per square; reduced by moisture and dirt, important for PCBs and switch housings. Most polymers are excellent insulators because electrons are held in covalent bonds; moisture absorption and polar groups lower these properties.

Q10. Write a note on optical properties of polymers. (4 marks)

Refractive index: n = c/v; about 1.49 for PMMA and 1.59 for PS; important for lenses and optical fibres. Transmittance: fraction of light transmitted; amorphous PMMA and polycarbonate are highly transparent and used for glazing, lenses, display covers, while crystalline polymers scatter light. Photoelectric property: some polymers conduct on illumination, e.g. poly(N-vinylcarbazole) in photocopiers, and conjugated polymers in organic solar cells and LEDs. Colour: from chromophores or added dyes and pigments; most pure polymers are colourless.

Exam tips

• In molecular weight numericals, make a table of Ni, Mi, NiMi and NiMi^2; it avoids mistakes and earns step marks.
• Check that Mw > Mn; if not, recheck your arithmetic.
• Use powers of ten for large numbers and give the final answer in g/mol.
• Tg answers should define Tg, mention glassy and rubbery states and list at least four factors.
• For property questions, give definition plus one example polymer and one application.
• Do not confuse Tg (amorphous, softening) with Tm (crystalline, melting).

FAQs

Why is Mw always greater than Mn?

Mw weights each molecule by its mass, so heavier chains count more; it equals Mn only if all chains have the same length.

Why is HDPE stronger than LDPE?

HDPE has linear chains that pack closely, giving higher crystallinity and density, whereas branching in LDPE prevents close packing.

Is a polymer used above or below Tg?

Rigid plastics like PS and PMMA are used below Tg; elastomers like natural rubber are used above Tg.

How do plasticisers work?

They are small molecules that go between chains, reduce intermolecular forces and increase free volume, lowering Tg and making the polymer flexible (e.g. plasticised PVC).

These notes follow the University of Mumbai first-year engineering syllabus (NEP 2020, Applied Chemistry) and were prepared with AI help and checked.