Polymer chemistry

In short

Polymer chemistry deals with macromolecules built by linking thousands of small repeating units (monomers) into chains, and with how chain length, architecture and intermolecular forces decide whether the material behaves like a pipe, a fibre, a rubber or a varnish. It is the backbone of India's largest chemical industry segment - petrochemicals, plastics, paints, adhesives, tyres and synthetic textiles - with Reliance Industries, IOCL, GAIL, OPaL, Haldia Petrochemicals, Supreme Industries, Finolex, SRF, Pidilite, Asian Paints, Apollo Tyres and Indorama among the big employers. In B.Sc/M.Sc papers it carries full questions on mechanisms, kinetics, molecular-weight averages and Tg; in CSIR-NET, GATE (CY/XL) and IIT-JAM it appears as numericals on Carothers' equation, Mn/Mw and Mark-Houwink. In placement technical rounds for QC, polymer processing and plant roles, interviewers ask about melt flow index, crystallinity, additives, and compliance with BIS standards and the Plastic Waste Management Rules.

Explained

Basic definitions and classification

• Monomer: small molecule that can join to others (ethene, vinyl chloride, styrene, caprolactam). Polymer: the macromolecule; repeat (structural) unit is the pattern that recurs; oligomer has only a few units.
• Functionality: number of reactive sites. Bifunctional monomers give linear chains; functionality greater than 2 gives branched or network polymers.
• Degree of polymerization (DP or n): number of repeat units per chain. Mn = DP × (mass of repeat unit).
• Classification by source: natural (cellulose, starch, natural rubber, proteins, DNA), semi-synthetic (cellulose acetate, vulcanised rubber), synthetic (PE, PP, PVC, PET, nylon).
• By structure: linear (HDPE, nylon), branched (LDPE), cross-linked/network (bakelite, vulcanised rubber, epoxy).
• By thermal behaviour: thermoplastics soften on heating and are re-mouldable (PE, PP, PVC, PS, PET, nylon); thermosets cure irreversibly into a network (phenol-formaldehyde, urea-formaldehyde, epoxy, unsaturated polyester); elastomers are lightly cross-linked, far above their Tg, and recover large deformations (natural rubber, SBR, nitrile, silicone).
• By mechanism: chain-growth (addition) versus step-growth (condensation) - the single most examined comparison.
• Homopolymer has one monomer; a copolymer has two or more, arranged as random (SBR), alternating, block (SBS thermoplastic elastomer) or graft (ABS, HIPS).
• Tacticity (for vinyl polymers with a substituted carbon): isotactic - all substituents on one side, crystalline, high melting (isotactic PP); syndiotactic - alternating; atactic - random, amorphous (atactic PP is a soft wax, atactic polystyrene is glassy and clear).
• Nomenclature: source-based (polystyrene, poly(vinyl chloride)); IUPAC structure-based (poly(1-phenylethylene)); common trade names (Teflon = PTFE, Perspex = PMMA, Nylon, Terylene/PET).

Chain-growth (addition) polymerisation

Addition of unsaturated monomers with no loss of small molecules; the repeat unit has the same formula as the monomer.

• Free-radical polymerisation - three steps:
• Initiation: an initiator decomposes to radicals - benzoyl peroxide, AIBN (thermal), or a redox pair such as persulphate/bisulphite; efficiency factor f (0.3-0.8) accounts for radicals lost to side reactions.
• Propagation: the radical adds monomer head-to-tail thousands of times in a fraction of a second.
• Termination: by combination (two radicals couple) or disproportionation (hydrogen transfer giving one saturated and one unsaturated end).
• Chain transfer: the radical abstracts an atom from monomer, solvent, polymer or a deliberate chain-transfer agent (dodecyl mercaptan); this shortens chains and controls molecular weight. Transfer to polymer causes the long-chain branching that makes LDPE.
• Inhibitors/retarders (hydroquinone, benzoquinone, oxygen) scavenge radicals - the reason monomers are stored with inhibitor and it is stripped before polymerisation.
• Gel (Trommsdorff/auto-acceleration) effect: at high conversion the viscous medium hinders radical diffusion, so kt falls, Rp and molecular weight shoot up and heat release can run away - a real plant hazard in bulk MMA polymerisation.
• Suitable monomers: ethene, styrene, vinyl chloride, vinyl acetate, acrylates, acrylonitrile.
• Cationic polymerisation: Lewis acid/protonic acid initiators (BF₃·H₂O, AlCl₃, H₂SO₄); needs electron-rich monomers - isobutylene (butyl rubber), vinyl ethers; very fast at low temperature.
• Anionic polymerisation: nucleophilic initiators (n-butyllithium, sodium naphthalenide); needs electron-poor monomers - styrene, butadiene, acrylonitrile, MMA. With no termination step it is a living polymerisation, giving narrow distributions (PDI near 1.0-1.1) and block copolymers (SBS).
• Coordination/Ziegler-Natta polymerisation: TiCl₄ + Al(C₂H₅)₃ (and modern supported MgCl₂/Ti and metallocene catalysts) gives stereoregular, linear, high-density product at low pressure - the basis of HDPE and isotactic PP. High-pressure free-radical process gives branched LDPE.
• Controlled radical methods (ATRP, RAFT, NMP): give living-like control with radical tolerance; examined as "controlled/living radical polymerisation".
• Ring-opening polymerisation: caprolactam to nylon-6, ethylene oxide to PEG, lactide to PLA.

Step-growth (condensation) polymerisation

• Bifunctional monomers react pairwise, usually eliminating a small molecule (H₂O, HCl, CH₃OH); any two species present can react, so monomer disappears early but high molecular weight appears only at very high conversion.
• Types: polyester (PET from terephthalic acid or DMT + ethylene glycol), polyamide (nylon-6,6 from adipic acid + hexamethylenediamine via nylon salt; nylon-6 from caprolactam), polycarbonate (bisphenol-A + phosgene or diphenyl carbonate), polyurethane (diisocyanate + diol, a stepwise *addition* polymerisation with no by-product), phenol-formaldehyde (novolac, acid-catalysed; resol, base-catalysed), urea- and melamine-formaldehyde, epoxy (bisphenol-A + epichlorohydrin, cured with amines or anhydrides).
• Conditions needed for high Mn: exact stoichiometry, pure bifunctional monomers, high conversion, and continuous removal of the by-product (vacuum, molten-state polycondensation).
• Interfacial polycondensation: the classic "nylon rope trick" - diacid chloride in an organic layer, diamine in water.
• Gelation: with any monomer of functionality more than 2, a three-dimensional network forms at a critical extent of reaction - Carothers' criterion DP → ∞ when p·f_av = 2.

Industrial polymerisation techniques and processing

• Bulk (mass): monomer + initiator only. Pure product, but heat removal is poor and the gel effect severe - used for PMMA sheet, PS.
• Solution: solvent controls viscosity and heat; needs solvent recovery; residual solvent limits food use.
• Suspension (bead/pearl): monomer droplets (0.05-0.5 mm) suspended in water with stabilisers (PVA, talc); initiator is monomer-soluble; gives beads - PVC (suspension grade), expandable PS.
• Emulsion: monomer emulsified with surfactant above the CMC; water-soluble initiator starts the reaction inside micelles, so high rate and high molecular weight together - unique to this technique. Gives latex used directly in paints and adhesives (Asian Paints emulsions, Pidilite PVA), plus SBR and NBR.
• Processing routes to learn: extrusion (pipes, films, profiles), injection moulding (crates, housings), blow moulding (bottles), calendering (PVC sheet), rotational moulding (water tanks), compression/transfer moulding (thermosets), thermoforming, melt spinning (polyester fibre), film blowing and biaxial orientation (BOPP, BOPET).
• Additives: plasticisers (DOP/DEHP in flexible PVC), heat stabilisers (Ca-Zn, previously lead - now restricted in potable-water pipe grades), antioxidants, UV stabilisers (HALS), fillers (CaCO₃, talc, carbon black), flame retardants, blowing agents, lubricants, pigments, impact modifiers.
• Rubber compounding and vulcanisation: sulphur + accelerator (MBTS, CBS) + activator (ZnO/stearic acid) cross-links rubber; raises strength and elasticity, removes tackiness.
• Quality-control tests asked in interviews: melt flow index (MFI, g/10 min), melt flow rate, density, Vicat softening point, HDT, tensile/flexural/impact (Izod), hardness (Shore), DSC (Tg, Tm, crystallinity), TGA, FTIR identification, GPC for distribution, ash and moisture content.

Molecular weight: averages, distribution and measurement

• A polymer sample is a mixture of chain lengths, so molecular weight is a distribution, not a single value.
• Mn (number-average): weights every molecule equally; measured by methods that count molecules - colligative/absolute methods: osmometry (membrane and vapour pressure), end-group titration, cryoscopy, ebullioscopy.
• Mw (weight-average): biases to heavy chains; measured by light scattering (absolute) and ultracentrifugation. Mw always ≥ Mn.
• Mv (viscosity-average): from dilute-solution viscosity via Mark-Houwink; relative method needing calibration. Mz weights still more heavily to large chains.
• Order: Mn < Mv < Mw < Mz for a polydisperse sample; all equal for a monodisperse one.
• PDI = Mw/Mn: 1.0 ideal monodisperse; ~1.05 anionic living; 1.5 (radical termination by combination) to 2 (disproportionation, and the "most probable" distribution of step-growth); 5-30 for Ziegler-Natta/free-radical LDPE.
• GPC/SEC (size-exclusion chromatography): separates by hydrodynamic volume - large molecules elute first; gives the whole distribution and all averages against standards.
• Why it matters practically: tensile strength and toughness rise with Mn up to a plateau; melt viscosity rises steeply with Mw, so very high Mw is hard to process. Broad distributions process easily but have weaker, more variable properties. UHMWPE (Mw in millions) must be ram-extruded or sintered.

Structure, thermal transitions and mechanical behaviour

• Crystallinity: regular, symmetric, unbranched, stereoregular chains with strong intermolecular forces pack into crystallites (HDPE, isotactic PP, nylon, PET). Bulky/irregular side groups and branching give amorphous polymers (atactic PS, PMMA, PVC). Polymers are semi-crystalline at best, never 100% crystalline.
• Glass transition temperature Tg: amorphous regions change from glassy and brittle to rubbery; a second-order transition seen as a step in heat capacity (DSC) and a drop in modulus. Tm (crystalline melting) is first-order and only exists in crystalline polymers. Rough rule Tg ≈ (0.5-0.7) Tm in kelvin.
• Tg is raised by: chain stiffness/aromatic backbone, polar groups and hydrogen bonding, bulky side groups, cross-linking, crystallinity (restrains amorphous chains). Lowered by: plasticisers, flexible -CH₂-/-Si-O- backbones, long flexible side chains, low molecular weight, copolymerisation with a soft comonomer.
• Typical Tg values: natural rubber ≈ −70 °C; LDPE ≈ −110 °C; PP ≈ −10 °C; PVC ≈ 80 °C; PS ≈ 100 °C; PMMA ≈ 105 °C; PET ≈ 70-80 °C (Tm ≈ 255-265 °C); nylon-6 Tm ≈ 220 °C; PTFE Tm ≈ 327 °C. Values vary with grade and measurement rate.
• Service rule: a plastic is used below Tg (rigid) or, if crystalline, between Tg and Tm; a rubber is used above Tg. PVC pipe is rigid because 27 °C is below its Tg; rubber bands are elastic because 27 °C is far above theirs.
• Viscoelasticity: polymers show both elastic and viscous response - creep under sustained load, stress relaxation, hysteresis, and time-temperature superposition (WLF equation). This is why a plastic water tank sags over years under its own load.
• Mechanical behaviour: elastomer (low modulus, huge elongation), flexible plastic (yields and draws, cold-drawing with necking), rigid brittle plastic, fibre (high modulus from drawn/oriented chains). Orientation by drawing greatly raises strength along the draw direction.

Degradation, recycling and Indian regulation

• Degradation routes: thermal (chain scission, dehydrochlorination of PVC), oxidative and photo-oxidative (UV initiates radicals; stabilisers delay it), hydrolytic (esters and amides - PET and nylon), mechanical (shear during repeated extrusion), biological (only for PLA, PHA, PBAT, starch blends under specified conditions).
• Recycling: mechanical (sort, wash, shred, re-extrude - only thermoplastics; properties fall each cycle), chemical/feedstock (glycolysis, methanolysis or hydrolysis of PET back to monomer; pyrolysis to oil), and energy recovery. Thermosets can only be ground as filler or chemically broken down.
• Resin identification codes 1-7 (PET, HDPE, PVC, LDPE, PP, PS, others) are required marking under India's plastic waste rules.
• Plastic Waste Management Rules, 2016 (as amended): manufacture, sale and use of identified single-use plastic items banned from 1 July 2022; plastic carry bags must be at least 120 micron thick (from 31 December 2022); mandatory marking of manufacturer and thickness; Extended Producer Responsibility (EPR) obligations on producers, importers and brand owners under the CPCB EPR portal, with categories for rigid, flexible, multilayered and compostable plastic packaging and year-wise recycling and recycled-content targets. Amendments are frequent - check the latest CPCB/MoEFCC notification before quoting a number.
• Compostable and biodegradable claims need certification against the Indian Standard for compostable plastics and CPCB marking; "biodegradable" is not a licence to litter.
• BIS: polymer products carry Indian Standards - for example PE pipes for water supply (IS 4984) and uPVC pipes for potable water (IS 4985), with grades specified by density, MFI and pressure rating; food-contact plastics are regulated by FSSAI packaging regulations alongside the relevant IS. Several polymers and plastic products are under BIS Quality Control Orders requiring ISI marking; the covered list changes, so verify currently notified items.
• Plant and safety context: monomers such as vinyl chloride (carcinogen), acrylonitrile, styrene and isocyanates are handled under the Manufacture, Storage and Import of Hazardous Chemical Rules and the Environment (Protection) Act, 1986; occupational safety in polymer plants now falls under the Occupational Safety, Health and Working Conditions Code, one of the four Labour Codes in force from 21 November 2025, which replaced the Factories Act. GST on most plastics and polymer articles is 18% under the slabs effective 22 September 2025; verify the HSN-wise rate.

Key points

• Polymer - macromolecule of repeating units; properties depend on chain length, structure and intermolecular forces, not just chemistry.
• DP - repeat units per chain; Mn = DP × repeat-unit mass.
• Addition polymerisation - no by-product, monomer formula = repeat-unit formula, needs C=C.
• Condensation polymerisation - small molecule eliminated; high Mn only at conversion very close to 1.
• Free-radical steps - initiation, propagation, termination (combination or disproportionation), plus chain transfer.
• Chain-transfer agent - deliberately added to cap molecular weight; does not slow the overall rate much.
• Gel effect - kt falls at high viscosity, so rate and Mw jump; a runaway-reaction risk.
• Anionic living polymerisation - no termination, PDI ≈ 1, makes block copolymers.
• Ziegler-Natta/metallocene - stereoregular linear HDPE and isotactic PP at low pressure; LDPE needs high-pressure radical route.
• Emulsion polymerisation - uniquely gives high rate and high molecular weight together; product is a usable latex.
• Mn, Mw, Mv, Mz - Mn from counting methods (osmometry, end-group), Mw from light scattering, Mv from viscosity, whole curve from GPC.
• PDI = Mw/Mn - 1 for monodisperse, 2 for most-probable step-growth, up to 20-30 for LDPE.
• Tg - amorphous glass-to-rubber transition (second order); Tm - crystalline melting (first order); only crystalline polymers have Tm.
• Tacticity - isotactic PP is crystalline and useful; atactic PP is a soft wax.
• Thermoplastic versus thermoset - re-mouldable linear chains versus permanent network; only the former is mechanically recyclable.
• Vulcanisation - sulphur cross-links rubber, converting a tacky gum into a strong elastomer.
• MFI - inverse indicator of melt viscosity and hence of molecular weight; the standard QC number for a resin grade.
• PWM Rules, 2016 (as amended) - single-use plastic ban (1 July 2022), 120-micron carry bags, resin codes, EPR targets on brand owners.

Formulas and examples

Example 1 - molecular-weight averages. A sample has 10 chains of 10,000 g/mol and 5 chains of 100,000 g/mol.

• Σni Mi = 10(10,000) + 5(100,000) = 100,000 + 500,000 = 600,000; Σni = 15.
• Mn = 600,000/15 = 40,000 g/mol.
• Σni Mi² = 10(1.0 × 10⁸) + 5(1.0 × 10¹⁰) = 1.0 × 10⁹ + 5.0 × 10¹⁰ = 5.1 × 10¹⁰.
• Mw = 5.1 × 10¹⁰ / 6.0 × 10⁵ = 85,000 g/mol; PDI = 85,000/40,000 = 2.125.
• Note the heavy chains are one-third of the molecules but five-sixths of the mass - which is why Mw ≫ Mn.

Example 2 - Carothers' equation, nylon-6,6. Adipic acid + hexamethylenediamine, exact stoichiometry, p = 0.990.

• DP = 1/(1 − 0.990) = 100 structural units.
• The repeat unit (one acid + one amine − 2H₂O) = 226 g/mol, so the average structural unit = 113 g/mol.
• Mn = 113 × 100 = 11,300 g/mol - still too low for fibre; p must reach ~0.998 (DP = 500, Mn ≈ 56,500).
• Now take p = 1 but a 1% excess of diamine, r = 0.99: DP = (1 + 0.99)/(1 − 0.99) = 1.99/0.01 = 199. A 1% imbalance caps DP at 199 however long you react (at exact stoichiometry DP → ∞ as p → 1) - the reason nylon salt is made first.

Example 3 - free-radical kinetics. [M] = 5.0 mol/L, [I] = 1.0 × 10⁻² mol/L, kd = 1.0 × 10⁻⁵ s⁻¹, f = 0.5, kp = 200 L mol⁻¹ s⁻¹, kt = 3.0 × 10⁷ L mol⁻¹ s⁻¹.

• Ri = 2(0.5)(1.0 × 10⁻⁵)(1.0 × 10⁻²) = 1.0 × 10⁻⁷ mol L⁻¹ s⁻¹.
• [M•] = (Ri/2kt)^½ = (1.0 × 10⁻⁷ / 6.0 × 10⁷)^½ = (1.667 × 10⁻¹⁵)^½ = 4.08 × 10⁻⁸ mol/L.
• Rp = 200 × 5.0 × 4.08 × 10⁻⁸ = 4.08 × 10⁻⁵ mol L⁻¹ s⁻¹.
• ν = Rp/Ri = 4.08 × 10⁻⁵ / 1.0 × 10⁻⁷ = 408; with termination by combination DPn ≈ 816.
• Doubling [I] multiplies Rp by √2 (= 1.41) but divides chain length by 1.41 - the classic rate-versus-molecular-weight trade-off.

Example 4 - Mark-Houwink. For a polymer-solvent pair K = 1.0 × 10⁻⁴ dL/g and a = 0.74; measured [η] = 1.00 dL/g.

• M = ([η]/K)^1/a = (1.00/1.0 × 10⁻⁴)^1/0.74 = (10⁴)^1.351 = 10^{4 × 1.351} = 10^5.405 = 2.54 × 10⁵ g/mol (a viscosity-average).

Example 5 - copolymer Tg (Fox). SBR with 70% styrene (Tg = 373 K) and 30% butadiene (Tg = 173 K) by mass.

• 1/Tg = 0.70/373 + 0.30/173 = 1.877 × 10⁻³ + 1.734 × 10⁻³ = 3.611 × 10⁻³.
• Tg = 1/3.611 × 10⁻³ = 277 K ≈ 4 °C - well below room temperature, so at 27 °C this composition is rubbery but stiff and leathery; raising butadiene content lowers Tg further into the useful elastomer range.

Where it is used

• Petrochemical and polymer plants: cracker and downstream units at Reliance (Jamnagar, Hazira, Dahej, Nagothane), IOCL (Panipat, Paradip), GAIL (Pata), OPaL (Dahej), Haldia Petrochemicals and HMEL make PE, PP, PVC, PET and polyester - roles in process, polymer QC and technical service.
• Plastic product manufacturing: Supreme Industries, Finolex, Astral, Prince and Nilkamal in pipes, fittings and moulded goods; QC roles test MFI, density, hydrostatic pressure and dimensions against the applicable Indian Standard.
• Paints, adhesives and coatings: Asian Paints, Berger, Nerolac (acrylic/vinyl emulsions, alkyds), Pidilite (PVA, cyanoacrylate, epoxy) - emulsion polymerisation and formulation labs.
• Tyres and rubber goods: MRF, Apollo, CEAT, JK Tyre - compounding, vulcanisation, rheometry; Reliance and others make SBR/PBR.
• Fibres and films: polyester staple fibre and filament, BOPP/BOPET film (SRF, Jindal Poly, Garware, Uflex, Cosmo) - orientation, coating and metallising.
• Pharma, medical and electronics: blister films, syringes, implant-grade polymers, encapsulants; roles in packaging development and extractable/leachable testing.
• Recycling and EPR services: PET recyclers and plastic waste processors registered on the CPCB portal; EPR compliance, environment and sustainability roles in brand-owner companies.

Interview questions

• Q: Why does molecular weight rise only at the very end in condensation polymerisation but immediately in addition polymerisation? A: In step-growth every molecule reacts with every other, so DP = 1/(1−p) and needs p near 1; in chain-growth each initiated chain grows to full length in seconds, so high-polymer exists from the start.
• Q: Why is Mw always greater than or equal to Mn? A: Mw weights each molecule by its mass, so larger chains count more; the two become equal only if all chains are identical in length.
• Q: Which methods give absolute Mn and which give absolute Mw? A: Osmometry, end-group analysis and other colligative methods give Mn; light scattering and sedimentation give Mw. Viscosity and GPC are relative and need calibration.
• Q: HDPE and LDPE are both polyethylene - why do their properties differ? A: LDPE is made by a high-pressure radical route and is heavily branched, so it packs poorly and is low in density and stiffness; HDPE from Ziegler-Natta catalysis is linear, more crystalline, stronger and stiffer.
• Q: What is the gel effect and why is it a safety concern? A: At high conversion the viscous medium suppresses radical-radical termination, so rate and molecular weight auto-accelerate; the exotherm can run away in a bulk reactor and must be controlled by cooling, dilution or staged conversion.
• Q: How do you reduce molecular weight without reducing the polymerisation rate much? A: Add a chain-transfer agent such as a mercaptan - it transfers the radical to a new chain instead of destroying it, so DP falls while Rp is nearly unchanged.
• Q: Why does adding a plasticiser soften PVC? A: It inserts between chains, increases free volume and weakens dipole interactions, lowering Tg below room temperature so the material becomes flexible.
• Q: Why can a thermoset not be remelted and recycled? A: Curing creates covalent cross-links into one network; heating degrades the bonds rather than allowing chain flow, so it can only be ground as filler or chemically depolymerised.
• Q: Which polymerisation technique would you choose for a paint binder and why? A: Emulsion polymerisation - it gives high rate with high molecular weight, excellent heat control, and a water-based latex that can be formulated directly without solvent recovery.
• Q: What does a high MFI tell you about a resin grade? A: Low melt viscosity and therefore lower molecular weight - easier to injection-mould thin parts, but lower strength and environmental stress-crack resistance; pipe grades use low MFI.
• Q: Why does nylon-6,6 melt much higher than polyethylene of similar chain length? A: Regularly spaced amide groups form strong interchain hydrogen bonds, needing far more energy to disrupt than PE's dispersion forces.
• Q: What are the main obligations of a brand owner under India's plastic waste rules? A: Registration on the CPCB EPR portal, mandatory marking and minimum thickness/resin-code compliance, and meeting year-wise collection, recycling, reuse and recycled-content targets for each packaging category, with the banned single-use items not to be used at all.

Common mistakes

• Computing Mw with the Mn formula (or forgetting that the Mw numerator uses Mi²), and reporting PDI less than 1.
• Using the repeat-unit mass of 226 for nylon-6,6 in Carothers' equation when the structural unit is 113 - it doubles the answer.
• Forgetting that Carothers' DP = 1/(1−p) assumes exact stoichiometry; ignoring the r-form when an excess is given.
• Saying Rp is proportional to [I] instead of [I]^½ in free-radical kinetics, and mixing up Rt = 2kt[M•]² with kt[M•]².
• Confusing Tg with Tm, or claiming an amorphous polymer like atactic polystyrene has a melting point.
• Treating polymers as 100% crystalline, or assuming crystallinity and cross-linking are the same thing.
• Calling every plastic recyclable, and quoting outdated carry-bag thickness or ban lists instead of checking the current amendment to the Plastic Waste Management Rules.
• Mixing units for intrinsic viscosity (dL/g versus mL/g) in Mark-Houwink, which shifts M by orders of magnitude.

Related topics

Green chemistry · Chemistry careers: QC labs, R&D and pharma · Chemical kinetics and reaction mechanisms · Petrochemicals and unit processes · Instrumental analysis: DSC, TGA, FTIR and chromatography · Physical chemistry of solutions and colligative properties