Emulsions & Surfactants

Emulsions are classified by which liquid forms the dispersed phase (droplets) and which forms the continuous phase (surrounding medium). In an oil-in-water (O/W) emulsion, oil droplets are dispersed throughout water; examples include milk, mayonnaise, and most skin lotions. In a water-in-oil (W/O) emulsion, tiny water droplets are dispersed in an oily continuous phase; butter and margarine are classic examples. The type formed depends largely on the geometry and polarity of the emulsifier used: emulsifiers with a larger hydrophilic head group tend to curve around oil droplets (favouring O/W), while those with bulkier hydrophobic tails favour W/O. This is quantified by the Hydrophile–Lipophile Balance (HLB) number — values above 8 typically stabilise O/W emulsions, and values below 6 stabilise W/O emulsions.

A typical soap molecule, sodium stearate ($\text{C}_{17}\text{H}_{35}\text{COO}^{-}\text{Na}^{+}$), has a long non-polar hydrocarbon chain (C₁₇H₃₅–) acting as the hydrophobic tail and a polar carboxylate group (–COO⁻) as the hydrophilic head. In water, the head is stabilised by ion–dipole interactions and hydrogen bonding, while the tail is repelled by water molecules (hydrophobic effect). At an air–water interface, surfactant molecules orient themselves with tails pointing away from the water surface, dramatically reducing surface tension. This surface-active behaviour gives the class its name.

Below the Critical Micelle Concentration (CMC), surfactant molecules exist as free monomers in solution. As concentration increases and reaches the CMC, it becomes thermodynamically favourable for molecules to aggregate: the hydrophobic tails cluster together in the interior of the micelle (away from water), while the hydrophilic heads face outward into the aqueous medium. A typical spherical micelle contains 40–100 surfactant molecules with an aggregation number (N) characteristic of each surfactant. For SDS in water, the CMC is approximately 8 × 10⁻³ mol L⁻¹ and N ≈ 62. Above the CMC, additional surfactant molecules join existing micelles rather than increasing the free monomer concentration, so many solution properties (conductivity, surface tension, osmotic pressure) show a sharp change at the CMC — the basis of experimental CMC determination. The thermodynamic driving force is the entropy gain from releasing ordered water molecules ('icebergs') that surrounded the hydrophobic tails; this is the classic hydrophobic effect described by ΔG°mic = RT ln(CMC).

Grease and oil on skin or fabric are non-polar and insoluble in water alone. When soap solution is applied, the hydrocarbon tails of surfactant molecules dissolve into the grease droplet (like dissolves like), while the ionic heads remain in the aqueous phase. As more molecules insert themselves at the grease–water interface, the grease is progressively surrounded by a layer of surfactant molecules oriented tails-inward, heads-outward. Mechanical agitation (rubbing, washing) breaks the grease into tiny droplets, each encapsulated in a micelle-like structure called an emulsion droplet or oil-in-water emulsion globule. The negatively charged outer surface of each droplet (from –COO⁻ or –OSO₃⁻ groups) creates electrostatic repulsion between droplets, preventing re-coalescence and keeping the grease stably suspended — it can then be rinsed away with water. Hard water contains Ca²⁺ and Mg²⁺ ions that react with soap to form insoluble calcium and magnesium stearate salts (scum): $2\,\text{C}_{17}\text{H}_{35}\text{COO}^{-} + \text{Ca}^{2+} \rightarrow (\text{C}_{17}\text{H}_{35}\text{COO})_2\text{Ca}\downarrow$. Synthetic detergents (sulphonate-based) do not form such precipitates and work effectively in hard water.

• \Delta G^\circ_{\text{mic}} — Standard Gibbs free energy of micellisation (J mol⁻¹): Energy released (negative value) when surfactant monomers self-assemble into micelles under standard conditions; a negative value indicates spontaneous micelle formation.
• R — Universal gas constant (J mol⁻¹ K⁻¹): R = 8.314 J mol⁻¹ K⁻¹; links macroscopic energy to molecular-scale thermal motion.
• T — Absolute temperature (K): Temperature in kelvin; higher temperature increases thermal agitation and affects the CMC.
• \text{CMC} — Critical Micelle Concentration (mol L⁻¹): The threshold surfactant concentration above which micelles spontaneously form; a lower CMC gives a more negative ΔG°mic, meaning micelle formation is more thermodynamically favourable.

Problem. Sodium dodecyl sulphate (SDS) has a CMC of 8.2 × 10⁻³ mol L⁻¹ at 298 K. (a) Calculate the standard Gibbs free energy of micellisation. (b) Is the process spontaneous? (c) A student prepares 500 mL of 0.020 mol L⁻¹ SDS solution. Explain whether micelles are present and estimate the approximate free monomer concentration.

Answer. ΔG°mic ≈ −11.9 kJ mol⁻¹ (spontaneous). Micelles are present; free monomer concentration ≈ 8.2 × 10⁻³ mol L⁻¹.

• Tyndall Effect and Colloidal Properties — Emulsions are a sub-class of colloids; understanding general colloidal properties (particle size, scattering, stability) provides the framework within which emulsion behaviour is explained.
• Adsorption and Surface Tension — Surfactants reduce surface tension by adsorbing at liquid–air and liquid–liquid interfaces; the Gibbs adsorption isotherm quantitatively links surface excess concentration to surface tension reduction.
• Gibbs Free Energy and Spontaneity — The thermodynamic criterion for micelle formation (ΔG°mic < 0) and the calculation of CMC from free energy require a solid understanding of ΔG, enthalpy, and entropy relationships.
• Hydrophobic Effect and Intermolecular Forces — The driving force for micelle assembly is the hydrophobic effect — entropy-driven release of structured water from around non-polar groups — which connects directly to intermolecular forces and solubility principles.