Physical chemistry

Colloids, emulsions, surfactants

Matter dispersed at the nanometre scale: why colloids neither dissolve nor settle, how surfactants build micelles and stabilise emulsions, and the forces — electrostatic, van der Waals, steric — that decide whether dispersions survive.

1 Lower secondary 2 Upper secondary 3 Undergraduate 4 Advanced 5 Research

IntuitionIntuition: dust that never lands

Milk, fog, paint, blood: none is a true solution, yet none settles out like sand in water. Their particles are colloidal — roughly 1 nm to 1 μm — big enough to scatter light but light enough for Brownian kicks from the solvent to fight gravity. Because nearly every atom of a small particle sits near its surface, the interface rules everything: coat the particles with charge or with molecules and you can make the dispersion last years, or collapse in seconds. Surfactants are molecules with a split personality — a water-loving head on an oil-loving tail — that do this coating on purpose.

A micelle built from surfactant molecules: hydrophilic heads face the water while hydrophobic tails pack into an oily core. Rotate the model and switch between the full micelle, heads only, and core only.

SchoolSchool: what a colloid is, and how to spot one

Definition: Colloid, Tyndall effect, emulsion, micelle

A colloid is a dispersion of particles of intermediate size (≈1 nm–1 μm) in a continuous medium — intermediate between true solutions (<1 nm) and coarse suspensions. Colloids scatter a light beam visibly (Tyndall effect) while true solutions do not. An emulsion is a liquid-in-liquid colloid (oil in water, or water in oil). A micelle is a self-assembled aggregate of surfactant molecules, typically 2–10 nm across, with polar heads outward and tails inward.

Table sugar vanishes into water; soapy water turns pearly. Soap molecules are surfactants: below a threshold concentration they sit at the water surface individually, but above the critical micelle concentration (CMC) they cooperatively form micelles so the greasy tails hide from water. That is why soap cleans: dirt and grease dissolve into micelle cores and rinse away with the water. Milk is stabilised the same way by casein proteins, mayonnaise by lecithin — biology and the kitchen run on colloid science.

Everyday colloids
Colloid	Dispersed phase / medium	Stabilised by
Milk	fat droplets / water	casein protein coat
Fog	water droplets / air	none needed (settles only slowly)
Blood	cells, proteins / plasma	charged glycoprotein surfaces
Ink	pigment particles / water	polymer dispersants

UndergraduateUniversity: self-assembly and why dispersions survive

Surfactant molecules pack according to geometry. The packing parameter P = v/(a₀l) compares the tail volume v and length l with the area a₀ each head group needs at the interface. Small P (bulky heads, slim tails) gives spherical micelles; larger P gives cylinders, then bilayers and vesicles; P near 1 and beyond gives flat membranes and inverted structures. The CMC itself is governed by the free energy of transferring a tail from water to oil-like environment — roughly −1 kT per CH₂ group.

P=\frac{v}{a_0 l}\qquad\begin{cases}P<1/3:\text{spherical micelles}\\1/3<P<1/2:\text{cylinders}\\1/2<P<1:\text{bilayers, vesicles}\\P>1:\text{inverted phases}\end{cases}

Why don’t bare colloidal particles just stick together and sink? DLVO theory adds two forces: an attractive van der Waals interaction (∝ −A_H/6r² between particles, with A_H the Hamaker constant) and a repulsive electrostatic term from the charged double layer each particle carries, decaying as exp(−κr) where κ⁻¹ is the Debye screening length. Their sum usually has a barrier at a few nanometres: particles must collide with enough energy to cross it. Adding salt shrinks κ⁻¹, lowers the barrier, and the sol flocculates — which is why river deltas silt up where fresh water meets brine, and why alum is dosed into drinking-water treatment.

V(r)\approx -\frac{A_H}{6}\frac{R}{r}\;+\;64\pi\epsilon R\,\frac{k_BT\,n_0}{\kappa^2}\tanh^2\!\Big(\frac{ze\psi_0}{4k_BT}\Big)e^{-\kappa r}

Example: Coagulating a gold sol

A citrate-stabilised gold sol stays red (dispersed) in pure water but turns blue and settles when 0.1 M NaCl is added. Explain in DLVO terms, and predict qualitatively whether 0.1 M CaCl₂ acts at lower, similar, or higher total ionic strength.

Solution

Na⁺ screens the negative citrate double layer: κ grows with √I, the Debye length falls, the DLVO barrier sinks below k_BT and particles aggregate; aggregation changes the plasmon colour red→blue. Divalent Ca²⁺ compresses double layers far more efficiently — the Schulze–Hardy rule puts the critical coagulation concentration roughly ∝ z⁻⁶ — so CaCl₂ flocculates at much lower ionic strength than NaCl.

AdvancedAdvanced: beyond DLVO — steric, depletion, Pickering

Real formulations add two more forces to the DLVO pair. Steric repulsion arises when grafted polymer layers on two particles overlap: compressing the coils costs entropy, giving a steep short-range repulsion that works even at high salt where charges are screened. Depletion attraction appears when small non-adsorbing polymers or micelles are excluded from the gap between particles; the osmotic pressure imbalance pushes the particles together, gently and reversibly. Emulsions can also be stabilised by solid particles that sit irreversibly at the interface (Pickering emulsions) — the droplets are armoured, not just charged.

References

Theory of Self-Assembly of Hydrocarbon Amphiphiles into Micelles and Bilayers · J. N. Israelachvili, D. J. Mitchell, B. W. Ninham, 1976
Emulsions · S. U. Pickering, 1907
Theory of the Stability of Lyophobic Colloids · B. Derjaguin, L. Landau, 1993