Colloids and Emulsions

01 / UNDERSTAND & APPLY

1. Classify the dispersed phase and the continuous medium separately

A colloidal dispersion contains structures large compared with ordinary small molecules but small enough that interfacial and thermal effects are important. A common introductory size range is roughly 1–1000 nm, but the boundaries are conventional and behaviour matters. A colloid can look uniform to the eye while remaining heterogeneous on a microscopic scale.

The dispersed phase consists of the particles, droplets or bubbles. The dispersion medium is the continuous surrounding material. Naming both prevents many classification errors: fog is liquid droplets in gas, smoke contains solid particles in gas, and an oil-in-water emulsion contains oil droplets in continuous water. A gas–gas mixture is molecularly mixed rather than a conventional colloidal dispersion.

A sol commonly means solid particles dispersed in a liquid. An emulsion is one liquid dispersed in another immiscible liquid. A foam has gas bubbles in a liquid or solid medium. An aerosol has liquid droplets or solid particles in a gas. A gel is a liquid-containing network with a solid-like mechanical response; treating every gel as isolated liquid spheres inside a rigid solid oversimplifies its structure.

Classification by phase differs from classification by how colloidal entities are formed. Multimolecular colloids contain aggregates of many small units, macromolecular colloids can consist of individual large polymer molecules, and associated colloids arise from reversible self-assembly such as micelles. The same word “particle” may therefore refer to a solid crystallite, a droplet or a molecular aggregate.

A molecular solution, colloid and coarse suspension form a continuum of sizes and behaviours rather than three materials separated by an exact visible boundary. Ordinary paper filtration often retains a coarse suspension but not a colloid; a suitable membrane can distinguish sizes more finely. Do not claim that every colloid is permanently stable or that every molecular solution scatters absolutely no light.

02 / UNDERSTAND & APPLY

2. Light scattering and Brownian motion reveal different aspects of a dispersion

The Tyndall effect is visible scattering of light by dispersed structures with sufficient size and refractive-index contrast. A beam can become visible from the side because some light is redirected toward the observer. The observed intensity depends on particle size, concentration, wavelength and refractive-index contrast, so lack of a dramatic visible beam does not alone prove a sample is a molecular solution.

Brownian motion is irregular motion of suspended particles driven by fluctuating molecular impacts from the surrounding fluid. It is not self-propulsion and is not the same as the motion of every solvent molecule. Thermal motion can help small particles remain distributed, but it does not by itself prevent them from sticking together after collision.

For dilute spherical particles in a simple continuum liquid, the Stokes–Einstein model gives D=k_BT/(6πηr), where D is translational diffusion coefficient, η viscosity and r hydrodynamic radius. At the same temperature and viscosity, smaller particles diffuse faster. A hydrated or polymer-coated particle’s hydrodynamic radius can exceed the size of its solid core.

For low-Reynolds-number settling of a dilute sphere, Stokes’ model gives speed v=2Δρgr²/(9η), with Δρ the density difference. Its r² dependence explains why aggregation can greatly accelerate settling. These formulas require their stated idealizations; concentrated, nonspherical or strongly interacting dispersions need more careful treatment.

A colloid may be kinetically long-lived even if aggregation would lower interfacial free energy. Slow settling and a barrier to particle attachment are distinct contributions to that persistence. Centrifugation increases the effective body force and can separate particles that settle very slowly under ordinary gravity.

03 / UNDERSTAND & APPLY

3. Preparation changes size; purification removes selected small species

Dispersion methods break larger material into colloidal-sized structures, while condensation methods assemble small molecular or ionic units into larger particles. Mechanical dispersion and controlled particle formation are broad concepts, not guarantees that every chemical system will yield a stable sol. A stabilizing surface environment is often needed to keep newly formed particles apart.

Peptization is conversion of a freshly formed aggregate or precipitate into a colloidal dispersion by a suitable adsorbing species or change in medium. Surface charging can help separate particles. It is not identical to dissolving the material into individual ions, even though both processes can make a coarse precipitate disappear from view.

Dialysis uses a membrane permeable to small ions or molecules but retaining the relevant colloidal species. Diffusion down a concentration gradient removes diffusible impurities from the retained compartment. The membrane cutoff and the sizes of all species matter; not every ion-selective or semipermeable membrane performs the same separation.

Electrodialysis uses an electric field with suitable membranes to enhance ion transport. Ultrafiltration uses a pressure-driven membrane to retain larger entities while allowing smaller components and solvent through. These are separations based on transport and selectivity, not chemical transformations of every impurity.

Removing too much electrolyte can sometimes change a sol’s stability if particular adsorbed ions help maintain its surface charge. Conversely, excess electrolyte can destabilize a charge-stabilized sol by screening repulsion. Purification therefore requires the actual colloid chemistry to be considered rather than an assumption that “less salt is always better”.

04 / UNDERSTAND & APPLY

4. Surface charge is surrounded by compensating ions

Colloidal particles can acquire charge through surface-group ionization, selective adsorption of ions or other interfacial processes. A negatively charged particle is accompanied by an excess of positive counterions in its surrounding liquid, preserving overall electroneutrality. The charge is not an isolated uncompensated creation of electricity.

A simplified electrical double layer contains charge near the particle surface and a more diffuse compensating ionic atmosphere. Two particles with like-sign charge can repel as these environments overlap. Electrolyte can shorten the range of this repulsion, while specifically adsorbed ions can also change the surface charge itself.

The zeta potential describes the potential at a hydrodynamic slipping plane relative to the bulk liquid, rather than necessarily the exact potential at the solid surface. Its sign and magnitude can help characterize electrokinetic behaviour, but it is not a universal standalone stability test for every sterically stabilized or complex dispersion.

In simple electrophoresis, charged particles move relative to the liquid in an applied electric field. A negative sol moves toward the positive electrode, the anode, in the usual externally powered arrangement. Electro-osmosis instead refers to liquid motion relative to a stationary charged surface. Confusing which component moves leads to a wrong identification.

The sign of a sol can depend on preparation conditions. For a standard silver iodide illustration, adsorption of excess iodide is associated with a negative particle surface, whereas excess silver ions can produce a positive surface. The compound formula AgI alone therefore does not uniquely specify the sol charge.

05 / UNDERSTAND & APPLY

5. Stability can be electrostatic, steric or both

Coagulation or aggregation occurs when particles attach to form larger structures. Flocculation often denotes formation of loose clusters, while coalescence is fusion of liquid droplets into larger droplets. Terminology varies somewhat by field, so identify the structural event rather than using every word as an exact synonym.

For many charge-stabilized lyophobic sols, increasing electrolyte concentration screens repulsion and allows attractive interactions to dominate. The critical coagulation concentration is the concentration associated with a defined rapid-aggregation criterion under a specified protocol. A smaller value indicates stronger coagulating action in that comparison.

The Hardy–Schulze rule is a qualitative trend that higher-charge counterions are often much more effective at coagulating oppositely charged lyophobic particles. It does not say that the co-ion controls the trend. Nor is a universal exact inverse-sixth-power concentration law guaranteed across all surfaces, ionic species and pH values.

Lyophilic means favourable interaction with the dispersion medium; hydrophilic is the water-specific case. Solvation and adsorbed or attached polymer layers can help stabilize particles. Steric stabilization occurs when approaching particles would compress or overlap solvated chains in an unfavourable way. Such a dispersion need not rely exclusively on a large surface charge.

A protective colloid can stabilize an otherwise sensitive sol by forming an appropriate interfacial layer. The traditional gold number compares the minimum protective-colloid mass required to prevent a specified gold-sol colour change in a standardized electrolyte test; smaller values indicate greater protective action only within the same test protocol. It is not an intrinsic number independent of the assay.

Polymer addition is not invariably protective. Too little coverage can promote bridging between particles, and changes in solvent quality can collapse a protective layer. Protein dispersions can aggregate when pH reduces net charge or heating changes structure. A stability explanation should name the particular barrier being strengthened or removed.

06 / UNDERSTAND & APPLY

6. Distinguish droplets, their interface and the surrounding phase

In an oil-in-water emulsion, oil is dispersed and water is continuous. In a water-in-oil emulsion, those roles reverse. Milk is commonly treated as an oil-in-water example, while butter has a water-in-fat continuous structure. Real foods can contain proteins, crystals and other dispersed components as well, so these labels describe their principal emulsion topology.

An emulsifier accumulates at the oil–water interface and can lower interfacial tension while providing electrostatic or steric barriers to droplet coalescence. A familiar amphiphile has a water-compatible head group and an oil-compatible hydrocarbon region. In an oil droplet surrounded by water, heads generally face the water and tails point into the oil-rich region.

Forming many small droplets creates more interfacial area than maintaining two large separated liquid layers. For a positive interfacial tension, creating this area has a free-energy cost. Ordinary emulsions are typically kinetically stabilized rather than automatically thermodynamically stable. Equilibrium microemulsions are a distinct class requiring suitable compositions; the prefix “micro” alone does not establish their nature.

Creaming is migration of droplets upward when they are less dense than the continuous phase; sedimentation is downward migration for denser droplets. Neither necessarily means the droplets have fused. Coalescence destroys the separating films and produces larger droplets. A creamed emulsion may redisperse, while a fully broken one may not recover by the same mild action.

Dilution and conductivity tests can help identify a continuous phase when their conditions are suitable: an oil-in-water emulsion often dilutes with water and conducts through its aqueous phase if ions are present. Conductivity alone is not infallible, because composition and additives influence it. Use several observations rather than one memorized label.

07 / UNDERSTAND & APPLY

7. Surface tension is force per length and reversible work per area

For a fluid interface at fixed temperature and appropriate composition, surface tension γ is the reversible free-energy cost per unit additional area. It also appears as a tangential force per unit contact-line length. Its SI units N m⁻¹ equal J m⁻². A liquid interface is not a literal solid skin, even though an elastic-sheet analogy can help visualize area reduction.

If γ is effectively constant, the reversible work to create additional total interfacial area is W=γΔA. A soap film has two liquid–air interfaces, so pulling a straight movable wire of length L requires force 2γL in the simple geometry. A single liquid interface contributes γL for the corresponding contact line. Counting surfaces is essential.

At an air–water interface, many amphiphiles arrange water-compatible heads in water while hydrophobic portions avoid water. Their adsorption can lower the interfacial free-energy cost, reducing surface tension. An ionic head can be anionic or cationic; nonionic and zwitterionic surfactants also exist. “Surfactant” is a functional class, not a synonym for one specific salt.

Sodium dodecyl sulfate contains a sulfate ester head, CH₃(CH₂)₁₁–O–SO₃⁻ with Na⁺. A sulfonate instead has a direct carbon–sulfur connection such as R–SO₃⁻. Those names and connectivities must not be interchanged. This distinction matters in interpreting structural formulas, even when both substances can act as surfactants.

Surface tension depends on temperature and composition. For many pure liquids it decreases as temperature rises toward the critical point. Surfactant adsorption can also take time, so a newly formed interface may have a different dynamic surface tension from its long-time equilibrium value. A single quoted γ should be used only for the state or approximation specified.

08 / UNDERSTAND & APPLY

8. Derive curvature pressure and capillary rise with the correct geometry

For a spherical liquid droplet of radius r with one interface, a small expansion gives dV=4πr²dr and dA=8πrdr. Balancing reversible pressure work ΔP dV with γdA gives ΔP=2γ/r. Here ΔP is the pressure inside minus outside for the convex droplet. A spherical gas bubble within a liquid also has one interface and the corresponding excess interior pressure is 2γ/r.

A thin soap bubble in air has inner and outer liquid–air interfaces of nearly equal radius. Their area contributions give approximately ΔP=4γ/r between the inner and outer gases, assuming the same surface tension on both faces and negligible film thickness. A rubber balloon has an elastic membrane with different mechanics, so one cannot automatically apply a constant-γ soap-bubble formula to it.

For a wetting liquid rising in a narrow cylindrical tube, the vertical surface-tension force is 2πrγ cosθ, with contact angle θ measured through the liquid. Balancing it against the weight πr²hρg gives h=2γ cosθ/(ρgr), neglecting gas density and the small meniscus-volume correction. If θ exceeds 90°, cosθ is negative and the formula describes depression rather than rise.

Breaking one spherical droplet of radius R into N equal spherical droplets conserves liquid volume: NR_small³=R³. The total final area is N4πR_small²=4πR²N^(1/3). Thus making more droplets raises area and requires reversible interfacial work if γ remains positive and constant. Surfactants can reduce that work but do not make the geometric increase disappear.

Use radius rather than diameter in these formulas, convert millimetres to metres, and distinguish total area from the area of one droplet. Check whether one or two interfaces are present before multiplying by a factor of two. These are model calculations for well-defined shapes, not a complete prediction of every emulsion’s flow or breakup.

09 / UNDERSTAND & APPLY

9. Micelles are dynamic molecular aggregates, not tiny soap bubbles

Above a suitable critical micelle concentration, CMC, many surfactants in water assemble into aggregates with hydrocarbon-rich interiors and water-compatible head groups exposed to the aqueous surroundings. A spherical micelle has no gas core and is not a thin liquid film enclosing air. Its molecules exchange with the surrounding monomer population.

The CMC is an operational concentration range associated with changes in properties such as surface tension or conductivity. It depends on surfactant structure, temperature, added electrolyte and solvent composition. For many ionic surfactants, a Krafft temperature marks a solubility-related threshold below which ordinary micelle formation is restricted; it is distinct from the concentration threshold CMC.

Above the CMC, a useful elementary approximation treats free monomer concentration as nearly fixed near the CMC and places most added surfactant into micelles. This is not exact at arbitrary concentration. Aggregation number is the number of surfactant molecules per micelle under the stated conditions, and it can change with environment and aggregate shape.

In a nonpolar solvent, reverse micelles can have polar head groups inward and hydrocarbon portions outward. Bilayers use a different arrangement: two molecular leaflets place hydrophobic tails against each other and expose polar heads on both outer faces. A vesicle encloses an aqueous compartment with such a bilayer; it is not structurally identical to a normal micelle.

Micellar solubilization can incorporate hydrophobic material into aggregate interiors, while emulsification stabilizes larger droplets with an interfacial layer. Both involve amphiphiles but are not the same size or structural process. Cleaning also involves wetting, detachment, dispersion and rinsing, so it should not be reduced to one static sphere drawing.

10 / UNDERSTAND & APPLY

10. Solved practice: classify, count and check the interface

The most useful final check is to name the continuous phase, the stabilizing mechanism and the object being counted. A counterion is selected by particle charge; a micelle count requires aggregation number; surface work requires total new area. The original exercises below keep these decisions explicit.