Chemistry · Analytical and physical chemistry · Year 2

Colloids and adsorption

Why do fine particles stick together and settle when aluminium sulfate is added to cloudy water?

The situation

Turbid water from the Chirchiq River flows into a water treatment plant in Tashkent; add a little aluminium sulfate and within a few minutes the fine particles stick together into flocs and sink to the bottom of the basin. Why do these particles not settle on their own for weeks, yet settle suddenly when a little salt is added? In the laboratory, meanwhile, activated carbon absorbs ethanoic acid, micelles appear in a soap solution, and a laser beam leaves a bright track in an iron(III) hydroxide sol. What laws govern the world of surfaces and nanometre-sized particles?

Topic

Colloid chemistry: adsorption, surfactants and sols. Water treatment plant in Tashkent: aluminium sulfate is added to the muddy water of the Chirchik river, and fine particles “stick together” and settle. In the laboratory…

Key ideas

Adsorption isotherm
Micelle and CMC
Coagulation

Formulas

a = a_{\infty} \frac{K c}{1 + K c}, \frac{c}{a} = \frac{1}{a_{\infty} K} + \frac{c}{a_{\infty}}, S = a_{\infty} N_{A} s_{0}

The Langmuir isotherm and the specific surface area of an adsorbent ( $s_{0}$ — the area occupied by one molecule).

Γ = - \frac{c}{R T} \frac{d σ}{d c}

The Gibbs adsorption equation: a substance that lowers the surface tension accumulates at the surface ( $Γ > 0$ ).

u = \frac{ε ε_{0} ζ}{η} E, v = \frac{2 r^{2} (ρ - ρ_{0}) g}{9 η}

The Smoluchowski equation (electrophoretic speed) and Stokes' equation (settling speed).

c_{k} \propto \frac{1}{z^{6}} : 1 : \frac{1}{64} : \frac{1}{729}

The Schulze–Hardy rule: the coagulation threshold is inversely proportional to the sixth power of the charge of the counter-ion.

U (h) = - \frac{A a}{12 h} + 32 π ε ε_{0} a {(\frac{k T}{z e})}^{2} γ^{2} e^{- κ h}

DLVO: van der Waals attraction and the repulsion of the electrical double layers; increasing the electrolyte $κ$ lowers the barrier.

Theory

Disperse systems and surface phenomena

A disperse system is one in which one substance (the dispersed phase) is spread as small particles through another (the dispersion medium). By particle size: true solutions (< 1 nm), colloidal systems (1–100 nm) and coarse disperse systems (suspensions, emulsions, > 100 nm–1 µm); by state of matter: sol, emulsion, foam, aerosol (fog, smoke), suspension, gel, solid foam. Systems strongly bound to the medium are lyophilic (solutions of proteins and starch), weakly bound ones are lyophobic (sols of metals, AgI, Fe(OH)₃). When a particle gets smaller, its specific surface area rises sharply (a cube of 1 cm reduced to 10 nm: from 6 cm²/cm³ to 600 m²/cm³), so surface energy becomes decisive — this is the basis of nanochemistry (nanoparticles, nanotubes, nanocomposites). Molecules in the surface layer are pulled inwards — this gives the surface tension σ (J/m² = N/m). Cohesion is the attraction between particles of the same substance, adhesion that between different substances; their ratio determines the contact angle (Young), the spreading of a liquid and its rise in capillaries (“Surface tension and capillarity”). Rebinder method (laboratory): the greatest pressure needed to push a bubble out of the tip of a capillary is $p = 2 σ / r$ ; the manometer reading is compared with that for water: $σ = σ_{0} Δ h / Δ h_{0}$ . From $σ (T)$ we get the surface entropy $- d σ / d T$ and the surface enthalpy $h = σ - T d σ / d T$ , and from the Eötvös rule $σ V_{m}^{2 / 3} = k (T_{c} - 6 - T)$ the critical temperature. Rebinder effect: adsorption of surfactants lowers the strength of a solid (used in drilling).

Adsorption: Henry, Freundlich, Langmuir, BET

Adsorption is the accumulation of a substance at a phase boundary; it occurs spontaneously ( $Δ G < 0$ ), and since the molecules become more ordered $Δ S < 0$ , so $Δ H < 0$ — it is exothermic (physical 5–40, chemical 40–400 kJ/mol). At low concentration Henry's law applies, $a = K_{H} c$ ( $K_{H}$ is Henry's constant); at intermediate concentration Freundlich, $a = k c^{1 / n}$ ; Langmuir theory assumes identical sites on the surface and a single layer — $a = a_{\infty} K c / (1 + K c)$ ; from the straight line of $c / a$ against $c$ we find $a_{\infty}$ and $K$ , and then the specific surface area $S = a_{\infty} N_{A} s_{0}$ . Multilayer adsorption is described by BET theory (linear form at $p / p_{0}$ = 0.05–0.3, N₂ at 77 K, $s_{0}$ = 0.162 nm²); the Polanyi potential theory and the Dubinin–Radushkevich equation describe the volume filling of micropores (activated carbon, 500–1500 m²/g); in mesopores capillary condensation (Kelvin equation) and adsorption hysteresis occur. Adsorbents: charcoal (gas masks, water filters), silica gel, alumina gel, zeolites; ion exchange (ion exchangers) is the basis of chromatography. Adsorption at the surface of a solution follows the Gibbs equation; for alcohols there is the Szyszkowski equation and Traube's rule: each CH₂ group raises the surface activity about 3.2 times. Laboratory: 1.00 g of charcoal and 50 mL of CH₃COOH of different concentrations are put in each of 6 flasks and shaken for 20 min; 10 mL of the filtrate is titrated with 0.1 mol/L NaOH using phenolphthalein: $a = (c_{0} - c) V / m$ . Safety: ethanoic acid and NaOH — wear goggles; do not breathe in charcoal dust.

Surfactants, micelles, emulsions and foams

A surfactant molecule has two parts: a hydrophobic hydrocarbon tail and a hydrophilic head. Types: anionic (soaps, sodium dodecyl sulfate — SDS), cationic (quaternary ammonium salts), non-ionic (ethoxylated alcohols), amphoteric. At low concentration the surfactant moves to the surface (σ falls); above the critical micelle concentration (CMC), spherical micelles appear in the solution (SDS: CMC ≈ 8.2 mmol/L at 25 °C; ≈ 60 molecules): σ hardly changes, and the molar conductivity falls sharply (counter-ions bind to the micelle) — this is the break point on the graph. Micelle formation is mainly an entropy-driven process (the hydrophobic effect: water molecules are freed), $Δ G \approx R T \ln (CMC)$ . Substances that dissolve in oil dissolve inside the micelle — solubilisation (the cleaning action; “Acids, esters and soap”). Emulsions: oil in water (O/W) and water in oil (W/O); by Bancroft's rule the phase in which the emulsifier is more soluble becomes the medium (Na soap → O/W, Ca soap → W/O); the type is determined by dilution, by dye (methylene blue — in water, Sudan III — in oil) and by electrical conductivity. Foams are stabilised by films of surfactant or protein. Biological membranes are phospholipid (sphingolipid, glycolipid) bilayers; cholesterol regulates membrane fluidity, and an excess of it in the blood leads to atherosclerosis; the membranes of prokaryotic and eukaryotic cells are built on this basis.

Sols: preparation, purification, molecular-kinetic and optical properties

Preparation: dispersion (colloid mill, ultrasound, sputtering of a metal in an electric arc — Bredig; peptisation — turning a fresh precipitate into a sol with an electrolyte) and condensation — chemical: $FeCl_{3} + 3 H_{2} O \overset{\overset{}{t}}{\to} Fe (OH)_{3} + 3 HCl$ (added dropwise to boiling water), $AgNO_{3} + KI \overset{}{\to} AgI + KNO_{3}$ ; physical: pouring an alcoholic solution of sulfur into water. Micelle structure (Paneth–Fajans rule: an excess ion that fits into the crystal lattice becomes the potential-determining ion): with excess KI, ${{[AgI]}_{m} n I^{-} (n - x) K^{+}}^{x -} x K^{+}$ , and for Fe(OH)₃, ${{[F e {(O H)}_{3}]}_{m} n F e O^{+} (n - x) C l^{-}}^{x +} x C l^{-}$ . Purification: dialysis (Graham), electrodialysis, ultrafiltration, ultracentrifuge. Molecular-kinetic properties: Brownian motion, diffusion $D = k T / (6 π η r)$ , the Perrin equation $n_{h} = n_{0} e^{- m^{'} g h / k T}$ , sedimentation (Stokes) and sedimentation–diffusion equilibrium; the osmotic pressure of colloids is very small (“Brownian motion and diffusion”). Sedimentation analysis: the mass of sediment $m (t)$ on a balance pan; from the breaks in the curve, $t_{i}$ → $r = \sqrt{9 η H / (2 Δ ρ g t)}$ . Optical properties: sideways scattering — the Tyndall effect (Rayleigh: $I \propto ν V^{2} / λ^{4}$ , blue light is scattered about 4 times more strongly than red), the nephelometer, the ultramicroscope (Zsigmondy), electron microscopy, X-ray diffraction; a gold sol is ruby red (plasmon absorption ≈ 520 nm).

Electrical properties: the electrical double layer and electrokinetic phenomena

Potential-determining ions are adsorbed on the particle surface, or surface groups dissociate — an electrical double layer forms. Helmholtz–Perrin: a plane capacitor; Gouy–Chapman: the counter-ions are spread through a diffuse layer by thermal motion, whose thickness is the Debye length $κ^{- 1}$ ≈ $0.304 / \sqrt{I}$ nm (1:1 electrolyte, 25 °C); Stern: a dense adsorbed layer plus a diffuse layer. The boundary of the liquid that moves along with the particle is the slipping plane, and the potential there is the zeta potential ζ. The movement of particles in an electric field is electrophoresis ( $u = ε ε_{0} ζ E / η$ , Smoluchowski), the movement of liquid through a porous barrier is electro-osmosis (Reuss, 1809); the reverse phenomena are the streaming potential and the sedimentation potential (Dorn). At a mercury–solution interface σ depends on the potential: the electrocapillary curve, Lippmann's first equation $\partial σ / \partial φ = - q$ and second equation $\partial^{2} σ / \partial φ^{2} = - C$ (capillary electrometer). Polyelectrolytes and proteins are charged macroions; if they are separated by a semipermeable membrane, small ions distribute unevenly — the Donnan equilibrium and the membrane potential. Laboratory: in a Burton U-tube buffer is carefully poured on top of the sol, 100–250 V is applied to the electrodes and the shift $s$ of the boundary is recorded against time: $ζ = η s / (ε ε_{0} E t)$ . Safety: high voltage — do not touch the electrodes until the supply is switched off.

Stability, coagulation, gels; safety and the model

A sol has kinetic stability (it does not settle) and aggregative stability (its particles do not stick together). In DLVO theory (Derjaguin, Landau, Verwey, Overbeek) the energy between particles is the sum of van der Waals attraction and the repulsion of the diffuse layers; if the barrier is several tens of $k T$ , the sol is stable. When electrolyte is added the diffuse layer shrinks ( $κ$ increases) and the barrier disappears — this is coagulation; the lowest concentration that starts it is the coagulation threshold $c_{k}$ . Schulze–Hardy rule: coagulation is caused by the ion of charge opposite to that of the particle, $c_{k} \propto z^{- 6}$ (As₂S₃ sol: NaCl 51, MgCl₂ 0.72, AlCl₃ 0.093 mmol/L). A mixture of electrolytes acts additively, antagonistically or synergistically; if there is an excess of a multiply charged ion, the sol is recharged (irregular series). Sols with opposite charges coagulate each other — mutual coagulation: in water treatment negatively charged clay particles stick to positive Al(OH)₃ flocs and settle; waste water, aerosols (electrostatic precipitators) and soil colloids obey the same laws. The rate of rapid coagulation is given by Smoluchowski's theory. Gels: setting, thixotropy (bentonite clay becomes fluid when shaken), syneresis (contraction of a gel), diffusion in a gel and Liesegang rings (periodic precipitate). Safety: AgNO₃ stains the skin black; FeCl₃ and HCl vapours — use a fume cupboard; do not point a laser beam at the eyes. Model: the Langmuir, BET, Szyszkowski and CMC parameters are model numbers of the same order as in the literature; in DLVO the Hamaker constant and surface potential are chosen so that the thresholds match classical values; the residual turbidity in the jar test is a model curve; time is accelerated.

Did you know?

The term “colloid” was introduced in 1861 by the Scottish chemist Thomas Graham (from the Greek “kolla”, glue); he also proposed dialysis — separating colloids from crystalloids through a parchment membrane.
Samples of ruby-red gold sol prepared by Michael Faraday in the 1850s are still kept at the Royal Institution in London.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Extraction and chromatography — Year 2
Spectra: determining structure — Year 2
Alloys: phase diagrams — Year 2
Chemical kinetics and Arrhenius — Year 2
Catalysis and enzymes — Year 2
Computational chemistry and docking — Year 2