Colloid and interface chemistry — IUPAC Division I / VI treatment of disperse systems and the thermodynamics of their bounding interfaces. Foundations: surface tension γ as the isothermal-isobaric Gibbs free-energy cost per unit new-area…
colloid-and-interface-chemistry
Young-Laplace overpressure ΔP = 2γ/R across a spherical meniscus
Young-Laplace equation (Young 1805, Laplace 1806): the pressure jump across a curved liquid-gas interface equals surface tension γ times…
Young equation γ_lv cos θ = γ_sv − γ_sl (three-phase contact)
Young equation (Young 1805): horizontal force balance at the liquid-solid-vapour contact line determines the contact angle θ. Complete…
DLVO total V(H) = V_vdW(H) + V_el(H) (van der Waals + double-layer)
DLVO theory (Derjaguin-Landau 1941; Verwey-Overbeek 1948): total interaction between two charged colloidal particles = attractive Hamaker…
ΔP = 2γ/R at γ=R=1 ⇒ ΔP = 2 (unit-droplet canonical)
Sympy-exact witness of the Young-Laplace 2γ/R scaling. At γ = R = 1 (dimensionless reference) the pressure jump across the interface is…
Young cos θ at (γ_sv, γ_sl, γ_lv) = (1, 0, 1): cos θ = 1 ⇒ θ = 0 (full wet)
Sympy-exact witness of the Young-equation full-wetting limit. Setup: γ_sv=1, γ_sl=0, γ_lv=1 gives cos θ = 1 exactly, θ = 0 (complete…
Micellisation ΔG_mic = −RT ln CMC: at ΔG=−RT ln 2 ⇒ CMC = 1/2
Sympy-exact witness of the critical-micelle-concentration signature at the one-bit free-energy threshold. Setup: take R=T=1…
Stokes-Einstein framework: D = k_B·T/(6πηR) (Brownian diffusion of a sphere in viscous fluid)
The Stokes-Einstein relation — Einstein 1905 doctoral-thesis derivation equating the fluctuation-dissipation pair (Brownian stochastic…
Langmuir adsorption framework: θ = K·p/(1 + K·p) (1:1 single-site surface equilibrium)
The Langmuir 1918 single-site adsorption isotherm — the canonical equilibrium-surface-coverage law derived from three textbook assumptions:…
Kelvin framework: ln(p/p_sat) = 2γ·V_m/(r·R·T) (curvature → vapor-pressure shift)
The Kelvin (Thomson 1871) equation — the thermodynamic consequence of Young-Laplace curvature pressure on a droplet's or meniscus's vapor…
Stokes-Einstein: D·(6π·η·R) = k_B·T (invariant product); R_H = k_B·T/(6π·η·D)
Sympy-exact symbolic witness of the Stokes-Einstein invariant. Setup: D = k_B·T/(6π·η·R) as a sympy expression with D, k_B, T, η, R all…
Langmuir: θ(Kp = 1) = 1/2 (half-coverage); dθ/dp|_{p=0} = K (Henry slope)
Sympy-exact symbolic witness of the Langmuir half-coverage anchor and Henry-law limit. Setup: θ(p) = K·p/(1 + K·p) with K, p positive…
Kelvin: ln(p/p_sat)|_r / ln(p/p_sat)|_{2r} = 2 (curvature-doubling fingerprint)
Sympy-exact symbolic witness of the Kelvin curvature-doubling fingerprint. Setup: ln(p/p_sat) = 2·γ·V_m/(r·R_gas·T) as a sympy expression…
Gibbs-Thomson effect
Equilibrium vapor pressure / solubility increases with curvature: ln(P/P0) = 2 gamma V_m / (r R T); drives Ostwald ripening (small…
DLVO theory (extended)
Derjaguin-Landau-Verwey-Overbeek 1941-48: total interaction = double-layer-repulsion + van-der-Waals-attraction; secondary minimum at ~10…
Zeta potential (electrokinetic)
Helmholtz-Smoluchowski 1879/1903: electrophoretic mobility u = epsilon zeta / eta; zeta-potential at slip-plane characterizes colloidal…
Contact angle (Young equation)
Young 1805: cos theta = (gamma_SV - gamma_SL) / gamma_LV; foundation of wettability + capillary phenomena; theta < 90 hydrophilic, > 90…
Emulsion stability (Bancroft rule)
Bancroft 1913: phase in which emulsifier is more soluble becomes the continuous phase; HLB hydrophilic-lipophilic-balance index (Griffin…
Steric stabilization (polymer-grafted)
Napper 1983: grafted polymer brushes on colloid prevent close approach via osmotic + entropic repulsion; PEG-coated nanoparticles stable in…
Pickering emulsion (particle-stabilized)
Pickering 1907: solid particles at o/w interface stabilize emulsions without surfactant; hydrophilic + hydrophobic particle balance…
Kelvin equation (1871)
Lord Kelvin 1871 ln(p/p0)=2γV/rRT; modern nanoporous + capillary-condensation + atmospheric-aerosol nucleation.
Young-Laplace (1805)
T Young-P S Laplace 1805 ΔP=γ(1/R1+1/R2); modern microfluidic-droplet + lung-surfactant + electrowetting EWOD.
Zsigmondy (1903)
R Zsigmondy 1903 (Nobel 1925) ultramicroscope colloidal-gold; modern dynamic-light-scattering DLS + nanoparticle-tracking analysis.
BET (Brunauer-Emmett-Teller 1938)
S Brunauer-P Emmett-E Teller 1938 BET-isotherm; modern multilayer-adsorption + N2-77K surface-area + MOFs 7000+ m²/g.
Pickering emulsion (1907)
S Pickering 1907 + Ramsden 1903 particle-stabilized emulsion; modern Janus-particles + bijel + active-Pickering colloid.
Self-assembly (Whitesides 2002)
G Whitesides 2002 self-assembly review; modern static + dynamic SA + DNA-mediated programmable nanoparticle crystals.