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…