Thermodynamics, kinetics, and structural physics of atoms and molecules at solid–vapour, solid–liquid, and solid–solid interfaces. Langmuir adsorption isotherm (Langmuir 1918, JACS 40:1361) — for non-interacting adsorbates on a uniform…
surface-science
Langmuir isotherm: θ(p) = Kp/(1 + Kp)
Langmuir adsorption isotherm (Langmuir 1918, JACS 40:1361) for non-interacting adsorbates on a uniform array of equivalent binding sites at…
BET: v/v_m = cx/((1−x)(1−(1−c)x)), x = p/p₀
Brunauer–Emmett–Teller multilayer isotherm (BET 1938, JACS 60:309) generalises Langmuir to physisorption where multilayer stacking is…
Wulff construction: h(n̂)/γ(n̂) = const
Wulff construction (Wulff 1901, Z. Krystallogr. Mineral 34:449) — the equilibrium shape of a single-component crystal minimises the total…
θ(Kp=1) = 1/2, lim_{p→∞} θ = 1, dθ/dp|₀ = K (exact)
Closed-form pins of the Langmuir isotherm at its three characteristic points. (i) Half-coverage — at the condition Kp = 1 (i.e. p = 1/K,…
BET at c=10, x=1/2: v/v_m = 20/11 (exact)
Closed-form rational evaluation of the BET isotherm at representative moderate-binding parameters c = 10 and intermediate-pressure x = p/p₀…
h_{110}/h_{100} = √2 at γ ratio √2 (exact)
Closed-form evaluation of the Wulff facet-distance ratio using the fcc hard-sphere nearest-neighbour-counting estimates. For an fcc…