Past exam of the quantum condensed matter course of the University of Cambridge 2007 Section A A4 a Solution Created 2026-10-18 Updated 2026-10-20
Creating a liquid surface changes the molecular environment and costs interfacial free energy. In the dispersion-only cleavage model, the attractive Van der Waals force per area has magnitude . Separating two contacting halves from a molecular cutoff to infinity takes work per areaHere denotes the Hamaker constant, to distinguish it from an area. Cleavage creates two free surfaces, giving the Hamaker estimate of liquid surface tensionThe continuum attraction diverges at zero separation and neglects molecular impenetrability and short-range repulsion. The cutoff is therefore an effective contact separation of molecular size, commonly of order –, not a limit that can be taken to zero.
An experimental limitation is the strong temperature dependence of surface tension. For water in equilibrium with its vapour, the recommended experimental values decrease from at to at , and the fitted tension vanishes at the critical point. A fixed pairwise cleavage energy misses interfacial entropy, changing density and many-body correlations.[ref]
Revised Release on Surface Tension of Ordinary Water Substance by International Association for the Properties of Water and Steam. 2014 release, printed pp. 3–4: temperature-dependent equation and Table 1
The dispersion-only model is unsuitable when cohesion is dominated by hydrogen bonds, ionic interactions or metallic bonding; liquid metals are a clear example of the latter failure.