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For two liquid half-spaces, integrate the magnitude of a dispersion attraction per area $A_H/(6\pi h^3)$ from a molecular contact cutoff $h_0$ to infinity. The work per area is $A_H/(12\pi h_0^2)$. Because cleavage creates two interfaces, each has the displayed surface tension in this approximation. The cutoff is essential: a continuum attraction cannot describe atomic overlap and short-range repulsion. This estimate neglects interfacial entropy, detailed density profiles and nonadditive interactions, and it cannot replace the metallic bonding or hydrogen bonds that dominate some liquids' cohesion.

At fixed temperature, a phase's Gibbs free energy satisfies $\mathrm{d}G=V\mathrm{d}p$. For the metallic-minus-molecular difference,Increasing pressure favors the smaller-volume metallic phase. With a pressure-independent volume approximation, $\Delta G(p)\simeq \Delta G(p_0)+(p-p_0)\Delta V$, so pressure can overcome an initially positive free-energy difference. The volume comparison explains the direction of stabilization; it does not by itself determine the transition pressure or the electronic origin of metallic bonding.

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 $A/(6\pi h^3)$. Separating two contacting halves from a molecular cutoff $h_0$ to infinity takes work per areaHere $A_H$ 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 $0.1$–$0.3\mathrm{nm}$, 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 $71.98\mathrm{mN}{\mathrm{m}}^{-1}$ at $25{}^{\circ }\mathrm{C}$ to $58.92\mathrm{mN}{\mathrm{m}}^{-1}$ at $100{}^{\circ }\mathrm{C}$, and the fitted tension vanishes at the critical point. A fixed pairwise cleavage energy misses interfacial entropy, changing density and many-body correlations.^[ref] 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.

The liquid does not wet the glass because $\cos 140^{\circ }<0$. The liquid meniscus is convex, with the capillary mercury level depressed below the reservoir. Balancing vertical surface-tension force against the hydrostatic column gives Jurin's law, using the inner radius $r=0.5\mathrm{mm}$:Thus the depression is approximately $10.1\mathrm{mm}$. The simple height law neglects small meniscus-volume corrections. Mercury's high surface tension reflects strong metallic bonding, not merely dispersion between weakly interacting molecular units.