Reduction in the surface energy of liquid interfaces at short length scales

Liquid–vapour interfaces, particularly those involving water, are common in both natural and artificial environments. They were first described as regions of continuous variation of density1, caused by density fluctuations within the bulk phases2,3,4. In contrast, the more recent capillary-wave model5,6 assumes a step-like local density profile across the liquid–vapour interface, whose width is the result of the propagation of thermally excited …