Density Profiles of Liquid/Vapor Interfaces Away from Their Critical   Point
  We examine the applicability of various model profiles for the liquid/vapor interface by X-ray reflectivities on water and ethanol and their mixtures at room temperature. Analysis of the X-ray reflecivities using various density profiles shows an error-function like profile is the most adequate within experimental error. Our finding, together with recent observations from simulation studies on liquid surfaces, strongly suggest that the capillary-wave dynamics shapes the interfacial density profile in terms of the error function. 
Wei Bu, Doseok Kim, and David Vaknin
cond-mat.soft