Density functional theory of size-dependent surface tension of Lennard-Jones fluid droplets using a double well type Helmholtz free energy functional

A double well type Helmholtz free energy density functional and a model density profile for a two phase vapor-liquid system are used to obtain the size-dependent interfacial properties of the vapor-liquid interface at coexistence condition along the lines of van der Waals and Cahn and Hilliard density functional formalism of the interface. The surface tension, temperature-density curve, density profile, and thickness of the interface of Lennard-Jones fluid droplet-vapor equilibrium, as predicted in this work are reported. The planar interfacial properties, obtained from consideration of large radius of the liquid drop, are in good agreement with the results of other earlier theories and experiments. The same free energy model has been tested by solving the equations numerically, and the results compare well with those from the use of model density profile. (C) 2011 American Institute of Physics. [doi:10.1063/1.3633475]