Fowler’s approximation for the surface tension and surface energy of Lennard-Jonesfluids revisited

Abstract

We present a detailed study of the validity of Fowler’s approximation forcalculating the surface tension and the surface energy of Lennard-Jones fluids. Todo so, we consider three different explicit analytical expressions for the radialdistribution function (RDF), including one proposed by our research group,together with very accurate expressions for the liquid and vapour densities, alsoproposed by our group. The calculation of the surface tension from the directcorrelation function using both the Percus–Yevick and the hypernetted-chainapproximations is also considered. Finally, our results are compared with thoseobtained by other authors by computer simulations or through relevant theoreticalapproximations. In particular, we consider the analytical expression proposed byKalikmanov and Hofmans (1994 J. Phys.: Condens. Matter 6 2207–14) forthe surface tension. Our results indicate that the values for the surfaceenergy in Fowler’s approximation obtained by other authors are adequate,and can be calculated from the RDF models. For the surface tension,however, the values considered as valid in previous works seem to beincorrect. The correct values can be obtained from our model for the RDF orfrom the Kalikmanov and Hofmans expression with suitable inputs.