Local density dependent potentials for an underlying van der Waals equation of state: a simulation and density functional theory analysis

There is an ever increasing use of local density dependent potentials in the mesoscale modelling of complex fluids. Questions remain, though, about the dependence of the thermodynamic and structural properties of such systems on the cut-off distance used to calculate these local densities. These questions are particularly acute when it comes to the stability and structure of the vapour/liquid interface. In this article we consider local density dependent potentials derived from an underlying van der Waals equation of state. We use simulation and density functional theory to examine how the bulk thermodynamic and interfacial properties vary with the cut-off distance, r_c, used to calculate the local densities. We show quantitatively how the simulation results for bulk thermodynamic properties and vapour-liquid equilibrium approach the van der Waals limit as r_c increases and demonstrate a scaling law for the radial distribution function in the large r_c limit. We show that the vapour-liquid interface is stable with a well-defined surface tension and that the interfacial density profile is oscillatory, except for temperatures close to critical. Finally we show that in the large r_c limit, the interfacial tension is proportional to r_c and thus, unlike the bulk thermodynamic properties, does not approach a constant value as r_c increases. We believe that these results give new insights into the properties of local density dependent potentials, in particular their unusual interfacial behaviour, which is relevant for modelling complex fluids in soft matter.