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 modeling of complex fluids. Questions remain, though, about the dependence of the thermodynamic and structural properties of such systems on the cutoff distance used to calculate these local densities. These questions are particularly acute when it comes to the stability and structure of the vapor/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 cutoff distance, rc, used to calculate the local densities. We show quantitatively how the simulation results for bulk thermodynamic properties and vapor-liquid equilibrium approach the van der Waals limit as rc increases and demonstrate a scaling law for the radial distribution function in the large rc limit. We show that the vapor-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 rc limit, the interfacial tension is proportional to rc and, therefore, unlike the bulk thermodynamic properties, does not approach a constant value as rc increases. We believe that these results give new insights into the properties of local density dependent potentials, in particular their unusual interfacial behavior, which is relevant for modeling complex fluids in soft matter.