Surface Tension Prediction From Density Profile Information by Polyatomic Molecular Dynamics Simulations

Surface tension prediction of liquid-vapor interfaces of polyatomic fluids using traditional methods in molecular dynamics simulations has shown to be difficult due to the requirement of evaluating complex intermolecular potentials even though these methods provide accurate predictions. In addition, the traditional methods may only be performed during a simulation run. However, analytical techniques have recently been developed that determine surface tension by using the characteristics of the density profile of the interfacial region between the bulk liquid and vapor regions. Since these characteristics are a standard result of many liquid-vapor interfacial region simulations, these data may be used in a post-simulation analysis. One such method, excess free density integration (EFEDI), provides results from the post-simulation analysis, but the expansion from monatomic to polyatomic fluids is not straightforward [1]. A more general and powerful approach to surface tension involves the application of a Redlich-Kwong-based mean-field theory [2], which has resulted in a single equation linking the surface tension of a fluid, σlv, with the density gradient at the center of the interfacial region, σlv=0.1065(1−T/Tc)−0.34Li2dρ^dzz=0aR0NA2bRNAT1/2ln1+ρ^lbRNA1+ρ^vbRNA(1) where z is the position normal to the interfacial region and is zero at its center, ρ^l and ρ^v are the liquid and vapor molar densities, respectively, TC is the critical temperature, NA is Avogadro’s number, Li is a characteristic length given by Li=kBTCPC1/3(2) and aR0 and bR are the coefficients in the Redlich-Kwong equation of state, P=NkBTV−bRN−aR0N2T1/2V(V+bRN)(3) Furthermore, PC is the critical pressure for the fluid. Reference [2] shows that the relation provided by Equation 1 provides a approximate prediction of surface tension for argon fluid using data from molecular dynamics simulations. The derivation of Equation 1 is based on the assumption that the density profile in the interfacial region follows ρ^−ρ^vρ^l−ρ^v=1e4z/δzi+1(4) where δzi is the interfacial region thickness,. Note that Equation 4 is more commonly expressed in the equivalent form ρ^(z)=12(ρ^l+ρ^v)−12(ρ^l−ρ^v)tanh2zδzi(5) Wemhoff and Carey [1] have recommended the use the fit curve relation given by Equation 5 for the liquid-vapor interfacial region of a diatomic nitrogen system. Therefore, Equation 1 may be used to predict the surface tension for diatomic nitrogen at various temperatures.