Dispersion Corrections to the Surface Tension at Planar Surfaces

Abstract

Molecular dynamics simulations are usually performed using cutoffs (r c ) for the short-ranged dispersion interactions (r −6 ). For isotropic systems, long-range interactions are often added in a continuum approximation. This usually leads to excellent results that are independent of the cutoff length down to about 1 nm. For systems with interfaces or other anisotropic systems the situation is more complicated. We study here planar interfaces, focusing on the surface tension, which is sensitive to cutoffs.Previous analytic results giving the long-range correction to the surface tension of a liquid-vapor interface as a two-or three-dimensional integral are revisited. They are generalized by introducing a dispersion density profile which makes it possible to handle multi-component systems. For the simple but common hyperbolic tangent profile the integral may be Taylor-expanded in the dimensionless parameter obtained by dividing the profile width with the cutoff length. This parameter is usually small and excellent agreement with numerical calculations of the integral is obtained by keeping two terms in the expansion. The results are compared to simulations with different lengths of the cutoff for some simple systems. The surface tension in the simulations varies linearlyc , although a small r −4 c -term may be added to improve the agreement. The slope of the r −2 c -line could in several cases be predicted from the change in dispersion density at the interface. The disagreements observed in some cases when comparing to theory, occur when the finite cutoff used in the simulations causes structural differences compared to long-range cutoffs or Ewald summation for the r −6 -interactions.

Scaled charges at work: Salting out and interfacial tension of methane with electrolyte solutions from computer simulations

“…This is very similar to the value obtained using a cutoff of 0.9 nm and including the long range corrections to g following the procedure described in Refs. [134]. For the vapor-liquid interface of pure water at this temperature the TIP4P/2005 underestimates the value of g by about 1e2 mJ/m 2 and it thus seems that a similar deviation is found for the methane-water interface.…”

“…It is important to point out that IFT are quite sensitive to the value of the cutoff at which the LJ part of the potential was truncated (Ewald sums in principle correctly include the long range ionic contributions). Thus, for a rigorous determination of g one should include long range corrections (LRC) [131e134] which give a positive contribution to g. We have implemented the methodology of Lundberg and Edholm [134] and estimated this correction to be about 2 mJ/m 2 for the methane-water interface (the thickness of the interface was 0.28 nm and the magnitude of the dispersion density difference squared was ðDr C6 Þ 2 Â 10 20 ¼ 0:15 J). This is in line with the small value of the correction found by Naeiji et al [135].…”

Molecular Dynamics Simulations of Liquid-Liquid Interfaces in an Electric Field: the Water-1,2-Dichloroethane Interface

“…Cases in point are the calculation of the self diffusion coefficient and the surface tension. 29,30 Because of the long-range nature of the Coulomb interaction, where the rate of decay is less than the increase in the radial density of charges, it was recognised early on that a short-range cutoff for the electrostatic interactions would have led to unphysical results. A variety of schemes have been developed throughout the years to efficiently compute the long-range electrostatic in-teractions in MD simulations.…”

“…The surface tension was computed for three values of the real space cutoff distance (1.1, 1.5 and 2 nm) and extrapolated to infinite cutoff to account for its dependence on the inverse of the cutoff radius squared. 30 The interface thickness was calculated by fitting the density profiles of one species along the z axis with a sigmoidal function…”

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff

“…21,56,57 Note that anisotropic mean-field variants have also been proposed for these situations, considering both electrostatic interactions 50,57 and LJ interactions. [58][59][60][61][62][63][64][65][66][67] See also Ref. 68 for an alternative route relying on emulating large cutoff distances in meanfield calculations using a lattice-sum scheme.…”