Relation between Tolman length and isothermal compressibility for simple liquids

Tolman length δ₀ of the liquid with a plane surface has attracted an increasing theoretical attention in recent years, while the expression of Tolman length in terms of observable quantities is still not very clear. In 2001, Bartell gave a simple expression of Tolman length δ₀ in terms of isothermal compressibility. However, this expression predicts that Tolman length is always negative, which is contrary to the results of molecular dynamics simulations (MDS) for simple liquids. In this paper, this contradiction is analyzed and the reason for the discrepancy in the sign is found. In addition, we introduce a new expression of Tolman length in terms of isothermal compressibility for simple fluids not near the critical points under some week restrictions. The Tolman length of simple liquids calculated by using this formula is consistent with that obtained using MDS regarding the sign.