Application of extended scaling law to the surface tension of fluids of wide range of molecular shapes

A linear correlation is presented between the reduced surface tension σ* and reduced temperature TextScal* by applying the extended scaling law. The correlation is applied quite accurately to 17 atomic, diatomic, and molecular fluid hydrocarbons of wide range of molecular shapes. The reduced surface entropy SextScals* is introduced, which has a value of 1.000 over the whole liquid range, indicating that the corresponding states principle is followed fully. The correlation for SextScals* contains a quantity Eμs, which is related to the surface energy Es, in the form Eμs=σ−(1/μ)T(∂σ/∂T), where σ is the surface tension, T the absolute temperature, μ the critical exponent for surface tension, and the surface entropy Ss = −(∂σ/∂T  ). Eμs is different form Es by an additional (1/μ) factor coupled to Ss. The form of the equation for Eμs is different from the equation for Es, which is a combination of the first and the second laws of thermodynamic for interface. The relation for SextScals* acts as an intermediate equation to derive a new analytical expression for Eμs in terms of intensive physical and thermodynamic properties of the particular fluid.