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 T extScal * 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 S extScal s * 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 S extScal s * contains a quantity E μ s , which is related to the surface energy Es, in the form E μ s = 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). E μ s is different form Es by an additional (1/μ) factor coupled to Ss. The form of the equation for E μ s 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 S extScal s * acts as an intermediate equation to derive a new analytical expression for E μ s in terms of intensive physical and thermodynamic properties of the particular fluid.