Application of Extended Scaling Law to the Surface Tension of Fluids of Wide Range of Molecular Shapes

Details Application of Extended Scaling Law to the Surface Tension of Fluids of Wide Range of Molecular Shapes Application of Extended Scaling Law to the Surface Tension of Fluids of Wide Range of Molecular Shapes

2006-10-31

arxiv.org/abs/cond-mat/0610883v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 4 Figures

Scientific paper

A linear correlation is presented between the reduced surface tension \sigma^* 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^{s^*}_{extScal} 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^{s^*}_{extScal} contains a quantity E^s_\mu, which is related to the surface energy E^s, in the form E^s_\mu = [\sigma - (1/\mu)T(d\sigma/dT)], where \sigma is the surface tension, T is the absolute temperature, miu is the critical exponent for surface tension, and the surface entropy S^s=-(d\sigma/dT). E^s_\mu is different from Es by an additional (1/\mu) factor coupled to S^s. The form of the equation of E^s_\mu is different from the equation of E^s, which is a combination of the first and the second laws of thermodynamic for interface. The relation for S^{s^*}_{extScal} acts as an intermediate equation to derive a new analytical expression for E^s_\mu in terms of intensive physical and thermodynamic properties of the particular fluid. Key words: Critical exponent; Extended scaling; Law of corresponding states; Surface energy; Correlation for Surface tension;

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