A comparison of semi-empirical density functional theories for nucleation

Density gradient theory with two different forms for the equation of state is used to model nonane nucleation. At each temperature considered, the two parameters in the equations of state are found by equating the equilibrium chemical potential and pressure in the liquid and vapour state. The coefficient of the square gradient is then chosen so that the surface tension for a planar surface calculated by density gradient theory matches the experimental value. Results for nucleation rates are compared with density functional calculations following the procedure described by Nyquist et al (Nyquist R M, Talanquer V and Oxtoby D W 1995 J. Chem. Phys. 103 1175). The density gradient values are within a factor of ten of the classical theory results and exhibit almost identical temperature dependences. In contrast, the density functional theory predicts rates that are much larger and exhibit weaker temperature dependence than classical theory. The two equations of state predict values that differ by a factor of about ten, indicating that the form of the equation of state in the unstable region is important in determining the nucleation rate from density functional theories. This conclusion is supported by calculations using a model equation of state, for which the chemical potential is three intersecting straight lines.