Differential theory of fluids below the critical temperature: Study of the Lennard-Jones fluid and of a model ofC60

The hierarchical reference theory (HRT) is applied to the Lennard-Jones fluid below the critical temperature ${\mathit{T}}_{\mathit{c}}$. This study completes a previous one performed above ${\mathit{T}}_{\mathit{c}}$ using the same kind of approximate closure for the direct correlation function. Results for several thermodynamic quantities and for the two-particle correlations are reported and compared both with other theories and with simulation data. In the two-phase region the theory correctly yields rigorously flat isotherms; this feature allows a straightforward and accurate determination of the coexistence curve without resorting to the Maxwell construction. In the critical region our analysis is consistent with the previously developed one for T>${\mathit{T}}_{\mathit{c}}$ and displays nontrivial critical exponents. We also study a fluid with the Girifalco model potential for ${\mathrm{C}}_{60}$. The critical point of the liquid-vapor transition is found at ${\mathit{T}}_{\mathit{c}}$=2138 K and ${\mathrm{\rho }}_{\mathit{c}}$=0.50 ${\mathrm{nm}}^{\mathrm{-}3}$. When the HRT result is supplemented with Verlet’s freezing criterion a triple point is found at ${\mathit{T}}_{\mathit{t}}$=1979 K and ${\mathrm{\rho }}_{\mathit{t}}$=0.848 ${\mathrm{nm}}^{\mathrm{-}3}$.