Surface critical behavior of fluids: Lennard-Jones fluid near a weakly attractive substrate

The phase behavior of fluids near weakly attractive substrates is studied by computer simulations of the coexistence curve of a Lennard-Jones (LJ) fluid confined in a slitlike pore. The temperature dependence of the density profiles of the LJ fluid was used to study the surface critical behavior. A universal critical behavior of the local order parameter, defined as the difference between the local densities of the coexisting liquid and vapor phases at some distance $\textit{z}$ from the pore walls, $\Delta\rho(\textit{z}) = (\rho_l(\textit{z}) - \rho_v(\textit{z}))/2$, is observed in a wide temperature range and found to be consistent with the surface critical behavior of the Ising model. Near the surface the dependence of the order parameter on the reduced temperature $\tau = (\textit{T}_c - \textit{T})/\textit{T}_c$ obeys a scaling law ~τβ1 with a critical exponent β1 of about 0.8, corresponding to the $\textit{ordinary}$ surface transition. A crossover from bulk-like to surface-like critical behavior occurs, when the distance to the surface is about twice the correlation length at the given temperature. Relations between the $\textit{ordinary}$ and $\textit{normal}$ transitions in Ising systems and the surface critical behavior of fluids are discussed.