Nonuniform one-dimensional classical fluids: Theory versus Monte Carlo experiments

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Abstract
Two types of approximate theory for nonuniform fluids are applied in the calculation of properties of nonuniform one-dimensional fluids whose particles interact via a Lennard-Jones (6-12) potential. The nonuniformity is produced by an external potential well which creates a local high-density "phase" in equilibrium with a low-density phase exterior to the well. The density and size of the local phase are varied by changing the depth and width of the well. The first type of theory invokes the density-functional (DF) approach. The authors examine a sequence of density functionals, all of which use the Percus-Yevick (PY) approximation for the interparticle interaction. Density profiles and free energies are found by means of the DF theories and compared with each other as well as with results obtained from Monte Carlo calculations for the same systems. The other type of theory, the linearized Percus-Yevick (LPY) treats the particle-well interaction in the Percus-Yevick approximation. This theory is used to obtain density profiles only. It is found that the results of the DF theories generally agree quite well with the numerical experiments while those of the LPY do not. The reason for the failure of the LPY is discussed in terms of an effective particle-well potential. Finally, important implications are derived concerning the reliability of the various DF theories for more realistic calculations in three dimensions.