DENSITY DISTRIBUTION-FUNCTIONS OF CONFINED TONKS-TAKAHASHI FLUIDS

The density distribution functions of a confined one-dimensional fluid of particles obeying the Tonks-Takahashi nearest neighbor two-body potential are reduced to simple functions of the grand canonical ensemble partition function. The resulting formulas are analogous to those found by Robledo and Rowlinson for a hard-rod fluid. In the absence of an external field the partition functions can be evaluated by the method of Laplace transforms. The dependence of the pressure P on the separation L of the confining walls is investigated for three model potentials: (i) hard rod, (ii) square well, and (iii) triangle well. P is an oscillating function of L in all three cases. The oscillations arise from the ordering effect of the repulsive forces between particles. The attractive interactions of the triangle-well potential reinforces the ordering whereas those of the square-well potential diminishes the ordering. Results for semiconfined and homogeneous fluids are also presented. © 1990 American Institute of Physics.