A theory for the 1-1/2 fluid

The 1-1/2 fluid is a conformal solution in which one species has a size parameter (diameter) of zero. This "point-particle" species nevertheless interacts with the other component of the mixture, as the collision diameter of a point particle and a finite particle is nonzero. A great simplifying feature of this model mixture is that the point particles do not interact with each other. For hard repulsive potentials, the properties of a 1-1/2 fluid can be obtained exactly in terms of the properties of the pure fluid obtained upon removal of all the point particles. For other potentials, the properties of the 1-1/2 fluid can be obtained only approximately. We develop two approaches to the description of the 1-1/2 fluid, both based on the methods of diagrammatic expansion and topological reduction. The first approach is an extended virial treatment, in which the free energy is expanded in the density ρ₁ of the full-sized species, keeping to all orders terms in the density ρ₂ of the point particles. A complementary approach takes the pure full-sized fluid as a reference, keeping all terms to ρ₁ while expanding in ρ₂. Monte Carlo simulation is used to show that, properly formulated, an expansion containing only terms first order in ρ₂ is capable of describing 1-1/2 fluid properties over a very broad range of conditions.