DIFFERENTIAL APPROACH TO THE THEORY OF FLUIDS

A detailed study of the hierarchical reference theory (HRT) of fluids is presented based on an Ornstein-Zernike closure, which can be considered a nontrivial extension of the optimized random-phase approximation. The resulting differential equations can be analyzed in the critical region following closely the spirit of the renormalization group. Universality of the critical behavior and scaling of thermodynamic quantities follow from such an analysis, which permits the explicit evaluation of the scaling function and critical exponents. At the same time, the short-range properties of the system can be described in a realistic way. Outside the critical region a detailed comparison with simulation results for thermodynamic and scattering quantities is presented for a Lennard-Jones potential and for hard spheres plus Lennard-Jones tail, showing that HRT is as successful as the best liquid-state theories. A comparison with experimental measurements is also presented and good agreement is found. © 1990 The American Physical Society.