Thermodynamically Consistent Theory of Classical Liquid Structure and Inverse Problem of Extracting Pair Potential

Abstract

The direct correlation function c(r) is divided into two parts, following the work of Kumar et al. One part, c(r) _potential ≡ c _p(r), contributes the entire compressibility and decays at large r as-φ(r)/K_BT, with φ(r) the density independent pair potential. The definition of c _p(r) as–φ(r)/K_BT{(1/6ρr ²)∂²/∂ρ∂r[ρ² r ³ g(r)]{ is motivated by the condition of thermodynamic consistency, and for a hard core liquid leads to c _p(r) small inside an atomic diameter.

The second part c(r) _cooperative ≡ c_c(r) is not expressible simply in terms of φ(r) and the pair function g(r), and is expected to differ in range between condensed rare gases and liquid metals say. Also, for a given liquid like argon, c_c(r) can be shorter or longer range than c _p(r) depending whether one is near the triple point, or near critical conditions. At the critical point, or alternatively in the presence of a collective mode as in liquid Rb, the long-range behaviour of c_c(r) can be dominated by cooperative effects.

To illustrate the theory, fluid argon well away from the critical point is considered. Here, it is argued that c_c(r) has the following properties: (i) it is short range compared with c _p(r), (ii) it is near to the direct correlation function for hard spheres inside an atomic diameter σ, and (iii) it has Ornstein-Zernike form e^−rl/r for r > σ.

The present work demonstrates the importance of knowledge of the density derivative ∂g(r)/∂r as well as g(r) in extracting density independent pair potentials from diffraction data.