Bounded inverse power potentials: Isomorphism and isosbestic points.

Abstract

Listen

Translate article

The bounded inverse power (BIP) interaction pair potential, ϕ(r)=1/(aq+rq)n/q, where a and the exponent, n, are constants which control the interaction softness, q is a positive integer, and r is the pair separation, is shown to exhibit isomorphic scaling as does the well-known inverse power potential, i.e., where a = 0. If T is the temperature and ρ is the number density of particles, two state points are isomorphic if a reference state, ρ0, T0, a0 and another state, ρ, T, a are related through the relationships ρn/3/T=ρ0 n/3/T0 and a=a0ρ0/ρ1/3=a0T0/T1/n. The potential form is therefore density dependent along an isomorph. Molecular dynamics simulations and solutions of the Ornstein-Zernike integral equation for q = 2 demonstrate the existence of isosbestic points (IBPs) in the radial distribution function and structure factor for 6 ≤ n ≤ 18 and a wide range of a and ρ values. For the BIP potentials with not too small a values and over a wide density range, the IBP distance is insensitive to the number density and is equal to the distance, rT, defined through ϕ(rT) = T. For exponential potentials of the general form, ϕ(r) = C exp(-rm) with 1 ≤ m ≤ 3, there are also IBPs which are at r values that are typically ∼10-15% larger than predicted by the formula for rT.