Extracting short-ranged interactions from structure factors

Ard Louis (1)

1 Rudolf Peierls Centre for Theoretical Physics

Inverting scattering experiments to obtain effective interparticle interactions is generally a poorly conditioned problem. L. Reatto (Phil. Mag. A {\bf 58}, 37 (1986)) showed that for atomic liquids close to the triple point, inversions are hard because the structure closely resembles that of an equivalent hard-sphere fluid. Here I demonstrate that at low concentrations and for particles with short-ranged attractive potentials, $S(k)$ also exhibits a very weak dependence on potential shape. Instead, different potentials all generate an $S(k)$ that closely resembles that of the Baxter model with a similar second-virial coefficient. By contrast, in this energetic fluid regime, the inversion of an attractive interaction from real-space correlations such as the radial distribution function $g(r)$ is well conditioned. Nevertheless, one may extract further information from $S(k)$ by measuring {\em isosbestic points}, values of $k$ where the scattering intensity $I(k)$ or the structure factor $S(k)$ is invariant to changes in interaction-potential well-depth. These points suggest a new extended corresponding states principle for particles in solution based on the packing fraction, the second osmotic virial coefficient, and a new measure of effective potential range.

Mots clés: Physical Sciences

Domaines: Matière Condensée [cond-mat]

Ard Louis. Extracting short-ranged interactions from structure factors. Molecular Physics, 2011, pp.1. ⟨10.1080/00268976.2011.611481⟩. ⟨hal-00746096⟩