Extracting short-ranged interactions from structure factors
Résumé
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.
Domaines
Matière Condensée [cond-mat]
Origine : Fichiers produits par l'(les) auteur(s)
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