Extracting short-ranged interactions from structure factors

Details Extracting short-ranged interactions from structure factors Extracting short-ranged interactions from structure factors

2012-01-20

arxiv.org/abs/1201.4235v1

Mol. Phys. 109, 2945 (2011)

Physics

Condensed Matter

Soft Condensed Matter

to appear in Molecular Physics, special issue in honour of Prof. Luciano Reatto. arXiv admin note: substantial text overlap wi

Scientific paper

10.1080/00268976.2011.611481

Inverting scattering experiments to obtain effective interparticle interactions is generally a poorly conditioned problem. L. Reatto (Phil. Mag. A 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 can 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 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.

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