Interaction Potentials in Liquids: the Inverse Problem
Abstract
This work advances a new method for extracting effective pairpotentials from static structure factors (accessible through radiation scattering measurements) of spherically symmetric dense fluids and supramolecular fluids such as colloids and micellar solutions. Liquidstate theories, including integralequation and perturbation theories, have traditionally concerned themselves with the prediction of structural and thermodynamic properties of fluids from assumed or known interparticle potentials. This is known as the forward problem. In contrast, the question of whether or not it is possible to calculate effective pairpotentials from experimental structure factors has so far received insufficient attention. This problem, known as the inverse problem, is the focus of this dissertation. First, we show that simple singlestep inversions based on closures to the OrnsteinZernike integral equation (which are, to this day, used in studying liquid metals) are inadequate for extracting reliable pairpotentials. We also illustrate, using specific examples, why the integral equation methods fail. Second, we demonstrate the robustness and accuracy of a recently introduced predictorcorrector inversion method based on perturbation theory for onecomponent systems. Both experimental and computationally generated structure factors for a wide variety of strongly interacting systems (liquids of rare gases, liquid metals as well as a model colloidal dispersion) are used for this purpose. An error analysis is also presented to identify the influence of experimental errors in the structure factors on the extracted potentials. Third, we extend the above method to twocomponent systems and apply it to theoretical partial structure factor data for a model binary LennardJones mixture to demonstrate that the original potentials can be recovered with remarkable accuracy. This method is the first formal solution of the inverse problem for binary mixtures, converges rapidly and is not numerically intensive. Our results demonstrate that structure factors retain many of the details concerning microscopic interaction forces and that these details can be recovered with remarkable accuracy in the case of both one and twocomponent systems using suitable methods, if sufficiently accurate experimental data over a wide range of scattering angles, including the smallangle region, are available.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1992
 Bibcode:
 1992PhDT.......103G
 Keywords:

 COLLOIDS;
 ATOMIC LIQUIDS;
 PERTURBATION THEORY;
 Engineering: Chemical; Physics: Molecular